.mwnqumm
‘ r," . .

7|

 

. "n“

9!

muumv-Mfiv

._:...‘J .
nvv a:
S...

y,»

9

pug-«”9”

.a.1

4 :u n.
I .:
Jtifig

. V

m‘Hv-nu"

.
a
a
d
a
a

.
n
.v
u:
n

n
..
d,
u

 

uv-|-fi.v u.gvg-l qt u71-1n‘

‘11..
.\.:s..

 

t
a" I
79.!

TATE unwsnsmv uamues

111111111111/1

"W 1

WIN/Hill!!!” NIH/ill

1 3 1293 01019 1959

This is to certify that the

dissertation entitled

REDUCTION OF PAVEMENT
RUTTING AND FATIGUE CRACKING

presented by
Hamid Mukhtar

has been accepted towards fulfillment
of the requirements for

Doctor of Philosophy degree in Civil Engineering

ilbert Baladi

 

 

 

Major professor

Date 11/17/93

 

MSU is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

LIBRARY

Michigan State
University

 

PLACE IN RETURN BOX to remove thle checkout from your record.

TO AVOID FINES return on or bdore dete due.

 

 

520'

DATE DUE DATEE [.6 ' DATE DUE

 

 

W3

 

 

 

 

 

 

 

L L
:lfi-‘H n
*%

 

 

 

 

 

——

 

 

 

 

MSU 1: A31 .“

REDUCTION OF PAVEMENT RUTTING
AND FATIGUE CRACKING

BY

Hamid Mukhtar

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

1993

ABSTRACT

 

Hamid Mukhtar

Flexible pavements are typically designed to provide a good ride quality and to
resist rutting and fatigue cracking. The two types of distress are mainly caused by wheel
loads and are accelerated by material and environmental factors. Although all the
pavement layers (base, subbase and roadbed soil) contribute to rutting and fatigue
cracking, the contribution of the asphalt concrete (AC) layer alone could be very
significant.

The pavement network in the State of Michigan is experiencing premature rutting
and fatigue cracking problems. The main objective of this study is to identify the AC
mix factors that affect pavement rutting and fatigue cracking.

Based on predetermined priority factors, forty-nine flexible and fifteen composite
pavement sections were selected from a large pool of pavements. For each selected
pavement section, rut and fatigue cracking measurements were made and for 13 sections,
full depth pavement cores were obtained. The cores were subjected to various laboratory
tests and the resilient, plastic, and fatigue life characteristics of the asphalt-aggregate
mixes were determined.

A multivariate regression analysis were performed to determine the relationship
of rut depth and laboratory fatigue life to the AC mix properties. The results showed that
high percent content of coarse angular aggregates (crushed on 3 or 4 sides), air voids
contents between 4 to 6 percent, and low amount of fine content can provide significant

improvement in the rut and fatigue cracking resistance of the AC mixes.

Hamid Mukhtar

Based on the analysis, shift factors between the fatigue lives of asphalt pavements
and the laboratory fatigue lives of the AC cores were developed and verified. Finally,
changes are recommended in the existing asphalt mix design and manufacturing processes

in the State of Michigan to reduce pavement rutting and fatigue cracking potential.

To my wife, children, parents, sister and brothers and to all peace loving humans.

iv

ACKNOWLEDGEMENT

Thanks to Allah Almighty for providing me with the opportunity to undertake and
complete this task. The writer wishes to express his appreciation to his major professor,
Dr. Gilbert Y. Baladi for his constant guidance and encouragement during the research.
Thanks also to members of the writer’s doctoral committee:
Dr. W.C.Taylor, Professor;
Dr. R.S. Harichandran, Associate Professor; and
Dr. R.V. Erickson, Professor.
Thanks are also extended to the Pakistan Military Engineering Services for partly
sponsoring my study program and to the Michigan Department of Transportation and the
University of Michigan Transportation Research Institute for sponsoring this study.
Thanks to the Technical Advisory Committee for this project from Michigan Department
of Transportation, including Dave Smiley, Jack DeFoe, Jerry Sweeny, and Ishvarlal
Patel, also deserve special thanks for their guidance and comments. The dedicated effort
of Kurt Bancroft in conducting the falling weight deflection tests and supervising coring
operation is also recognized and appreciated. Help and guidance provided by Leo
Defrain in programming is also appreciated.

Efforts of S. Stuart, Bill E., Guy N., John A., Erich T., and others in data

acquisition and reduction is appreciated.

TABLE OF CONTENTS

CHAPTER 1
W ....................................... l
1.1 GENERAL ...................................... 1
1.2 PROBLEM STATEMENT ............................. 2
1.3 RESEARCH OBJECTIVE ............................. 2
CHAPTER 2
W .................................. 4
2.1 GENERAL ...................................... 4
2.2 MECHANICS OF PERMANENT DEFORMATION AND FATIGUE
CRACKING ...................................... 8
2.2.1 Permanent Deformation (Rut) ....................... 8
2.2.2 Fatigue Life ................................. 10
2.3 FACTORS AFFECTING RUTTING AND FATIGUE CRACKING OF
ASPHALT SURFACED PAVEMENTS ..................... 12
2.3.1 Tire Inflation And Tire-Pavement Contact Pressures ......... 12
2.3.2 Consolidation And Field Compaction .................. 19
2.3.3 Aggregates .................................. 24
2.3.4 Sand and Mineral Filler .......................... 29
2.3.5 Asphalt Type And Content ......................... 29
2.3.6 Environmental Factors ........................... 34
2.3.7 AAMAS Mixture Properties Related to Pavement
Performance ................................. 38
2.3.8 Effects of Mix Manufacturing and Field Placement on AC Mix
Performance ................................. 41
2.4 PERMANENT DEFORMATION PREDICTION MODELS ......... 43
2.5 LABORATORY FATIGUE CRACKING MODELS ............. 48

vi

2.6 . MATERIAL ALTERATION ........................... 49

2.7 MATERIAL CHARACTERIZATION ...................... 54

2.7.1 State of Stress ................................ 54
2.8 TEST PARAMETERS ................................ 61
2.8.1 Pulse Shape .................................. 62
2.8.2 Pulse Duration and Rest Period ...................... 62
2.9 SUMMARY ...................................... 63
CHAPTER 3
WAN ...................................... 67
3.1 INTRODUCTION .................................. 67
3.2 RESEARCH PLAN ................................. 74
CHAPTER 4
FIELD AND LABORATORY
INVESTIGATION ...................................... 77
4.1 PAVEMENT SELECTION ............................. 77
4.2 MARKING, CODING, CORING AND NDT ................. 83
4.3 LABORATORY INVESTIGATIONS ....................... 85
4.3.1 Indirect Cyclic Load Tensile Test fer Bituminous Mixtures ..... 87
4.3.2 Maximum Theoretical Specific gravity Tests .............. 92
4.3.3 Extraction Tests ............................... 93
4.3.4 Recovered Asphalt Penetration ...................... 96
4.3.5 Sieve Analysis ................................ 96
4.3.6 Aggregate Angularity ............................ 97
CHAPTER 5
W ............................. 101
5 1 General ........................................ 101
5.2 STATISTICAL ANALYSIS TECHNIQUES AND ISSUES ........ 104
5.3 DEFINITION OF TERMS ............................ 109
5.4 ANALYSIS AND DISCUSSION OF FATIGUE LIFE ........... 110
5.4.1 Field Cores, Laboratory Samples, and the INCL Tests ....... 116

vii

5.4.2 Test Results ................................. 117

5.4.3 Analysis and Discussion of the Test Results ............. 124
5.4.4 Regression Analysis ............................ 132
5.4.5 Sensitivity Analysis and Engineering Interpretation ......... 141
5.5 RUT ANALYSIS .................................. 155
5.5.1 Determination of Material Properties for a Core Location ..... 157
5.5.2 Analysis of Rut as a Function of Material Properties ........ 160
5.5.2.1 Regression Analysis ................... 167
5.5.2.2 Sensitivity Analysis and Engineering
Interpretation ....................... 175
5.5.2.3 Rut Prediction Based on Assigned Material
Properties ......................... 187
5.5.3 Analysis of Rut as a Function of the Pavement
Deflection ................................... 198
5.5.3. 1 Introduction ......................... 198
5.5.3.2 Statistical Analysis ..................... 201
5.5.3.3 Regression Analysis .................... 209
5.5.3.3.1 Statistical Analysis Based on
Strings of Variables ............... 211
5 .5 .3.3.2 Regression Analysis Based on
Cluster of Variables ............... 217
5.5.3.4 Observations and Discussion ............... 227
5.6 ERRORS ........................................ 229
5.7 VERIFICATION OF THE SHIFT FACTORS OF THE FATIGUE
LIFE .......................................... 232
CHAPTER 6
W
W .............................. 224
6.1 SUMMARY ..................................... 224
6.2 ACCOMPLISHMENTS .............................. 224
6.3 CONCLUSIONS .................................. 225
6.4 RECOMMENDATIONS ............................. 226
REFERENCES ....................................... 244

viii

APPENDICES

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

ix

Table 2.1 :
Table 2.2 :
Table 2.3 :

Table 2.4 :

Table 2.5 :
Table 2.6 :

Table 2.7 :
Table 2.8 :

Table 2.9 :

Table 2.10 :

Table 3.1 :

Table 3.2 :

Table 3.3 :

Table 3.4 :

LIST OF TABLES

Average rut (percent of total rut) in each layer of section 51

of the AASHO Road Test (5) ....................... 11
Percent rutting in various layers due to distortion, section 51

of AASHO Road Test, 1960 (5). ..................... 11
Effect of tire type and tire inflation pressure on the maximum

tire -pavement contact pressure (8). ................... 14
Summary of mix densities (lbs/c.ft)(27) ................. 27
Effect of asphalt cement factors on

pavement distress (34). ........................... 33
Summary of ranking of mixture properties related to pavement
performance (38). .............................. 40
Gradation ranges for asphalt concrete mixes (24) ........... 51
Different binder modifiers ......................... 53
Analysis of SHA questionnaire: Modifiers most commonly used

(52) ....................................... 56
Analysis of SHA questionnaire: Primary targeted pavement
distress, (52). ................................. 56
MDOT specifications and tolerance limits for various AC courses

(prior to 1979) ................................ 68
MDOT specification and tolerance limits for various AC courses
(1979-1992) .................................. 69
MDOT AC mix design criteria (1992) .................. 70

MDOT specifications and tolerance limits for AC mixes (1992) . . 72

Table 3.5 :
Table 3.6 :
Table 4.1 :
Table 4.2 :
Table 4.3 :
Table 4.4 :

Table 4.5 :

Table 4.6 :
Table 5.1 :
Table 5.2 :
Table 5.3 :
Table 5.4 :

Table 5.5 :

Table 5.6 :
Table 5.7 :
Table 5.8 :
Table 5.9 :
Table 5.10 :
Table 5.11 :
Table 5.12 :

Table 5.13 :

MDOT AC mix selection criteria (1992) ................
Recommended AC mix placement thickness (1992) ..........
Criteria for finial section selection ....................
Selected flexible sections ..........................
Selected composite sections ........................
List of cored pavement sections ......................
Results of extraction, penetration and maximum theoretical

specific gravity tests for all AC courses of the cored pavement
sections. ....................................
Results of sieve analysis for each AC course ..............
Data for the 57 INCL test samples ...................
Descriptive statistics of the properties of all test samples .....
Correlation matrix for fatigue life and independent variables . . .

Correlation matrix for the final variables ...............

Collinearity diagnostics ( eigenvalues, condition indices and the
proportion of the variance attributable to the eigenvalue) .....

Collinearity diagnostics: TOL and VIP ................
Results of regression analysis ......................
Regression matrix for laboratory fatigue life .............
Residual statistics of the data ......................
Ten worst Residual ............................
Shift factor for the flexible pavement sections ............
Material properties for the 19 core locations .............

Descriptive statistics of the properties of the 19 pavement cores .

72
73
78
8O
8 1

34

94
99
119
121
126

134

136
136
138
138

150
158

159

Table 5.14 :
Table 5.15 :
Table 5.16 :'

Table 5.17 :

Correlation matrix for the 19 extracted core locations ....... 161
Correlation matrix for rate of rutting (RRUT) ............ 166
Correlation matrix for the final variables ............... 169

Collinearity diagnostics (eigenvalue, condition indices and the

proportion of the variance attributable to the eigenvalue) ..... 169
Table 5.18 : Collineerity diagnostics TOL and VIP ................. 171
Table 5.19 : Results of regression analysis ...................... 171
Table 5.20: Regression matrix for rate of rutting .................. 172
Table 5.21 : Residual statistics of equation 5.5 ................... 174
Table 5.22 : Ten worst Residuals ............................ 174
Table 5.23 : Material properties for the 107 core locations ............ 190
Table 5.24 : Descriptive statistics of the data ...................... 202
Table 5.25 : Correlation matrix for rut and sensors deflection ............ 208
Table 5.26 : Results of regression analysis ....................... 212
Table 5.27 : Regression matrix for rutting ....................... 213
Table 5.28 : Residual statistics of equation 5 .6 ..................... 215
Table 5.29 : Ten worst residuals .............................. 215
Table 5.30 : Results of regression analysis ........................ 221
Table 5.31 : Regression matrix for rutting ........................ 221
Table 5.32 : Residual statistics of equation 5 .7 ..................... 223
Table 5.33 : Ten worst residuals .............................. 223

Table 5.34 : The maximum, minimum, and the average values of the shift factors

for the indicated pavement section ..................... 233

xii

Table 5.35 : Predicted and observed fatigue lives of two pavement sections with
fatigue cracks .................................. 238

xiii

Figure 2.1 :

Figure 2.2 :

Figure 2.3 :

Figure 2.4 :

Figure 2.5 :

Figure 2.6 :

Figure 2.7 :

Figure 2.8 :

Figure 2.9 :

Figure 2.10 :

Figure 2.11 :

Figure 2.12 :

LIST OF FIGURES

Illustration of critical stress/ strain locations in a typical
pavement structure. ............................. 6

Trench study of the transverse profile of loops 4 and 6 of the
AASHO ROAD TEST (4) ......................... 9

Variation of tensile strain at the bottom of the AC surface for
different AC thicknesses and two tire inflation pressures, (10). . . 17

Variation of tensile strain at the bottom of a 2-inch thick
surface pavement with lateral distance from the center of the

tire, treated tire with 90 psi pressure, (10) ............... 17
Variation of compressive strain at the top of the subgrade for
different thickness and tire pressure, (10). ............... 18
Variation of compressive strain at the top of the subgrade for
different thickness and two level of loads (10). ............ 18
Fatigue life variation for different thickness and tire inflation
pressure (10) .................................. 20
Fatigue life variation for different thickness and tire loads

(10) ....................................... 20
Pavement subgrade rutting damage life for different thickness and

loads (10). .................................. 21
Fatigue life ratio of two asphalt mixes compacted at 50 and 75

blows Marshall compaction versus the asphalt content, (11) . . . . 21
Rutting as a function of the voids in the total mix (VTM) (7) . . . 23
Relationship between rut depth and stability (16) ........... 25

xiv

Figure 2.13 :

Figure 2.14 :

Figure 2.15 :

Figure 2.16 :

Figure 2.17 :

Figure 2.18 :

Figure 2.19 :

Figure 2.20 :

Figure 2.21 :
Figure 2.22 :
Figure 2.23 :

Figure 2.24:

Figure 3.1 :

Figure 4.1 :
Figure 5.1 :
Figure 5.2 :

Figure 5.3 :

Effect of aggregate top size upon the percent voids in mineral

aggregate, (27) ................................ 28
Effect of aggregate top size on the percent air voids in the mix,

(27) ....................................... 28
Binder contribution to different distresses. ............... 31

Effect of asphalt cement on fatigue life- Califomia medium grading,
Basalt aggregate, 60-70 penetration asphalt (l7) ............ 35

Bending stress vs. application to failure , for mixes of
different stiffness-California graded mixes, granite aggregate,
85-100, 60-70 and 40-50 penetration asphalt, 6 percent

asphalt (l7). ................................. 35
Interaction between traffic related and aging related fatigue
cracking in bituminous surfacing (37) .................. 37
Permanent defamation as a function of time (Brampton Road Test
section 3), (6) ................................ 46
Aggregate gradation curves and mix design criteria: SMA
compared with MDOT 20AAA (51) ................... 52
Modifier ranking bar chart for fatigue cracking, (52) ......... 55
Modifier ranking bar chart for permanent deformation, (52) . . . . 55
Typical pavement stress distribution under static loading ..... 57
Typical stress states in the asphalt concrete layer with wheel

load applied .................................. 59
Overall research plan ............................ 76
Baladi indirect tensile test apparatus ................... 88
Performance period of a pavement .................... 111
Service life of a pavement ......................... 111
Remaining service life (RSL) of a pavement .............. 112

XV

Figure 5.4 :

Figure 5.5a :

Figure 5.5b :

Figure 5.6 :

Figure 5.7a :

Figure 5.7b :

Figure 5.8 :

Figure 5.9 :

Figure 5.10 :

Figure 5.11 :

Figure 5.12 :

Figure 5.13 :

Figure 5.14 :

Figure 5.15 :

Figure 5.16 :

Figure 5.17 :

Fatigue cracking index (FCI) as a function of time .......... 114

Resilient modulus, horizontal plastic and total deformation as
a function of the number of load applications ............. 123

Deformation ratio (horizontal plastic/vertical plastic) as a function

of the number of load applications. ................... 123
Histrogram standardized residual ..................... 142
Observed versus the predicted laboratory fatigue lives of the 55
test samples .................................. 143
Percent difference between the observed and the predicted
laboratory fatigue lives for the 55 test samples ............ 144
Laboratory fatigue life as a function of aggregate angularity, for
different levels of service life ....................... 146
Laboratory fatigue life as a function of pavement service life, for
different levels of coarse aggregate angularity ............. 148
Laboratory fatigue life as a function of sample bulk specific
gravity, for different levels of coarse aggregate angularity ..... 151
Laboratory fatigue life as a function of fines, for different levels
of coarse aggregate angularity ....................... 153
Laboratory fatigue life as a function of AC content, for different
levels of coarse aggregate angularity ................... 154
Observed versus the predicted rate of rutting at the 19 core
locations .................................... 176
Percent differences between the observed and the predicted rate of
rutting for the 19 core locations ..................... 177
Rut depth as a function of the percent fine content, for three levels
of coarse aggregate angularity ....................... 179
Rut depth as a function of the percent air voids for three levels of
coarse aggregate angularity ........................ 181
Rut depth as a function of percent AC content, for three levels of
aggregate angularity ............................. 182

xvi

Figure 5.18 :

Figure 5.19 :

Figure 5.20 :

Figure 5.21 :

Figure 5.22 :

Figure 5.23 :
Figure 5 .24 :
Figure 5 .25 :

Figure 5.26 :

Figure 5.27 :

Figure 5.28 :

Figure 5 .29 :

Figure 5.30 :

Figure 5.31 :

Rut depth as a function of coarse aggregate angularity, for three
levels of the percent fine content ..................... 184

Rut depth as a function of l8-kip ESAL, for three levels of
aggregate angularity ............................. 186

Percent difference between the proposed and as-constructed AC

courses thicknesses ............................. 188
Observed versus the predicted rut depths at 107 core locations . . . 195
Percent differences between the observed and the predicted rut
depths for the 107 core locations ..................... 196
Average peak deflection variation along section 43F ......... 197
Pavement deflection as a function of time ............... 204
Observed versus predicted rut depths .................. 216
Percent error between the observed and the predicted rut depth
values ..................................... 218
Observed versus predicted rut depths for the 563 pavement
locations .................................... 219
Observed versus predicted rut depths .................. 224
Percent error between the observed and the predicted rut depth
values ..................................... 225
Observed versus predicted rut depths for the 5 63 pavement
locations .................................... 226
The maximum, minimum, and average values of the shift factors
of the fatigue life versus the indicated pavement section number . 236

xvii

CHAPTER 1
INTRODUCTION

1.1 GENERAL

The structural design of flexible highway pavements and bituminous overlays has
been an evolutionary processes based primarily on the experience and judgement of
highway engineers, expanded by empirical relationships developed through research and
field observations. The proper design of asphalt concrete pavements and asphalt overlays
requires the consideration of several complex and interrelated factors. Recent efforts
considering the interaction of these factors have resulted in the development of rational
new design models using the elastic and visco-elastic theories. Today, design methods
for flexible pavements and bituminous overlays could be divided into two groups:
empirical approaches, and mechanistic-empirical approaches. The main design
considerations in both groups are to limit the compressive strains induced at the top of
the subgrade to control permanent defamation (roadbed rutting), and to limit the tensile
strain induced at the bottom of the asphalt layer to minimize fatigue cracking. Both
approaches have their advantages and disadvantages. Empirical procedures are relatively
easy to use, are mainly derived from experience (they lack theoretical background), and
are often custom designed, thus, limiting their applications. Mechanistic-empirical design
approaches are based and supported by theory. However, they are unable to model the
interaction of different factors (e, g. , environmental, drainage etc.) which cause pavement
distress.

Rutting of flexible pavements and bituminous overlays is defined as accumulation
of permanent deformation in the wheel path whereas, fatigue cracks are load induced
cracks that can be found in both wheel paths and are accelerated by environmental
factors. Both rutting and fatigue cracking are load related distresses. Rutting and fatigue

cracking potentials are affected by traffic volume and load, material properties,

2

construction quality, layer thicknesses, and the environment. Therefore, any

methodology solely based on empirical or mechanistic approach, will fail to model the

pavement behavior efficiently.

1.2

PROBLEM STATEMENT

A good portion of the pavement network in the State of Michigan is experiencing

premature rutting and fatigue cracking problem. The two types of distresses are caused

by several factors including:

1.

2
3.
4

Heavy vehicle loads and high number of multi-axle trailers.
The existing asphalt mix design practices.

The pavement design process.

Existing construction and quality control practices.

Hence, the need to determine the asphalt mix properties and asphalt mix design

factors that affect the two distresses have been recognized.

1.3

RESEARCH OBJECTIVE

The objectives of this research study are to:

Determine the asphalt mix properties (i,e. percent aggregate, sand and fine,
aggregate angularity, binder type and content, and percent air content) that affect
pavement rutting and fatigue cracking.

Model the rut and fatigue cracks as functions of the asphalt mix properties, traffic
load and volume, and the pavement cross-section.

Recommend changes in the existing asphalt mix design, and construction practices

to decrease rut and fatigue cracking potentials.

To this end, this dissertation is organized into six chapters and two appendices as

follows:

9995“!"

Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Appendix A

Appendix B

3
Literature review.
Research plan.
Field and laboratory investigation.
Analysis and discussion.
Conclusions.
Data acquisition and reduction software for indirect tensile
test.
Pavement cross-section and deflection data for 564

pavement locations.

CHAPTER 2
LITERATURE REVIEW

2.1 GENERAL

The load carrying capacity of flexible pavements is brought about by the load-
distributing characteristics of their layered systems. In general, flexible pavements
consist of a series of layers with the highest quality material placed at or near the
surface. Hence, their strengths are the result of building up thick layers and thereby
distributing the load over the roadbed soil (1). Two types of load related distress can be
found in flexible pavements:

l. Rut - Rut can be defined as the sum of the plastic (permanent) deformations in
the AC, base, subbase, and roadbed soil. Rut is mainly caused by wheel loads
and is accelerated by environmental factors. In general, rut can be minimized by
using stiff materials in all layers and by proper pavement design and construction
practices.

2. Fatigue cracking - Fatigue or Alligator cracking is a series of interconnecting
cracks caused by fatigue failure of the asphalt concrete surface (or stabilized base)
under repeated traffic loading. It is a load associated distress that can be found
in both wheel paths and are accelerated by environmental factors. Fatigue
cracking potential of any pavement can be minimized by using the appropriate
pavement materials, proper design procedure, and good construction practices.
It should be noted that the contribution of the AC layer to the total pavement

rutting due to densification is negligible since, this layer is typically compacted to near

its theoretical maximum density during construction. Permanent deformation in the AC

layer is mainly the results of lateral distortion due to repeated shear deformation (5).
The tensile stresses or strains induced at the bottom of the AC layer due to a

wheel load cause fatigue cracking. In general, fatigue cracks start at the bottom of the

4

5

AC layer and they propagate upwards towards the surface. Hence, fatigue cracks may

exist in a pavement structure for several years before they can be observed.

Consequently, there is no universally adopted standard definition of fatigue failure of

asphalt pavements.

In the laboratory, the fatigue life of a compacted asphalt specimen is defined by
the number of load applications that causes fatigue failure of the specimen. The
definition of fatigue failure, however, varies from one researcher to another. For
example, Santucci and Schmidt (2) defined laboratory fatigue failure as the number of
load applications required to reduce the stiffness of the specimen by 60 percent of its
initial stiffness measured at 200 load applications. Baladi (3), on the other hand, defined
the fatigue life (of a laboratory compacted Marshall size specimen tested by using the
indirect tensile cyclic load test) as the number of load applications at which the
cumulative horizontal plastic defamation (measured along the horizontal diameter of the
specimen) reaches a value equal to 95 percent of the total horizontal defamation of a
duplicate specimen tested to failure in the indirect tensile test mode.

Rut and fatigue cracking potentials of pavement can be minimized by taking
balanced engineering steps during the material design (asphalt mix design), pavement
design process and during construction. These include:

1. Engineered asphalt mix design that can withstand the expected traffic loading
without plastic yielding, resists the induced tensile stress without cracking, and
resists low temperature cracking.

2. Balanced pavement design process that provides adequate layer thicknesses to
reduce the induced compressive stresses at the top of the base and subbase layers
and at the top of the roadbed soil, which causes plastic defamation (rut) of these
layers, and minimizes the tensile stress and strain induced at the bottom of the
AC thereby, increasing the fatigue life of the asphalt layer (see Figure 2.1).

3. Good construction practices that deliver adequate and unifom compaction of the

 

 

 

 

 

 

 

 

 

> :;;_-.;g,_' Compteedveetteutop
v‘r» otbeee

AC

 

,, Cornpreeelve etreee top of
eubbeee

Base :axééiaaafséiiééééi;tii
Base:iizéééiaz:wwiviiisiaas
Road:axsziizziésééééizséi:
Bed ”32:33?Liaééiiihziflr":.z353‘:935:235T::55‘I5:5“I;.=-'3‘L3;i‘=fi;315:f;:¥’53?519’s???

 

 

 

 

 

 

 

 

Figure 2.1 : Illustration of critical stress/strain locations in a typical pavement
structure.

various pavement layers.

Existing flexible pavement design methods can be divided into two categories;
empirical and mechanistic-empirical. Mast empirical design methods are based on
statistical equations derived from field observations of pavement rutting and surface
roughness. Mechanistic-empirical design methods, on the other hand, are mainly based
on two criteria:

1. Minimizing the rut potential of each pavement layer by limiting the magnitude of
the compressive stress induced at the top of that layer by a moving wheel load.

2. Maximizing the fatigue life of the AC layer by minimizing the induced tensile
stress at the bottom of the layer due to a moving wheel load.

Regardless of the pavement design method (empirical or mechanistic-empirical)
employed in the design of flexible pavements, the design process involves two major
steps as follows:

1. The design of the asphalt mix which involves the praportianing of the different '
ingredients (coarse and fine aggregates, mineral fillers, and asphalt cement) in the
mix and the compaction effort.

2. The thickness design of the AC course and the other pavement layers (base and
subbase), which involves the evaluation of the behavior of these layers under the
anticipated traffic load and environmental conditions.

Since the outcomes of the asphalt mix design process (step 1) affect the
engineering properties of the mix, the thickness design of the pavement, and the
pavement perfomance, the two steps (mix design and thickness design) and construction
practices must be considered in a comprehensive way so that the desired pavement

perfomance is assured.

8

2.2 MECHANICS OF PERMANENT DEFORMATION AND FATIGUE
CRACKING

2.2.1 Permanent Defamation (Rut)

Pemanent defamation in flexible pavements manifest itself as rutting in the
wheel paths thereby, causing pemanent distortion in the transverse profile. In addition,
pavement uplift may occur along the sides of the rut. In many instances, ruts are
noticeable only after a rainfall, when the wheel paths are filled with water. Nevertheless,
pemanent defamation of the pavement surface is the result of rutting of the roadbed
soil, the subbase and base layers, and the AC surface. Pavement rutting is mainly caused
by densification or lateral distortion due to traffic loading, hence, rut is a load related
distress. Several other factors affect the magnitude of rut and its time rate of
accumulation. These include:

1. Construction factors including inadequate compaction (either low compaction
effort or compaction at lower temperatures than those specified).

2. Asphalt mix factors that include soft (low viscosity or high penetration) asphalt
cement, high air voids, rounded aggregate, and excess sand in the mix.

3. Environmental factors that include high temperatures which soften the AC layers,
and high moisture content or saturation of the lower layers (base and subbase) due
to inadequate drainage.

4. Tire factors such as studded tires and high tire pressures.

As stated earlier, pavement rutting is the sum of the rut in the AC, base and
subbase layers and in the roadbed soil. Figure 2.2 shows the results of a study of the
transverse profile of loops 4 and 6 of the AASHO Road Test (4). It can be seen that
rutting has taken place in all pavement layers and in the roadbed soil. The contribution
of each layer to the total pavement rut varies from one pavement to another. For

example, the average rut in each layer as a percent of the total pavement rut of section

 

      
 
   
   

Loop 6 6-3-8 Design
30 Kip Single Axle Load
”i"..-_£ ______ .i _______

 
    

 

F .

our1

1 ‘7 .

"1'4. , L.

 

0 2

 

1 .......... ' 1511:“: ________ 1

 

    

 

 

.~ .5~ IJ

 

 

 

1
‘ aeo

J'\

I I

m\\\\\\\

'i' //;i

  
  
      
      

 

\%

 
   
 
   
   

 

Dame: ,

    
  

 

N6
SUBBASE
38‘ IN PK'I’CH

0?

  
 
   
 
   

4 5 4
32 Kip

 

 

,. WW

    
 
  

   

10
51 of the AASHO Road Test, is shown in Table 2.1.

Table 2.2 provides a list of the relative percentages of the pemanent defamation
of section 51 of the AASHO Road Test that are attributable to distortion alone. It can
be seen that, in general, pemanent defamation is largely due to lateral distortion.

Based on laboratory data, Morris (5) concluded that densificatian and lateral
distortion in compacted asphalt concrete specimens are largely a function of the test
conditions. He added that, in the field, asphalt pavements are subjected to densification
in the compression zone and to lateral distortion in the tension zone. Tests on asphalt
concrete used at the Brampton Test Road (6), confirmed the above observations. It was
noted that the rut potential in the tension zone in asphalt concrete pavements is higher

than that in the compression zone because of distortion.
2.2.2 Fatigue Life

With the passage of each wheel load, a cyclic tensile stress is induced at the
bottom of the AC layer which causes cyclic tensile strains. This strain is composed of
three components as follows:

1. Elastic strain which is recoverable upon the removal of the load.

2. Viscoelastic strain which is recoverable after the load has been removed for a
certain time period.

3. Plastic strain which is pemanent in nature and causes the asphalt cement to
stretch and crack.

As the number of load applications increases, the cumulative plastic tensile strains
increases causing further stretching of the asphalt cement until a crack is developed.
Additional load applications causes the crack to widen and to propagate upward toward
the pavement surface where it manifest itself as alligator (fatigue) cracks. Hence, the

plastic strain is the sole cause of the fatigue cracking. A perfectly elastic material

11

Table 2.1 : Average rut (percent of total rut) in each layer of section 51 of

the AASHO Road Test (5).

AC
32

 

Percent of the total rut.
Subbase I Roadbed soil I

IBasel

14

45

9

Table 2.2 : Percent rutting in various layers due to distortion, section 51
of AASHO Road Test, 1960, (5).

 

l

 

 

 

 

 

 

 

 

 

MATERIAL % Rutting due to distortion during a AVERAGE
given season
SPRING SUMMER FALL

A/C SURFACE 82 82 76 80

BASE 0 70 NO Figs.inconsistent
MEASUR.

SUBBASE 9‘7 96 NO 95.5
MEASUR.

 

12
will never develop fatigue cracking (3).

It should be noted that as the fatigue crack initiates at the bottom of the AC, the
tensile strength of the AC is reduced and hence its resistance to tensile cracking
decreases. Therefore, the rate of tensile cracks propagation increases as the width and
length of the crack increases.

Over the last 30-year period, large quantities of laboratory fatigue life data for
compacted asphalt mixtures have been obtained. Traditionally, the data are presented as
stress or strain amplitude versus the number of load repetitions to failure. The resulting
curves are known as the S-N curves. Like metals and other engineering materials, the
fatigue life of compacted asphalt mixtures steadily increases with decreasing stress or
strain amplitude until the stress or strain level of the fatigue limit is reached, below
which the fatigue life becomes infinitely long. In general, tensile stresses at or below
the fatigue limit causes only elastic strains. Based on laboratory fatigue tests conducted
by using indirect tensile and flexural beam tests, Baladi (3) concluded that the fatigue
limit of compacted asphalt mixtures is reached when the tensile stress is about 35 percent

of the indirect tensile strength of those mixtures.

2.3 FACTORS AFFECTING RUTTING AND FATIGUE CRACKING OF
ASPHALT SURFACED PAVEMENTS

2.3.1 Tire Inflation And Tire-Pavement Contact Pressures

In the U.S.A. asphalt surfaced pavements are experiencing premature rutting and
fatigue cracking due to increased traffic volume, loads and/or increased truck tire
pressure. Surveys in the States of Illinois and Texas indicate that the tire pressures have
increased substantially over the last few decades. An average tire pressure of 96 psi with

a maximum of 130 psi were recorded in the Illinois survey. The Texas survey showed

an average tire pressure of 110 psi with a maximum pressure of 155 psi (7).

13
Typically, the rut potential of asphalt pavements has been evaluated on the basis

of the magnitude of the compressive stresses induced at the top of the base layer and

roadbed soil due to an 18-kip single axle load and a constant tire pressures (typically 85

psi). Experimental studies conducted by GoodYear tires and Rubber Company indicate

that (8):

1.

For a constant tire load, increasing the tire inflation pressure causes a shift in the
point of maximum contact pressure to the center region of the contact area
between the tire and the pavement surface.

For a constant tire pressure, increasing tire loads causes a shift of the point of
maximum contact pressure towards the perimeter of the contact area between the
tire and the pavement surface.

Regardless of the tire load and tire pressure, the tire-pavement contact pressure
is not unifom within the tire-pavement contact area. The distribution of the
contact pressure is a function of the tire type and design. For example, contact
pressures as high as twice the tire inflation pressure were measured for three tire
types as shown in Table 2.3.

Smith and Bonquist (9) studied the influence of tire type and tire inflation pressure

on pavement perfomance. They conducted full-scale pavement tests using the Federal

Highway Administration (FHWA) Accelerated Loading Facility (ALF) located at Turner

Fairbank Highway Research Center in Mclean, Virginia. The study examined the effects

of tire pressure, tire load, pavement cross-section, and environmental conditions on

pavement response (stresses and strains) and on pavement perfomance (rut potential and

fatigue life). They made the following conclusions:

1.

The effect of wheel load on pavement responses is greater than the effect of tire
pressure. The measured pavement responses (stresses and strains) doubled for
an increase in load from 9,400 pounds to 19,000 pounds, while increasing the tire

inflation pressure from 76 psi to 140 psi resulted in a less than 10 percent

l4

 

 

 

 

 

 

 

 

 

 

 

Table 2.3 : Effect of tire type and tire inflation pressure on the maximum
tire -pavement contact pressure, (8).
Tire type and Tire-inflation Max. contact. RatioMCP/TIP)
load pressure (TIP) Pressure (MCP).
(psi) (psi)

11-24.5 65 117 1.8
i 4250113. 75 114 1.5
I 95 118 1.2
11124.5 75 122 1.6
H 42501113 95 152 1.6
115 182 1.6

385/65R22.5 100 200 2.0 II
120 226 1.9
140 252 1.8

 

 

 

 

15

increase in the measured response. This conclusion support the results of
mechanistic analysis of flexible pavement structures. For example, Baladi
(unpublished data) used MICHPAVE (a linear/nonlinear finite element computer
program) to analyze the stresses and strains induced in the pavement layers due
to various wheel loads and tire inflation pressures. He reported that the effects of
increasing tire pressure on the induced stresses and strains in the pavement are
much smaller than those due to increasing wheel load.

2. Increasing tire pressure from 76 psi to 140 psi causes less than 30 percent
increase in the expected fatigue damage. Increasing the wheel load from 9,400
pounds to 14,100 pounds, on the other hand, causes an increase in the expected
fatigue damage by 350 to 650 percent. Based on mechanistic analysis of flexible
pavements and the rut and fatigue prediction models embedded in MICHPAVE,
similar conclusion was also made by Baladi (unpublished data). He reported that
an increase in the wheel load by 50 percent causes an increase in the pavement
rut by a factor of 1.4 to 3 and a decreases in the fatigue life by a factor of 5 to
10 depending on the layer thicknesses and material quality. He added that
increasing the tire pressure by a factor of 2, on the other hand, decreases the
fatigue life by a factor of 1.2 to 2 depending on the layer thicknesses and material
quality.

3. The effects of tire pressure and/or wheel load on pavement rutting are much
higher for thin pavement sections (less than 2-inch AC surface) than for typical
or thick sections (more than 4-inch thick AC surface). Further, higher
temperatures cause higher rut potential. Hence, the combinations of high tire
pressure, high wheel load, high temperatures, and thin pavement sections are
extremely damaging to flexible pavements.

Although, the average truck tire inflation pressure has increased by about 20 psi

over the last thirty-year period, the above findings suggest that this increase has an

l6

insignificant effect on pavement rutting and a moderate effect on fatigue life. On the

other hand, the reported increase in wheel load (e.g. , the average wheel-load in Michigan

has increased by 4000 pounds over the last twenty-year period) has significant effect on
both the rut potential and the fatigue life of flexible pavements.

Chen (10) employed the three dimensional Texas Grain Analysis (TEXGAP-3D)
program (a 3-D linear finite element computer program) to study the effects of various
wheel loads, nonunifom tire pressures, and nonunifom tire-pavement contact pressures
on the induced stresses and strains and the resulting damage in asphalt concrete
pavements. Results of the analysis were also compared with those of the ELSYMS
computer program which uses a circular contaCt area with unifom contact pressure
distribution. Chen used two field fatigue distress models developed by Finn et al (one
model is applicable to 10 percent or less of fatigue cracks per area of wheel path and the
other for 45 percent or more). Chen used the two models to analyze the effect of tire
pressure and load on fatigue life. He also utilized a rutting model developed from the
AASHO Road Test data to analyze pavement rutting. He made the following
observations:

1. For a constant load of 4500 pounds, a variation of the tire inflation pressures
from 75 to 110 psi have more influence on the strains at the bottom of a thin
pavement surface layer than on a thick one (see Figure 2.3).

2. For a thin surface course, higher loads consistently produce higher tensile strains
even at a distance of 6-inch from the tire centerline as shown in Figure 2.4.

3. For a constant axle load of 4500 pounds, a 47 percent increase in the tire inflation
pressure produces less than 2 percent increase in the compressive strain developed
at the top of the subgrade as shown in Figure 2.5.

4. For a constant inflation pressure, a 20 percent increase in the axle load produces

approximately a 20 percent increase in the subgrade compressive strain at the top

of the subgrade as shown in Figure 2.6.

17

4 ‘ “A
Tire pressure

1
. 75
2
15 - r _

 

(a)
Q 01

AC thickness (inches)
N
at

 

 

 

topsi
pm
'140 160 180 200 220 240 260 280 300
Tensile strain bottom at AC surface (microstrain)

Figure 2.3 : Variation of tensile strain at the bottom of the AC surface for
different AC thicknesses and two tire inflation pressures (10).

Meloed
sebum swam

1 2 3 4 5 6
Transverse distance from tire centerine (inches)

 

dub-0‘
sssa§

Tensile etreln bottom of AC thickness (mieroetreln)
8

 

 

 

Figure 2.4 : Variation of tensile strain at the bottom of a 2-in. thick surface
pavement with lateral distance from the center of the tire, treated tire
with 90 psi pressure (10).

Figure2.5:

Figure 2.6 :

18

 

O

 

ac thickness (inches)
1°
(I

 

 

 

 

1 .5 r ‘
300 350 400 450 500 550 600 650

Compressive strain top at subgrade (microstrain)

Variation of compressive strain at the top of the subgrade for different
thickness and tire pressure (10).

 

‘ u

3.5

so thickness (inches)

 

 

 

 

1.5 - r -
300 350 400 450 500 550 600 650 700 750 800
Compressive strain top at subgrade (microstrain)

' Variation of compressive strain at the top of the arbgrade for different

AC thicknesses and two Axle loads (10).

2.3.2

19

For a 2-inch thick AC surface pavement and a constant axle load, a 47 percent
increase in the tire inflation pressure results in a 48 percent reduction in fatigue
life using the 10 percent fatigue model as shown in Figure 2.7. whereas, for a 4-
inch thick AC surface pavement and a constant tire inflation pressure, a 20
percent increase in axle load causes a 36 percent reduction in fatigue life for both
the 10 percent and the 45 percent fatigue models as shown in Figure 2.8.

For the same tire inflation pressure, increase in axle load from 4500 pounds to
5400 pounds results in a 50 percent reduction in pavement life based on subgrade
compressive strain as shown in Figure 2.9.

Based on these observations Chen et al. made the following conclusions:

High inflation pressure and heavy load causes higher tensile strains at the bottom

of the asphalt concrete and a significant reduction in the pavement fatigue life.

(The axial load not the inflation pressure has a major influence on subgrade

rutting.

Consolidation And Field Compaction

Proper specifications and quality assurance regarding asphalt mixture composition

and compaction decrease the rutting potential due to densification and offers a benefit in

terms of increased fatigue life.

Barksdale (l l) conducted laboratory study on compacted asphalt mixes composed

of AC-20 asphalt cement and crushed granitic genesis aggregate. He concluded, that for

a range of asphalt content from about 4 to 5 .5 percent, the fatigue life of all specimens

compacted by using 75 blows Marshall compaction is higher than those compacted at 50

blows as shown in Figure 2.10. He added that, the benefits of higher compaction efforts

decrease as the percent asphalt cement content increases from about 4 to 5.5 percent.

Barksdale also cited the work of Raithby, Epps and Acott, and reported that asphalt

20

 

 

 

 

 

 

s
3.5
4“ Tire preset” 75 psi
2 110 “i
'5
a
((3 Treeded tire

2.5

2 . 3K—
1 2 a 4 5 5
Fatigue lite (millions oi cycles)
Figure 2.7 : Fatigue life variation for different AC thicknesses and tire inflation

pressures (10).

 

 

 

 

 

 

 

 

‘ * I —
m r 4‘ / A .
3.5 ,
i as. lead
g t ‘ 4500 pastes
C
'o‘ 3 1
c
it
5
2
2.5 Treeded tire
2 . -
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Fatigue lite (millions oi cycles)

Figure 2.8 : Fatigue life variation for different thickness and tire loads (10).

21

 

 

ac thickness (inches)

 

 

 

 

0 510 152025 3035 404550
Subgrade rutting (millions oi cycles)

Figure 2.9 : Pavement subgrade rutting damage life for different thickness and

 

 

 

 

 

 

 

loads (10).
20
crushes Grenltlc Gneiss
Slendero Greoetloo
0 Ac-zo no r
'2
B
.2
E 9.
=5 5. 10
£- 2
2 z
a
n
I I; L-
E
S
0
4 5 6
Asphalt content (percent)
figure 2.10 : Fatigue life ratio of two asphalt mixes compacted at 50 and 75

blows Marshall compaction versus the asphalt content (1 1).

22
mixes placed in the field at a compaction level equal to the 50 blows Marshall
compaction experienced gradual compaction and densification due to traffic loading.

Several other researchers (12-16) have shown that the fatigue life of asphalt
cement is reduced by about 10 to 30 percent for each 1 percent increase in air voids over
the nomal range of 4 to 7 percent. Finn and Epps (13) evaluated two flexible pavements
with AC thicknesses of 4 and 6-inch. He reported that, when the percent air voids (due
to compaction) is increased from a desirable level of 7 percent to a very poor compaction
level of 12 percent, the 4-inch thick AC layer effectively lasts only as long as the 2-inch
thick layer. Likewise, the life of the 6-inch AC layer is reduced to that of the 4-inch
thick layer. Similarly, Epps and Monismith (17) reported that asphalt mixes placed at
higher percent air voids due to inadequate field compaction experienced shorter fatigue
life and densification under traffic loading. They added that the changes in the fatigue
life due to variations in air void contents cannot be entirely explained by changes in the
mixture stiffness produced by the same variation in air void contents. That is higher
percent air voids produces softer mix and shorter fatigue life. The implication of their
findings is that stiffness alone cannot be used to model the fatigue life of AC mixes.
Higher AC mix stiffness could be produced by higher compaction efforts, higher
viscosity asphalt cement in the mix, and different arrangements of the aggregate matrix
in the mix. Increasing mix stiffness due to compaction is beneficial and it tends to extend
the fatigue life of the mix. On the other hand, increasing the mix stiffness by using
higher viscosity asphalt cement reduces the fatigue life of the mix. Similar findings were
also reported by Baladi (3).

Huges and Maupin (7) monitored the rut depth of asphalt pavements made by
using different asphalt mixes (see Figure 2.11). They measured the rut depth right after
construction, six months, and one year after construction. They reported that mix 1 with
the highest initial voids in the total mix (VTM) has rutted more quickly than Mix 4
which had the lowest initial VTM. This supports the widely held belief that improving

23

0.15

 

0.1 r

 

 

 

 

g 0.05- \
5' o
a \ \‘\$\jmx.
-0.05~ '
-0.1 4 ‘ ‘
5 6 7 8 9

VTMS

Figure 2.11 : Rutting as a fuction of the voids in the total mix (VTM),(7).

24
density during construction reduces rut depth.

Miller (16), based on results obtained from 24 test sites in Arkansas, stated that
asphalt mixtures placed and compacted at air voids between 2.5 to 5 percent provide an
acceptable level of rutting. He added that pavements with deep rutting have air void
contents of less than 1.0 percent. Brown (18) stated that in place air void contents above
3 percent are needed to decrease the probability of premature rutting throughout the life
of the pavement, whereas, air voids of less than 3 percent greatly increase the probability
of premature rutting. Huber and Heiman (19) reached similar conclusion and suggested

that asphalt mixes should be compacted above a threshold value of 4 percent air voids.

2.3.3 Aggregates

The perfomance of asphalt mixes depend on providing adequate aggregate
interlock for resisting and distributing the wheel load rather than on the shear strength
of the asphalt cement. Therefore, the size, shape and angularity, and quality of the
aggregates play an important role in the perfomance of the AC mix. Hence, every
precaution should be taken to insure that a face to face aggregate contact and aggregate
interlocking are provided for the high quality AC mixes.

The maximum aggregate size, aggregate shape, and angularity, and the percent
aggregate content in the mix influence the rut and the fatigue life of asphalt pavements
and Marshall stability and flow of the asphalt mix. Higher aggregate angularity produces
higher Marshall stability, lower flow, and lower pavement rutting (l6,l9,21,22).
Figure 2-12 depicts the rut depth as a function of Marshall stability. Larger top size
aggregate in the asphalt mix, on the other hand, produces higher stability, higher resilient
modulus, higher compressive strength and lower rut potential (24,25).

Herrin and Goetz (26) studied the effects of the percent aggregate in the mix and

aggregate shape on the stability of the mix. They observed that as the percent aggregate

25

3 ..

U ‘0 g

.E

e 3

230% 993! Fitted Eauotion

"' L99 RUI ' 1598 - 0.00496 STAB

92 i 0.490. RMSE a 0.180

aRUT DEPTH3

 

Iii

v vvvvvvv vvvv'v'v'vvv vvvv‘v v‘v vv' vvv vvvvv vvvvv 2‘2'0

"wk.”
JMD MARSZHALL‘O STABILITY“o - 100 lbs

Figure 2-12 : Relationship between rut depth and stability (16) .

26

in the mix decreases, its influence on the stability of the mix decreases. This may be
explained by the fact that as the percent aggregate decreases and the percent sand
increases, face to face aggregate contact is lost producing a ball bearing effect. That is
higher percent sand contents cause the aggregate particles to float in the sand matrix
thereby, reducing friction and stability. Indeed the European Stone Mastic Asphalt (SMA)
mix consists of 70 to 80 percent crushed aggregate. The SMA is well known for its low
rutting potential. In addition for a constant asphalt content, large size aggregates causes
an increase in the density of the compacted asphalt mixtures (27). The increase in density
is more pronounced when the aggregate top size is increased from 3/4 to 2-inch as it can
be seen from Table 2.4. Further, increasing the aggregate top size in a mix causes an
increase in the percent air void and in the percent void in the mineral aggregates (VMA)
as shown in Figure 2.13 and 2.14 (27).

Similarly, based on literature review conducted by Button at e1. (28), he
concluded that the rutting problem can be addressed by using large top size aggregates
(l to l'A-inch), increasing the percent void in mineral aggregate requirements (14 to 15
percent minimum), replacing most or all the natural sand in the mix with manufactured
angular particles, increasing the minimum allowable air void in the laboratory compacted
mix to
4 percent and limiting the ratio by weight of mineral filler to bitumen to about 1.2. Epps
and Monismith (17) reported that crushed (angular) aggregates produce AC mixtures with
high rut and fatigue resistance. Typical requirement for crushed coarse aggregate are:
l. A minimum of 75 percent of particles with two crushed faces.

2. A minimum of 90 percent of particles with one crushed face.

Table 2.4 :

27
Summary of mix densities (lbs/c.fl),(27).

 

 

 

 

 

 

 

 

 

 

 

 

Asphalt Aggregate Top Size
Content
it " 1" 1%“ 2" 2%“
3% - - - 148.77 150.00
4% 143.71 145.50 148.19 151.30 151.38
5% 144.14 148.02 149.68 150.25 149.65
5% 142.96 145.88 148.98 - -

 

 

Figure 2.13 :

Percent Air Voids in the Mix

Figure 2.14 :

Percent Voids in Mineral Aggregate

28

 

20

 

15‘

 

 

 

10 I

Asphalt Content
at by weight of Aggregate

 

 

 

 

 

 

 

 

5 * 3 -o- s
-o- 4 -iv-- a
a 1 L
172 an 1 r 2 r 2 11:
Aggregate Top Size (inches)

Effect of aggregate tap size upon the percent voids in mineral
aggregate (27) .

 

Asphalt Content.
1% by weight o: Aggregate)

+3! +5!

 

1
\t .0.“ .9.“

7“"
/'

 

 

 

 

\.___.
\

 

 

 

 

 

 

 

 

 

 

U2 3/4 1. 1 1/2 2 2 1/2 3

Aggregate Top Size (inches)

Effect of aggregate tap size on the percent air voids in the mix
(27) .

29
2.3.4 Sand and Mineral Filler

The angularity and shape of the sand particles, the percent sand content in the AC
mix, and the type of mineral filler influence the rut and fatigue life perfomance of
asphalt pavements. The Federal Highway Administration (FHWA) recommends that
natural sand (rounded sand particles) be limited to 15 to 20 percent of the total weight
of aggregates for high volume roads and to 20 to 25 percent for medium and low volume
roads (29). Similarly, Button et al. (28) suggested that for high traffic volume roads
limiting the natural (uncrushed) sand particle content of the asphalt mixes to about 10 to
15 percent reduces rut and fatigue cracking potentials. Young (30) cited Barksdale and
Hicks, and reported a significant increase in pavement rutting due to an increase in the
percent sand contents.

Barksdale (11) studied the effect of three types of mineral filler (the dust produced
from crushing aggregates, fly ash and portland cement) on the fatigue properties of
asphalt pavements. He reported that the use of fly ash as mineral filler resulted in a

lower fatigue life than the other two types of fillers.

2.3.5 Asphalt Type And Content

The type of the asphalt cement and its content in an asphalt mix impact the rut
and fatigue life of the asphalt mixes. Typically, the type'of asphalt cement used in an
asphalt mix depends on the environmental conditions. Higher temperature regions require
harder (higher viscosity or lower penetration) asphalts. On the contrary, softer asphalts
are used in the construction of asphalt pavements in cold regions. The asphalt cement
hardness or viscosity affects three types of distress.

1. Fatigue life which is affected by the AC viscosity at inservice temperatures.
2. Rutting- Softer asphalt tends to cause higher rutting potential. Hence, rut is

affected by the AC viscosity at high temperatures.

30
3. Cold temperature cracking- Stiff asphalt cements tends to harden at lower
temperatures and loose its flexibility. Thus, cold temperature cracking is affected
by the AC viscosity at low temperatures.

The effects of the asphalt binder on the various distress modes vary. For
example, a study conducted by the National Research council, Strategic Highway
Research Program (SHRP), found that the binder contribution to the rut potential of the
asphalt course is about 40 percent as shown in Figure 2.15. The other 60 percent is
attributed to the other ingredients in the mix (aggregate, sand and mineral filler) and their
proportions and to the construction practices. Also shown in the Figure is that the binder
contribution to the fatigue life of the asphalt layer is about 60 percent. The other 40
percent is related to the pavement layer thicknesses and properties. Finally, the asphalt
binder contribution to the low temperature cracking potential is about 80 percent.

Traditionally, asphalt binders are classified and specified according to their
viscosities at a given temperature. Two AC binders of the same grade (e,g., AC-20)
may have the same viscosity at the specified temperature. However, their viscosities at
higher or lower temperatures may differ substantially and so their behaviors. This fact
has been recognized in the new SHRP binder specifications which consider three types
of distress: pemanent defamation, themal cracking and fatigue cracking. These
distresses are related to the rheological properties of the binder at high, low, and
intemediate temperatures, respectively.

Huber and Heiman (19) stated that penetration and viscosity of the AC binder do
not possess a significant effect on rutting rate because an asphalt grade typically
produces a similar penetration and viscosity after mixing. They attributed the rutting
perfomance to air voids, voids filled with asphalt and asphalt content. Huges and
Maupin (7) on the other hand, stated that binder type is not as important as aggregate
gradation in minimizing early pavement rutting. Kruts (31) evaluated the impact of

moisture on rutting potential of polymer modified mixtures. He reported that moisture

31

80

70

50

Percent contribution at the AC binder
8

  

10

 

Rutting Fatigue Low Temp. Cracking

Figure 2.15 : Binder contribution to different distresses.

32
conditioning of laboratory specimens before detemining their pemanent defamation
potential yielded a fairly consistent pemanent defamation results for all mixtures
regardless of the grade of the asphalt cement binder.

An excessive amount of asphalt or a very soft grade asphalt can often produce a
mix with high Marshall flow values. A maximum Marshall flow of 16 is often specified
for mix design and construction control. Brown and Cross (32) reported that Marshall
flow is a good indicator of rutting potential. Higher amount of rutting is associated with
mixes having flow values above 10.

Mixes with large aggregates have less asphalt requirement to coat the aggregate.
Case studies of rutted pavements in Oklahoma conducted by Hensley and Leahy (33)
showed that missing intemediate fines in stone-filled mixtures make them less sensitive
to asphalt content. This is due to the fact that intemediate fines increase the surface area
to be coated with asphalt cement and increase their ball bearings effects. Thus, their
absence not only reduces the asphalt requirement but also reduces the sensitivity of the
mix to increased asphalt contents.

Decker and Goodrich (34) ranked five asphalt cement factors relative to their
effects on asphalt pavement distresses. They used a ranking scale from 0 to 5. A
ranking of 0 indicates no effect whereas 5 indicates significant affect. Since, asphalt
cement properties are mainly governed by the source of the crude, they found that the
refining process has a very minor effect on rutting and fatigue cracking. Decker and
Goodrich studied and ranked the physical properties (such as stiffness, temperature
susceptibility) and rheology of the AC binders (see Table 2.5). They made the following
conclusions:

1. Increasing the viscosity of the AC binder causes an increase in the stiffness of the

AC mix which in turn improves the rut resistance.

2. For a thick pavement section, fatigue resistance can be increased by increasing

the binder stiffness. Whereas, softer mixes provide a better resistance for thin

33

Table 2.5 : Effect of asphalt cement factors on
pavement distress (34).

 

ASPHALT FACTORS

PAVEMENT PERFORMANCE

 

 

 

 

 

 

 

 

 

 

 

THERMAL FATIGUE RUTTING MOISTURE

CRACKING CRACKING DAMAGE
REFINING TECHNIQUE 1 1 1 0
PNYSICAL PROPERTIES 6 3 2 1.5
CHEMICAL PROPERTIES 2 2 2 2
AGING 1 3 1 1.5
MODIFICATION 2.5 2.5 2.5 2.5

 

 

34

pavement sections. The reason for this is that aging of the binder causes the AC
mix to stiffen and to loose its flexibility to contract due to low temperatures. For
thin AC pavements, the aged binder may influence the tension zone in the AC
layer thereby, causing less resistance to fatigue cracking. For thick AC
pavements, on the other hand, the aging process affect the upper part of the AC
layer causing higher stiffness in the compression zone and lower tensile stress in
the tension zone. Hence, the fatigue life is increased.

Epps and Monismith (17) conducted tests to detemine the effects of mixture
variables on the flexural fatigue properties of asphalt mixes and reported an asphalt
content of 6.7 percent reduces fatigue cracking (see Figure 2.16). They argued the fact
that increased viscosity or decreased penetration should increase the stiffness of the AC
mix, which in turn should increase the fatigue life at a particular stress level as shown
in Figure 2.17. They cited Jimenez and Heukelom and Klomp for reaching similar
conclusion.

Kim et al. (35) used indirect tensile test to detemined the significance of the
asphalt content on fatigue life of the sample. They reported a significant improvement
in the fatigue resistance of the AC mixes when asphalt content of 0.6 percent above the

optimum asphalt content at 32° P (not at 68° F) is used.
2.3.6 Environmental Factors

Exposure to environment causes the bituminous material to harden over time.
With the passage of time, the bituminous binder becomes so brittle that it can no longer
sustain the strains affiliated with daily temperature changes and with traffic loads. The
rate of hardening is a function of the oxidation-resistance of the binder, temperature, and
thickness of the asphalt film. Therefore, the rate of hardening vary with the binder type,

climate and material design. It should be noted that most of the asphalt hardening takes

35

 

8

/'\
\\
/ \

/£ 0 -Kefser-Chrm
0 e 0 4c: -Ceneerd
/’

 

\ x
N Oi
\

 

 

 

Q

Fatigue L 170 - s [0’

G

 

 

 

 

 

 

 

 

 

5 6 7 a 9
Asphalt Connnr— percent

Figure 2.16 : Effect of asphalt cement on fatigue life- California medium
grading, Basalt aggregate, 60-70 penetration asphalt (l7).

 

ii

 

 

 

 

 

 

it

warm: leper sen

 

 

    

as

 

 

 

 

 

 

 

 

’0 \W
0' 10’ p‘ , 0’ 10‘ 10’
Wbreileve- 4
Figure 2.17 : Bending stress vs. application to failure , for mixes of different

stiffness-California graded mixes, granite aggregate, 85-100,
60-70 and 40-50 penetration asphalt, 6 percent asphalt (l7).

36

place during mixing, agitating, transporting, and construction.

Asphalt durability can be defined as its resistance to change in its
original properties during mixing, construction, and service life. Durability of the asphalt
is not a factor that effects rutting directly. In fact the embrittlement of the asphalt due
to aging can cause increases in both the cohesion and the stiffness of the binder, which
result in a greater resistance to pemanent defamation under loading. Asphalt hardening
on the other hand, adversely affects its fatigue life and low temperature cracking.

Huges and Maupin (7) reported that early pavement rutting is a function of the
temperature of the pavements when it is opened to traffic. They suggested pavement
temperatures of less than 150 °F lead to a stable asphalt mix under traffic.

Vallerga et al. (36) evaluated the effect of asphalt aging (they used the Rolling
Thin Film Oven to produce an aged asphalt) on the fatigue perfomance of AC mixes.
They reported that for a particular stiffness modulus, the aged asphalt resulted in a
greater number of load repetitions to failure. However, it is conceivable that continued
‘ embrittlement of the asphalt through aging beyond some point, adversely affect the
fatigue cracking of the AC pavement.

Paterson (37) reported that bituminous binder hardens due to environmental
exposure, which substantially reduces the fatigue life of thin to medium thick asphalt
pavements. Whereas, the fatigue life of thick asphalt pavements is less effected due to
aging because they behave according to controlled-stress conditions. He suggested that
the timing of fracture is governed by three mechanisms, which are effected by the
interaction of aging and traffic as shown in Figure 2.18. These mechanisms are:

1. Aging mechanism - After construction, the aging of the asphalt course is almost
unifom across its thickness. Because of exposure to the environment, the top side
of the asphalt course will age more rapidly than the bottom side. Therefore,
since the fatigue life is dependent on aging, the available fatigue life at the top of

the AC course decreases more rapidly than that at the bottom side as it is shown

37

 

 

 

ii
A WWII:
mam
Arum
8 ' ,Airietoochgs
3 ~ \
gr. , \
Fruciueot
um delherrnd
otSuioce
hociueDue
”W
D 1 1 1 3
o 2 4 o a 10 12
mite-(wan)
Figure 2.18 : Interaction between traffic related and aging related fatigue

cracking in bituminous surfacing (37) .

38
by curves “A" and ”B" of Figure 2.18.

2. Load induced strains - When the cumulative plastic strain due to repeated load
application reaches the available fatigue life, the AC will fatigue crack. For thin
pavements (high tensile strains at the top of the AC), the top side of the AC
surface will crack first as shown by curve "C' of Figure 2.18. For thick
pavements, on the other hand, the bottom side of the AC surface will crack first.

3. Themal strain - Due to temperature changes, plastic strain will accumulate at the
top and bottom sides of the AC layer. This themal plastic strain is much higher
at the top of the AC than at the bottom because of the temperature variation
throughout the AC thickness. Hence, the top side will experience low temperature
cracking first, as it is shown by curve ”D" of Figure 2.18.

It should be noted that the relative location of curves ”C” and "D" (load induced
or themal strain induced cracking) depends on the traffic volume and the environmental

conditions of the region.
2.3.7 AAMAS Mixture Properties Related to Pavement Performance

A comprehensive study of the effects of asphalt mixture variables on the
perfomance of flexible pavements and on the engineering properties of the mixtures was
sponsored by the National Cooperative Highway Research Program (NCHRP). The title
of the project is Asphalt Aggregate Mixture Analysis System (AAMAS). The asphalt
mix design factors included in this study are: compaction, resilient and creep. modulus,
indirect tensile strength and strain at failure and the compressive strength. Each factor
was ranked on a scale from 0 to 5. A ranking of 0 indicates that the factor has no effect
on the pavement perfomance. A ranking of 5 indicates significant effects (38).

Two static creep and repeated load tests were used in the AAMAS study, the

uniaxial compression and the indirect tensile. The values of the resilient modulus

39
obtained from the first test were used to evaluate the rut potential of the compacted
asphalt mixes. The values obtained from the second test were used to assess the fatigue
cracking potential.

Table 2.6 provides a list of the ranking of the various test outputs. It can be seen

that:

1. The resilient modulus of asphalt mixtures possesses a significant effect on the
fatigue cracking potential, a moderate effect on rut and themal cracking
potentials, and a minor effect on the moisture damage potential.

2. The creep modulus of the AC mixture has significant effect on the rut and
themal cracking potentials, a moderate effect on fatigue cracking, and a minor
effect on moisture damage potential. ’

3. The tensile strength at failure and the indirect tensile strength have significant
effects on both the themal and fatigue cracking potentials and minor effects on
rut and moisture damage potentials.

4. The compressive strength has a moderate effect on rut potential, a minor effect

on moisture damage, and no effects on the fatigue and themal cracking
potentials of the mixes.

Other mix factors such as aggregate particles orientation, which is affected
by the compaction method (the gyratory compaction technique was recommended by the
AAMAS study), the slope and intercept of the creep-time curve (also known as the alpha
and gnu parameters), the tensile stress to tensile strength ratio, and the compressive stress
to compressive strength ratio were also included in the AAMAS study. Their respective
ratings are listed in Table 2.6.

The AAMAS findings and conclusions tend to confim those reported earlier by
Baladi (3), who also provided correlations of the test factors to some of the basic
properties of the mix. For example, Baladi stated that the indirect tensile strain at failure

decreases with increasing the kinematic viscosity of the asphalt binder. The tensile

40

Table 2.6: Summary of ranking of mixture properties related to pavement
perfomance, (38).

 

 

 

 

FACTORS DISTRESS MANI FESTATIONS
Fundamental Engineering Permanent Thermal Fatigue Moisture
Properties: Deformation Cracking Cracking Damage
Resilient Modulus 3 3 S 1
Creep Modulus 5 S 3 I

 

Tensile Strain
At Failure 1 4 S 1

 

Indirect Tensile
Strength 3 0 0 1

 

Other Properties 8 Factors:

 

 

 

 

Particle Orientation 3 3 3 0
Alpha and Gnu 5 1 2 0
Tensile Strength Ratio 2 0 3 5
Resilient Modulus Ratio 3 0 2 4

 

Compressive Strength
Ratio 2 0 0 2

 

 

 

 

 

 

 

41
strength, on the other hand, was related to the test temperature, air voids in the mix, the
’ aggregate angularity, and the kinematic viscosity of the asphalt. He stated that higher
indirect tensile strength implies higher fatigue life and higher resilient modulus of the AC
mix. The higher tensile strength can be obtained by using a lower air void in the mix,
higher aggregate angularity, higher kinematic viscosity of the AC binder, lower
temperatures, or by combination thereof. It should be noted that aggregate angularity was
qualified relative to three descriptive toms: rounded, a mix of 50 percent by weight
crushed and 50 percent rounded, and 100 percent crushed. No attempt was made to

differentiate between those aggregates that were crushed on 1, 2, 3, or 4 faces.
2.3.8 Effects of Mix Manufacturing and Field Placement on AC Mix Perfomance

The objectives of the asphalt concrete mix design include the detemination of the
aggregate gradation that meets the required specifications in terms of percent voids in
mineral aggregates (VMA), percent air voids, density, and stability. Any change from
the specifications will affect both the rut and the fatigue life of the AC mix. The rut and
fatigue potentials of AC mix are significantly affected by the compacted density of the
mix. Hence, factors related to manufacturing, laying, and compacting asphalt mixes that
affect the density will also affect the pavement rut and fatigue cracking potentials.
Further, most of the aging of the AC binder takes place during the mix manufacturing
and transporting, and during pavement construction. Hence, these factors affects the
fatigue and low temperature cracldng potentials.

Scherocman and Acott (39) studied the affect of AC mix manufacturing,
transportation, and placement on pavement performance and reported that:

1. Manufacturing- A number of factors can affect the quality of the aggregate
during mix production. The most important one is the proportion of each

aggregate delivered from the cold fwd bins of asphalt plant. Secondary factors

42

are segregation and contamination with foreign material and dust. The handling
of the asphalt cement during the production of the asphalt concrete mixture can
affect the properties of the produced mix in a number of ways. A reduction in
the stiffness of the asphalt concrete mix (caused by a variation in the asphalt
content) can greatly change the characteristics of the mix. The second most
significant factor is the aging or hardening of the binder during production.
Proper storage of the AC binder in the asphalt plant tank, will not cause
appreciable hardening of AC binder. On the other hand, if the material is
overheated, excessive hardening of the binder asphalt cement can occur.

Placement - Ambient temperature, wind velocity, and rain at the time of mix
placement affect the ability of the paver to properly distribute the asphalt mixture
across the roadway and to compact them. The ambient temperature will affect
the rate of cooling of the mix and thus, its change in stiffness. Although,
environmental conditions during placement does not directly affect the rut and
fatigue cracking potentials, they affect the compaction process which in turn
influences the mix perfomance. Further, inadequate placing can produce a
teared and rough surface causing increase in the air void contents. The higher
air contents affect both the rutting and fatigue cracking potentials of the AC mix.
Compaction - The primary effect of environmental conditions on the compaction
of an asphalt concrete mix is on the time available for compaction. Higher air
temperatures, cause a lower rate of cooling and provide a longer time period for
compaction (typical minimum compaction temperature is 175°F). Three types of
compaction equipment are nomally used to compact asphalt concrete mixtures:
static steel wheel rollers, pneumatic tire rollers, and vibratory rollers. Each type
of roller exerts its own compaction efforts. Compaction equipment which is
capable of densifying the mix more quickly produces lower air voids in the mix.

In general, vibratory rollers are able to impart a greater degree of density per

43
pass to the mix than are pneumatic tire rollers and static rollers. All roller types
however, can achieve the same level of density in the mix if enough time is

available for proper compaction.

2.4 PERMANENT DEFORMATION PREDICTION MODELS

The proper pavement design and pavement management systems must be capable
of predicting the pavement perfomance with time, the service life, and the remaining
service life of the pavement structures. Rut is one type of distress that must be predicted
during the pavement design and the pavement evaluation processes. In several countries,
an overlay is applied when the rut depth of the pavement is of the order of 20 to 30 mm.
In the U.S.A., the maximum acceptable rut varies from one State Highway Agency
(SHA) to another and it depends on the pavement class (interstate versus farm to market
roads).

Current rut prediction models can be divided, in general, into two groups:
mechanistic and mechanistic/empirical. The mechanistic models are based either on the
theory of elasticity, theory of plasticity, or the Viscoelastic theory.

Barksdale (40,41), Heukelon and Klomp (42), Romain (43) and others have
suggested that layered elastic theory can be used to calculate the induced stresses and
strains in the pavement due to traffic. The plastic strain can be assumed to be
proportional to the elastic strain and the number of load repetitions. In this type of
analysis, the relationship between the plastic strain and the applied stress for each
pavement component can be obtained from laboratory repeated load test along with either
linear or nonlinear elastic theory. Nonlinear theory should provide more accurate results,
but its use has been limited because of its complex nature. Rut prediction cannot be
made directly from plastic stress-strain relationship although, it provides a considerable

insight regarding material behavior.

44

Barksdale and Leonards (44) suggested that rutting can be estimated by assuming
that the pavement can be represented as a Viscoelastic layered system. The plastic strain
can then be predicted by using the material characteristics obtained in the laboratory from
the creep tests. Elliot and Moavenzadeh (45) suggested the use of the linear rather than
the nonlinear Viscoelastic theory due to its mathematical complexities for predicting
structural response.

Morris (5) cited Kenis and a study conducted at Washington State University Test
Track and reported that the rut prediction obtained by using linear Viscoelastic theory
were substantially lower than the actual measured rut depth. For the test track, after
247,000 load repetitions, the linear Viscoelastic theory predicted rut depth in the order
of 5 to 10 percent of the actual measured ones.

The complexities involved with the theoretical prediction models tempted the
researchers to develop mechanistic/empirical models to predict rutting. Some of these
models are presented below.

Leahy and Witczak (46) assessed the influence of repeated triaxial test conditions
and mix parameters on the pemanent defamation characteristics of asphalt concrete and

presented a statistical model of the fam:

log“ 6, = -15.83+7.132 x log,.m+l.los xlog,. (S)-0.118 x Iog,,(V)+2.155 x
log..(EAC)+l.117 xlog,. (VOL)+0.986 x mm!" x VMAW') x

'08" “4”) (2.1)
R2 =0. 82

Where;
= pemanent defamation;
test temperature (°F);

= deviator stress (lb/inz);

<‘D—im
Ii

= viscosity at 70° F (10° poise);
EAC = effective asphalt content (percent by volume);

45
VOL = percent air void;
TTEMP = test temperature (°F);
VMA = percent void in mineral aggregates; and
LN = load repetition.

A sensitivity analysis of the above equation showed that the temperature is by far
the most significant variable. The model is less sensitive to loading conditions, material
type and mix parameters (46).

Based on laboratory test data Morris et al. (6) presented the following regression

equation, to predict pavement rutting:

E, =f(o,,a,,T,N):l:E (2.2)
Where

e, = amount of pemanent strain;

a, = vertical stress;

or2 = horizontal stress;

T = temperature;

= number of load applications; and
E = The estimate of error associated with any attempt to predict
or, as a function of the other four factors.

The laboratory developed model was used to predict the observed rutting at the
Barmpton Road Test. Although the model does not account for the effect of the AC
thickness, the binder type, and the percent air voids, the overall predicted and observed
values were comparable as shown in Figure 2.19.

Baladi (47) correlated AC mix and other pavement layers properties to predict the

rut depth in the AC layer. He presented an equation of the fam:

46

 

 

 

 

5' as - .
. -"'0-- MEASURED
E —x-— neucrzn I
3 05i- 1 seat confluence unravel. [/1
i
g . ‘ l’e
p. 0.4 -
5 I l’
a.
g ”L I -'.’ ’1'”
ML 1 r g]. 1 r
i '9 2 E E E E E
5 § 5 i § § i 3
TIME
figure 2.19 : Permanent deformation as a function of time (Brampton Road

Test section 3), (6).

47

LOG(RD) = -1.6 + 0.067 x(AV) - 1.4x(log(TAC)) + 0.07 x(AAT)
- 0.000434x(KV) + 0.15x(log(ESAL)) - 0.4x (log(MR.,)
- 0.50x(log(MR,) + 0.1x(log(SD)) + 0.01x(log(CS))

- 0.7xaog('rn,o)) + 0.09x(log(50-(TAC + T3,, m (2.3)
where

LOG = natural log;

RD = rut depth (inch);

AV = the percent air void in the mix;

TAC = thickness of AC layer (inch);

AAT = average annual temperature (°F);

KV = kinematic viscosity at 275 °F (AASHTO T-201)
(centi strokes);

ESAL = the number of 18-Kip ESALs at which the rut depth is
being calculated;

MR” = resilient modulus of roadbed soil (psi);

MR3 = resilient modulus of the base material (psi);

SD = pavement surface deflection (inch);

CS = compressive strain at the bottom of the AC layer; and

TBBQ = equivalent thickness of base material (inch), which is the

actual thickness of the base layer plus the equivalent
thickness of the subbase layer; equivalent thickness of the
subbase layer is equal to the actual thickness of the subbase
layer reduced by the ratio of the modulus of the subbase to
that of the base material.

Baladi, concluded that air voids is the most important factor affecting rut and

higher air voids lead to higher rut potential.

48
2.5 LABORATORY FATIGUE CRACKING MODELS

Several Phenomenological and mechanistic models have been suggested to
represent fatigue cracking. Phenomenological models are based on Miner’s law. They
express ”intemal damage" in terms of crack geometry, stress, strain and the energy in
the vicinity of the damaged region irrespective of the molecular mechanisms involved.
The main drawbacks of these models are that they do not satisfactorily account for the
influence of pavement geometry and material heterogeneities and they do not provide a
quantitative measure of the extent of cracking in pavements. Mechanistic models are
complex, impractical to use, although they do provide quantitative description of the
degree of cracking in pavements (48).

Pell and Cooper (49) studied the effects of AC mix factors on the laboratory
fatigue life of asphalt mixes. Mix variables were correlated to the laboratory fatigue life

and the following regression equation with a correlation coefficient of R2 = 0.877 was

reported.
log N = 4.13 x logrv,)+6.9s x raging-11.13 (2.4)
where
N = laboratory fatigue life;
Va = volume of binder(percent of total volume); and
Tm, = ring and ball temperature.

To make use of laboratory results they didn’t suggested any shift factor. Based
on their study they concluded that asphalt content is the most important variable affecting
the fatigue life.

Baladi (3) used the results of stress-controlled indirect tensile tests on Marshall
size specimens, to develop a fatigue model using statistical methods. His model is
presented below:

LOGINJ = 36.631 - 0.1402X(T'I') - 2.300XLOG(CL) - .5095X(AV) -
.001306 x (KV) + .06403 x (ANG) (2.5)

49

where
LOG = natural log;
Nf = laboratory fatigue life;
'I'I‘ = test temperature (°F);
CL = cyclic load (pounds);
AV = air void (percent);
KV = kinematic viscosity (centistoke);
ANG = aggregate angularity.

Based on limited field observations of in-service flexible pavements in Michigan
and Indiana, Baladi reported that the predicted laboratory fatigue life of asphalt samples
were 20 times less than the fatigue life of the observed pavements.

Irrespective of the procedure used, fatigue life of a pavement cannot be predicted
with a reasonable accuracy due to the following reasons:

1. Fatigue life is dependent upon the stress distribution in the materials and other
environmental and material factors.
2. The stress distribution in a pavement system depends upon the thickness and the

characteristics of the different pavement layers.

2.6 MATERIAL ALTERATION

Rutting and Fatigue cracking are the primary load related distresses in flexible and
composite pavements. Efforts are being made to overcome this problem by changing the
design methodology, altering the material properties and by use of additives. Various
asphalt additives are being promoted to increase the stability of asphalt mixes and to
improve their perfomance. For example, the use of large size aggregates and little fines
is often arbitrary recommended to optimize the interaction and contact among the coarse

aggregate particles in the mixes and to overcome the problem of rotting. Brown et al

50

(24) evaluated the perfomance of different aggregate gradations using aggregate maxi-
mum nominal size of 1% to lA-inch (see Table 2-7). They observed significant increases
in the creep perfomance, resilient modulus and tensile strength as the maximum nominal
size increases: whereas, the maximum nominal size has no significant effect on Marshall
stability. Other researchers (25, 28, 50) also recommended the use of larger size crushed
aggregates with low angular sand content to improve the resistance of asphalt mixes to
rutting and fatigue cracking.

Recent development in Europe produced AC mixes that consist of high percent
contents of coarse aggregate, asphalt binder, and low percent content of sand-size
particles (the mix is called Stone Mastic Asphalt ,SMA) (51). SMA mixtures are being
used in the U.S.A and in the State of Michigan. Comparison of the aggregate gradation
for SMA and Michigan 20AAA rut resistance mix are shown in Figure 2.20. Due to an
increase amount of crushed aggregate, which provides face to face aggregate contacts and
interlocking, the SMA gradation provides a better guard against rutting. Presently, the
Federal Highway Administration is in the process of evaluating the SMA’s feasibility for
its implementation in the U.S.A.

To improve the perfomance of asphalt concrete, a variety of materials have been
promoted over the years as asphalt binder modifiers. For a modifier to be successful,
the benefits offered by its use should offset the increase in the cost of production of the
asphalt mix. Binder modifiers can be classified into 6 generic types as shown in Table
2.8. The most common modifiers used by State Highway Agencies are polymers.

Polymer modified asphalts have the following potential benefits over straight asphalts:

1. Increasing the viscosity of the binder at high temperature.
2 Reducing the themal susceptibility of the binder.

3. Increasing the cohesion of the bitumen.

4 Increasing the resistance to pemanent defamation.

51

Table 2.7 : Gradation ranges for asphalt concrete mixes, (24).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grading Designation
Sieve A B C D E
Designation
2 inch 100 -- .. .. ..
I '16 inch 97-100 100 - - -
1 inch - 97-100 100 - -
16 inch 66-80 - 97-100 100 -
V2 inch - - 76-88 97-100 -
Vs inch 48-60 53-70 -- - 100
No. 4 33-45 40-52 49-59 57-69 97-100
No. 8 25-33 25-39 36-45 57-69 62-81
No. 40 9-17 10-19 14-22 14-22 22-37
No. 200 3-8 3-8 3-7 3-8 7-16
(Federal Highway Administration)
1 _ nan—=—

 

 

PERCENT "SM

52

STEVIOPCMW
cases a as a a s s s a s s
00000 c- «N v 0 O 2 a a 8 a

 

 

 

 

 

 

 

 

ABSCISSA SCALEO TO STEVE
OPENINGS. 1N MILLIME‘I’ERS
RAISED T0015 men.
assess Q I 15 fl 0 4 m m m been i-ncn Ih-tncn M m
use-
mm
Figure 2.20 : Aggregate gradation curves and mix design criteria: SMA

compared with MDOT 20AAA (51).

0390".“ INIOW

53

Table 2.8 : Different binder modifiers.

 

 

 

 

 

 

Modifier Type Modifiers Encountered Most Promising
Modifiers
Dispersed Polyethylene (PE), Ethylene acrylic copolymer PE
Thermoplastics Atectic polypropylene (APP), Polypropylene Uax
(PPM), Ethylene acrylic copolymers,
hydroxylterminated Polybutadiene (HTPB)
Network Neoprene, Styrene-butadiene-styrene (SSS), SBS/SEBS,SBR
Thermoplastics Styrene-ethylene-butadine-styrene (SE85),
Styrene-butadiene copolymer (SBR), Styrene-
butadiene latex, Ethylene-vinyl acetate (EVA)
Reacting Epoxy, Elvaloy, AM, Furfursl, Maleic anhydride Epoxy
Polymers (MAM), Chromium trioxide (Crag) I
Fiber Cellulose fiber, Mineral fiber, Glass fiber, Cellulose fiber
Polyester fiber.
Rubber Microfil 8, Crumb rubber modifiers (CRM) from Microfil 8, CRM

passenger car and truck tires

 

 

Others

 

 

 

 

 

54

Collins et al. (53) reported that an AC mix containing 6 percent by weight of
Thermo Block Copolymers (TBC) lead to a 7.5-fold increase in rut resistance. Based on
a comprehensive series of laboratory tests using polymer additives, Carpenter and
Vandam (54) concluded that polymer modified asphalt cement, particularly at high
temperatures, slightly increased the fatigue resistance of bituminous mixtures and
significant improved rotting at 100 °F.

Under the SHRP program (52), 38 asphalt modifiers were evaluated by surveying
various State Highway (SHA) and binder manufacturers. Based on the results of the

survey, the following conclusions were made:

1. Polymers were identified to be the best suited against permanent deformation (see

Figure 2.21, 2.22 and Table 2.9,2.10).

2. Polymer and reclaimed rubber improve the asphalt mix resistance against fatigue
cracking.

Higgins (55) suggested the use of liquid modifiers and reported that Manganese-
based modifiers improve the strength and reduce the deflection of full-depth asphalt
concrete so that heavy loads may be supported over an extended time period.

Today, a number of asphalt additives are sold in the market with the claims of
improving the asphalt mix resistance against key distresses. These additives usually add
significantly to project cost, therefore, it is important to determine their effectiveness

under field conditions and to evaluate the cost effectiveness of their use.

2.7 MATERIAL CHARACTERIZATION

2.7.1 State of Stress

Under a static load uniformly applied to a circular area at the top of a full depth
asphalt, the elements immediately below the center of the loaded area are subjected to

principal stresses vertical "a,” and horizontal "a3” . Figure 2.23 shows the distribution

55

 

8

 

Performance Ranking
0

 

 

 

I Polymer U Uta-ens and lease
lialmd Rubber 86m»
(50) '- /uum’ ’M-Gaodant o.”
\I'Iller
21313234352519725368141127336
Modifier Identification Number
Figure 2.21 : Modifier ranking bar chart for fatigue cracking. (52).

 

lOO

  
 

53-“ 0.3:: «.23: 43.2):

0'
O

62.2! 42.3): OLIX

 

 

 

 

 

I Polymer g Catalyst "' 2x

B Bitumen and Ileana In."
(50)

Performance Ranking
0

E Reclaimed Rubber 6 Anti-Oxidant

filler

 

 

 

{100)
21 25 32 34 19 31 8 27 6 28 1‘ 38 24' 35

Modifier Identification Number

Figure 2.22 : Modifier ranking bar chart for permanent defamation (52).

56
Table 2.9 : Analysis of SHA questionnaire: Modifiers most commonly used (52).

 

 

 

 

 

 

 

 

 

 

 

 

 

Responses
Modifiers (Percent)
A. Polymers 86
B. Anti-Stripping Agents 77
C. Fillers/Fiberlextendera 59
0. Recycling Agents 43
E. Catalyst 25
F. Aging Inhibitors 16
6. Others:
36

Ground Tire Rubber

Gilsonite 9

Trinidad Lake Asphalt 7

 

 

 

 

Table 2.10 : Analysis of SHA questionnaire: Primary targeted pavement distress

 

 

 

 

 

 

 

(52).
r:—
Responses
Distress iPeroentl
A. Permanent deformation 24
8. Fatigue Cracking 20
C. Moisture Susceptibility 21
D. Low Temperature Cracking 20
E. Aging 15

 

 

 

 

 

ASPHALT CONCRETE

I SUBGRADE £

 

 

(o) ELEMENTAL
STRESSES

57

 

Nausea ‘

 

 

 

 

c - COMPRESSION
1 - TENSION

(b) DISTRIBUTION (c) DISTRIBUTION
' OF 0’. OF 0',

Figure 2.23 : Typical pavement stress distribution under static loading.

58

of a, and a, with depth. Different state of stress are induced in asphalt concrete
pavements due to a wheel load as shown in Figure 2.24. These states of stress and their
relative locations are:
1. Compression at the surface and immediately underneath the wheel.
2. Lateral tension combined with vertical compression at the
bottom of the AC layer and immediately underneath the load.
3. Lateral tension at the surface at some distance from the load.
4. Lateral compression at the bottom of the AC layer at some distance from the
load.

These state of stresses cannot be duplicated in the laboratory. Consequently,
different tests are needed to represent different stress states. To evaluate the asphalt mix
properties, several tests are presently being used. The Marshall, Hveem and Hubbard
tests are used to determine the proportioning of the different components in the mix.
Triaxial, indirect tensile and flexural tests are used to determine structural properties
needed as input to mechanistic and mechanistic-empirical pavement design methods.
Presently, the only laboratory technique that can be used to closely duplicate the field
stress conditions is the wheel tracking test. A scaled model of the pavement section
representing field condition is constructed in the laboratory and traffic loading is
simulated by a loading wheel mechanism capable of applying different load intensities.
The wheel tracking test however, is not available in most of the research facilities.
Hence, researchers often utilize conventional testing techniques.

Asphalt mix tests (e,g.. Marshall) provide information relative to proportioning

of different components in the mix. However, they do not provide any information

59

 

__!A5E ___1_: Triaxiai Compression
CASE 3: Primarily Lateral Tension

Tension
Compression

 

Tension
Compression

 

 
  

Compression

    

Tension

cxse I: Primarily Lateral Acsrahaltt
Compression oncre e

CASE 2: Vertical Compression
Lateral Tension

 

 

 

 

 

Figure 2.24: Typical stress states in the asphalt concrete layer with wheel load
applied.

60
regarding the structural properties (e. g, permanent deformation, fatigue life) which are
needed for the design of the pavement structure (3). Hence, a second group of tests
(triaxial, indirect and fiexure) are used to determine the structural properties of the
mixes.

Triaxial test was recommended and used by researchers (6,56,57,58) for material
characterization due to its low cost and relatively accurate estimates of material proper-
ties. In this test, cylindrical samples are used to determine the stress-strain behavior.
The samples may be subjected to a lateral confining stress and an axial stress is applied
to the ends of the sample. In a conventional triaxial test, the axial load is steadily
increased and the sample defamation is monitored until failure. In the triaxial cyclic
load test, the sample is subjected to a constant or a pulsating confining pressure, and a
cyclic axle load (simulating a moving load). The main limitations of triaxial tests are
(30,59):

1. The presence of end friction between the specimen’s cap and the loading
mechanism which restricts lateral deformations.
2. Lack of capability to apply shear stresses to simulate a moving load.

Recall that the critical location for fatigue cracking and rutting (due to lateral
distortion in the tension zone) of the asphalt layer is located at the bottom of the layer
(see Figure 2.1), where tensile stresses can be found along with vertical compression.
This configuration of stresses can be simulated in the indirect tensile test.

Several researchers recommended (6,60,61) the use of tensile test to characterize
the pavement deformations. Reynaldo (62) cited Roque and Ruth and reported that
modulus values determined using strain gauge measurements obtained in the vicinity of
the center of the face of an indirect tension specimen resulted in admirable predictions
of the strain and deflections measured on full scale pavements at low in-service
temperatures. Baladi (63), pointed out the problems with the existing indirect tensile test

apparatus (Schmidt’s apparatus). He devised a new indirect tensile test apparatus and

61

after testing 412 Marshall size test samples using the new apparatus reported that:

l.
2.

The test results were consistent and very reasonable.

Maximum of only seven percent difference was observed between results for any
triplicate.

Poisson’s ratio was found to be a function of the mix variable and its value varied
from 0.2 to 0.42 for all specimens. For any triplicate specimen, the values were
almost the same.

More meaningful, reasonable and consistent fatigue lives were obtained for all
test specimen as compared to fiexural cyclic load tests.

The plastic deformation can be analyzed both in compression and tension modes
and the test results were more consistent than those obtained from cyclic load
triaxial tests.

The indirect cyclic tensile test procedure recommended for the Baladi’s apparatus

is practically the same as that found in the ASTM D-4123 with the exception that

deformations can be measured in all three directions. The indirect tensile testing mode

seems to be both practical and versatile for determining the properties of asphalt concrete

and it was employed in this research.

2.8

TEST PARAMETERS

In order to predict the behavior of inservice pavement from the results of

laboratory tests on different pavement components, it is essential to perform the testing

in a way to simulate field conditions. Hence, the test parameters must be chosen to

closely represent the most realistic field conditions. The effects of test parameters on the

test results are discussed in the following subsections.

62
2.8.1 Pulse Shape

Barksdale (64) noted that, in the field, the form of the stress pulse changes with
depth. He reported that vertical stress pulse varies from a near sinusoidal near the top
of the pavement structure to a more triangular shape at the lower portion of the base
course. Allan and Thompson (65) described the vertical stress pulse as generally
sinusoidal with a sharper peak near the surface and a flatter top in deeper portions of the
base course. In general, sinusoidal wave form simulates traffic loading better than any

other wave form and it was adopted in this study.

2.8.2 Pulse Duration and Rest Period

The stress pulse applied by a moving wheel loads (under actual in-service
conditions) lasts about 0.01 to 0.1 of a second (30). This duration time is mainly
dependent upon the speed of the vehicle and the position of the element under
consideration within the pavement structure. The speed of a vehicle is inversely related
to the load duration. That is, the load duration decreases with the increase in the veloci-
ty of the vehicle.

Maclean (cited by Morris (5)) reported that (for a limited number of load
applications) the rest period is an important factor affecting permanent deformation.
Snaith (cited by Morris (5)) conducted his testing with and without rest periods for higher
number of load repetitions. He concluded that the rest period is not a significant
variable. Bonnaure et al. (66), tested 9 by 1.2 by 0.8-inch rectangular beam specimens
in the stress and strain controlled modes and reported the effects of the rest period upon
the fatigue characteristics of asphalt concrete mixes. They observed higher number of
load cycles to failure for longer rest periods. They concluded that the most beneficial
rest period is equal to 25 times the loading period. Young (30) reported insignificant

effects of the rest period on the resilient modulus of a bituminous mixture for the

63
conditions of short stress duration and low temperature. However, it has significant
effects at higher temperatures when the behavior of the asphalt mixes is nonlinear.
Baladi (3) and Roque (67) used a rest period of 0.4 seconds for their studies. In general,
conflicting data exists on the effects of stress duration and rest period. For the purpose
of this study a load duration period of 0.1 second and a rest period of 0.4 second were
selected. These two periods, simulate the loading time of one axle load and the time
delay at a point between two consecutive axles of a vehicle travelling at 55 miles per

hour.

Brown and Snaith (56) reported an increase in the permanent strain with a
decrease in the frequency of the applied vertical stress. They added that permanent strain
is time dependent for frequencies of more than 1 cycle per second. Terrel and Awad (68)
reported similar findings to those of Brown and Snaith. Monismith et al. (69) studied
the effects of load frequency and stress reversal on the fatigue properties of asphalt
mixtures. They used a frequency range from 3 to 30 cycles per minute. They concluded
that, for a given load level, higher frequencies causes lower strain and that the test
frequency has no effect upon the mix behavior in repeated flexure. Many researchers
(56,63,68) have employed 0.1 second loading time and 0.4 second relaxation period

which are considered to appropriately simulate traffic loading.

2.9 SUMNIARY

Rotting and fatigue cracking of asphalt surfaced pavement structures are load-
related distresses that are affected by several factors including:
1. The asphalt mix properties.
2 Inadequate construction practices (e. g. , compaction, segregation).
3. Softening of the asphalt binder due to high temperatures.
4

Strength and type of the materials used in the various pavement layers.

64
5. Softening of the base, subbase, and roadbed materials due to moisture infiltration
and freeze-thaw cycles.
6. Heavy multi-axle vehicles.

Although all the pavement layers (AC, base, subbase and roadbed soil) contribute
to rutting and fatigue cracking, the contribution of the asphalt concrete (AC) layer alone
could be very significant. Adequate asphalt mix design, manufacturing, and construction
practices, increase the resistance of the AC layer to rat and fatigue cracking. The AC

mix variables that affects rutting and fatigue cracking potentials include:

1. The percent coarse aggregates and sand contents in the mix.
2. The aggregate angularity.

3. The percent asphalt content.

4. The asphalt grade (viscosity or penetration).

5. The percent air voids.

Numerous statistical fatigue cracking and rut depth models for AC surfaced
pavements have been developed. Generally, the models are based on laboratory data
(laboratory prepared samples) and are extended to predict field rut and fatigue cracking
by using a transfer or a shift function. These models are either based, solely on the
material properties or they take into account the effect of 18-kip ESAL. Further,
existing shift factors are generalized for all pavement sections.

The use of laboratory prepared samples to evaluate AC mixes have some
drawbacks. For example, the laboratory prepared samples may or may not represent the
actual conditions in the field such as the level of compaction. Hence, the use of core
samples eliminates this problem.

The significance of the AC mix variables affecting rut and fatigue cracking
potentials using laboratory prepared samples is affected by the test conditions and the
range of the values of the variable in question. For example, a low percent contents of

coarse aggregate has an insignificant impact on the rut and fatigue cracking resistance of

65
the AC mix. However, investigating the coarse aggregate at high contents will have a
significant affect on the rut and fatigue cracking resistance as the aggregate interlocking
is mobilized due to aggregate face to face contact (26, 51).

The effect of the aggregate angularity on rut and fatigue cracking potential is
often evaluated in terms of the percent contents of angular (crushed) and rounded
(uncrushed such as river gravel) particles without considering the number of the crushed
faces (3). For example, aggregates crushed on one face only would not have the same
effects as those crushed on 3 or 4 faces.

The objectives of the asphalt concrete mix design include the determination of the
aggregate gradation that meets the required specifications in terms of the percent voids
in mineral aggregates, the percent air voids in the mix, density, and stability. Any
change from the specifications will affect rut and fatigue life of the AC mix. Hence,
manufacturing, laying, and compacting asphalt mix practices that cause appreciable
variation in the properties of the compacted AC mix would impact the pavement rut and
fatigue cracking potentials.

To this end, the objectives of this study are to:

1. Select test sections that are representative of the various pavement sections
encountered throughout the State of Michigan and are subjected to various levels

of traffic load and volume.

2. Obtain representative core samples.
3. Test the pavement cores to determine their physical and engineering properties.
4. For each cored pavement section, determine the variability of the material and

layer thicknesses along the section. This information can be used to calibrate the
construction practices and to enhance the existing quality control.

5. Develop a test procedure to characterize aggregate angularity in terms of the
number of crushed faces.

6. Determine the combined effects of traffic and material properties on pavement

66
rutting.
Asses the laboratory fatigue life of the pavement cores and develop a relationship
between the fatigue life and the asphalt mix properties.

Develop shift factors relating the laboratory and field fatigue lives.

3.1

CHAPTER 3

RESEARCH PLAN

INTRODUCTION

The research plan for this study has evolved around the policy, practices, and

acceptance specifications of the Michigan Department of Transportation (MDOT)

regarding the asphalt mix design procedure. Thus, for completion, the MDOT policy

and standard specifications are addressed below.

As is the case for most State Highway Agencies (SHA), the MDOT policy and

standard specifications for asphalt mix design have changed over time. Three sets of

specifications that belong to three time periods can be identified as follows:

1.
2.
3.

AC mixes made prior to 1979 (see Table 3.1).
AC mixes made between 1979 and 1992 (see Table 3.2).
AC mixes made after 1992 (see Table 3.3).

As it can be seen from Tables 3.1 and 3.2, the basic features of, and differences

between, the early (prior to 1979) AC mixes and those made between 1979 and 1992 are:

l.

The specifications and tolerance limits for the AC, base and binder courses are
the same in both sets of specifications. For the base course, the percent passing
of six sieves (1.5", 1", 3/8", No. 8, No. 30, and No. 200) are specified. For the
binder course, on the other hand, the percent passing of 4 sieves are specified.
The maximum possible percent sand (passing the number 8 sieve) contents for the
base and binder courses are 65 and 45 percent, respectively.

For the two sets of AC mixes number 4.09 and 4.11; and 4.13 and 4.22; the
specifications and tolerance limits in both sets are the same.

For the AC mix number 4.12, the earlier specifications have been enhanced by
adding tolerance limits for sieve number 4 and modifying the percent passing for

67

(58

 

.26.. cow. .2. 95.3.. 53 3.3. .359 >289 >1 .3235 of 63: 2a 3223! 221a- oecuosoe .8 can: 8:33 :23

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o.o.m.o .mp.s o~.mn oo..oo co. u.n.uun.<.n neon nos-ou-oca

o.o.m.o .m..~ oh-mm ac..uo co. a.n.«un.<m~ u..gn.¢ neon -..

m.—.m.o co. m.n.uun econ ecu-ou-oca

o.o.n.n a... co. ”an.mun u..ga.< econ n...
o..« o..m oo.o~ oo..oo co. man.aon.<.n L.>L.c.o:
a.“ 9-. o~.om oo..oo oo— aan.uun.<.n s.>p...oa
a.“ o-n mo.mm oo..no oo— aan.mun.<m~ :u.>..c.o:
o.m u.e oh-me oo..oo co. .man.mun.¢m~ u.>»....:
c.. «-9 me-m~ oo..oo ca. «an.mun.<.n .:._.s.4
o.. «-9 ne-m~ oo..uo co. u.n.«un.<m~ .c...sun
o-e n.o m¢-m~ oo..oo cc. «an.aun.<o touc.u ~_.c
L.m o,.n os.o~ mo.o¢ oo.oo co. <a~ seaso>oa
A.“ o.-n me.o~ o~.ms oo.mo oo..mo cc. <<c~ .oo‘...o F..¢
9v ~T~ 9.8 2-3 no.3 oo— 8~ e958
o.. o..~ o..o~ mo.oe oo.ao oo— ‘a~ ou.ctam
o.e o..~ me.o~ o~-me oo.mo oo..no co. <¢a~ ..a<.._o oo.e
o.n ~.-o me.me mo.on oo.mm co..oo on, uc~ oucaou «an. me.»

83... 8.2. 92. “.2. .5... .5... .5... .5; 5.5
a ego...” .263 8.228.. .58... ~58... .33 880.32 88: mafia-fin

 

 

 

 

 

.85 3 See 838 3. 82.: .3 £5: 8:823 e... 82.858& .582 a 3 use...

 

69

 

n. 39 26.. 3 3:38.. an :2. .8er season «9:.— as» .o aceucoo cola... e5 .3953 ~ 5 one:

.0953 c3 22 co» 3.:er- IIZao e u :23 5.53 see. accused

e..e 3.5:? 085 c2! 2.

.25.- 8~ .o: 9:33 .3» 3...: segue >290... El .3835 05 .33 see 3323! Seine ocean-soc co can: eoueeaae :25 e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o.o-m.o .m..~ o~.mn oo..oo co. «an.mun.<pn ac.“ nos.ou..aa
o.o-m.o .m..~ o~-mm oo.-oo as. u.n.mun.<m~ u..ga.< an.“ -.oz -.c
m...m.° co. «an.mun ucam ou~aou..aa u:aa.uota
o.o.m.m o.-. co. «an.mun u.-;a.< neon nF.oz n...
9.-“ o..« 99.95 oo,.oo co. «an.mun.<pn L.>»..-a: L:~..oa
o-“ 9-. m¢-m~ 95.9“ mo-oo oc..oo co. «an.mun.<.n x.>L.c-g: z:~..oa
a-“ o.n me.m~ mo.mm ms.mm oo.-oo co. man.mun.<m~ :u.>h.t.oa :o:~_.oa
a.“ o.« m¢-m~ o~.ne n~.mm oo..oo co. .man.uun.<m~ u.>».toga u:~..oa
o.. n-o mn.m. mq-m~ oo.on oo..oo co. «an.uun.<—n oc..o>od L4~p.oa
n.. m.o mn.m. me.m~ oo.on oc..uo cc. man.mun.<m~ u:..o>od u.~..oz
o.. m.o ne-m~ oo..oo co. «an.mun.< touc.. ¢~..oa ~..c
..~-m o—.n cq-o~ mo.oe ao.ao oo- «aN “cases-a ¢o~....oa
..L.m o.-n m¢.o~ °~.nq oo.mo oo..mo so. ¢<o~ ..u<.u_. ¢<o~....oa ...q
..u.« ~..~ me.o~ o~.oe mo.oo co. .o~ outaou uo~.o.oa
..o.n o_.~ o¢.o~ mo.oe oo.oo co. <o~ caucus“ <o~.o.o=
..c.m o..~ mc-o~ oh-nq mo.no oo,.mo co. <<o~ .uu<.u.. <<c~.o.oz oo.4
o.n ~..o mc.m. mo-on oo.mm oo.-°o co? uo~ oacaou anon n.oa no.n
x.: c.» oo~.o= on.oz o.o. m.o= e.oa .c. a .c. s. .c. a .c. p .c.:. so. cqecoa
clad; age.“ 33:33.. 9:33 aceocea .33 330.52 ease: 9552: 305:5;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANS—AR: 82:8 3. 2.2.5 .8 5.5. 8:833 E; 8:858... see:

u N5 035—.

 

70
Table 3.3 : MDOT AC mix design criteria (1992).

 

 

 

 

MIXTURE MO. 2 3 6

MIXTURE TYPE C B C B C 8 13A 13 11A 36A 368
VMA MIM X 12.5 12.0 16.5 16.0 15.5 15.0 16.5 16.0 12.0 16.0 15.5
AIR V0105 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
XTARGET

 

FINES/ASPHALT 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
RATIO MAX

 

FLOM MUMDERTMS

 

0F AM IMCM 8°16 8-16 8-16 8-16 8-16 8-16 8-16 8-16 8-16 8-16 8-16
L. A. ABRASIOM 60 60 6O 60 60 60 60 60 50 60 60
MAX. 1 LOSS

 

SOFT PARTICLE 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0
MAX.(%by weight)

 

 

 

 

 

 

 

 

 

 

 

 

 

FIME AGO. 6.0 3.0 6.0 3.0 6.0 3.0 2.5 2.0 2.5 3.0 2.5
AMGULARITY

 

 

71
sieve number 8.
The 1979-1992 specifications requires that (for AC mixes placed in two courses),
the percent AC binder of the lower course be 0.5 percent lower than that of the
upper course.
Both sets of specifications do not address the percent air voids in the mix or the
percent voids in mineral aggregates.

The 1992 specifications (see Tables 3.3 through 3.6) are based on several criteria

including:

1.

2
3.
4
5

S"

The percent air voids in the AC mix and the percent voids in mineral aggregates.
The maximum ratio by weight of the fines to the AC binder.

The angularity of the fine aggregates (sand). 6

The Marshall flow.

Maximum losses by weight of 40 and 50 percent based on the Los Angeles
abrasion tests. A

One directional commercial average daily traffic (ADT).

Thickness of the AC layer.

The new specifications ( 1992) are more strict in terms of the percent passing

through any particular sieve. For example, comparing the new base mixes 2C (see Table

3.4) and No. 5 base mix (see Table 3.2) it can be seen that, for the No. 5 mix the

percent by weight in the mix of the aggregate larger than the 93-inch sieve, can be any

where from 10 to 45. Whereas, for base mix 2C, the maximum percent passing the %

sieve has been specified, thus, ensuring that the mix contain more of the coarser

aggregate. Comparison between the new (1992) and the old (1979) specifications

indicates that, in general, the new specifications calls for less amount of fine (minus #200

sieve) and higher percent of crushed aggregates (plus #4 sieve) depending on the one

directional commercial ADT in the design lane (see Table 3.5). Table 3.6 presents the

recommended placement thickness and usage of the mixes. The new specifieations were

72
Table 3.4 : MDOT specifications and tolerance limits for AC mixes (1992).

 

MIXTURE NO. 2 3 6

 

MIXTURE TYPE C 0 C B C 8 13A 13 11A 36A 368

 

BITUMEN X 3-6 3-6 6-7 6-7 5-8 5-8 5-8 5-8 6-6 5-8 5-8

 

 

 

 

 

 

 

 

 

 

 

 

 

STEVE NO. - PERCENT PASSING TNE INDICATED STEVE

1 5 inch - - - - - - - - 100 - -

1 inch 100 100 - - - - - - 80-95 - -

5 inch 90 max 90 max 100 100 - - 100 100 70-90 - -

6 inch 73 max 78 max 90 max 90 max 100 100 75-95 75-95 60-80 100 100
N inch 70 max 70 max 77 max 77 max 90 max 90 max 60-90 60-90 55-80 92-100 92-100
Mo. 6 52 max 52 max 57 max 57 max 67 max 67 max 45-80 65-80 35-75 65-90 65-90
No. 6 20-60 20-40 28-45 28-45 33-52 33-52 30-65 30-65 25-65 55-75 55-75
No. 16 10-30 10-30 18-33 18-33 20-37 20-37 20-50 20-50 20-50 - -
No. 30 8-22 8-22 10-25 10-25 15-27 15-27 15-40 15-60 15-60 25-50 25-50
No. 50 5-17 5-17 5-19 5-19 10-20 10-20 10-25 10-25 8-25 - -
No. 100 4-15 4-15 5-15 5-15 5-15 5-15 5-15 5-15 4-15 - -
No. 200 3-6 3-6 4-6 4-6 6-6 4-6 3-6 3-6 3-6 4-10 6-10
Crushed 95 50 95 50 95 50 25 O 25 60 40
Min X

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3.5 : MDOT AC mix selection criteria (1992).

 

 

One Hey Crushed
Commercial Mixture Aggregate
ADT Type 1 by Height
0-99 13 or 11A 0 or 25
100-250 A 25
251-10000 B 50
1001-3500 C 95

Over 3500 Special Provision

 

 

 

 

 

73
Table 3.6 : Recommended AC mix placement thickness (1992).

 

 

Mix Course Single Course
Type (lift) Thickness (inch)
28, 2C* Base 2 to 2'].

3B, 36* Base, Level lit to Z'I:

68, 60 Top 1 to 1%

11A * Base 2 to 31$

13, 13A* Base, Level, Top 1ll to 2'1:

 

 

 

 

 

Use bituminous mixture-11A for any base course over 2%" total thickness
(regardless of commercial ADT) except for rubbelized concrete projects. For
rubbelized concrete projects use bituminous mixture-C or B for the base course
regardless of the thickness. First layer over rubbelized concrete shall be a
minimum of two inch.

74
adopted (April 1992) after the start of this study. Therefore, the new mixes are not
included in this study.

3.2 RESEARCH PLAN

Over the last few decades, the number of heavy multi-axle trailers using Michigan
roads has substantially increased. This resulted in higher rutting and fatigue cracking
potentials. The resistance of the AC mixes to rut and fatigue cracks is a function of the
AC mix properties (percent coarse and fine aggregate, angularity of the aggregate, and
the asphalt binder content and viscosity), the pavement design process, construction
practices and environmental factors. Recall that (see Chapter 2) one of the SHRP studies
concluded that forty percent of rotting, sixty percent of fatigue cracking and eighty
percent of thermal cracking potential may be attributable to the asphalt binder alone
whereas, the remaining percentages of the respective distresses can be attributed to the
other properties of the AC mix and to the overall design-of the pavements. This suggests
that rat and fatigue cracking resistance of AC mixes can be enhanced by changing the
properties of the AC mixes to withstand the present day traffic conditions and to perform
satisfactorily over the design life.

Research studies nwd to be conducted to establish the AC mix factors that
enhance the resistance against rutting and fatigue cracking of the mix. Study of factors
affecting the rut and fatigue cracking potentials of the AC mixes involves several steps
including (see Figure 3.1):

1. Selection of existing pavement sections having various asphalt grades and percent
asphalt contents, aggregate types and angularity, gradation, and various types of
fines and percent fine contents, various AC thicknesses, different levels of traffic
volume and load, and different service lives.

2. For each selected pavement section, the rut and fatigue cracking data are

75

measured and core samples are obtained. Because of economical reasons and
time constraints, the number of cores have to be limited. Variations of the
pavement properties along the pavement sections can be analyzed by using
nondestructive deflection testing data. The deflection basins may also be used to
analyze the rut potential of those pavements.

3. The cored samples are then brought to the laboratory for testing to determine the
asphalt mix properties. These include the elastic, Viscoelastic and plastic
properties, gradation, the asphalt content, the air voids and the angularity of the
aggregate.

4. A statistical study whereby the properties obtained in step 3 are related to the rut
and fatigue cracking data of step 2.

5. A sensitivity analysis whereby the effects of the various parameters of the
statistical models of step 4 on the rut and fatigue life are assessed.

Details of the pavement site selection and the field and laboratory investigations

are presented in Chapter 4.

 

 

 

76

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Obtain
traffic
data P-]
Obtain __J
construction
history
Conduct Statistical]
Obtain -— laboratory —- mechanistic
cores tests analysis
Make
rutting and

fatigue cracking

”ISUPMES

 

 

 

 

Figure 3.1 : Overall research plan.

 

Determine
factors
affecting
rutting and

fatigue
cracking

 

 

 

Conduct
sensitivity
analysis

 

 

 

 

4.1

CHAPTER 4
FIELD AND LABORATORY
INVESTIGATION

PAVEMENT SELECTION

The pavement section selection was accomplished in consultation with personnel

from the Michigan Department of Transportation (MDOT). The main criterion used in

this selection is that the selected sections should represents the spectrum of pavement

cross-sections, paving materials, and traffic volume and load found throughout the State

of Michigan. In this regard, the following variables were identified and prioritized prior

to the selection of the pavement sections.

1.

Asphalt Course Thicknesses - Thin (less than 3-inch), moderately thick (3- to 6-
inch), and thick (more than 6-inch) asphalt surface.

Traffic Volume and Load - Heavy, moderate, and light traffic loads and volumes
in terms of the 18-kip equivalent single axle load (ESAL).

Pavement Types - flexible pavement without overlays, flexible pavements with
overlays, and FCC pavements with overlays.

Cross-Sections - One layer (AC only), two layers (AC and base), and three layers
(AC, base and subbase).

AC Mixes - Stability based and standard type mixes.

Roadbed Type - Cohesive and cohesionless soils.

Pavement Surface Age - Newly constructed and/or rehabilitated (less than 3-year
old) and older pavement sections.

Distress Types - Rut and fatigue cracking.

Table 4.1 provides a list of the combination of variables used to prioritize the

various flexible and composite pavement sections and the weight factors assigned to each

variable. The values of the weight factors are based on the importance of the variable in

77

Table 4.1 : Criteria for finial section selection.

78

 

 

 

 

 

 

 

 

 

 

 

 

Flexible Pavemems Composite
Pavemefls
Factor eight Factor Weight
raffic (ESAL) Traffic (ESAL)
Us!“ 3 Us!“ 3
Heavy 4 Heavy 4
‘ knees (inch) Thickness (inch)
Thin < 3' 3 This < 3' 2
Medium 3 To 6" 2 Medium 3 To 6" 3
Thick > 6' 2 Thick > 6" 4
Cross Section AC Overlay
2 Layers 3 1 Course 2
3 layers 2 2 Cause 2
4 layers 2 3 or more 3
Courses
AC Courses (no Number of Overlays
overlay). 1 Overlay 2
Less than 3 l 2 or more 2
More than 3 l Overlays
IAC (overlay) l erlay Age (years)
Less than 3 2
. New Mix 2
Sad
Sand 2 Old Mix 2
Clay 2
Pavemera Age (years) iPavemsm Dim .
less than 3 2 Fatigue 2
New Mix 2 Rut 2
Old Mix 2 fatigue and Rut 2
Pavemem biases
Fatigue 2
Rut 2
Fatigue and Rut 4
T

 

 

 

79

question to this study. For example, heavy traffic loads (high percent commercial
vehicles travelling the pavement section) were assigned a weight factor of 4 while light
traffic loads were assigned a weight factor of 3. likewise, a weight factor of 2 was
assigned to each of the following types of distress, fatigue cracking and rat. Hence, the
weight factor of a pavement section showing either rut or fatigue cracking is 2 the weight
factor for a pavement showing both fatigue cracking and rut is 4, and the weight factor
of a pavement section with no fatigue cracks and/or rut is zero.

Based on the above criteria and the various variables, 200 pavement sections (150
flexible and 50 composite) of variable lengths (one to several miles) were initially
selected. For each pavement section, the MDOT pavement management system data
base and the MDOT 1987 sufficiency rating book were used to obtain the location
reference point, construction and rehabilitation history, rut, fatigue cracking, shipping,
other distress data, traffic volume and load, cross-sectional data (layer thicknesses and
types), and other general information. The data was then tabulated in a spreadsheet.

For each of the 150 flexible and 50 composite pavement sections, a score (based
on the variables and their weight factors) was then calculated. A pavement score consists
of the sum of the weight factors assigned to each variable. The pavement section with
the highest score was given the highest priority. Based on the pavement score (priority),
the 49 flexible and 15 composite pavement sections with the highest priorities were
chosen and they are included in this study. Tables 4.2 and 4.3 provide lists of the
flexible and composite pavement sections chosen in this study. Other data such as
pavement type, route number, direction (north, south, east, or west bound), district,
control section number, and the beginning and ending mile post of each pavement section I
are also listed in the Tables.

For each of the 49 flexible and 15 composite pavement sections, the pavement
condition data (obtained from MDOT data bank) was examined. It should be noted that
the MDOT data bank does not identify fatigue cracking as a separate distress category.

Table 4.2 :

80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Selected flexible section's.
ction Pave Route Dir. District Central Mile Post
a. ment i - 1 1 N s 1 Section From To
Type US-22 S-2
M -33 E-3
W-4
1 AC 3366 1 3 40061 2.00 13.00
2 AC 3350 3 8 23052 1.30 14.00
3 AC 3334 3 6 46041 1 .50 1 1 .20
4 AC 3372 3 3 40023 0.00 6.00
5 AC 3326 3 1 66022 3.00 14.40
6 AC 3350 4 5 34021 4.50 8.00
7 AC 22131 1 S 54014 8.00 11.10
6 AC 33136 3 6 79011 1 6.70 19.90
9 AC 3320 4 5 54022 0.00 0.60
10 AC 3326 3 1 31021 4.60 9.60
1 1 AC 3344 3 5 41051 4.20 5.20
12 AC 1196 3 5 61152 1.20 5.40
13 AC 2227 1 8 18034 1.61 1.80
14 AC 3377 1 2 75052 8.00 1 0.00
15 AC 2227 2 4 20016 0.00 6.30
16 AC 22131 1 3 63031 2.50 3.00
17 AC 22131 1 5 54013 0.50 8.41
16 AC 2227 1 4 20016 0.00 6.30
19 AC 1 175 1 4 69013 0.00 6.00
20 AC 3366 1 5 59051 1 1 .90 13.20
21 AC 3319 1 6 74032 0.00 10.00
22 AC 3362 4 5 62041 0.00 5.90
23 AC 3326 3 1 66023 6.60 1 1 .00
24 AC 3399 1 8 3301 1 4.30 4.60
25 AC 22131 2 3 63031 3.00 2.00
26 AC 3357 3 6 25102 2.85 2.95
27 AC 1 175 1 4 72061 7.00 1 3.40
28 AC 1175 1 4 1 6093 0.00 5.90
29 AC 3399 1 8 23092 2.20 7.30
30 AC 1 175 1 4 69013 6.00 7.00
31 AC 3326 4 1 66051 0.00 4.00
32 AC 22131 1 5 59012 11.00 11.10
33 AC 22131 2 5 54014 8.50 8.60
34 AC 33129 1 2 17072 12.10 19.30
35 AC 1 175 1 4 16091 0.00 1.50
36 AC 1175 2 4 72061 13.30 7.00
37 AC 1 175 1 4 72061 19.00 23.66
36 AC 3366 1 3 57013 6.20 12.71
39 AC 222 3 2 21024 4.60 14.60
40 AC 1175 1 4 20015 4.10 9.10
41 AC 1175 1 4 20015 9.10 14.20
42 AC/RC 1194 3 7 11015 13.00 15.00
43 AC 1194 3 7 11015 3.00 7.00
44 AC 2223 1 4 71073 24.70 26.71
45 AC 1 175 1 4 20015 0.00 1.00
46 AC 3366 1 3 40061 0.00 1 .22
47 AC 3361 8 3 16041 8.65 8.92
46 AC 3349 1 8 - 30011 1 1 .00 17.00
49 AC 1 175 2 4 72061 16.60 17.50

 

 

 

81'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.3 : Selected composite sections.
Section Eavement Fioute Dir. District Control Mile Post
Lo. Type I =1 1 N=1 Section From To
US= 22 S: 2
M =33 E=3
W=4
1 Composite 1194 4 6 81 104 5.60 7.90
2 Composite 1194 4 8 81104 1.90 5.60
3 Composite 3350 3 6 46081 1 .10 3.00
4 Composite 22127 1 6 30071 0.00 4.90
5 Composite 2241 1 1 7023 6.48 14.01
6 Composite 22223 3 8 46061 2.60 3.60
7 Composite 22127 1 6 4601 1 4.50 5.18
6 Composite 3350 3 6 46061 6.30 13.20
9 Composite 2241 1 1 7013 0.00 3.10
10 Composite 3350 - 3 8 46081 3.00 8.30
' 1 1 Composite 3325 3 6 32012 12.00 19.90
1 2 Composite 3325 3 6 3201 2 1 9.90 27.90
13 Composite 22127 1 8 30071 9.80 10.30
14 Composite 22127 1 8 30071 4.90 9.80
15 Composite 1 175 1 9 63173 9.25 9.50

 

 

 

 

 

 

 

 

 

82

Rather, it identifies the severity and extent of smoking (which includes all types of
cracking). That is, when cracking data is found in the data base, it implies that the
cracked pavement section may have edge cracking, temperature cracking, fatigue
cracking, transverse cracking, or a combination thereof. Consequently, only the rut data
in the MDOT data bank were considered accurate and relevant. Nevertheless, the rut
data for each pavement section was examined and, within each section, several loo-feet
long pavement sites showing rutting problem were identified and they were labeled as test
sites. For some pavement sections, the test sites were adjacent to each others while for
some others, they were separate.

During the Summer of 1991, four members of the Michigan State University
(MSU) research team visited each test site. The purposes of the visit were to:
1. Verify the location reference point, pavement type, and general conditions.
2. Mark the test sites.
3. Inspect, measure, and record the extent and severity of rutting, fatigue cracking

and other types of distress.
4. Identify those test sites to be cored by MDOT.
5. Mark locations for nondestructive deflection tests (NDT) within each test site.
The rut depth was measured by using a six foot straight-edge leveling rod, a graduated
triangular wedge with an accuracy of 0.025-inch and a scale with accuracy of 0.06-inch.
The rut was measured in the outer wheel path over each marked core location and at
several other locations along the test site. The fatigue crack was recorded in terms of
severity and the percent of the loo-feet long test site showing alligator cracking.
Further, a total of 107 loeations were designated for pavement coring. Each test site and
NDT and core locations were given specific designation numbers. The coring method

and the designation numbers are presented in the next section.

83
4.2 MARKING, CODING, CORING AND NDT

Each test site was designated by a two-number system. One number designates
the pavement section and the other designates the test site. For example, a test site
designation of 29-1 indicates the first test site of pavement section number 29. It should
be noted that, for all pavement sections, the test site number increases from south to
north and from west to east.

Some test sections were selected for coring (see Table 4.4). The cores were
located either in the outer wheel path, between the wheel paths, or in the inner wheel
path of the traffic lane. In addition, some cores were located over an existing longitudinal
crack. Each core location was designated using a seven digit number. Starting at the
left-most digit, the first two digits indicate pavement section number; the third digit
indicates pavement type (1 for flexible and 2 for composite); the fourth digit designates
the site number; the fifth and sixth digits indicate the distance of the core loeation from
the beginning of the site; and the seventh digit indicates the core number within that site.
For example, a core loeation designation of 2712402 indicates (left to right) that the test
is conducted on section 27, flexible pavement, test site number 2, at 40 feet from the
beginning of the site, and is the second core at the site.

The cores were obtained by using a power auger equipped with a 6—inch coring
bit. A hand auger was preferred over a power auger to obtain disturbed samples from
non-stabilized base, subbase and roadbed soil. The reason for this is that different layers
can be easily identified. Most of the cores obtained from the wheel paths were utilized
for resilient modulus and, extraction testing to determine material properties and fatigue
life. The laboratory test procedures are presented in section 4.3 of this chapter.

Non—destructive deflection tests (NDT) using a falling weight deflectometer
(FWD) were also conducted at several locations along each test site. The NDT tests

were divided into two categories as follows.

Table 4.4 :

34

List or cored sections.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ection Proposed
0. Total AC Concrete Base Subbase
Thickness Thickness Thickness Thickness
Gnohes‘l
7P 7.2 0 4 18
10F 4.54 0 6 18
13F 4.17 0 6 32
14F 2.93 0 6 16
19F 3.75 0 6 8
29F 13.5 0 11 0
35F 7.25 0 8 28
43F 12.44 0 6 18
10 10.5 8 0 0
4C 2.75 6 0 0
5C 5.9 6 0 0
BC 4.5 6 0 0
1 10 4.09 8 0 0

 

 

 

 

 

 

 

85
1). Regular tests - Each test site (100’ long) was subjected to five FWD tests (a test
is 3 drops). The tests were conducted at equal intervals of 20’ starting at the
beginning of the test site.
2). Additional tests - For cored test sites, additional FWD tests were conducted over
the core location.

Each FWD test is designated by using an eight digit number. Starting at the left
most digit, the first two digits indicate pavement section number; the third digit indicates
pavement type (1 for flexible and 2 for composite); the fourth digit designates the site
number; the fifth and sixth digits indieate the distance of the test location from the
beginning of the site; the seventh digit indieates the sequential drop number (drop number
1, 2 or 3); and the eighth (right most) digit indieates test location (0 indicates regular test
in the outer wheel path, 1 for additional test in the outer wheel path, 2 for additional test
at the center of the lane, 3 for additional test in the inner wheel path, 4 for a test at a‘
joint in the outer wheel path, and 5 for a test at a joint in the inner wheel path). For
example, an FWD test designation of 27124020 indicates (left to right) that the test is
conducted on section 27 , flexible pavement, test site number 2, at 40’ from the beginning
of the site, and is the second drop of a regular test in the wheel path.

4.3 LABORATORY INVESTIGATIONS

This section provides a summary of the laboratory test procedures used to
determine the physical and engineering characteristics of the materials. Various
laboratory tests were conducted to assess the properties of the core materials obtained
from the various test sites. Since these tests are standards of the American Society for
Testing and Material (ASTM), only the ASTM test designation numbers and the purpose
of the tests are mentioned. For details of the test procedure, the reader is referred to the
“Annual Book of ASTM Standards” Volume 4.03.

86
As noted earlier, all pavement cores were obtained by MDOT. The cores were
then transported to the MSU laboratories and they were:

1. Inspected to document the possible existence of distress such as cracking and
stripping, and to determine the thicknesses of the various AC courses.

2. Subjected to specific gravity tests to determine the bulk specific gravity (ASTM
D-2726) before cutting and handling.

3. Cut by sawing to obtain 2.5-inch thick test samples.

The 2.5-inch thick, 6-inch diameter samples were then subjected to the following
tests.

1. Bulk specific gravity (ASTM D-2726).

2. Indirect cyclic load test to determine the resilient modulus, fatigue life, and
permanent deformation characteristics along the horizontal and vertieal diameters
of the samples.

After the completion of the indirect tensile tests, several test samples of similar

AC courses and thicknesses were combined along with some of the untested cores. The

combined materials were then subjected to extraction tests. The purpose of the extraction

tests are to determine:

1. The percent asphalt, fine, sand, and coarse aggregate contents.

The penetration of the recovered asphalt cement.

The top size and gradation of the aggregates.

The coarse aggregate angularity.

9'95”!”

The theoretical maximum specific gravity of the AC mix.
A brief description of each test procedure and data reduction are presented in the

next sections.

87
4.3.1 Indirect Cyclic Load Tensile Test for Bituminous Mixtures

Several researchers recommended the use of indirect tensile test to characterize
compacted asphalt mixes (6,59,60,6l,62). Baladi (62,70,71), pointed out some of the
problems associated with some existing indirect tensile test apparatus (e,g. , the Schmidt’s
apparatus) and devised a new one. He concluded that tests conducted by using the new
apparatus are:

l. Consistent and very reasonable.

2. Repeatable (a maximum of only seven percent difference was observed between
results obtained from any triplicate specimens).

3. More meaningful, reasonable, and consistent fatigue lives were obtained for all
test specimen as compared to flexural cyclic load tests.

Hence, the Baladi’s new device (see Figure 4.1) along with an MTS closed loop servo-

hydraulic system were used in this study. Details regarding the testing equipment can

be found else where (72). The data acquisition software is contained in appendix “A”.

A modified version of the ASTM standard test procedure D-4123 was used to determine

the resilient characteristics and fatigue lives of the asphalt mixes. Modifieations of the

D-4123 test procedure include:

1. A 50 pounds sustained load was used. The ASTM standard procedure does not
specify any value for the sustained load.

2. The ASTM recommended cyclic load range is 10 to 50 percent of the tensile
strength of the test sample. The older specifications recommended cyclic load of

25 pounds. A cyclic load of 300 pounds was used.

The reasons for these modifications are:

a). Under a 25 pounds cyclic load, the sample deformation along its thickness

was within the accuracy of the measuring system (Linear variable

differential transformers with .00001-inch accuracy).

88

Loading Head

Frictionless

. é—sGuiding System

   
 
  
   
 
 

Top Loading
strip

Asphalt Sample

LVDT
LVDT

LVDT
Bottom Strip

Figure 4.1 : Baladi indirect tensile test apparatus.

89

b). The test results obtained by using the 300 pounds cyclic load were more

consistent than those using the 25 pounds cyclic load.

All the indirect cyclic load tensile tests were conducted to failure. During each
test, the sample resilient and permanent deformations were collected along the vertical
and horizontal diameters and along the thickness of the sample. Since only the
deformation from any 2—directions are required to calculate the resilient modulus and
Possion’s ratio of the specimen, the least square technique was used such that the sum
of the errors between the properties calculated by using the data from any 2-directions
were minimized (3,62,70,71). This resulted in the following equations for resilient
modulus and Possion’s ratio of a 6-inch diameter sample (Harichandran, R. S. , 1992,
private communication, Department of Civil Engineering, Michigan State University,
East Lansing):

D = 1.1045791 (H’+ W-l-A’) - (H - 0.0627461 V + 0.319145 A)’ (4.1)
MR = (0.253680 H - 3.9702876 V - 0.0142874 A)ID (4.2)
v = (0.225127 11’ - 0.269895 V’ - 0.086136 AH - 3.570975 HV - 1.145064 AV)ID (4.3)
where;

H = Dfl LIP;

V = DV UP;

A = DA /P;

DH = the horizontal resilient or total deformation of the specimen along

the horizontal diameter (inch);

D" = the vertical resilient or total defermation of the specimen along the
vertical diameter (inch);

D A = the longitudinal resilient or total deformation along the longitudinal

axis (thickness) of the specimen (inch);

90

P = the magnitude of the applied cyclic load (pounds);

MR = the total or resilient modulus depending on the type of deformation
used (psi);

L = the sample thickness (inch); and

v = the total or resilient Possion’s ratio.

The resilient modulus and Possion’s ratio were calculated at load cycle number

500 by using equations 4.1 through 4.3. Further, the following protocol was used for

all samples:

1.

For each cored pavement section, 3 cores were used to obtain 6-inch diameter
and 2.5-inch thick test samples. The bulk specific gravity of the sample was
determined prior to the commencement of the cyclic test.

On the average, 2 test samples of 2.5-inch thick were obtained from each core.
The location of each test sample within the core was a function of the thickness
of the core and the thicknesses of the various asphalt courses within the core.

Care was taken as not to include more than one asphalt course in one sample.

.For all cores with an asphalt course thickness of more than 2.2-inch, a test

sample was sawed from the core such that the sample consisted of only one
asphalt course.

For all cores with an asphalt course thickness of less than the required minimum
of 2.2-inch, the test sample was sawed from the core such that one test sample
consisted of two or more courses. Hence, only the global behavior of the asphalt
courses were determined.

No tests were conducted on any friction course.

For test samples with more than one asphalt course, the age of all courses within
the sample were the same. Asphalt courses having different ages were not
combined in one test sample.

For all pavement sections that were subjected to more than one rehabilitation

91

activity and historical rut and fatigue cracking data were not available, the test

samples were obtained from those asphalt courses for which distress data was

available.

8. A total of 78 samples were tested in the cyclic load indirect tensile test. This
implies that at least 2 samples from each of three cores of the 13 cored test
sections were tested.

Based on the above protocol, the test samples were sawed as close to the 2.5-inch
thickness as possible. The samples were then marked using the respective code of the
core with an extension of one more digit. For example, a test sample designation
number of 29172711-1 indicates (left to right) that the test sample is from pavement
section 29, flexible pavement, test site 7, at 27 feet from the beginning of the site, first
core in the site, located in the wheelpath and the extension of 1 indicates that the sample
was obtained from the top 2.5-inch portion of the core.

After sawing, the bulk specific gravity of each test sample was determined and
the sample was left to dry for a 48-hour period at room temperature. After drying, each
sample was inspected. Those samples that showed uneven and rough vertical surfaces
were rejected.

The cyclic load indirect tensile tests were conducted at room temperature (about
75°F). First, the test sample was placed on the lower loading strip of the indirect tensile
test apparatus such that its vertical diameter was parallel to the MTS actuator. Five
LVDT’s were then mounted and their initial (reference) readings were recorded. The
sample was then preconditioned under 100 load cycles using 300 pounds cyclic load.
During the preconditioning, the sample position on the lower loading strip was adjusted
as to eliminate any measurable differential horizontal movement. After sample
conditioning, the test was commenced and continued until failure. Throughout the test
the 300 pounds cyclic load was applied at a frequency of 2 cycles per second. Each load
cycle consisted of 0.1 second loading and unloading time, followed by a 0.4 second

92
relaxation period.

4.3.2 Maximum Theoretical Speciflc gravity Tests

The maximum theoretical specific gravity (Gmm) of each AC course was
determined by using the ASTM D 2041 standard test procedure. After the test, the
percent air voids in the AC mix was calculated by using the following equation:

P.=100( G" G”) “-"
Where
P, = the air voids in the compacted asphalt mixture, percent of total
volume;
6..., = the maximum tireoretical specific gravity of the paving mixture;
and
G”, = the bulk specific gravity of the compacted mixture.

The ASTM D-2726 standard test procedure defines bulk specific gravity as the
ratio of the mass of a given volume of material at 25° C to the mass of an equal volume
of water at the same temperature. This test method is only recommended for dense
graded or practically non absorptive compacted mixtures. The bulk specific gravities of
the entire core prior to cutting and of the indirect cyclic test samples were determined
by using the above ASTM procedure. The core specific gravity data was used to
determine the air voids of the entire core whereas, the test sample specific gravity of
each test sample was used to determine its air voids content.

After failure of the test samples in the indirect tensile mode, they were sawed
down to individual layers presenting different AC mixes. The bulk and maximum
theoretical specific gravities were determined according to the ASTM D 2726 and D

93

2041 procedures. The maximum theoretical specific gravity procedure requires a
minimum sample weight of 2000 grams for maximum aggregate size of 31-inch.
Whenever it was not possible to obtain enough material for the maximum theoretical
specific gravity test, layers (same AC mix) from two different cores of the same section
were combined to obtain enough material. The maximum theoretical specific gravities
for different layers of 13 cored sections are presented in Table 4.5. Cores or test
samples having more than one layer, the maximum theoretical specific gravity and the
bulk specific gravity were calculated for each individual layer. Further, the weighted
average (the sum of the products of the specific gravity of each layer and its respective
thickness divided by the entire thickness of the core! test sample) specific gravity was
also calculated.

4.3.3 Extraction Tests

After the determination of the maximum theoretical specific gravity, the samples
were subjected to extraction test in accordance with the ASTM D 2172 standard test
procedure. The tests were conducted to determine the AC mix composition. This test
separates the asphalt cement in the AC mix from the aggregate. Thus, the AC mix
composition such as, the percent asphalt, fine, sand and aggregate contents can be
determined. It should be noted that, the test results may be affected by the age of the
asphalt mix. Older mixes tend to yield slightly lower bitumen content due to aggregate
absorption. It is difficult to remove all the asphalt .when some aggregate types are used
and some chlorides may remain within the mineral matter affecting the measured asphalt
content. Nevertheless, trichloroethylene was used as solvent and bitumen content was
established by difference from the mass of the extracted aggregate, moisture content, and
mineral matter in the extract. The bitumen content (see Table 4.5) was expressed as

percent by the weight of the moisture-free mixtures as follows:

94

Table 4.5 : Results of extraction, penetration and maximum theoretical specific
gravity tests for all AC courses of the cored pavement sections.

 

95

Table 4.5 : Results of extraction, penetration and maximum theoretical specific
gravity tests for all AC courses of the cored pavement sections,
(continued).

 

96

(Wr'wa) "W3+W4)

 

AC=[ (W142) ]x100 (4.5)
Where,
AC = asphalt content (percent by total weight of mix);
WI = mass of test portion;
W2 = mass of water in test portion;
W3 = mass of the extracted mineral aggregate; and
W, = mass of the mineral matter in the extract.

After extraction of the bitumen from the AC mix, the recovered bitumen, the
aggregate and the fine material were further tested to determine the recovered asphalt
penetration and the gradation and angularity of the aggregate.

4.3.4 Recovered Asphalt Penetration

The ASTM D5-86 standard test procedure was used to measure the penetration
(consistency) of the recovered bituminous material. Higher values of penetration indicate
softer asphalt or lower viscosity. Penetration is defined as the consistency of a
bituminous material expressed as the distance in tenths of a millimeter that a standard
needle vertically penetrates a sample of the material under known conditions of loading,

time, and temperature. The recovered asphalt penetrations are listed in Table 4.5.

4.3.5 Sieve Analysis

The particle size distribution of the aggregate and sand obtained from the
extraction tests was determined by using sieve analysis in accordance with the ASTM C
136-84a standard test procedure. The tests were conducted by passing a weighed sample

97

of dry aggregate through a series of sieves of progressively smaller openings. Table 4.6

lists the percent by weight of aggregate passing through each sieve.

4.3.6 Aggregate Angularity

Since, there is no standard test procedure for determining the coarse aggregate

(retained on sieve number 4) angularity, the number of crushed faces of an individual

aggregate particle was used as a measure of the angularity. Numbers ranging from 1

(rounded and subrounded) to 5 (crushed on all four faces) were assigned to the

aggregates depending on the number of crushed faces. The test procedure consists of the

following steps:

1.

A 300 gram aggregate sample was obtained irrespective of the amount of the
coarse aggregates in the AC mix.

The aggregates were then divided into different piles depending on the number
of crushed faces. Each pile was inspected and an angularity number was assigned
according to the number of crushed faces of the aggregates. For example, the
pile which consists of aggregate particles crushed on only one face (one side) was
given an angularity of 2. Likewise, the pile that consists of aggregate particles
crushed on all four faces was assigned an angularity number of 5.

The weight of each pile as a percent by weight of the 300 grams sample was
determined.

The angularity of the aggregate sample was then determined as the sum of the
percent by weight of each aggregate pile times the assigned angularity of each
pile and divided by the total weight of 300 grams.

For AC samples with more than one AC course, the angularity of the sample was
determined by calculating the weighed average angularity of the aggregates in the

various AC courses.

98

The above procedure implies that the angularity of the coarse aggregate is
independent of the amount of the coarse aggregate in the AC mix. That is two samples
with 20 and 50 percent coarse aggregate contents may yield the same angularity. The
drawback of this procedure is that, asphalt mixes with low coarse aggregate contents may
have the same aggregate angularity as those mixes made with high coarse aggregate
contents. At low coarse aggregate contents, the aggregate particles float in the sand
matrix which causes separation of the particles. Hence, the aggregate interlocking and
fiiction are decreased. This scenario implies that care should be taken when analyzing
the effects of the coarse aggregate angularity on the AC mix performance. The
aggregate angularity must be considered in view of the percent aggregate contents in the
mix. That is, higher coarse aggregate content in the mix leads to more mobilization of
the aggregate angularity. Nevertheless, the test procedure and the method of calculating
the angularity were adopted to minimize the dependency of the angularity on the percent
aggregate or to minimize the collinearity between these two factors as discussed in
chapter five. It should be that this test procedure represents a departure from those
procedures used by other researchers. In their test method, the aggregate angularity is
defined by three categories (rounded, subrounded, and angular). The sample angularity
is calculated as the weighted average angularity of the three categories based on their
weights. The method do not differentiate between aggregates crushed on 1, 2, 3, or 4
faces.

The angularity of sand size particles (passing standard sieve number 4 and
retained on sieve number 200) can be determined by using the Michigan standard test
method (MTM) 118-90. The test procedure however, requires a minimum sample size
of 1500 grams which was not available in this study. Hence, the sand angularity was not

determined and it is not considered in any further analysis.

99
Table 4.6 : Results of sieve analysis for each AC course.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[1 8191196129
BecamNaI11/2] 1 [31411121379194]991919L9301950I910019200
1’um
7F
uyen 100 100 100 99.9 99.2 93.4 49.4 42.9 39.5 21.9 9.4 9.4
Lam 100 100 97 93 73.9 59.5 47.2 41.9 39.9 17.9 5.3 3.9
Tam 100 100 99.3 94.9 90.9 71.9 90.7 50.9 40.3 17.7 4.7 3.1
10F
_u_¥¢1 100 100 100 97.7 99.9 99.1 59.2 49.3 41.3 23.2 9.9 5.3
um 100 100 100 99.7 99.9 997 57.2 439 40.1 25 12.7 7.9
Layers 100 100 100 94.3 99.4 724 57.2 45.9 34.9 221 139 10.3
13F
Layert 100 100 100 99.1 92.9 47.2 39.1 35.1 31.7 20.9 9.1 3.9
3.2 100 100 100 99.2 99.3 90.4 49.3 43.1 39.3 231 12.4 7
Layers 100 100 94.2 55.7 47.9 41.2 37.2 39.2 31.3 20.9 7.7 3.9
14F
Leyen 100 100 99.1 97.4 79.5 92.1 51.5 42.7 34.7 21.4 10.9 7.2
w 100 100 99.3 93.7 72.9 57.9 49.1 41.9 33.9 19.7 10.9 9.4
Layers 100 100 100 100 93.3 55.1 33.3 29.4 20.2 12.3 9.9 4.9
19F

 

100 100 100 100 91.7 ”.1 14.5 9.5 5.9 3.4 1.9 1.2

 

100 100 100 ”.8 ”.1 ”.9 50.2 43.8 3.9 18.8 8.8 8.5

 

100 100 .100 97.5 87.2 82 0.3 43.2 37.1 19.2 8.8 8.8

 

 

100 100 100 ”.9 ”.3 81.8 ”.5 44.8 31.9 18.8 9.1 7.1

 

100 100 100 97.4 79.3 48.8 ”.9 22.2 15.8 9.1 3.8 2.5

 

100 100 “.3 ”.1 84.7 70.7 55.2 41.9 27.2 13.2 8.3 4.3

 

 

100 100 100 ”.8 91.1 73.8 58.8 44.9 31.9 15 8.3 8.2

 

100 100 100 97.2 81.3 49.8 33.4 .28.7 20.1 10.4 8.2 5.1

 

100 100 100 91.9 77.5 53.5 $3 32.1 ”.7 12.9 8.1 8.5

 

 

100 100 98.4 91.4 85.5 51.3 41.8 33.3 20 9.7 8.9

 

100 100 100 “.5 ”.8 88.5 51.9 42.4 32.7 17.7 9.3 8.9

 

100 100 “.8 87.8 78.8 81.4 48.5 37.2 3.1 17.4 9.4 7

 

100 100 $ 79.8 “.9 51.8 “.2 32.2 8.3 17.4 10.8 8.3

 

 

100 100 100 97.2 84.8 ..9 47.4 3.7 8.7 18.1 9.5 8.9

 

100 100 100 97.2 84.2 57.5 42.4 33.1 24.2 15.3 9.8 7.2

 

100 100 “.1 “.5 81.2 57.4 42.2 33.1 25.3 18.4 9.8 7.1

 

 

100 100 100 97 ”.8 81.4 48.4 35.9 28.4 14.5 7.4 5.8

 

iiiiiiailiiigiiirii'igiii

100 100 100 97.1 84 50.2 41.7 3.4 ”.4 27.8 13.2 7.5

 

”7 100 100 75.9 47.8 38.8 3.4 3.1 ”.4 24.2 17.8 7.8 3.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100
Table 4.6 : Results of sieve analysis for each AC course, (continued).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[ miz-
beeiimNaI11/2I113/4L1/2T 379194f 99191914fl950191o0l 9200
Percent PM
4c
mm 100 100 100 95.4 97.2 99.7 59.3 49.2 35.4 21.7 11.9 7.9
45412 100 100 100 100 94.9 59.4 43.7 37.4 29.9 19.9 7.4 4.9
so
um 100 100 100 99 99 70 54.7 43.1 33.1 22 139 10
um 100 100 100 99.9 97.3 97 524 41.9 325 21.9 13.1 9.2
Lam 100 100 100 99 91.9 99.3 54.5 43.9 35.2 24 12.9 7.9
gm 100 100 100 99.9 90.2 95.1 49.3 37.1 27.3 17.9 11.2 9.3
so
um 100 100 100 99.4 99.3 99.5 50.9 421 34.4 22 10.7 7.5
1.932 100 100 100 99 99 54.9 44.2 41.1 39.7 27.1 14.9 7.5
Layer.) 100 99.5 92.9 52 39.5 31.7 29.4 27.9 24.4 17 9.2 3.9
no
um 100 100 100 95.9 97.4 97.1 51.4 43 33.1 20.9 11.4 9.9
Lam 100 100 100 97 99.7 99.3 53.2 44.2 35.5 22.5 10.9 9.9
mm 100 100 100 97.7 92.1 55.2 42.4 35.1 29.9 19.5 9.9 9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 5
ANALYSIS AND DISCUSSION

5 .1 General

A wheel load moving on a pavement structure causes three types of responses;
elastic, Viscoelastic, and plastic. Although the three responses are dependent on the
material properties, the elastic one is time independent while the Viscoelastic and plastic
responses are time dependent. The plastic response of asphalt pavements manifests itself
as rut (permanent deformation) and/ or fatigue (alligator) cracks.

As is the case for most solids, asphalt concrete pavements exhibit a greater variety
of mechanical behavior than liquid or gases. It is extremely difficult to arrive at a single
set of equations that realistically describes or models the interplay of the elastic,
Viscoelastic, and plastic responses under a combined set of stresses and boundary
conditions. Even if such equations could be developed, they would be far too complex
for the practical analysis of stresses and strains induced in the pavement structure. To
simplify the problem, in the early work on plastic solids, the yield condition and plastic
flow rule were trusted as independent ingredients of a theory of plasticity. For example,
an experimental based yield condition was advanced by Tresca (73). Later, Saint Venant
(74) and Levy (75) adopted Tresca’s condition and developed a plastic flow rule whose
form was inspired by the theory of elasticity. In his theory of plasticity, Von (76)
retained the plastic flow rule and modified (for the purpose of mathematical convenience)
the Tresca yield condition.

Recently, the plastic flow rule and yield condition for asphalt surfaced pavements
were further simplified and fatigue and rut models were developed. Each model is based
on a single variable, the radial strain for the fatigue model and the compressive strain for
the rut model. Both radial and vertical compressive strains are calculated by using elastic
layer theory. Examples of these models are those developed by the AASHTO/ARE (77)

101

102
and Maj idzadeh and Ilve (78). The main limitations of the models are that:
1. They are independent of the plastic properties of the paving materials.
2. They cannot be used to assess the effects of material properties on the fatigue life
and rut potential of asphalt pavements.
3. Their accuracy is poor at best.

Numerous statistical fatigue cracking and rut depth models for AC surfaced
pavements have also been developed. The models express the fatigue life and rut depth
in terms of the asphalt-aggregate mix properties and compositions. These models are
presented in Chapter 2 of this dissertation. It should be noted that the fatigue life and
rut depth of asphalt pavements are functions of not only the AC layer properties but also
the properties of the base and subbase layers, the characteristics of the roadbed soils, the
traffic load and volume and the environmental factors.

As stated in Chapter 1, the objectives of this study are to determine the asphalt
mix variables that affect the structural performance (rut and fatigue cracks) of flexible
and composite pavements and to recommend changes in the existing asphalt mix design
procedure and standard specifications. To accomplish these objectives, the outputs of
' this study must include relationships between pavement performance and asphalt mix
variables such that the sensitivity of the pavement performance to the various asphalt mix
variables can be assessed. Therefore, the data analysis procedure to be employed must
account for the variability of the asphalt mix and must be capable of:

1. Providing a good description of the sensitivity of the response variables to the
input parameters (independent variables).

2. Developing realistic models whereby the relationships between the dependent and
independent variables are reasonable and have good engineering interpretations.

3. Predicting pavement responses in terms of rutting and fatigue cracking potentials
for the range of the given variables.

Two types of analysis can be employed; mechanistic and statistical. The former

103

is typically based on existing theory (e.g., elastic, plastic, Viscoelastic) and it requires
substantial inputs regarding material properties. Because of the limited resources, such
inputs cannot be obtained. Further, the resulting mechanistic models are not practical
and they cannot be used by State Highway Agencies. Consequently, a statistical type
analysis was selected in this study. The inputs to the statistical models include the
engineering and physical properties of the AC materials as well as traffic loading, volume
and pavement service life (age).

The main advantage of the statistical analysis is its simplicity and low cost. The
main disadvantage is that the resulting statistical models are applicable only within the
range of data from which the models have been developed. This disadvantage can be
minimized if the range of material properties used in developing the statistical model
represents the spectrum of the properties used in the field. Therefore, the selection of
the experiment is very crucial to the success of the analysis. The experiment should
include:

1. A representative range of the properties and variability of the asphalt mixes used
in the construction of various pavement sections that are:

3) expected to experience light, medium, and heavy traffic;

b) located in the various environmental regions;

c) supported by different roadbed soils;

(1) constructed by using different base and subbase materials; and

e) consisted of various cross-sections.

2. A representative range of the properties and variability of each of the materials
used in the compacted asphalt mixes.

The details of the experiment in this study are presented in Chapter 3. The
statistical package (computer program) used in the study is “Statistical Package for Social
Sciences (SPSS)". The reasons for this selection include:

1. The simplicity and user friendliness of the program.

104
The various options that are embedded in the program which allow the users to
examine the various statistical parameters of the output models.
Its graphic capability whereby each input and output variable can be plotted and
examined for engineering interpretation.
The capability of the program to access the data through a common spreadsheet
and/or data base.
The flexibility of the program which allows the users to input the desired form
of equations relating the dependent and independent variables.
Most statistical procedures are generally based on the least squares criteria

(minimization of the sum of the square of the differences between the predicted and the

observed data). Again most procedures are simple and easy to use provided that the

proper relationship between each independent variable and the dependent one is properly

specified. The issues here are that the relationship must:

1.
2.

Have the proper engineering interpretations.

Be representative of the observed trend between the dependent and independent
variables.

Model other data reported in the literature.

Several aspects relative to these issues and some specific comments regarding the

statistical procedure used in this study are presented in the next section.

5.2

STATISTICAL ANALYSIS TECHNIQUES AND ISSUES

The most important issues regarding statistical analysis of engineering data

include:

1.

2.

The number of variables to be included in the analysis, their significance level,
and their collinearity if any.

The form of the equation(s) relating each independent variable and/or clusters of

105
independent variables to the dependent one.

3. The engineering interpretations of the final correlation equation.

If the only purpose of the statistical analysis is to express the behavior of the response
(dependent) variable in terms of the independent variables and to minimize the residual
sum of squares, then the best suited model is the one that include all the available
independent variables regardless of whether or not the variables are causally related or
the model is realistic. A model having fewer variables, on the other hand, has the appeal
of simplicity, and economic advantage in terms of obtaining the necessary information.
The elimination of some variables from the model, however, is obtained at the expense
of biases and loss of predictability of the model. Thus, the exclusion of any variable with
a significant correlation coefficient causes a bias penalty (79).

Regardless of the number of variables to be included in the final model, the
results of any statistical analysis that is based solely on the least square technique reflect
only the correlational structure of the data being analyzed. This structure may or may not
be representative of the true engineering relationships between the dependent and
independent variables. Another problematic aspect of variable selection is that the
relative importance of a variable as manifested in the sample may not necessarily reflect
its relative importance in the population. Important variables in a sample may appear
unimportant in the population and vice versa. That is, the best set of variables in a
sample might not be the best set in the population. The choice of variables in the final
model depends on prior knowledge and experience and on the variable clusters used to
model a behavior. Further, statistical correlations between independent variables (9, g. ,
material properties), and the dependent variable (e, g. , pavement perfomance in terms
of rut and fatigue cracking) may lead to several possible outcomes including:

1. Certain material properties (e.g. , air void) appear to have specific effects on
pavement performance which can be related to certain observed patterns.

2. Certain material properties appear to have no effect on pavement performance.

106

That is, regardless of the range of the property and its variation, the pavement

performance is more or less constant for the entire range of that property.
3. Variation in the values of the pavement performance appear to have similar

pattern that can be related to variations in the material properties.

Nevertheless, in this study, the statistical analysis were conducted by using the
SPSS computer program. The statistical models (regression equations) were developed
by using four steps. A brief discussion of each of these steps is provided here and a

detailed discussion is contained in the model development.
Step 1 Determination of a Simple Correlation Matrix

In this step, a simple correlation coefficient between the dependent and each of
the independent variables was computed and tabulated in a matrix format. Each
coefficient was then examined to determine the trend between the dependent and each of
the independent variables and the significance of the latter on the former. The trends and
the significant levels were also compared to field observations and experience. The
simple correlation matrix also provides information regarding the degree of collinearity
between any two independent variables (a situation when two or more independent
variables are correlated among themselves). A higher degree of collinearity between any
two independent variables, causes more difficulty in separating the effect of each
independent variable on the response variable (80). Because of its importance, the
degrees of collinearity between the independent variables were also examined in steps 2
and 3.

Step 2 Computation of Eigenvalues and Condition Indices

The eigenvalues of a symmetric (square) matrix 'A(an)" are a set of 'n" non-

negative scalars ”A," such that their product with n non-zero vectors ”2,, i=1...n" of the

107
matrix is the same as the product of the matrix with the z, vectors. That is "Az, = A}
z,“ . The eigenvalues are typically used to examine the collinearity between the
independent variables. In addition, the scaled uncentered cross-products matrix and the
decomposition of the regression variance corresponding to these eigenvalues were
computed. There is an indication of near dependency of variables, when there is a high
proportion of the variance of two or more coefficients that are associated with the same

eigenvalue (81). Hence, the condition index which is defined below can be calculated.

Cond. Index I=[ eigenvalue... I eigenvalue, 1” (5.1)

The presence of collinearity results in small eigenvalues and consequently, larger
condition index values. Furthermore, the number of large condition index values

corresponds to the number of cases of collinearity between the independent variables.
Step 3 Computation of Variable Tolerance and Variance Inflation Factor (VIF)

Variable tolerance and variable inflection factors (VIF) are other measures of
collinearity between the independent variables. The variable tolerance and the VIF are
defined as (73):

Tolerance a (l-R,’) (5.2)
vrr = [1/ (1.33)] (5.3)
where

Ri = the multiple correlation coefficient of the ith independent variable when
it is predicted from other independent variables.
If the tolerance of an independent variable is small, or its VIF is high, then the variable

is collinear with one or more independent variables.

108
Step 4 Variable Selection Methods

In this step, the independent variables to be included in the statistical model are
selected. Several variable selection methods are available to the user of the SPSS
program. In this study, the stepwise regression method is used. This method identifies
a good (not necessarily the best) set of variables to be included in the development of the
statistical model. The statistical model is constructed by considering one variable at a
time that having the greatest or the least impact on the residual sum of squares of the
model. Three stepwise techniques can be identified (76); forward selection, backward
elimination and stepwise selection. These three techniques are addressed below.
Forward Selection - In the forward selection technique, the first independent variable
to be considered in the development of the statistical model is that which accounts for the
largest amount of variation in the dependent variable. At each successive step, the
independent variable (from the independent variable pool) that causes the largest decrease
in the residual sum of squares of the existing model is added. In the absence of any
termination rule the process continues until all the variables are included in the model.
Backward Elimination - In the backward elimination technique, first the statistical
model is developed by including all the independent variables in the pool. At each
consequent step, a variable whose deletion causes the least increase in the residual sum
of squares is dropped. If no termination rule is specified the deletion process continues
until only one independent variable is left in the model.

Stepwise Selection - The stepwise selection technique is basically a forward selection
process that at every step reexamines the significance of the previously added variables.
If the partial sum of squares of any previously added variable does not meet a minimum
specified criterion, the variable is dropped from the model and the selection process
changes to backward elimination. The variable elimination process continues until all of

the variables remaining in the model meet a minimum specified criterion after which the

109

forward stepwise selection process is resumed. It should be noted that, at every step, the
significance of all variables relative to the model is reexamined. Hence, any variable
that has been deleted from the model in earlier steps may be added back to the model
when it meets the minimum specified criterion.

Neither the forward selection nor the backward elimination techniques consider
the impacts of adding or deleting a variable on the remaining variables in the model. A
variable added to the model in the forward selection technique may become insignificant
after other variables have been added. Similarly, the significance of a deleted variable
may increase as other variables are deleted from or added to the model.

The stepwise selection technique was used in this study because the process allows
a better chance of selecting the best independent variables relative to the other two
techniques. Nevertheless, the forward selection and the backward elimination techniques
were occasionally used to compare the resulting statistical models. For each statistical
model, the null hypothesis of no relationship between the dependent and independent
variables were tested. Finally, the residual analysis and the comparison of the predicted
versus observed values were performed.

To this end, several technical terms relating to the pavement performance are used
throughout the remaining parts of this thesis. These terms are defined in the next

section.
5 .3 DEFINITION OF TERMS

For the benefits of the readers, the following pavement performance terms are
defined in this section.
1. Design Life - The design life of a pavement structure is defined as that period of
time (typically in years) assumed during the pavement design process. Pavement

design life could be greater, equal, or less than the actual pavement performance

5.4

110
period. _
Performance Period - A pavement performance period is defined (see Figure
5.1) by the time period in years between construction and rehabilitation or
between two rehabilitation activities during which the pavement was opened to
traffic and its conditions were equal to or better than the specified threshold
value.
Service Life - A pavement service life is defined by the time period in years
between construction/ rehabilitation and the present time as shown in Figure 5.2.
Hence, a pavement service life is always shorter than the pavement performance
period. However, the pavement service life could be longer, equal, or shorter
than the pavement design life.
Remaining Service Life — The remaining service life (RSL) of a pavement
structure is defined by the future (predicted) time period in years between the
present time and that point in time where a pavement distress reaches its
minimum specified threshold value as shown in Figure 5.3. Hence, for any
pavement structure several RSL values could be calculated (one value for each
type of distress). The RSL of the pavement structure could be assigned as the
smallest of the RSL values or it could be calculated on the basis of the weighted
average of all types of pavement distress.

ANALYSIS AND DISCUSSION OF FATIGUE LIFE

Recall that (see Chapter 2 - Literature Review) fatigue cracks are the results of

the tensile strains induced at the bottom of the AC layer due to a moving wheel load.

These tensile strains are the sum of three components; elastic, Viscoelastic, and plastic.

While the first two components are recoverable upon the removal of the load and with

time, the plastic tensile strain is permanent in nature. The magnitude of the plastic

111

Distress

   
 

Acceptable pavement
condition

.......... -1. ll 5......

T value
erformance period Unacceptable

 

 

Performance period

 

 

Time (years)

Figure 5.1 : Performance period of a pavement.

Distress

Acceptable pavement

. condltlon
servrce life

5 9 l
I
...................... _ - .. _ .— Thfgghold

T .5...

Unacceptable

 

1

Present time

./
Time

(years)

 

Figure 5.2 : Service life of a pavement.

112

Actual

Distress /

Service life

 

 

RSL

Predicted

\ \ \ Acceptable pavement

\ condition

---------- \r- - - - - Threshold

7. iii .5...

Unacceptable

 

 

Time (years)

Figure 5.3 : Remaining service life (RSL) of a pavement.

113

tensile strain depends on the material properties and the magnitude of the wheel load.

Higher loads cause higher strains. Further, as the number of wheel load applications

increases, the cumulative plastic (permanent) strain increases until the asphalt cement

cannot stretch any longer. Hence, cracks will develop and with further load applications,
the cracks will propagate toward the pavement surface where they manifest themself as
alligator or fatigue cracks.

Various fatigue cracking models for asphalt concrete pavements have been
established by numerous investigators based on both field performance data and
laboratory fatigue data. The laboratory based fatigue models generally predict failure
much sooner than is observed in the field. The reason for this is that most laboratory
models predict crack initiation. In the field, fatigue cracks start at the bottom of the AC
layer and after some time (few months to few years depending on the pavement cross-
section), they propagate upward toward the pavement surface. Hence, fatigue cracks in
asphalt pavements may exist for a long time period before they can be detected at the
surface of the pavements. Figure 5.4 illustrates a generalized fatigue cracking
performance model for asphalt pavements. The scale on the vertical axis indicates the
fatigue cracking index (FCI). An FCI value of 100 indicates no fatigue cracks can be
seen on the pavement surface. An index value of less than 100, on the other hand,
indicates the presence of fatigue cracks. As the severity and intensity of the fatigue
cracks increase, the value of the FCI decreases. Three important observations can be
made from Figure 5.4. These are:

1. An FCI value of 100 implies that no fatigue cracks can be seen on the pavement
surface. This however, does not imply that the pavement is free from fatigue
cracks. Indeed, the time of fatigue cracks initiation could be anywhere along the
horizontal line ab as shown in Figure 5.4.

2. The time period between the first observation of fatigue cracks and failure of the

pavement structure due to fatigue cracks is much shorter than the period between

114

 

 

 

a b
100

l
I
I
ACI '
I
FCI 5° T :
I
I
I
I
0 4

Time

Figure 5.4 : Fatigue cracking index. (FCI) as a function of time.

l 15

construction or rehabilitation and the first observation of fatigue cracks.
Because of the above two observations, no universal definition of fatigue crack
failure has been adopted. Some State Highway Agencies (SHA) define fatigue
failure in terms of the area of the cracked pavement. Some others, in terms of
the percent of the pavement section that showing fatigue crack. Still others,
define fatigue crack failure by the combination of the areas of the pavement that
show low, medium, and high severity fatigue cracking.

To this end, and because accurate and historical filed fatigue cracking data were

not available to this study, the results of laboratory tests are used to assess the effects of

the properties and compositions of the asphalt-aggregate mixes on their fatigue lives.

Hence, the following assumptions were made at the onset of this study.

1.

If an asphalt-aggregate mix variable has an adverse or favorable effects on the
laboratory determined fatigue life of the mixes then that variable has and adverse
or favorable effects on the fatigue life of the AC layer in the field.

For the type and range of the variables included in this study, the order of
significance each variable has on the laboratory determined fatigue life is the
same as the order of significance in the field. That is, if variable "XX” is the
most significant variable affecting the laboratory determined fatigue life then
”XX" is also the most significant variable affecting the fatigue life of the

pavements.

The above two assumptions are reasonable because of the following reasons:

1.

The absence of accurate and historical field fatigue data and the absence of a
definition of pavement fatigue life make it impossible to relate material properties
to the fatigue life of the pavements.

The objective herein is not to quantify or predict the pavement fatigue life but to
assess the effects of each mix variable on the pavement fatigue life.

The fatigue life of AC pavement is also affected by traffic load, volume and by

116

the thicknesses and stiffnesses of the other pavement layers and the roadbed soils.

While for each pavement section included in the study, the traffic data is

available, layer stiffnesses and the stiffness of the roadbed soil were not available.

Nevertheless, as stated in Chapter 3, the laboratory samples were obtained from
field cores and they were tested by using the indirect cyclic load (INCL) tests.
Observations regarding the field cores, laboratory samples, and the INCL tests are
presented in the next section.

5.4.1 Field Cores, Laboratory Samples, and the INCL Tests

Presently, different laboratory techniques are used to evaluate the fatigue potential
of asphalt mixes in the laboratory. As noted in Chapter 2, the indirect cyclic load
(INCL) tensile test has several advantages over other testing methods and it was used in
this study. The INCL tests were conducted on core samples by using an MTS closed
loop servo—hydraulic system and the Baladi’s indirect tensile test (INTS) device (3).
Initial tests were conducted by using a fixed and a hinged 0.5 inch loading strips. The
test data indicated that, for test samples consisted of more than two courses ( i,e. leveling
and surface courses), the fixed loading strip delivered most of the load to the stiffer
course. The resulting fatigue life was much shorter than that of compatible sample tested
by using the hinged loading strip. Further, since all the test samples were obtained from
field cores (the cores lacked smooth and vertical surface), the fixed loading strip did not
make a full contact with the samples. Consequently, the hinged loading strip was used
throughout the testing program.

The 6-inch diameter test samples were sawed from asphalt concrete cores that
were obtained by MDOT from pavement sections selected for coring. The cores were
composed of surface, leveling and base courses (see Table 4.5). The thicknesses of the

various AC courses varied from one core to another. For example, the combined

l 17

thicknesses of the surface and leveling courses varied from about 2 to about 3 inch.
Whereas, the AC base course thickness varied from about 3 to about 9 inch. The INCL
test samples were prepared by sawing about 2.5-inch thick portion from the 6-inch
diameter cores (see sample preparation, Chapter 4). Because of the limited thicknesses
of the surface and leveling courses, it was not possible to obtain 2.5-inch test sample
from each course. Therefore, combinations of the surface and leveling courses and,
occasionally the base course were included in the test samples. That is some of the test
samples contained only surface and leveling courses while others contained surface,
leveling and base courses. This implies that the test results reflect the global behavior
of the combined courses rather than the individual course behavior. It should be noted
that extreme care was taken as not to include any base course material in test samples
made from the surface and leveling courses. For a few samples however, this was not
possible and a minimum amount of the AC base course was included (a minimum sample
thickness of 2.2-inch was specified in this study). The above scenario presented no
problems for all test samples obtained from the base course (all cores contained more
than 2.5-inch thick base coarse).

Trial INCL tests were also conducted by using a constant sustained load of 50
pounds and two cyclic load levels of 500 and 300 pounds. It was observed that some
samples tested under the 500 pounds cyclic load were failing in shear (punching of the
loading strip along the vertical diameter of the sample) rather than in fatigue. Therefore,
a cyclic load of 300 pounds was selected and used throughout the testing program.

5.4.2 Test Results

A total of one-hundred and six full-depth 6-inch diameter cores were obtained
from thirteen cored pavement sections. Each core was carefully examined and defects

such as stripping, cracking, and smoothness of the core side were noted and the

1 18
thicknesses of each AC course (surface, leveling, and base) were measured and recorded.

After examining the cores, one-hundred test samples (approximately 2.5-inch
thick) were carefully sawed. Each test sample was then inspected for possible defects
and the thickness of each AC course in the sample was measured and recorded. It was
observed that the vertical sides of 43 test samples were highly uneven due to the coring
process. Uneven sample side is known to cause a rocking motion in the sample during
the application of cyclic load, hence, these samples were rejected. Thus, 55 test samples
were accepted for testing. Prior to the commencement of the INCL tests, the bulk
specific gravity of each of the 55 test samples were measured by using the ASTM D-
2726 standard test procedure. The test results are listed in Table 5.1.

After the completion of the INCL tests, similar test samples (that have the same,
leveling and/or base courses) and some of the 43 rejected samples were combined and
asphalt extraction tests were conducted. The reason for combining several samples is to
obtain adequate materials for the asphalt extraction tests. The extraction tests were
conducted according to the ASTM D-2172 standard test procedure which specifies that
a minimum material weight of 2000 grams be used. The extracted asphalt cement and
the recovered aggregate were used to determine:

1. The recovered penetration of the AC cement.
2. The percentages by weight of the:

a) coarse aggregate (plus number 4 standard sieve);

b) fine aggregate (minus number 4 and plus number 200 standard sieves);

c) fines (minus the number 200 sieve).

d) asphalt cement.

3. The maximum theoretical specific gravity of the asphalt mix.
4. The weighted average angularity of the coarse aggregate.
Tables 5 .1 and 5 .2 summarize the test results. These include the sample

designation number, thickness, specific gravity, the recovered penetration of the asphalt

119

.9399 .9. .52. B 2: .5. 5.5

 

» 1m 933,—.

120

835.83 9.588 .9. .67: R 2.. he «a:

 

u fin 039,—.

121

.3353 .8. :3 he 3:92—95 05 .9 8.3.59 32.3.53:

 

« fin 035,—.

122

cement, the percent by weight of the AC, fine, sand, and coarse aggregate in the asphalt

mix, the angularity of the coarse aggregates, the percent air voids, the magnitude of the

cyclic load, the INCL test temperature,the resilient modulus of the sample calculated at

load application number 500, the maximum compressive and tensile stresses induced in
the sample during the test, the service life of the pavement section (the period in year
between construction or last rehabilitation and the time of coring), the cumulative 18-kip

ESAL experienced by the pavement section in question during its service life, and the

fatigue life of the sample.

For each sample, the test data were analyzed and several procedures were used
to determine its fatigue life. These specify that the fatigue life of the sample corresponds
to:

1. The number of load repetitions at which the value of the resilient modulus of the
test sample is equal to half of its original value.

2. The number of load repetitions at which the rate of change (the slope) of the
logarithmic value of the accumulated plastic and total deformation (along the
vertical and horizontal diameters of the sample) relative to the logarithmic value
of the total number of load applications increases significantly (see Figure 5 .5a).

3. The number of load applications at which the rate of change of the plastic
deformation ratio (the ratio of the accumulated plastic deformation along the
horizontal diameter to that along the vertical diameter) relative to the logarithmic
value of the number of load applications increases significantly as shown in
Figure 5.6b. 9 L

4. The number of load applications at which a crack along the vertical diameter was
observed. The width of the crack, however, varied from one sample to another.

The second method (the slope of the line representing the logarithmic values of the

cumulative plastic deformation along the horizontal diameter of the sample versus the

logarithmic values of the total number of load applications) produced good results.

123

 

280 100

 

 

 

 

 

 

 

 

an + 9194.11.17.11“. x Tot.hor.dai. +
g. 200 — +
E 1
i : ~ 10 ‘3
g 180 - I ‘5’
2' . .3.
2 q). I g
g 100 - I g
E I - 1
5
5': ”it are as as x + 3‘ *3?“
I
0 ‘ ' I 0.1
100 1000 10000 100000
Load Applications (thousands)
Figure 5.5a : Resilient modulus, horizontal plastic and total deformation as
a function of the number of load applications.
0.8
0.4 - ,
s; 0.2 l. .
0
ll '
0.1 - I
I
l
o . ' . l
100 1000 10000 100000
Load Applications (thousands)
Figure 5.5b : Deformation ratio (horizontal plastic/ vertical plastic) as a

function of the number of load applications.

124

However, locating the point where the slope shows an increase was subjective in nature

due to the nonlinear nature of the data at the higher numbers of load applications. The

third procedure yielded more consistent results and hence, it was used for all the test
samples. This procedure consisted of three steps as follows:

1. The ratios of the cumulative plastic deformation measured along the horizontal
diameter to that measured along the vertical diameter were calculated at several
number of load applications and plotted against the logarithmic values of the
number of load applications as shown in Figure 5.6. It should be noted that the
test data for the first 100 load applications was not included due to sample seating
and/ or sample conditioning.

2. Two best fit lines prescribing the data were then drawn and their intersection was
found.

3. The laboratory fatigue life of the test sample was then defined by the number of
load applications corresponding to the intersection of the two best fit lines.
Table 5.1 provides a list of the fatigue lives of the 55 test samples estimated by

using the above procedure.

5.4.3 Analysis and Discussion of the Test Results

Statistical analyses were conducted to relate the fatigue life of the test samples to
the test and the asphalt-aggregate mix variables. In the analysis, the fatigue life was
assumed to be the dependent variable and the test and asphalt mix variables were
assumed to be the independent ones. In reality, the test and mix variables are not truly
independent variables. For example, the recovered asphalt penetration is a function of
the asphalt cement aging process which, in turn, is a function of the original asphalt
mixing process, storage time, the percent aggregate and sand in the mix, the service life

of the pavements, and the environmental conditions. Likewise, the percent aggregate in

125

the asphalt mix is a function of the l8-kip ESAL experienced by the pavement structure
since construction. This is a direct result of the MDOT pavement design practices. For
example, the asphalt course layer of a pavement structure expected to carry high number
of l8-kip ESAL is typically designed to have higher percent aggregate, angular
aggregate, and low percent sand. Hence, these three factors are not truly independent
of the number of 18-kip ESAL. Consequently, extreme caution should be taken while
conducting the statistical analysis and explaining the engineering interpretation of the
statistical equations.

The above scenario implies that various degrees of collinearity (collinearity
between two variables implies that the two variables are related) exist between the
independent variables. This is evident from the correlation matrix where the coefficient
of correlations between the dependent (the logarithmic value of the fatigue life) and the
original values of the independent variables (asphalt mix properties and test parameters)
and between the independent variables themselves are listed in Table 5.3. A coefficient
correlation value of 0.0 implies no linear relationship or collinearity between the
variables. A value of 1.0, on the other hand, implies 100 percent collinearity. Further,
a positive value indicates a direct relationship (increasing value of one variable causes
an increase in the value of the other variable) while a negative value marks an inverse
relationship. It can be seen that the degrees of collinearity between the various
independent variables vary from a negative 0.001 (between the tensile strain "TS“ at
failure and the aggregate angularity 'AG"), an insignificant collinearity, to -0.976
(between the percent aggregate ”A66" and the percent sand “SAND” in the mix), which
implies significant collinearity. Some of these collinearities can be eliminated. For
example, the sand content can be expressed in terms of the aggregate and the percent fine
content ”FINE” as follows:

SAND = 100 - (AGG + FINE)

However, most other collinearities cannot be eliminated by substitution. For example,

126

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.ec:._90 an 0.99»- e..eeoa e 0»
2.8. 3.89.. 22:8,. .. a.
5... 23249.3 :3 a 2
«5.003930 use. 9090.). e 00
«>u.>aco 0.0.0000 8.30 9.0:ee e phuam
ux_a 0¢ :. no.00ucaa «00 03.00 909000009 09 >u_ce.:0ca 9 03¢
“Ruse—ea >0 00900900 :06 u¢ c. .00 03.00 909090009 9 00¢
2222. B 980.80 x... 04 5 2: .. mg:
228! 3 2.8.98 5.. 3 5 9.: a 9.4...
222... >0 959.8. 959:8 22.38 a 2
«09.09009090 0.90099 voco>ooec e 300..
no... 930.090 ucouaceaa_ e 45
«09. .903000 e 000
000.— 000.. 00.. 000.. 00~. .00.. 00p.. pun. 00p. -0. 00.. 00... 00
000.9 cm... 0-. ~n0.. 00—. ~nn. .. n0~.. pon.. n00.. 00m. «x
000.. ~00. 00p. 00w. 50.. men. ps~.. 00m. p00.. m0~. p.»
000.. 0n—.. '~—.. pp... 500.- 0—5. 0~w.. 050. 000.- 0.0
000.. Amp. 0P0.. 050. 000.. whw. n00. n0~. .>»0am
000.. ~50. sen. 00s.. n0~. 0~0.. 0N0. 02¢
000.p ~0~. 050.. —n0.. 00F.. 00m. .00¢
000.— ~00.. 050. 000. 050.- ms.»
000.. 000.. ~00. n0n.. 02¢m
000.p p0~. 00n.. 0¢
000.. 0~0.. 205.:
000.— .400000
00¢ ma: 03¢m u¢
m» a: 5 .5 >500 02¢ «£0.03 3 0:90.50 .33.: 3:00..

 

 

.8339: 0000090000. 000 0.:— 05028 .50 5.30:. 00:59:00 " 0.0 333.0

127

the coefficient of correlation between the specific gravity 'SPGTY" of the samples and

the recovered penetration "R.PEN" of the asphalt cement is 0.443 (see Table 5.3). This

is reasonable (not coincidental) and it can be explained. That is, higher values of specific
gravity indicate higher densities and lower air voids and hence, lower rates of oxidation
of the asphalt cement which result in a higher recovered penetration. However, one term
cannot be substituted by the other due to the lack of a proper transformation model (the
rate of oxidation is affected by numerous other factors whose effects are not fully
understood at this time).

The problem of collinearity between the independent variables can be partially
resolved by several methods including:

1. Stratifying the data by grouping it such that only the value of one independent
variable changes at one time. For the type and nature of the data of this study,
this method is not practical and it cannot be applied. The reason is that, the
experiment matrix will have to have a large number of entries. Stated differently,
the size of the experiment and the number of the samples that needed to be tested
make the cost of this study prohibitive.

2. Excluding those variables which show high collinearity to other variables from
the statistical model. This solution can cause some bias in the resulting statistical
model.

3. Creating clusters of variables whereby two or more independent and collinear
variables are clustered together and the values of the cluster are used to represent
the collective influence of the independent variables. Although this method is
sound where the independent variables can be expressed through a transformation
function or theoretical models, it is not applicable to this data.

Nevertheless, the values of the coefficient of correlation between the dependent
and independent variables listed in Table 5 .3 reflects the relationship between the
logarithmic values of the fatigue life and the original (untransformed) values of the

128

independent variables. Examination of the values of the coefficient of correlations leads

to the following statistical observations:

1.

The most significant variable (corresponding to the highest value of the coefficient
of correlations of Table 5.3) affecting the fatigue life of the asphalt mixes is the
aggregate angularity. Increasing aggregate angularity causes an increase in the
fatigue life. This result is reasonable and it was expected. Higher aggregate
angularity provides a better aggregate interlocking which causes a better stress
distribution (i.e. , lesser compressive and tensile stresses).
The second most important variable is the asphalt cement in the mix. In this
regard, two factors adversely affect the fatigue life. In their order of
significance, these two factors are the recovered penetration of the asphalt cement
and the percent asphalt content. Increasing values of any of these two variables
cause a decrease in the fatigue life. In reference to Table 5 .3, two important
observations can be made as follows:

a) The recovered asphalt penetration shows some degrees of collinearity to
the percent fine and to the aggregate angularity. Higher percentage of
fine cause denser mixes and lower air voids. Hence, the rate of field
oxidation decreases. On the other hand, using angular aggregates in the
asphalt mix causes lower densities and higher air voids which increase the
rate of oxidation in the field.

b) The percent asphalt content shows a relatively high degree of collinearity
to the percent fine and a relatively low one to the aggregate angularity.
While the latter observation is not significant, the former one implies that
higher percent fine content causes higher asphalt contents. Once again,
this is reasonable because higher fine contents increases the total surface
area that needs to be coated with asphalt. Hence, the effects of the
asphalt content on the fatigue life cannot be assessed unless the percent

129

fine is held constant and the percent asphalt content increased. While this

solution is possible for laboratory compacted samples, it is not practical

for core samples.
The two observations noted above implies that the values of the coefficient of
correlations between the fatigue life, on one hand, and the percent asphalt content
and the recovered penetration, on the other hand, should not be taken at their face
values. The collinearity between these two variables and other independent
variables should be addresses. In other words, the above observations are
statistical in nature and they should not be taken at face values when considering
their engineering interpretations. To illustrate, consider the value of the
coefficient of correlation of the recovered asphalt penetration of "-.424" (see
Table 5.3). This implies that if the values of the recovered asphalt penetration
is truly an independent variable, then increasing values result in a shorter fatigue
life. Recall that the recovered penetration of the asphalt cement is a function of
the asphalt mix processing practice and temperature, storage time, age (service
life) of the pavement, the air voids in the asphalt mix and the composition of the
aggregate and sand in the AC mix. Hence, the coefficient of correlation of the
recovered penetration (PEN) of "-.424" reflects the global effects of the above
noted factors. Hence, this correlation cannot be taken at its face value. That is
one cannot conclude that softer asphalts have a better ability to withstand plastic
deformation without cracking than that of harder asphalt. Moreover, the
correlation matrix of Table 5.3 provides information relative to the relationship
between the fatigue life and the unprocessed (original) values of the independent
variables. The values of the coefficient of correlation listed in the Table and the
order of significance of the independent variables may change as their values are
transformed. For example, if the value of the recovered asphalt penetration are

expressed by an exponential function, then their coefficient of correlation to

130

fatigue life and their order of significance will change.

Further, examination of the values of the coefficient of correlation of
Table 5.3 indicates that the variables contributing the most to the fatigue life of
the AC mix is the angularity of the coarse aggregate and the second one is the
recovered asphalt penetration. This however, does not imply that the recovered
penetration of the asphalt cement will be included as a variable in the final
statistical equation. The reason for this is that the recovered penetration shows
a certain degree of collinearity to the aggregate angularity and other variables.
Indeed, the final statistical equation based on the untransformed values of the
independent variables did not include the recovered asphalt penetration as a
variable. The significance of this term was below the specified criterion. This
criterion for variable inclusion in the final statistical model specifies that if the
probability associated with the 'F' statistics for the hypothesis that the coefficient
of the variable is zero is equal to or less than five percent (0.05), then the
variable is excluded from the model. In the SPSS computer program, this
probability is designated by "FIN".
The percent aggregate, sand and fine contents affect the fatigue life of the asphalt
mixes in the respective order of significance. Increasing the percent aggregate
content cause an increase in the fatigue life. Whereas, increasing sand and fine
contents leads to a decrease in the fatigue life. Once again, these results were
expected and confirm the data reported in the literature. One point should be
noted here is that, the aggregate in the asphalt mix affects the fatigue life in two
ways, the aggregate content and the angularity of the aggregate. Further, the
effects of the aggregate on fatigue life cannot be had unless the aggregates are not
floating in the sand matrix. That is, a full contact between the aggregates is fully
mobilized.
The effects of the other asphalt mix variables (such as the resilient modulus and

131

the specific gravity or air voids of the samples) on the fatigue life also confirm

those reported in the literature (3, and 12 through 16). Increasing either the

specific gravity (decreasing the air voids) or the resilient modulus cause an
increase in the fatigue life.

5 . The effects of the test variables (such as the temperature and the magnitude of the
applied load) on the fatigue life are statistically insignificant. The reasons being
are:

a) All tests were conducted at room temperature where the measured

temperature (see Table 5.1) varied from about 74 to about 82 °F. Most
tests were conducted at about 75 “F.

b) The cyclic load was carefully controlled to within the accuracy of the
MTS system. Although the magnitude of the cyclic load varied from one
sample to another, most samples were tested under a 300 pounds cyclic
load. '

The above observations concerning the effects of the independent variables on the
independent one are only relevant to the untransformed values of the independent
variables. These observations may be altered or totally changed when the values of each
variable are transformed by using the proper transformation form based on the
observation of the trend between the dependent and the independent variables. For
example, the coefficient of correlation of the most contributing significant variable (the
aggregate angularity) of 0.47 may not be the optimum value. That is if the value of the
aggregate angularity are used in a transformed form then its coefficient of correlation will
change. For this reason, several transformed forms of the independent variables were
used. First the independent variable in question was plotted against the logarithmic
values of the dependent variable (fatigue life). From the plot, several transformation
forms that simulate the trend between the dependent and the independent variables were
used and the forms that showed the highest coefficient of correlation and the least

132
standard error were selected for the final analysis. These and other issues are presented

in the next section ”Regression Analysis“ .

5.4.4 Regression Analysis

The fatigue life of the asphalt mix core samples is a function of the asphalt mix
variables, the test conditions and the previous loading history. Although, the test
variables were kept constant throughout the testing program, some variations were
observed in the applied cyclic load and the test temperature (see Table 5.1). Therefore,
the test variables were considered as independent variables affecting the fatigue life of
the samples. Further, since the test samples were obtained from pavement cores, the age
(service life) of the pavement structure, the cumulative 18-kip ESAL that had travelled
on the pavements were also included in the analysis. It should be noted that the service
lives of the composite pavement sections were not included in the analysis. The reason
for this is that due to the thickness and stiffness of the portland cement concrete (PCC)
slab located beneath the AC layer, the neutral axis of the composite pavement is located
below the AC overlay. That is, the AC surface was not subjected to tensile stress or
strain due to traffic loading. The tensile strains induced in the AC layer due to the
expansion and contraction of the concrete slab and the AC surface were neglected. Such
strains cannot be calculated unless the state of cracks of the PCC slab is fully known.
As stated earlier, the criterion for excluding a variable from the statistical model specifies
”FIN" value of 5 percent or better. Prior to the analysis, each independent variable was
plotted against the logarithmic values of the fatigue life. The trend of the data was then
modeled using several equation forms (e, g. logarithmic, cubical, polynomial). During the
analysis, the various equation forms for each variable were analyzed. The form that
yielded the lowest "FIN” value, highest coefficient of correlation, highest significance

level, and lowest standard error in the presence of the other independent variables was

133

then selected for the final analysis.

Again, all the sample and test variables were included in the analysis. Variables

that did not meet the specified ”FIN" criterion were excluded from the model. Table 5.4

provides a list of the correlation matrix for those variables that satisfied the ”PIN"

criterion. It can be seen that only 5 variables are included in the final model. These

variables are listed below in their order of explaining the observed variations in the

fatigue life.

1.

2
3.
4
5

Aggregate angularity.
Asphalt content.

Specific gravity.

Percent fine.

Pavement age or service life.

Examination of the values of the coefficient of correlation matrix of Table 5 .4

indicates that:

1.

The coarse aggregate angularity has the highest correlation coefficient (the most
significant variable) with the fatigue life. Increasing aggregate angularity causes
an increase in the fatigue life. In addition, the aggregate angularity has a positive
(direct) degree of collinearity with the service life. That is higher aggregate
angularity is associated with higher service life. This collinearity can be directly
attributed to the MDOT pavement and mix design practices. Typically, more
angular aggregates are used for those pavements designed to have higher service
life and higher traffic volumes.

The asphalt content (LOGAC) and the sample bulk specific gravity (SPGTY2)
have some degrees of collinearity with. the percent fine (LOGFINE). As stated
earlier this was expected because higher amount of fines causes an increase in the
surface area of the sample to be coated with asphalt thus, increasing the asphalt
content in the AC mix. Further, fines fill the intermediate voids between the

134

Table 5.4 : Correlation matrix for the final variables.

 

 

 

 

 

 

 

 

 

 

 

LOGFL A1103 LOGAC SPGTYZ LOGFIIIE 5L

LOGFL 1.000

A1103 .490 1.000

LOGAC -.310 .204 1.000

SPGTYZ .264 .142 .322 1 .000

LOGFlliE -.096 .281 .687 .603 1.000

SL -.001 .456 -.144 .064 -.134 1.000
L00 8 base 10 logarithmic;
FL - laboratory fatigue life (thousands of load applications);
A1163 8 (angularity of the coarse particles (plus 44) in the ac aix)’;
A0 I asphalt content, (percent by weight);

SPGTYZI (samle bulk specific gravity)”;
FiliE I Fine, (percent by weight): and
$1. I pavement service life from construction mtil coring.

135

larger aggregates thereby affecting the bulk specific gravity of the AC mix.

Nevertheless, the degree of collinearity between the independent variables listed
in Table 5.4 were examined. Table 5.5 provides a list of the six eigenvalues and
condition indices, and the variance proportion (the percent of the variance attributable
to the eigenvalue) of each variable for each eigenvalue. It should be noted that, for each
variable, the sum of the values of its variance proportion over the eight eigenvalues is
equal to 1.0. That is, the variance of each variable has a different degree of
proportionality to the various eigenvalues such that their sum is equal to 1.0. For
example, a value of the variance proportion of the aggregate angularity (AN G) of
0.00564 implies that .564 percent of the variance of ANG is attributed to the first
eigenvalue. Likewise, the ANG variance proportion of 0.01049 indicates that 1.05
percent of the variance of AN G is attributed to the 6th eigenvalue. Nonetheless, the
values of the variance proportion and the eigenvalue indicate the degree of collinearity
or multicollinearity of the variable in question to the other variables. Higher values of
the variance proportion for the lowest eigenvalue implies a high degree of collinearity.
For example, the two terms "SL" (service life) and "constant” have high variance
proportion values of 0.87275 and 0.94560, respectively, for the minimum eigenvalue of
0.0. These values indicate, as it should be expected, a high degree of collinearity
between the two terms. Since, the other variables have small variance proportion values
for the 6th eigenvalue, they do not seem to have a significant multicollinearity. In
addition the tolerance and the variance inflation factors (VIF) were ealculated for each
variable and are listed in Table 5.6. The low VIF values for the-variables indieate that
they are not collinear, and authenticate the previous finding based on eigenvalues and
condition index. These diagnostics indicate that no significant degree of collinearity
exists among the variables.

The results of the regression analysis are listed in Table 5.7. Once again, all the
variables that are included in the resulting equation satisfy the specified criterion for the

136

Collinearity diagnostics ( eigenvalues, condition indices and the
proportion of the variance attributable to the eigenvalue).

Table 5.5 :

 

 

 

 

Cond Percent of variance attributed to the eigenvalues
lumber Eigenval index Constant 4863 LOGAC 396112 St LOGFlIE
1 5.32541 1.000 .00004 ,ggfigg .00009 .00018 .00004 .00762
2 .48260 3.322 .00013 .02986 .00030 .00065 .00012 .50661
3 .18158 5.416 .00017 .81789 .00018 .0000? .00015 .32286
4 .00751 26.623 .04390 . 12803 .00024 .45946 .00885 . 11645
5 .00231 48.000 .01015 .00808 .77616 .09755 .11809 .02455
6 .00058 95.504 ‘25569 .01049 .22303 .44210 ‘81215 .02191

 

 

 

 

 

 

 

 

 

Table 5.6 : Collinearity diagnostics: TOL and VIF

 

 

 

Variable tolerance VlF
ANG3 .655789 1.525
LOGAC .512891 1.950
SL .675476 1.480
SPGTY2 .588911 1.698
LOGFlIE .327870 3.05

 

 

 

 

 

137

variable inclusion. It can be seen from Table 5.7 that all the variables in the equation
have a "T" significance values of less than 0.05. Hence, they are significant variables.
The results of the regression analysis listed in Table 5.7 indicate that the standard error
of the resulting model is 0.14923. The value of the coefficient of determination (R2) is
0.78 and the adjusted R2 is 0.75. The numbers listed under the column designated 'B"
are the regression constants for the indicated variables. The stepwise development of the
model is addressed below.

Table 5.8 provides a list of the regression constants and the values of the R2 and
the standard error obtained from each step of the stepwise method of the SPSS computer
program. It can be seen that the aggregate angularity “ANG" is the most significant
variable and this term alone explains 24 percent of the variation of the logarithmic values
of the fatigue life (the dependent variable) of the asphalt samples. This percentage
increases, as it should be expected, with the inclusion of more variables in the model.

The final model can be expressed as follows:

LOG(FL) = 2.1261 + .0068 (ANG)3 - 2.4266 (LOG(AC)) - .0183 (81.) + .7520 (SPGTYP - 1.484
0.00m» (5.4)
R2 = 0.731, SE = 0.149, F = 34.97, PM, = 0.000

where
LOG = base 10 logarithm;
FL = laboratory fatigue life (thousands of load applications);
ANG = angularity of the coarse aggregate particles in the AC mix
(1 =rounded, 5=crushed on all sideS);
AC = asphalt content (percent by weight of the total AC mix);
SL = pavement service life from construction or last

rehabilitation to coring (years);

SPGTY = sample bulk specific gravity;

138

Table 5.7 : Results of regresion analysis.

 

 

Multiple R .88380
R Square .78110
Adjusted R Square .75877
Standard Error .14923
Analysis of Variance

OF SI. of Sqrares Mean Sqrare
Regression 5 3.89390 .7787!
Residual 49 1.09122 .02227
F - 34.97017 Signif F c .0000
‘ * * ' N U L T l P L E R E G R E S 5 l 0 fl * * * *
Equation laser 1 Dependent Variable.. LOGFL
------------------ Variables in the Equation ------------------
Variable 8 SE 8 Beta T Sig T
ANG3 .006869 6.350888-04 .892749 10.817 .0000
LOGAC -2.426645 .525708 -.430794 -4.616 .0000
SL -.018319 .002592 -.574717 -7.067 .0000
SPGYYZ .752051 .106965 .612354 7.031 .0000
LOGFlRE -1.483891 .348211 -.497427 -4.261 .0001
(Constant) 2.126127 .575990 3.691 .0006

 

 

Table 5 .8 : Regression matrix for laboratory fatigue life.

 

 

 

 

Laboratory intercept Regression coefficient of independent variables

Fatigue life

LOGCFL) AMOS LOGAC SL $90112 LOGFlIE R.8q. 5.E
3.325366 .003773 .240 .267
5.100313 .004444 -2.4114 .416 .236
5.591363 .006169 -3.0284 -.01412 .560 .207
3.442994 .006075 -3.7687 -.01535 .4890 .699 .173
2.126127 .006869 -2.4266 -.01832 .7521 -1.4839 .781 .149

 

 

 

 

 

 

 

 

variables sane as correlation aatrix.

 

139

FINE = fine (percent by weight);

R2 = coefficient of determination;
SE = standard error;

F = F statistic; and

F®= significance of F.

Based on the statistics of the model, the following two observations were made:
1. The null hypothesis of no linear relationship between the independent variables
and the laboratory fatigue life was rejected and it was concluded that at a
probability of F =0.000, 78 percent of the variation in the laboratory fatigue life
is explained by the above listed independent variables.
2. The largest value of the ”T” significance is 0.0001. This implies that all
variables in the model are statistically significant.
In addition, the following statistics were calculated to study the residuals and the
predicted values and are listed in Table 5 .9.

l. PRED = the unstandardized predicted values;
2. RESID = the unstandardized residuals;

3. ZPRED = the standardized predicted values;
4. ZRESID = the standardized residuals; and

5. D.W.S = the Durbin-Watson statistics.

The Durbin-Watson statistics is a measure of the autocorrelation between the

residuals. The regression analysis assumes that the residuals are uncorrelated, in which
case the value for Durbin-Watson test should be close to 2. The calculated value of 2.14
for the model signifies a satisfactory lack of correlation between the residuals.
Further, the maximum, minimum, mean! and standard deviation of the unstandardized and
standardized predicted values and the residuals are also presented in Table 5.9. Based
on the values of the residuals and the standardized residuals the ten worst residuals are
listed in Table 5.10.

140
Table 5.9 : Residual statisties of the data.

 

 

 

 

 

 

 

 

 

Min Max Mean Std Dev R
*PRED 3.1525 4.0739 3.5532 .2685 55
*RESlD -.2916 .2848 .0000 .1422 55
*ZPRED -1.4922 1.9391 .0000 1.0000 55
*ZRESlD -1.9538 1.9088 .0000 .9526 55
Durbin-Uatson Test 8 2.14477

 

Table 5.10 : Ten worst Residual.

 

 

 

 

 

Case 8 ‘RESID 'ZRESID
16 -.2916 -1.95378
42 .2848 1.90878
15 .2565 1.71892
24 -.2387 '1.59939
20 .2327 1.55961

3 .2315 1.55162
6 -.2254 -1.51032
13 .2205 1.47733
26 -.2129 -1.42690
5 .2128 1.42625

 

 

 

141

A histogram of the standardized residuals of equation 5 .4 is presented in Figure
5.6. ”N” represents the observed number of residuals in an interval whereas, ”Exp N”
indieates the expected number of residuals in that interval. The extreme interval labeled
as ”out” contain more than 3 standard deviations from the mean of the residuals. The
expected frequency and the overlap between expected and observed are indicated by a
period and a colon respectively. The presented histogram is fairly normal indicating that
the statistical model has no significant bias. '

To this end, the sensitivity of the statistical model to the various input parameters
and comparison between the observed and predicted values are presented in the next

section.
5 .4.5 Sensitivity Analysis and Engineering Interpretation

The statistical model presented by equation 5 .4 was used to predict the fatigue life
of the test samples. Figure 5.7a depicts the values of the predicted fatigue life versus
the laboratory observed one. The straight line in the Figure represents the locus of those
points where the observed and predicted fatigue lives are equal. It can be seen that most
predicted values are reasonably close to the observed ones. Figure 5 .7b depicts the
percent errors between the predicted and the observed fatigue life values. A negative
percent error implies that the statistical model under predicts the fatigue life of the
indicated sample. A positive error on the other hand, indicates an over prediction.
Examination of the Figure indicates that the predicted fatigue lives of 89 percent of the
samples (about 50 samples) are within 50 percent of the observed values. This indicates
that the statistical model is relatively accurate.

One additional point should be made herein is that, the fatigue life of a pavement
structure is a function of several variables including the stiffnesses and thicknesses of the

various pavement layers, the properties of the materials in the AC mix, the traffic

142

 

 

.m.

m

m

a.

u n

c 3.2.. .3“

al I

... .33er..-
Mm.em.eMNamsam..mn.mm

3222111 1412223

N
mummwmumuunnmuuoumwmmm
I I I I I I I I I I I I I I I I I I I I I
E 1136567656311
"000013257763963210000

 

 

Figure 5.6 : Histogram standar ' d residual

143

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14
12 T
4.
10
+
2 +
j 8
i. a .
= +
v: i
8 + +
% LE— 6 ,jfl
a. + +
a + + +
4 +
+ 3
t
~101- + " 3
2 .24 1:; +
$ 3'" g + +
G
0 2 4 6 8 10 12 14
Observed Laboratory Fatigue Life
(Thousands)
Figure 5.7a : Observed versus the predicted laboratory fatigue lives of the 55

' test samples.

144

 

 

 

 

 

4

 

 

 

 

 

Percent difference between the observed and the predicted

laboratory fatigue lives for the 55 test samples.

0"
Figure 5.7b :

145

volume, load, and environmental factors. In this study, only the asphalt mix properties

and the traffic load and volume data are used. Since, all of the test samples were

obtained from field cores, they were subjected to a history of stresses/strains that is a

function of the above listed factors. Consequently, one should not expect the statistieal

model presented in equation 5 .4 to fully explain the variations in the fatigue life.
In any event, the sensitivity of the statistical model to variations in each
independent variable and the engineering interpretations of the model are presented in the
next section.
Sensitivity analysis of equation 5 .4 was performed to determine the effect of each
variable in the equation on the predicted fatigue life of the test samples. The sensitivity
of the model to each variable was analyzed such that:
1. The values of three variables in the equation were held constant.
2. The value of a fourth variable was changed from a low, to a medium, to a high
value within the range of that variable.
3. The value of the variable in question was varied from one end of its range to the
other.
Results of the sensitivity analysis are presented and discussed below.
Aggregate Angularity - Figure 5.8 depicts the sensitivity of the predicted fatigue life to
the aggregate angularity for constant values of the asphalt and fine contents, and
the specific gravity of the sample, and for three levels of service life (1, 15, and
20 years). Examination of the Figure indicates that:
1. Increasing aggregate angularity from 1 (rounded aggregate such as river
gravel) to 5 (aggregate crushed on all sides) causes an increase in the
fatigue life by a factor of about 7.

2. The rate of increase in the fatigue life varies from one value of the
aggregate angularity to the other. For example, using aggregate crushed
on only two sides (aggregate angularity of 3) causes the fatigue life of the

Fatigue Life

146

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14000
L
Fpgty- 2.38. AC -s.71. Fine- 5.39 /
12000
10000 gt Data Range
SIMCO 1110 I 1
8000 /
600C /
/
400C /
/ 15 /
v ’1‘
T Ti
0 r
1 2 3 4
com M97993" Angularity

5

Figure 5.8 : Laboratory fatigue life as a function of aggregate angularity, for
different levels of service life.

147
asphalt mixes to increase by a factor of only 1.5 relative to those made by
using rounded aggregate. Given that the difference in cost between
crushing the aggregate on one side and on all sides is not significant, the
benefit to cost ratio will be maximized by using aggregate crushed on all

sides.

For all values of the service life, the rate of increase in the predicted

fatigue life is the same.

Service Life — Figure 5 .9 shows the sensitivity of the predicted fatigue life to the service

life of the pavement structure for constant values of the asphalt and fine contents,

and the specific gravity of the sample, and for three levels of aggregate angularity
(l , 3 and 5). Examination of the Figure indicates that:

1.

Increasing the service life (older pavements) from zero (after construction)
to 30 years causes a decrease in the predicted fatigue life by a factor of
about 3.5. Recall that a longer service life of a pavement structure
indicates that the pavement was subjected to a higher traffic volume.
Higher traffic volumes cause higher accumulation of plastic (permanent)
strain in the asphalt which is the main cause of fatigue cracking. Thus,
the term ”service life” herein represents the stress and/or strain history of
the asphalt course. If the asphalt course was subjected to higher stress
and/or strain levels during its service life then its remaining service life
(RSL) should be expected to decrease.

The rate of increase in the fatigue life of the asphalt samples with respect
to the service life of the pavement structure is almost constant (near linear
relationship). This implies that the data can be used to obtain a shift factor
whereby the laboratory measured/predicted fatigue life of an asphalt mix
can be used to calculate the fatigue life of a pavement structure made by

using the same asphalt mix. Such a shift factor will be constant for all

 

148

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14000?
\[spgry- 2.3a. AC -s.71, Fine- 3.39
12000 \ '
10000.th Data Range ——2
a \
g 8000 \l I Coarse aggregate angularity - 5 —
3'2.” \
o
1.1. 6000 a. \‘
4000 \ .«r
..\ if
2000\ T\ I?
'\ 1r\ 0
V '\'~-\\x~r
c0 5 10 15 20 . 2‘5 3'0

3 Figure 5.9 : Laboratory fatigue life as a function of pavement service life, for
different leveb of coarse aggregate angularity.

149
pavement structures provided that the service lives of the pavements are
used. On the other hand, if one is interested to predict the fatigue life of
the pavement structure in terms of the number of 18-kip ESAL, then the
shift factor becomes site specific. In this regard, the number of l8-kip
ESAL can be calculated by using the average daily traffic (ADT), the
percent commercial, and the ESAL factor for the pavement in question.
Table 5.11 provides a list of the values of the shift factors in terms of
service life and the number of 18-kip ESAL for the flexible pavement
sections included in this study. Verification of the shift factors is presented

in section 5.7.

Bulk Specific Gravity - Figure 5.10 shows the predicted fatigue life as a firnction of the

bulk specific gravity of the samples for constant values of the asphalt and fine

contents and service life and for three levels of aggregate angularity of 1, 3 and

5. Examination of the Figure indicates that:

1.

Increasing the sample bulk specific gravity from 2.2 to 2.5 causes an
increase in the fatigue life by a factor of about 11.5. This observation
however, should not be interpreted as higher bulk specific gravity eauses
a better pavement performance. Other types of pavement distress such as
rut need to be evaluated before a decision can be made. Tire reason being
is that higher bulk specific gravity values imply lower air voids. Although,
lower air void values (lower than about 2 percent) cause higher fatigue
life, percent air voids in the order of 2 or less causes distortion and rutting
in the pavement structures. One other point should be noted herein is that
very low bulk specific gravity values (lower than about 2.25) may eause
bearing capacity failure of the pavement structure.

The rate of change in the fatigue life with respect to the bulk specific
gravity increases at the higher values of the specific gravity. This implies

150

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o... 4.8. 88. 8a.. .m. 8 84.4. a... me 3 “a. 3
pm. 2... 83 «8. 86 a. 2.3 ..m as am ......
..m 8m .2“ mace «we . and 3 we as “a.
8.. $8 83 8:. ...... ... 8a.“ a... S 3 ”an
88 8 2..“ 88 Ed . «Ba 3 2. no “.9.
an. 3.. can 28 3.. .. m8.“ «.6 me an ”a.
8a «a. 83 88 2.... .. as.“ as e... a... a8
8. 8m. 88 89. mu. . can.“ an a... v... n:
...m 23 - 3.2:: 283 emmwl .wfi 8.“. o<
3. s... a:
8.8". 2.9.3. Susan. .23 a: .o
, aim 60:22.5 do... .93 .E:0 8.26m aoEoromtotofis. .m>< eczuom

 

6:388 «c.2522. 03.5: a... ..8 .38.... 5.5 u 3% 623—.

151

 

 

 

 

AC -5.71. SL- 9.4 .Fino- 0.39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

25000
‘——_ Date Range .
20000 at;
.2
3
a 15000 /
3 Con to la - 5
'2 no aggrega angu rlty \ .

 

 

 

 

10000 i/

 

 

 

 

 

 

 

 

50°C / /.
/ 0/
+/ ////\/
‘L -
cugigf “1”;1' / [fl

 

I l l
2.20 2.25 2.30 2.35 2.40 2.45 2.50
Sample Bulk Sp. Gravity

Figure 5.10 : Laboratory fatigue life as a function of sample bulk specific
gravity, for different levels of coarse aggregate angularity.

152
that the incremental benefits of compaction increases as the compaction
efforts (the number of roller paths) increases. However, the rate of
increase in the bulk specific gravity with respect to increasing compaction
efforts decreases at the higher values of specific gravity. Consequently,
economic analysis regarding the benefits and costs should be conducted
before a decision regarding the proper compaction effort can be reached.

Fine - Figure 5.11 depicts the fatigue life (predicted by using equation 5 .4) as a
function of the fine content for constant values of the asphalt content, service life
and bulk specific gravity of the samples, and for three levels of aggregate
angularity. It can be seen that fine content has a detrimental effect on the fatigue
life. Higher fine contents cause lower fatigue life. Increasing the fine content
from 4 to 10 percent (the data range) causes a decrease in the fatigue life by a
factor of about 4.5 . This observation should not be taken independent of that
regarding the bulk specific gravity. Lower fine contents cause lower bulk specific
gravity and lower asphalt content. Thus, either the combined effects of fine
content, bulk specific gravity, and asphalt content should be addressed or the
effects of each variable should be studied separately by stratifying the three
variables. Due to the nature of the test samples in this study (core samples), the
latter avenue was not possible. The former one can be analyzed through an
example by using hypothetical data. Such an example is given at the end of the
next paragraph.

Asphalt Content - Figure 5 . 12 displays the relationship between the predicted fatigue
life and the asphalt content for constant values of the service life, bulk specific
gravity of the sample, and fine content, and for three levels of aggregate
angularity. It can be seen that higher asphalt contents cause lower fatigue life.
As is the case for the fine content, the effects of the asphalt content should not
be taken herein at face value. The asphalt content of an asphalt mix is affected

153

 

 

 

 

 

AC -5.71. SL- 9.4 . Spgty -2.aa

 

 

 

 

 

18000 \
16000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D taRango ———>
14000 \ .
*\

12000 *t Coamaggregato angularity - 5
o
5
S 10000 i
a? \
a
n.

6000 T \

\

 

 

 

 

 

 

 

 

 

 

 

 

 

El! \ .\ E:+:i 1% .L‘l
. . I 1"" T—t
4 5 6 7 a 9 1o 11 12
FinoContentmorcentbyweight)
Figure 5.11 : Laboratory fatigue life as a function of fines, for different

levels of coarse aggregate angularity.

154

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

450001
40000 \\ Nice lite- 9.4. Spgty- 2.36. Fine- 6.39
35000 ‘
\ ‘ Datafiange '-
30000
\ Aggregate angularity - 5
g 25000
.1 V
g .
E 20000 \\
15000 '
10°00 \ ‘\ ...
3] \
1 I \ ”r" 4L k
c . r ‘1‘ :1=—". 1
3.0 3.5 4.0 4.5 5.0 5.5 6.0 5.5 7.0 7.5 8.0
AC Content(percentby weight)
Figure 5 .12 : Laboratory fatigue life as a function of AC content, for

different levels of coarse aggregate angularity.

155
by the fine content and it influences the bulk specific gravity of the sample.
Hence, the combined effects of the three variables (fine and asphalt contents and
the bulk specific gravity is addressed by using an example in the next paragraph.

The Combined Effects of Bulk Specific Gravity and Asphalt and fine Contents -

5.5

Consider an AC mix with a bulk specific gravity of 2.193, an AC content of 4. 10
percent, a fine content of 3.10 percent, aggregate angularity of 2 and a service
life of 15 years will yield a fatigue life of 2028 load repetitions using equation
5.4. Increasing the percent fine content of the mix to 7 percent will also increase
the bulk specific gravity to 2.275. For new values of the percent fine content and
the bulk specific gravity (rest of the variables same as before) equation 5.4 yields
a fatigue life of 1142 load repetitions. The implieation of the above observation
is that although, increasing the fine content in the AC mix causes an increase in
the bulk specific gravity of the mix, but the negative affect due to increase in the
fine content on the fatigue life is overwhelming as compared to the positive affect
of the bulk specific gravity. Similarly, if the AC content in the mix is increase
from 4.10 to 4.5 , 5.0, and 5.5 percent, the respective increased values of the
bulk specific gravity are 2.202, 2.213 and 2.224 and the predicted fatigue lives
are 517, 436 and 376. Again the increase in the AC content has an
overwhelming negative affect on the fatigue life as compared to the positive affect

of the bulk specific gravity.
RUT ANALYSIS

Rut or plastic deformation of a pavement structure is a function of the

construction practices, the properties and thicknesses of the AC, base, and subbase

layers, the properties of the roadbed soil, environmental factors and traffic load and

volume (1). Unfortunately, the properties of the base, subbase, and roadbed materials

156

are not available to this study. Hence, the following assumptions were made at the onset

of this analysis.

1.

Rutting in flexible and composite pavements ean be analyzed as a function of the
AC layer and its material properties.
The material properties, layer thicknesses, construction specifieations/practices

and the construction quality remain the same within one job number.

The two assumptions are reasonable because of the following reasons:

1.

In the absence of material properties for base, subbase. and roadbed soil, their
effects on the rotting of flexible pavements cannot be assessed. Whereas, in the
case of composite pavements the entire rotting can be attributed to the AC layer
due to the presence of a stiff concrete layer.

In this study the selected test sites within one pavement control section number
(a number, used by MDOT to identify a pavement section) have had the same job
number (a number, used by MDOT to identify a construction/rehabilitation
project). It is the MDOT practice to divide longer pavement control sections into
several smaller job sections for construction and/or rehabilitation purposes. The
pavement thickness design, the material properties, and the specifieations are then
kept the same within the same job section (number) depending on the existing
pavement, roadbed soil, and the traffic conditions. Thus, any pavement section
within the same job number will have similar layers thicknesses and material
properties.

Due to the first assumption, one should expect some bias in the deve10ped rut

model. That is, given the lack of information regarding the properties of the base,

subbase and roadbed soils, their effects cannot be incorporated. Further, the assumption

of constant material properties may not hold. Even though, in the presence of the same

specifications and design, variations due to construction practices are always present in

the form of the AC mix manufacturing, placement, and compaction. Nevertheless, the

157
thickness of each AC layer in the pavement was obtained from the cores and the overall

global AC mix properties for each core was determined as presented in the next section.

5.5.1 Determination of Material Properties for a Core Location

Based on the second assumption and due to economic and time constrains, it was
decided to perform one extraction test per asphalt course for all 13 cored pavement
sections to obtain the material properties of each AC course. For example, section 43F
has four AC courses (see Table 4.5) therefore, one extraction test per AC course was
performed to obtain its properties. Thus, four extraction tests were performed for
section 43F. The global properties of each core were determined as the weighted
average properties of the various AC courses of that core.

As stated in the fatigue analysis, the same AC courses of two or more cores
obtained from one pavement site were combined to yield enough material for a single
extraction test. For the combined cores the average material properties along with the
average measured rut depth were assigned to the locations of those cores. This resulted
in a total of 45 layer extraction tests for the 19 core locations of the 13 cored sections.
Table 5.12 summarizes the global material properties for the 19 cored locations. These
include the core designation number, AC thickness, Coarse aggregate angularity, air
void, percent contents by weight of the AC, sand, fine and coarse aggregate in the
asphalt mix, the service life of the pavement section, the cumulative 18-kip ESAL
experienced by the pavement section in question during its service life, and the average
rut depth of the core location. Table 5.13 summarizes the minimum, maximum,average,
and standard deviation of each data entry of Table 5.12.

Two types of analysis were conducted in this study. One analysis is based on the
properties of the paving materials, the other, on the measured deflection basins. The two
types are presented below.

158

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

09.0 0w.0 0— w? 5 N0 0.0 00 N0 ?p.0 ?mN 0p5wN—?p 0..
??.0 00.0 N N? 5 N0 —.0 00 —.0 00.0 00.? :0w0Nw _ 0—
N0 p00 0 F0 0 00 0.0 00 0.? 00.0 00.N —N000N0 5w
0—.0 ?54 0F ?0 0 0? 0.0 5N N.0 00.? 00.0 :0PON0 0—.
0rd ?5.— 0w ?0 0 0? 0.0 5N 0.0 00.? F00 :OwNNO 0—
0rd NN.0 5 00 0 N0 0.0 N0 0.0 N5.0 0?.0 :0—0w0w ?w
0 —.0 50. w ?w 0? 0 —.0 0.0 ?N 0.5 05.? ?0.0 p000p —00 0F
00.0 05.0 F 0? 0 0? 0.0 m? 0.0 05.0 00.0 :0Nm—0? N—
000 05.0 _. ?? 0 0? 0.0 ?? 0.0 00.0 ?0.0w :0w0w0? ..—
00.0 05.0 p ?? 0 0? 0.0 m? 0.0 N0.0 p0.0— :0p?—0? 0..
00.0 00.0 0 00 0 00 0.0 00 0. p 50.N 00.N _. —0N — N? 0
00.0 00.0 0 00 0 00 0.0 00 0.— 50.N 0N.N :00NN? 0
00.0 N — .0 0 N0 5 ..0 0.0 N0 N.0 0N.0 N0.N :08pr 5
00.0 Nw.0 0 N0 5 '0 0.0 N0 N0 0N.0 0?.N «N05mN: 0
0N.0 00.— FF 0? 0 . ?0 0.0 ?? 0.0 0?.0 0N.0 2.30—0— 0
0N.0 004 pp 00 0 00 0.0 ?? 0.0 0?.0 0P0 :000p0w ?
0.20 05.0 2. p0 ? 00 5.? 0? 0.5 00. w 00.?w —N55w —0N 0
0—.0 F04 00 N0 0 0? 0.0 5? N0 00.? 55.? ..N—5ww0p N
—0.0 0N... 5 ?0 ? N0 ?.? . ?? 0.0 ?N.N ?N.0 :N —0 —5 w
22.. 9.5% 33¢ 22... .3532
5%.. ._<mm a: 62 2m use 9 8:82... 20> .32.: 5.22.6 62
Eu .5: e .353 3 Easefi 022.3 “E DE DK 20w Ten-

 

.2232: 9.8 3 o... .5. 8:02.95 3.532 a «fin «Ema.

159

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

«..o 8... s e. . s ...o o. 3.. 86 8.0 58.2...
86 86 a 3 s 3 an 3 .3 8d a...» we.
3... can 8 «a a 8 an 8 «a 86 on... .52
3o «.... . .o v 3 v... 8 o.. 8.. 8.... .....2
32.. 2.2. .28.. 22..
£9... #8 ...... .22 E... .85 3 8:32.... 20> a... ...sfi
Sc ...50 axiom £10.25 3 .5030? 022.030 .2 .392 o<

 

.830 28:82... a a... .e 8.22.9... o... ..e 8.5....» 9.3.880 . 3d 03:...

 

160
5.5.2 Analysis of Rut as a Function of Material Properties

The objectives of this analysis are to :

1. Determine the influential factors affecting pavement rutting.

2. Recommend changes to the existing asphalt mix design and pavement construction
practices to decrease the rut potential.

Statistical analysis were conducted to relate the measured pavement rut depth to
the AC mix variables and the traffic volume. During the analysis, several collinearity
problems were encountered. For example, as noted earlier, by the MDOT practices,
higher angular aggregate contents, better construction practices, and stricter quality
control are commonly used for most pavements designed for higher traffic volumes. By
the nature of this practice, collinearity between the independent variables (the material
properties, layer thicknesses, and traffic volume) exists as shown by the simple
correlation matrix in Table 5.14. For example, the term ESAL (the cumulative 18-kip
equivalent single axle load applications) has positive collinearities with the AC thickness,
the percent aggregate and the aggregate angularity; and negative collinearities with the
percent sand and fine contents, the recovered penetration, the amount of asphalt in the
AC mix and with the air voids. The reason for this is that, in most pavement design
methods (see Chapter 2), the traffic volume has the most influence on the thickness of .
the individual layers in a pavement structure. Thus, for higher traffic volumes, higher
thicknesses, and higher quality materials are used to safeguard against excessive rotting
and fatigue cracking. In the correlation matrix of Table 5.14, the positive correlation of
ESAL to the coarse aggregate angularity and the percent coarse aggregate content and
negative correlation with the percent sand and the fine contents, substantiate the fact that
the MDOT pavement design practice is balanced and that better materials are being used
for higher volume roads. It has already been proven (16,19,21,22) that the performance
of AC mixes depends on providing adequate aggregate interlock and distributing the

161

Table 5.14 : Correlation matrix for the 19 extracted core locations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RU! ESAL A01“ PEN Percent by weight ANG AV
A0 A66 SAND F 1 IE
RUT 1.000
ESAL .453 1.000
A0 TH .513 .099 1.000
PEI -.264 -.617 -.393 1.000
A0 -.445 -.420 -.613 .493 1.000
A00 .205 .541 -.001 -.387 .131 1.000
SAND -.251 -.488 .027 .355 -.227 -.983 1.000
FINE .214 -.360 -.136 .224 .490 -.237 .054 1.000
ANG .037 .357 -.224 -.462 .400 .755 -.814 .200 1.000
AV .392 -.056 .408 -.074 -.486 -.318 .307 .107 -.200 1.000
Rut I rut depth (inch);
ESAL I 18-kip cumulative ESAL during the service life;
Ac iflI thickness of A: layer (inch);
PEA I recovered asphalt penetration;
A0 I asphalt content (percent by weight);
A00 I aggregate (plus #4) in Ac nix (percent by weight);
SAID I send in Ac nix (percent by weight);
FINE I fine in Ac nix (percent by weight);
ANG I angularity of coarse aggregate (plus #4) in Ac nix; and
AV I air voids in Ac nix.

 

162

‘ wheel load. Increases in the percent aggregate, reduce the amount of the sand and the

fine in the AC mix. This leads to a better aggregate face to face contact and reduces the

ball bearing effect due to the presence of excessive sand and fine in the AC mix.

The above scenario implies that the statistical analysis between the dependent and

independent variables must be conducted on the basis of engineering knowledge rather

than on the basis of statistic alone. This point ean be illustrated by examination of the

values of the correlation coefficients between the dependent variables (rut depth) and the

independent variables (material properties, traffic volume, and service life). Such an

examination leads to the following observations:

1.

The rut depth increases with increasing the number of cumulative ESAL. This

observation was expected and it is consistent with that reported in the literature.

‘ The reason for this is that pavement rutting is mainly eaused by wheel loads and

is accelerated by material and environmental factors.

The rut depth increases with increasing the thickness of the AC layer. This
observation was not expected. Thicker AC thicknesses eause a decrease in the
compressive stress and strain delivered to the base and subbase layers and to the
roadbed soil. Further, such an observation should not lead to the conclusion that
the rut depth potential can be decreased by decreasing the AC thickness. This
observation is mainly a statistical one and it is caused by the collinearity between
the traffic volume and the AC thickness. Once again, by the nature of the design
and construction practices of most State Highway Agencies (SI-IA) including
MDOT, pavements that are expected to carry higher traffic volumes are designed
with thicker AC layers. Thus, the observation that a thicker AC layer leads to
a higher rut depth may as well be interpreted as higher traffic volumes eause
higher rut depths. The important point here is that the true effects of the
thickness of the AC layer on rut depth cannot be understood unless the

collinearity between the AC thickness and the traffic volume is resolved.

163

The rut depth increases with the decrease in the recovered asphalt penetration.

This observation is not reasonable and it is not consistent with the literature.

Softer asphalts produce softer asphalt mixes with lower resistance to rutting.

Once again, the collinearity between the recovered asphalt penetration and the

pavement service life presents a problem in interpreting the data. Longer service

life of a pavement structure leads to more oxidation and hardening of the asphalt
cement which should result in a lower future rut depth. However, a longer
service life implies higher cumulative traffic volume and hence, higher rut depths.

This supports the discussion made in item 2 above. The true effects of the

recovered asphalt penetration cannot be found unless the collinearity problem

between this variable and service life is resolved.

The rut depth decreases with an increase in the asphalt content in the mix. Two

points can be made relative to this observation. These are:

a) Higher traffic volume roads are typically built with thicker AC
thicknesses. In general, the AC layer consists of several AC courses, with
larger AC layer thiclmesses requiring a larger number of courses. For
example, a 7.5-inch AC layer may consists of a 1.5-inch surface course,
a 3-inch leveling course, and a 3-inch base course. On the other hand, a
3-inch thick AC layer may consists of 1.5-inch surface course and a 1.5-
inch base course. Hence, commonly, no leveling course is used in thin
pavements. Since, in the State of Michigan, the AC content of the
leveling course is a half-percent lower than that of the surface course, and
the AC content of the base course is about 4.5 percent, higher traffic
volume roads have lower asphalt contents. This can also be seen through
the examination of the degree of collinearity between the AC content and
the cumulative ESAL (see Table 5.14). A negative collinearity implies
that higher ESAL volumes lead to lower AC contents. Again, this

164
collinearity problem needs to be resolved prior to making any engineering
decision.
b) The range of the AC content data is rather narrow, hence, the trend of the
data may be affected by its variability.

5. The rut depth increases with increasing percent of coarse aggregate and with
decreasing percent sand contents in the mix. Once again, both observations are
not reasonable and they are the direct results of the pavement design practices.
Higher percent coarse aggregate and lower percent sand contents are typieally
used in the construction of higher volume roads. Hence, the increase or decrease
in the rut depth is mainly affected by the traffic volume.

6. The rut depth increases with increasing percent fine (passing sieve number 200)
content. This observation is reasonable and consistent with that reported in the
literature. Although, a certain degree of collinearity between the percent fine
content and the cumulative ESAL exists, it appears that its effects is not
significant to cause a reversal in the effects of the fine on the rut depth.

7. The rut depth increases with increasing aggregate angularity. For the same
reasons stated above this observation is not reasonable and inconsistent with that
reported in the literature.

8. Finally, the rut depth increases with increasing percent air voids. This observation
is reasonable and consistent with that reported in the literature. One point should
be noted is that no significant degree of collinearity can be found between the
percent air voids and the cumulative ESAL. However, certain degrees of
collinearity exist with other variables such as the percent coarse aggregate and
sand contents.

The above observations indicate that the degrees of collinearity between the
cumulative number of ESAL and the other variables are problematic. Stratification of

the data to resolve the collinearity problem is not possible because of the nature of the

165

field experiment. Hence, another solution must be found before balanced statistical and

engineering analyses can be conducted.

In order to alleviate the problem and to analyze the rut depth as a function of the
material variables without a significant interference by the traffic volume, a new term is
introduced herein ”Rate of Rutting (RRUT)". The rate of rotting or rut rate is defined
as the amount of rut per million ESAL. Hence, a new dependent variable 'RRUT" can
be used and the independent variable ”cumulative ESAL" can be eliminated from the
pool of independent variables thereby eliminating significant degrees of collinearity. This
solution however, does not necessarily eliminate other collinearity problems as discussed
below.

Table 5.15 provides a list of the values of the correlation coefficients between the
dependent variable (RRUT) and the independent variables ”material properties“ .
Examination of these values indicates that some degrees of collinearity between the
independent variables still exist. These are:

l. The collinearity between the sand and aggregate contents. This can be eliminated
by expressing the percent coarse aggregate contents in terms of the fine and sand
contents as follows:

AGG = 100 - (Fine + Sand)
where AGG, Fine, and Sand are the percent aggregate, fine, and sand contents,
. respectively.

2. The collinearity between the thickness of the AC layer (AC TH) and the percent
AC content (AC). The reason for this degree of collinearity was explained
earlier. Unfortunately, because of the nature of this dependency, this collinearity
problem cannot be resolved by expressing one variable in terms of the other.

3. The collinearity between the percent fine and the percent AC contents. This
collinearity cannot be resolved prior to the statistieal analysis. However, the
combined effects of both variables can be assessed by using the resulting

166

Table 5.15 : Correlation matrix for rate of rutting (RRUT).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

31107 AC 1'11 PEN Percent by acid“ A110 AV
A0 A00 SAID FlNE
RRUT 1.000
A0 TN -.088 1.000
PEN .638 -.393 1.000
A0 .325 -.613 .493 1.000
A00 -.368 -.001 -.387 .131 1.000
SAND .251 .027 .355 -.227 -.903 1.000
FINE .670 -.136 .224 .490 -.Z37 .054 1.000
ANG -.205 -.224 -.462 .400 .755 -.014 .200 1.000
AV .472 .400 -.074 -.406 -.310 .307 .107 -.200 1.000
RRUT I rut/ia-lrips cmlative ESAL; and rest of the variables are sane as Table

5.13.

 

167

statistical models along with some assumptions to express one variable in terms

of the other.

4. The degrees of collinearity between the recovered asphalt penetration (PEN) and
the percent AC content, the aggregate angularity, and the percent sand and
aggregate contents. Once again, these collinarities cannot be resolved prior to the
statistical analysis. Consequently, several statistical analysis were conducted
whereby various transformations were used to express each independent variable.
It was found that the elimination of the recovered asphalt penetration (PEN)
variable from the pool of variables did not causes any significant bias in the
resulting model. Therefore, the variable PEN was not included in the final
analysis.

Based on the results of the statistical analyses presented in Tables 5.14 and 5 .15,
the discussion presented above, and the elimination of the variable PEN from the pool
of variables, a third statistical analysis was conducted to obtain a regression equation
relating the dependent and independent variables. This analysis is presented in the next

section.

5.5.2.1 Regression Analysis

Prior to the commencement of the statistical analysis, the dependent
variable (RRUT) was plotted against each of the independent variables. From the
plots, the trend between the dependent and each of the independent variables was
observed. For each independent variable, the observed trend was then modeled
by using several transformations (e.g. ,logarithmic, cubieal, polynomial). The
form that yielded the lowest FIN value, highest coefficient of correlation, highest
significance level and lowest standard error in the presence of the other

independent variables was selected for inclusion in the model.

168

Table 5 . 16 provides a list of the values of the correlation coefficients for
all variables that satisfied the variable inclusion criteria (FIN) in the final model.

It can be seen that only six variables are included. In their order of significance,

these variables are:

1. the percent fine and sand content (F+S);

2. the percent air voids (AV) of the AC mix which is included in a
polynomial form as AVI , AV2, and AV3;

3. the percent AC content (AC); and

4. the angularity of the coarse aggregate (ANG);

where;

RRUT

F+S
Fine
Sand
AVl
AV2
AV3
ANGl
AV
log

Rut/cumulative 18-kips ESAL over the
service life (inch/million ESAL);
Fine’ + Sand;

percent fine content;

percent sand content;

e“ ;

AV2 ;

AV3 ;

log (AN 6):

percent air voids; and

base 10 logarithm.

The degree of collinearity between the independent variables listed in

Table 5.16 were examined. Table 5 . 17 provides, for each independent variable,

a list of the seven eigenvalues and condition indices and the percent of variance

attributed to each eigenvalue. The results indicate that the different terms of air

void (AVl, AV2, and AV3) have high variance proportion values for the 7th

eigenvalue thus indicating significant multicollinearity. A similar conclusion was

169
Table 5.16 : Correlation matrix for the final variables.

 

 

RRUT F+S AV1 AC3 AN01 AVZ AV3
RRUT 1.000
F+S .697 1.000
AV1 .529 -.001 1.000
AC3 .346 .344 -.Z35 1.000
AN01 -.127 .214 -.359 .411 1.000
AVZ .496 .119 .826 -.459 -.375 1.000
AV3 .490 .073 .905 -.422 -.404 .984 1.000

 

 

 

 

 

 

 

 

 

 

RRUTIrate of rotting per nillion ESAL;
F+s I(percent fine) apercent sand;
AV1 Iexp(air void);

AC3 I(percent AC content)’;
AN01Ilog(engularity);

AV2 I(air void)’:and

AV3 I(air void)’.

 

 

 

 

Table 5 .17 : Collinearlty diagnostics (eigenvalue, condition indices
and the proportion of the variance attributable to the
eigenvalue).

Cond Percent of variance attributed to the eigenvalue
Nurber Eigenval index Constant HS AV1 AC3 AN01 AV2 AV3
1 5.69448 1.000 .00036 .00336 .0001.9 .0005: .0006: .00006 .0000:
2 1.03648 2.31.1. .0007: .00939 .01288 .00201 .0021.0 .0001: .00027
: .11.162 6.341 .00891 .66514 .0039: .009:2 .01551 .00016 .00006
1. .0996: 7.558 .00155 .07967 .1291: .0175: .00002 .00660 .0022:
5 .0105: 17.528 .02739 .02672 .0251.2 .:57:: .76259 .0001.1 .00068
6 .00825 26.272 .96070 .19463 .05262 .61323 .1458 .007:9 .00286
7 .00096 77.146 .ooo:6 .02109 .3550 .00005 .07327 .2552; m

 

 

 

 

 

 

 

 

 

 

 

170
also made based on the tolerance and VIF values listed in Table 5.18. These
diagnostics indicate that a significant degree of collinearity exist only among the
various polynomial terms of the same independent variable (the percent air void
AV). Note that the presence of such a collinearity does not affect the estimated
parameter of the other independent variables.

The results of the regression analysis are listed in Table 5.19. All the
variables that are included in the resulting equation satisfy the specified criterion
for the variable inclusion. It can be seen from the Table that all the variables
- have a "T" significance value of less than 0.05. Hence, they are statistically
significant variables. The results of the regression analysis listed in Table 5.19
indicate that the standard error (S.E.) of the resulting model is 0.0797, the value
of the coefficient of determination (R2) is 0.93 and the adjusted R2 is 0.90. The
numbers listed under the column designated 'B" in Table 5.19 are the regression
constants for the indicated variables. Table 5.20 provides a list of the regression
constants and the values of the R2 and the standard error obtained from each step
of the stepwise method of the SPSS computer program. It can be seen that the
term percent fine and sand content (F+S) is the most significant variable and it
alone explains 48 percent of the variation of the pavements rate of rotting (the
dependent variable). This percentage increases, as it should be expected, with the
inclusion of more variables in the model. The final model can be expressed as

follows:

RRUT= -.3656 + .00068 ((FINE)’ +SAND) +.00012 (EXP(AV)) + .0289 (AV’) -
.0037 (AV’) + .00314 (AC’) - .6614 (LOG(ANG)) (5.5)

R2= 0.93, SE = .079, F = 27.94, F“, = .000
where

all the variables are the same as before.

Table 5.18 :

171
Collinearity diagnostics TOL and VIF.

 

 

Variable Tolerance VlF
F+S .666348 1.501
AV1 .042814 23.357
AC3 .490252 2.040
ANG1 .694469 1.440
AV2 .007450 134.234
AV3 .004235 236.112

 

 

 

 

 

Table 5.19 : Results of regression analysis.

 

Multiple

Equation

Variable

F+8
AV1
AC3
Al01
AV2
AV3

 

R 96603

R Square :93321
Adjusted R Square .89982
Standand Error .07965
Analysis of Variance

or an of Separea ilean Sure
Regression 6 1.06385 .17731
Residual 12 .07614 .00634
F I 27.94516 Signif E - .0000

' ' ' ‘ H U L T l P L E I E 0 R E S S l 0 I * * * '

timber 1 Dependent Variable.. R1101

--------- Variables in the Equation ------------------
0 SE I Data 1 Sin 1

6.840148E-04 1.20564E-04 .518512 5.673 .0001
1.1867275‘04 3.26269E-05 1.311425 3.637 .0034
.003135 7.58457E-04 .440393 4.133 .0014
-.661445 .212961 -.278054 -3.106 .0091
.028855 .008632 2.889327 3.343 .0059
-.003734 .001224 -3.496769 -3.050 .0101

(Constant) °.365607 .162551 -2.249 .0441

 

 

172

 

 

 

Table 5.20: Regression matrix for rate of rutting.
RRU‘I’ intercept Regression coefficient of independent variable

HS AV1 AC3 A1101 AVZ AV3 R.Sq. S.E.

-.0159 .0009 .1.60 .1:57

-.0952 .0009 .00005 .767 .1269

-.3905 .0006 .00005 .0020 .631 .1131.

-.1956 .0006 .00005 .0021. -.1.992 .864 .1053

-.3797 .0007 .00003 .0032 -.1.667 .0031 .661 .1020

-.3656 .0007 .00012 .0031 -.6615 .0269 -.0037 .933 .0797

 

 

 

 

 

 

 

 

 

 

 

173
Based on the statistics of the model (equation 5 .5), the following
observations were noted.

1. The null hypothesis of no linear relationship between the independent
variables and RRUT was rejected and it was concluded that at a
probability F“, of zero, 93 percent of the variation of the dependent
variable (RRUT) is explained by the independent variables included in the
equation.

2. The largest value of "T" significance is .04. This implies that all the
variables in the model are statistically significant.

In addition, the following statistics were calculated to study the values of
the residuals and the predicted RRUT values and are listed in Table 5.21. '

l. PRED = the unstandardized predicted values;
2. RESID = the unstandardized residual values;
3. ZPRED = the standardized predicted values;

4. ZRESID = the standardized residual values; and
5. D.W.S. = the Durbin Watson statistics.

The Durbin-Watson statistics of equation 5.5 listed in Table 5.21 signifies
a satisfactory non autocorrelation between the residuals. Further, the maximum,
minimum, mean and standard deviation of the unstandardized and standardized
predicted values and the residuals are also listed in the Table. Based on the
values of the residuals and the standardized residuals, the ten worst residual cases
are listed in Table 5.22. It should be noted that the ten worst residual cases are
based on the absolute difference and not on the percent error between the
predicted and measured RRUT values.

174

 

 

Table 5.21 : Residual statistics of equation 5 .5.
Min Max Nean Std Dev I
mm .0126 .9715 .3256 .2431 19
*assro -.1030 .1042 .0000 .0650 19
529950 -1.2672 2.6560 .0000 1.0000 19
11295510 -1.2935 1.3067 .0000 .6165 19

 

 

 

 

 

 

 

 

Durbin-Hatson Test 8 1.48605

 

Table 5.22 : Ten worst Residuals.

 

Case # 'Resid *ZRESID

10 .1042 1.30870
13 -.1030 °1.29352
11 .1017 1.27703
12 .0883 1.10899
19 -.0855 °1.07324
4 -.0825 -1.03583
2 .0820 1.02939
17 -.0819 -1.02829
5 -.0794 -.99707
3 .0383 .48024

 

 

 

 

 

 

175
5 .5 .2.2 Sensitivity Analysis and Engineering Interpretation

The statistical model presented by equation 5.5 was used to predict the
rate of rutting at the 19 core locations. Figure 5.13 depicts the values of the
predicted rate of rutting versus the observed one. The straight line in the Figure
represents the locus of those points where the observed and predicted rut depth
are equal. It can be seen that all of the predicted values are close to the observed
ones. Figure 5.14 depicts the percent errors between the predicted and the
observed rate of rutting. Examination of the Figure indicates that most predicted
rates of rutting are within 50 percent of the observed values. This indicates that
the statistical model is relatively accurate.

One additional point should be made herein is that, the rut depth of a
pavement structure is a function of several variables including the stiffnesses and
thicknesses of the various pavement layers, the properties of the materials in the
AC mix, the traffic volume, load, and environmental factors. In this study, only
the asphalt mix properties and the traffic load and volume data are used.
Consequently, one should not expect the statistical model presented in equation
5.5 to fully explain the variations in the rate of rutting.

The statistical model of equation 5.5 expresses the dependent variables as
the ratio of rut depth to the cumulative number of ESAL. Hence, the model can

be rewritten as follows:

RUT= ESAL (-.3656 + .00068 ((FINE)3 +SAND) +.00012 (EXP(AV))
+ .0289 (AV’) - .0037 (AV’) + .00314 (AC’) - .6614
(LOG(ANG))) - (5.6)

where

all the variables are the same as before.

176

 

1.00

 

0.90

 

0.80

 

0.70

 

0.60

 

0.50

 

0.40

Predicted Rate of Rutting

 

0.30

1* -

 

0.20

 

0.10

a

4

 

 

0.00
0.00

Figure 5.13 :

 

 

 

 

 

 

 

 

 

 

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Observed Rate of Rutting

Observed versus the predicted rate of rutting at the 19 core
locations.

 

177

 

 

 

 

 

n\\\\-m
.\\\\

¥\\ 1mm
.\ \
#\\\N “P

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ s .

 

 

 

 

 

 

  

 

 

/ / / /
..u ..e e ..4 m.

Percent differences between the observed and the predicted

rate of rutting for the 19 core locations.

Figure 5.14 :

178

The sensitivity of equation 5.6 to variations in each independent variable
and the engineering interpretations of the model are presented below.

A sensitivity analysis of equation 5 .6 was performed to determine the
effect of each variable in the equation on the predicted rut depth at the 19 core
locations. The sensitivity of the model to each variable was analyzed such that:
1. The values of four variables in the equation were held constant.

2. The value of a fifth, variable (the coarse aggregate angularity) was
changed from a low, to a medium, to a high value within the range of
values of that variable.

3. The value of the variable in question was varied from one end of its range
to the other.

Results of the sensitivity analysis are presented and discussed below.

Fine - Figure 5.15 shows the relationship between the predicted rut depth and the
percent fine content in the AC mix for constant values of the sand content,
the percent air voids, the AC content, ESAL and for three levels of coarse
aggregate angularity (1, 3, and 5). It can be seen that:

1. Increasing the percent fine content from 0 to 10 causes increases

in the rut depth by factors of about 2, 5 and 33 for the respective
aggregate angularity of l, 3, and 5.

2. There is no appreciable increase in rut depth as the percent fine
content increases from 0 to about 5 percent. Further increase in
the percent fine content causes substantial increase in pavement
rutting. The implieation of these two observations is that fine
contents in the order of 0 to 5 percent will have a minimum impact

on pavement rutting.

179

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.20 l
EMU-54. AV-5.7. AC8 5.5 . ESAL-.99
1.00
" Data Range —%
-r

0.80 /‘. /

E / I / l
C to -1 ..

5;, oarse aggrega angularity I - / /
50. 0.60 / / /
8 / u / . x
E a -___,__,___.. / /

0.40

/ 1’
E \ r /. ‘ x/
/’ /
0.20 0 __4’ ’_______ 0’44 air/
E ~N /
/
0.00? i #7 T/I
0 1 3 5 6 7 8 9 10
Fine Content (percent by weight)

Figure 5.15 :

Rut depth as a function of the percent fine content, for three
levels of coarse aggregate angularity.

180

Air Voids -Figure 5.16 depicts the sensitivity of the predicted rut depth to the
percent air voids for constant values of the fine, sand and asphalt contents,
and the l8-kip ESAL, and for three levels of coarse aggregate angularity
(l, 3, and 5). Examination of the Figure indicates that:

1. Increasing the percent air voids from 3 to 10 percent causes
increases in the rut depth by factors of about 4, 10 and 42 for the
respective aggregate angularity of l, 3, and 5 .

2. Increasing the percent air voids from 1 to 6 percent causes an
insignificant increase in the rut depth. Increasing the percent air
voids above the 6 percent level eauses a substantial increase in rut.
The implication of the above observation is that the effects of the
air void content on pavement rutting ean be minimized by
specifying a maximum of 3 to 6 percent air voids in the AC mix.
It should be noted that percent air void contents between 0 and 2
percent eause high shear deformation and consequently rutting and
bleeding.

Asphalt Content - Figure 5.17 represents the relationship between the predicted
rut depth and the asphalt content for constant values of the percent fine,
sand, and air voids contents, and ESAL and for three levels of coarse
aggregate angularity (l, 3, 5). It can be seen that increasing asphalt
content from 4 to 8 percent causes an increase in the rut depth by factors
of 3, 7 and 33 for the respective aggregate angularity of l, 3, and 5.
Recall that MDOT uses 4.5 percent AC content for most asphalt base
courses. The above observation supports the MDOT practice. It should
be noted that AC contents much lower than the 4.5 percent may cause
stripping and low adhesion of the AC.

181

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15° 1 l 1 I
FINE-6. SAND-54. AC- 5.5. ESAL-.99
2.00
‘ Data Flange ’
g 1.50
5.
«5
8'
D
E 1.00
I
Coarse aggregate angularity - 1 \/ /
/ I’l -— I -/1 ,.
0.50 / I/T 15" 4’
a/ . . l—\ 7
1/ ¢".——— “I {P
4» / ’ <
ir/ x / T J + ha
0.00 ‘ ‘f/ , 1 r
1 2 3 4 5 6 7 8 9 10
Percent Air Voids
Figure 5.16 : Rut depth as a function of the percent air voids for three levels

of coarse aggregate angularity.

182

 

1.80 [

 

FINE - 8 . SAND-I 54. AVIS. ESAL- .99 /'

WWW... \/ ..
1.20 4— Data Range _> / /‘
// /
_ /f/

:T/ //i/
0.00:-="'//gL/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rut Depth (inches)

 

 

 

 

 

 

 

 

 

- 6 7 8
AC Content (percent by weight)
Figure 5.17 : Rut depth as a function of percent AC content, for three levels

of aggregate angularity.

183

Aggregate Angularity - Figure 5.18 depicts the sensitivity of the predicted rut

depth to the aggregate angularity for constant values of the percent sand , air

voids and AC contents, and ESAL and for three levels of the percent fine content
(4, 7, and 9 ). Examination of the Figure indicates that:

l.
2.

The relationship is almost linear.

Increasing aggregate angularity from 1 (rounded aggregate such as
river gravel) to 5 (aggregate crushed on all sides) causes a
decrease in the rut depth by factors of about 8, 3 and 2 for the
respective fine contents of 4, 7, and 9 percent. The implieation of
these observations is that the use of angular aggregates in the AC
mix of a pavement structure decreases its rut potential. However,
the benefit of using such aggregates diminishes as the percent fine
and the percent sand contents increase. These findings were
expected because as the percent fine and/or the percent sand
contents increase, the ball beefing effects increase causing a
decreaseinthefacetofacecontactbetweentheaggregate
particles. Further increases in the percent fine and sand contents
cause, the coarse aggregates to float in the fine and sand matrix.
One important point should be noted here is that the benefits of
using angular aggregates in terms of decreased rut depth potential
should be evaluated against the expected service life and the costs
of the pavement structure in question. For example, the use of
angular aggregates (higher cost) in a pavement structure cannot be
justified if that pavement is designed for a shorter service life
period than the period during which the rut depth of the pavement
will exceed the maximum acceptable rut. That is, if the pavement
design process assumes that the pavement will be rehabilitated (for

184

 

1'00}: i

\ AV-5.7. ac- 5.5. ESAL- .90
0 90

. \ J‘ Data Range +
0.80
\/ Fine .Sand I 9. 54

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.70,"\ \T\
£050., \‘ ‘*\
5 0.50 ‘ ‘

 

0.30 \
‘—_‘ \ ..
0.20 \ T<

 

 

 

 

 

 

 

 

 

 

0.10 \\
0.00 l l l l
1 2 3 4
Coarse Aggregate Angularity
Figure 5.18 : Rut depth as a function of coarse aggregate angularity, for

three levels of the percent fine content.

185

roughness, temperature cracking, or other expected types of
distress) within a ten-year period after construction and that the
expected rut depth of that pavement during the same period is less
than the maximum acceptable standard, then it would not be wise
to use expensive crushed aggregates in the AC mix to extend the
pavement service life relative to rutting to 20-years. Stated
differently, the benefits of using crushed aggregates in the AC mix
should be assessed during a systematic and comprehensive design
processes whereby the expected pavement service lives relative to
each of the expected distress types are evaluated.

ESAL - Figure 5.19 depicts the relationship between the rut depth and the
cumulative 18-kip ESAL for the constant values of fine, sand, air voids,
and asphalt contents shown in the Figure, and for three levels of coarse
aggregate angularity of l, 3, and 5. It ean be seen that the rut depth
increases linearly with increasing number of l8-kip ESAL (e.g.,
increasing the number of ESAL by a factor of 10 causes an increase in the
rut depth by the same factor). This observation was not expected and it
cannot be supported by either field or laboratory data. In general, the rate
of pavement rutting decreases as the number of l8-kip ESAL increases.
One of the reasons for this discrepancy between the model and the
observed data could be the collinearity of the variable ESAL with. the
other independent variables such as the percent aggregate, sand, fine, and
asphalt contents that was discussed earlier. Another reason is the MDOT
practice regarding the collection of traffic data and the computation of
ESAL (the average daily traffic (ADT) data is multiplied by an estimated
percent commercial and by an estimated average ESAL per vehicle). This
practice ean be enhanced by collecting weigh in motion (WIM) data which

186

 

2.50

 

 

 

 

 

FINE-6. SAND- 54. AV-SJ. AC-5.5 .

 

 

 

 

 

 

 

 

 

2.00. 4 Data Range /,

Coarse aggregate angularity -1 /
N:-

 

 

 

 

 

 

 

 

 

\

 

Rut Depth (inches)

’6

/

 

 

 

 

 

 

 

 

 

 

0'50 / i r l ; /
a .. /
‘i/ i
...—z?!
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
18-Kip ESAL (millions)
Figure 5.19 : Rut depth as a function of 18-kip ESAL, for three levels of

aggregate angularity.

187
can be used to directly calculate, not assume, the ESAL per vehicle and
the total number of 18-kip ESAL.

5.5.2.3 Rut Prediction Based on Assigned Material Properties

Recall that the statistical rut depth model presented by equation 5 .6 was

developed by using the material data for the 19 extracted core loeations. In this

study, the pavement rut depths at 88 other cored locations were also measured.

However, no material data are available at these locations. In order to apply the

model to the other locations, the following assumptions were made:

1.

The material properties determined from each extracted AC course
represent the properties and the tirickrress of similar AC course
encountered at other cored loeations. A

The global properties of each core were determined as the weighted

average properties of the various AC courses of that core.

In regard to the above assumptions, several points should be made. These are:

1.

Because of economical and other constraints, it is not practical nor is
possible to conduct extraction tests to obtain the properties for each core
location. The reason is that several cores must be combined in order to
obtain enough materials to conduct extraction tests. Hence, only the
average material properties obtained from several cores can be
determined.

The cross-sectional data obtained from MDOT regarding the layer
thicknesses represent the as-designed thicknesses not the as—constructed
ones. Variations between the MDOT cross-sectional data and the layer
thicknesses obtained from the cores were observed. Figure 5.20
represents the percent difference between the AC layer thicknesses

 

188

 

 

 

 

m m _NVM\.\M\V.\.\V\.\.\.\.\ m
w u m m

c m u _

9 W o _

an a. C “.11
.m mam sm
6. w - u & B «w

 

 

41-60 61-80
Percent Error

 

1_M\\\\\\\\\
_\\§w\\\\x§§a
_
:1... --1 21-11.--. ....1.11! 11.V\\\\\\\\\\\\\\\\\x
A ..\. RX\\\\\R\\\\\\ ..\\\\\N\.\\\\\\\\\\\\\\\\\\\\\.\X\\\\\.\\M
IIIIiIII=III!
1. 1-- 1.111-511 ! - -,---.--!-...-1--1 1-111-11..-.--1...
_§§§§§§§

. . .... wt... v.V.J\\..\\.\\\,m\\\x.\\\\\\s\\\\\&..\\..\.RGN.H\\\\\\V\\\.\\\\\\\N\R\\N\\«\N\\...\\

       

 

 

 

_.

21-40

 

0-20

 

 

 

 

 

 

 

- m i e. 1m m. e. m
m w m m m 0
33ch30 .0 33632

Percent difference between the proposedand as-constructed AC
courses thicknesses.

Figure 5.20

189

obtained from the MDOT cross-section data file and the AC thickness

determined from the cores of the 107 core locations. It can be seen that

variations by as much as 100 percent was observed for the base course
whereas, variation upto 40 to 60 percent was common for wearing and
leveling courses.

Nevertheless, material properties for the other 88 core locations were
assigned based on the above two assumptions. Table 5.23 summarizes the core
designation number, the coarse aggregate angularity, the percent air voids, the
percent AC, fine, sand, and aggregate contents, the pavement service life, the
estimated cumulative l8-kip ESAL, the measured rut depths, the rut depths
predicted by using equation 5.6, and the percent difference between the predicted
and the measured values. Figure 5.21 shows the predicted and the measured rut
depths of 107 pavement locations (open squares in the Figure indicate the 19 core
locations for which equation 5.6 was developed). Once again, the locus of the
straight line in the Figure represents those points where the predicted rut depth
values are equal to the measured ones.

The variations between the predicted and measured rut depths shown in
Figure 5.22 are expected. As stated earlier, the reasons for these variations are:
1. Because of construction practices and variations, the as-constructed layer

thicknesses and material properties vary from one point to another. For

example, Figure 5.20 depicts the percent difference between the as-
designed layer thicknesses (obtained from the MDOT files) and the actual
thickness determined for the 107 core locations.

2. Figure 5 .23 shows the variations in the average peak pavement deflection
along pavement control section number 43F. This section was designed
and it was supposedly constructed by using the same material properties
and layer thicknesses. However, the peak pavement deflection which

190

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00.00 00.0 00.0 00.0 0 0 0 0 0.0 0.0 00.0 $00.90
00.0 0.0 0.0 05.0 9 .0 v 00 5.0 0.5 .0. . .u><
0.0. 0.0 9.0 05.0 . . 00 v 00 5.0 0.5 50.. 02 .0000 .00 00
0.0. 0 . .0 9.0 05.0 . . 00 v 00 5.0 0.5 00. . 02 .0005 .00 00
0 . .0 00.0 05.0 . . .0 v 00 5.0 0.5 00. . oz . .000 .00 .0
0.00. 0.0 00.0 05.0 9 00 v 00 5.0 0.5 00. . oz . .000 .00 00
0.9. ...0 9.0 05.0 9 .0 v 00 5.0 0.5 00.. oz ..5. . .00 0.
0.0.. ...0 9.0 05.0 9 .0 v 00 5.0 0.5 00. . 02 9500.00 0.
5.0.. ...0 9.0 05.0 9 .0 v 00 5... 0.5 00. . 00> .055. .00 5.
0.? 0.0 9.0 05.0 .. 00 v 00 5.0 0.5 00. . o2 . .505 .00 0.
50.0. 00.0 00.0 00.0 0 0 0 0 0.0 ..0 .0.0 $00.90
00.0. .. 00.0. 0.0 .0. . 00 00 0 00 0.0 0.0 00.0 .03.
0.09. 00.0. 0.0 .0.. 00 00 v 00 0.0 0.0 00.0 oz 9000.0. 0.
0.0... 00.0. 0.0 .0.. 00 00 0 00 0.0 0.0 00.0 02 90.0.0. 9
0.0. .. 00.0. 9.0 .0. . 00 00 0 00 0.0 0.0 50.0 02 00000 .9 9
5.9.- 00.0. 00.0 .0. . 00 00 v 0.. 0.0 0.0 00.0 02 9000 .9 0.
0.00. 00.0 9.0 .0. 00 00 0 0w 0.0 0.0 00.0 00> .0.590. 9
0.00.. 00.0. .0.0 .0. . 00 00 0 0.. 0.0 0.0 00.0 02 9000.0. 0.
0.09. 00.0. 0 . .0 .0. . 00 00 0 00 0.0 0.0 00.0 oz . .0090. 0
0..0.. 3.0. 0.0 .0.. 00 00 0 0v 0.0 0.0 00.0 02 0000.0. 0
00.0. . 0 . .0 0 . .0 00.0 0 . 0 . 0.0 0.0 00.0 $00.90
00. .5 00.0 00.0 00. . 5 00 v .0 1.0 0.0 00.0 Jada
0.00. 0.0 00.0 00. . 5 00 v 00 0.0 0.0 00.0 02 90.95 5
0.0. 50.0 .00 00. . 5 v0 . v 00 0.0 0.0 00.0 00> 90.0.5 0
0. .0 00.0 00.0 00. . 5 00 v .0 ...v 0.0 00.0 02 00000 .5 0
0.00 50.0 0. .0 00.. 5 00 v .0 0.0 0.0 00.0 02 .0550 .5 v
0.0? 00.0 00.0 00. . 5 00 v .0 0.0 0.0 50.0 02 00050 .5 0
0.500 00.0 0 . .0 00. . 5 00 v .0 0.0 0.0 0.0 oz . .000 .5 0
0.000 00.0 0.0 00. . 5 00 v 00 0.0 0.0 .00 oz . .0095 .
$220 28.0 flea 2.5 «an... .3552
85:05 50 .200 a... a? 2E 0.30 o< 26> 2.3392 .260 5:20.30 .6
EEIELEE 20532.6... .2 a. 32.00pr ..

003.08. 0.80 50. 0:. ..8 000.300.:— 30032 n 00.0 030,—.

191

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.6 .66 86 86 6 . o . 66 ..6 86 68.6.6
666. 86 «66 86 6 66 6 56 6.6 66 56.« 1.010
.... 566 86 666 6 8 6 8 6.6 6.. 56.« 66> ..6«.«.. 6..
566 86 666 6 66 6 8 6.6 ... 56.6 oz 888.. 6..
86 86 666 6 66 6 8 6.6 «6 66.« 62 8658.. 8
566 86 86 6 66 6 8 6.6 6.. 56.« oz :886 66
66. 566 86 666 6 8 6 8 6.6 6.. 56.« 66> :886 «..
8.8 86 86 86 6 6 o 6 66 .6 .66 58.6.6
66..«. 86 6.6 «.6 6 «6 5 .6 6.6 «.6 ««.6 .63.
6.56. 86 6.6 «.6 6 «6 5 .6 6.6 6.6 8.6 oz :88: ...
«.. 86 86 «.6 6 «6 5 .6 6.6 «.6 ««.6 oz «8.8: 66
6.8. 86 6.6 «.6 6 «6 5 .6 6.6 ..6 8.6 oz «858: 8
66 86 86 «.6 6 «6 5 .6 6.6 «.6 8.6 66> :88: 66
6.. 86 86 «.6 6 «6 5 .6 6.6 «.6 ««.6 oz .«88: 56
66 86 86 «.6 6 «6 5 .6 6.6 «.6 8.6 ..> .«658: 8
8.... «66 86 86 6 . 6 . 66 .6 .86 5868'
8.8 86 ««6 8.. .. 8 6 8 6.6 6.6 66.6 .64 ,
6.6 86 86 8.. : 8 6 8 «.6 6.6 56.6 62 8.8.6. 8
6.8 86 86 8.. : 8 6 8 6.6 5.6 «...6 oz ..«.6.6. ..6
6.56 86 86 8.. .. 66 6 8 6.6 6.6 8.6 62 8.8.6. 8
«.65 86 86 8.. .. 8 6 8 6.6 6.6 66.6 62 .8568. «6
6.56 ..66 86 8.. .. 6.. 6 8 6.6 6.6 66.6 oz .888. .6
.66 86 86 8.. .. 66 6 8 6.6 6.6 8.6 oz .888. 8
6.8 .66 86 8.. : «.. 6 66 ...6 «.6 66.6 62 ..8:6. 8
..55 86 86 8.. : 6.. 6 8 6.6 6.6 66.6 66> ....6.6. 8
6.65 86 86 8.. .. 8 6 8 6.6 6.6 66.6 66> :68.6. 5«
6.«6 566 86 8.. : 8 6 8 6.6 6.6 66.6 62 886.6. 8
6.66 86 86 8.. : 8 6 8 6.6 6.6 56.6 62 ..6.6.6. 8
6.8 86 86 8.. : 8 6 8 6.6 5.6 66.6 62 88:6. 8
4.66.66. £26 32.. as. .860 .3652
622.65 5.. .28 6.... 8... .6... 668 o... 26> 5.66.665. .260 666666.68 .6
.0020 E SE .80” 0050M u 0...: E 00< 00.02...” 0B 0:“

.000—.5880 602.08. 83 50. 0... .8. 8056080 3.8.02 . 00.0 030.0

192

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

05.50 00.0 00.0 00.0 0 . 0 . ..0 ..0 .0.0 $00.90 I .
00.00 .00 9.0 50. . 9 0.. 0 .0 0.0 0.5 05.0 493.
0.00 00.0 9.0 50.. 9 0e 0 .0 0.0 0.5 05... oz .005900 05
..00. 00.0 9.0 50.. 9 00 0 .0 0.0 0.5 05.0 oz 990.00 00
0.00 00.0 00.0 50. . 9 00 0 .0 0.0 0.5 05... oz .0 .00 .00 00
0.50 00.0 00.0 50. . 9 00 0 .0 0.0 0.5 05.0 oz . .000.00 50
0.50 00.0 0 ..0 50. . 9 00 0 00 0.0 0.0 05.0 oz . .00.. .00 00
0.00. 00.0 9.0 50. . 9 00 0 .0 0.0 0.5 05.0 oz 900900 00
0.00 00.0 9.0 50. . 9 00 0 00 0.0 0.5 05.0 oz . .000.00 00
0.00. 00.0 9.0 50. . 9 00 0 .0 0.0 0.5 05.0 oz .0000 .00 00
0.00. 00.0 9.0 50. . 9 00 0 .0 0.0 0.0 05.0 oz . .000.00 00
0.09 50.0 0.0 50. . 9 00 0 00 0.0 5.5 05.0 oz 0009 .00 .0
0.50 00.0 0 . .0 50. . 9 00 0 .0 0.0 0.5 05.0 00> .000. .00 00
0.0. 00.0 00.0 50. . 9 00 0 .0 0.0 0.5 05.0 oz .000900 00
9.05. .0.0 9.0 00.0 0 0 0 0 0.0 ..0 00.0 $00.20
.000. 00.0 00.0 05.0 . 00 0 00 0.0 0.0 00.0 dd
5.00. 00.0 0 ..0 05.0 . ..v 0 00 0.0 0.0 00.0 oz . ... .0 .00 00
0.000 00.0 00.0 05.0 . 0v 0 00 0.0 0.0 00.0 oz 0.0900 50
5.000 00.0 00.0 05.0 . 0v 0 00 0.0 0.0 00.0 02 .0005 .00 00
0.0 .. .0.0 00.0 05.0 . vv 0 00 0.0 0.0 00.0 oz . .90 .00 00
....0. 00.0 00.0 05.0 . 3 .0 00 ...0 0.0 00.0 oz 000090.. 00
0.00 .00 00.0 05.0 . 0v 0 00 0.0 0.0 00.0 oz . .0 .0 .00 00
0.50 00.0 9.0 05.0 . vv 0 0.. 0.0 5.0 00.0 oz . .5. . .0.. 00
0.0.. 00.0 00.0 05.0 . 0.. 0 00 0.0 0.0 05.0 00> . .000.00 .0
0.000 00.0 00.0 05.0 . 0v 0 00 0.0 0.0 00.0 oz 0. .05.00 00
0.0.. .0.0 00.0 05.0 . ..v 0 00 0.0 0.0 00.0 00> . .9900 00
0.0.. .0.0 00.0 05.0 . vv 0 00 0.0 0.0 00.0 00> . .9900 00
0.00. 00.0 00.0 05.0 . 0v 0 00 0.0 0.0 00.0 oz 3.00900 50
66.66. £20 32... ....E. .6665. .8562
622...... .60 .28. ...... 80 E... 668 o... 26> 5.66.665. .260 66668.80 .6
.0020n mac—men Eu .8...” 0 Z 390‘; .5 .000.00 ._< 00< 00.09%. 0.6 0:

.88....8. 68:68. 88 56. e... .6. 8.086.... .6036: . 8.6 6.66.5

 

193

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

05.00 .0.0 0.0 00.0 0 . 0 . 0.0 0.0 00.0 oz $00.20
05.0. 00.0 .00 .00 0 00 0 00 0.0 0.0 00.0 oz i0?
0.00. 00.0 00.0 .00 0 00 0 00 0.0 0.0 00.0 oz .000.00 00
5.0 00.0 00.0 .00 0 .0 0 00 0.0 5.0 00.0 oz 0.5.000 00
0.00 00.0 0.0 .00 0 .0 0 00 0.0 0.0 00.0 oz . .3000 00
5.0... 00.0 00.0 .00 0 00 0 00 0.0 0.0 00.0 oz .000000 50
..0. 00.0 00.0 .00 0 .0 0 00 0.0 0.0 00.0 00> .000000 00
.000 00.0 00.0 00.0 0 . 0 . 0.0 ..0 00.0 5000.0
00.00 0.0 0.0 ..5.. 0. 00 0 ... 0.0 0.0 00.0 .03.
0.0.. 00.0 00.0 ..5.. 0. 00 0 00 0.0 0.0 00.0 oz . .0300 00
0. .0. 0.0 00.0 05.. 0. 00 0 00 0.0 ..0 50.0 oz ..0. .00 00
0.00 0.0 00.0 05.. 0. 00 0 .0 0.0 0.0 00.0 oz ..0.000 00
..00. 0.0 0.0 ..5.. 0. 00 0 00 0.0 0.0 00.0 00> ..0.000 00
..0.. ...0 0.0 ..5.. 0. 00 0 00 0.0 0.0 00.0 00> ..0.000 .0
0.00. 0.0 00.0 05.. 0. .0 0 00 5.0 0.0 00.0 oz 000.000 00
5.00. 0.0 00.0 05.. 0. .0 0 00 5.0 0.0 00.0 oz ..00000 05
0.00. 0.0 00.0 05.. 0. 00 0 .0 0.0 0.0 00.0 oz 0000.00 05
00.00 3.0 ....0 00.0 0 . . 0 0.0 0.. 00.0 $00.20
50.0. 0.0 00.0 00.0 5 .0 0 .0 0.0 0.0 50.0 J90
5.0. 0.0 0.0 00.0 5 .0 0 .0 0.0 0.0 00.0 oz .00.0.0. 55
5.0... 0.0 00.0 00.0 5 00 . 5 .0 0.5 0.0 00.0 oz ..5. . .0. 05
0.00. 0.0 00.0 00.0 5 00 5 .0 ..5 0.0 00.0 oz 0005. .0. 05
0.00. 00.0 00.0 00.0 5 00 0 .0 0.5 0.0 00.0 oz .050. .0. ..5
0.00. 0.0 00.0 00.0 5 00 0 .0 5.0 0.5 .5.0 oz 3000.0. 05
0.50. ...0 0 ..0 00.0 5 00 0 .0 0.0 5.5 05.0 oz .0 .00 .0. 05
0.0. 0.0 0.0 00.0 5 00 0 00 0.0 0.0 05.0 00> ..0.0.0. .5
000.00. 20.... £20 2.5 “0.0000 30:52
020.050 s: #00 0.: 00< 00m 0000 9. 06> 0.00.0050 00.8 5020.000 6
.000.0& ”0.0—m00n SK .an 00“>00m 29M; 0 n .coofi .2 00< 00.000xm. 0.0 0:

.6005.080 000008. 88 50. 0.0 ..0. 8.0.2.80 300.02 0 00.0 030...

 

194

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00.050 00.. 5.0 00.0 0 0 o 0 ..0 0.. 00.0 500.000
00.500 00.0 00.0 0.0 0. 00 5 .0 0.0 0.0. 5..0 .02
0.000 00.0 0.0 0.0 0. 00 5 .0 0.0 0.0. 5.0 oz ..500.0. 50.
0.005 00.0 0.0 0.0 0. 00 5 .0 ..0 5.0. 0.0 oz .0050.0. 00.
0.5. 50.0 00.0 0.0 0. 00 5 .0 0.0 0.0. 0.0 oz 00000.0. 00.
00.0 8.0 0.0 0. 00 5 00 ..0 5.0. 0.0 oz 00000.0. 00.
5.00. 00.0 00.0 0.0 0. .0 5 .0 0.0 5.0 0.0 oz 0002.0. 00.
... 0.0 0.0 0.0 0. .0 5 00 0.0 0.0 .0..0 00> 0.5.0.0. 00.
0.00. 0.0 00.0 0.0 0. .0 5 00 0.0 0.0 0.0 oz 00.00.! .0.
0.000 00.. 0.0 0.0 0. 00 5 .0 ..0 0... 0.0 oz 0.0.0.0. 00.
0.050 00.0 00.0 0.0 0. 00 5 00 0.0 0.0. 00.0 oz 0.0.0.0. 00
.5.50 0.0 0.0 00.0 o 0 0 0 ..0 0.0 5.0 5000.0
.000 00.0 00.0 00.0 0 00 0 00 0.0 0.0 00.0 L02
0.00 00.0 .00 00.0 0 50 0 50 0.0 0.0 00.0 oz . . .0.0. 00
0.0 00.0 00.0 00.0 0 50 0 50 0.0 0.0 05.0 oz ..5.00. 50
0.5.. .00 0.0 00.0 0 00 0 50 0.0 0.0 00.0 oz ..0000. 00
..00. .00 00.0 00.0 0 00 0 00 ..0 0.0 0.0 oz .080. 00
0.. .00 .00 00.0 0 50 0 50 0.0 0.0 00.0 oz ..0050. 00
0.. .00 .00 00.0 0 00 0 00 0.0 0.0 5..0 oz ..0000. 00
0.00 05.0 00.0 00.0 0 00 5 00 ..0 ..0 00.0 00> . .0 .00. 00
..00. 00.0 00.0 00.0 0 00 0 00 ..0 0.0 00.0 oz ..0.00. .0
00200. 2000 £80 .....5 .2000 00:52
0000.050 50 .200 0.... 000 00.0 0:00 00 03> 0.00.005. 00.8 8020.000 6
, Exxon Elk-PE 0 :0 E .02.E.0020P 0< 00< 00.08.“le 0..

 

.6005.080 000008. 88 50. 0.0 ..0. 00.0.0020 300.02 0 00.0 0.00...

 

1.20
+
1.00
{g 0.80 0 0 U
‘5
0‘,
5
8 t
0 0.60
‘5
n:
.31
.9 4D
3 ;
l 0.40 3 ‘r v
* + + 1 u 0
+ + n g *
+ * + ++‘ + E 0
"‘ m ++
0.20 0
...
4' 0
0» ++ + *
:= * 1»
II +
O
0.00 = i t
0.00 0.10 0.20 ' 0.30 0.40 0.50 0.60
Observed Rut Depth (Inches)
Figure 5 .21 : Observed versus the predicted rut depths at 107 core locations.

195

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.70

196

 

 

 

 

  

 

\ \
x
\x \

 

. 4 . . a
“0““ ‘FFIP'I .{D dwvdbo.

\
\\ ,_ .\

..§H\0\H\\I\L\\\0\w\\\\v\w z 5» 7.5;.[1h‘k5t

0
[I'm

stilt 5:13.? 09:15:? .tof'thl'

 

 

I; .0

v... iii 1|}? Ellil'pvn .A‘lfypvitgv‘

 

35‘

30-

 

/—
0

00000 .o 03:52 320050

       

 

m

Percent differences between the observed and the predicted rut

depths for the 107 core locations.

Figure 5.22 :

197

 

7.4

 

 

306661435: I

 

 

 

 

 

 

 

Average

 

6.6i

 

6.4

 

Average Peak Deflection (mils)

 

CD
I

 

5.8

 

 

 

 

 

 

 

 

 

 

4 5 6 7 8
Site Number

Figure 5.23 : Average peak deflection variation along section 43F.

198
represents the pavement response to a 9000 pounds load vary from one
location to another. Variations in the pavement deflection is the direct
consequence of variations in the material properties and layer thicknesses
between one point and another.

3. Measured rut depth is also a function of the other layers in the pavement
structure besides the AC course. Since, most of the extreme eases are of
the over prediction, the contribution of rut due to other pavement layers
such as base, subbase and roadbed soil can easily be ruled out. Thus, it
can be concluded that the assumption of similar material properties within
a section can be questionable if proper quality controls are not exercised.

5 .5 .3 Analysis of Rut as a Function of the Pavement Deflection

5.5.3.1 Introduction

Nondestructive deflection tests (NDT) have evolved over time from the
Benkelman beam (introduced by A.C. Benkelman in connection with the Western
Association of State Highway Officials (WASHO)) to the falling weight
deflectometer (FWD) introduced during the 1980.3. The NDT tests are currently
very popular and are used by most State Highway Agencies. The tests are easy
to perform and they do not require the closing of the highway pavement to traffic
for a prolonged period of time. Using the FWD, the NDT test consists of raising
a calibrated weight to a certain height, dropping the weight on a steel plate, and
measuring the resulting dynamic load and the pavement response (deflections).
It should be noted that pavement deflection represents the pavement system
(surface, base, and subbase layers and the roadbed soil) response to load. It is a
direct consequence of the mechanics by which the energy induced into the
pavement structure attenuate with distance and depth from the point of load

199

application. Deflection data is generally affected by the following factors:

1. The structural integrity and capacity of the pavement, which include the
stiffnesses and thicknesses of all pavement layers, the stiffness of the
roadbed soil, and the depth to a stiff layer such as the bedrock.

2. The environmental conditions including moisture and temperature.

3. The pavement conditions such as the type, extent, and severity of the
distress (e.g., rut, fatigue cracks, and other types of cracks).

4. The applied load magnitude, frequency, and duration.

5 . The test location relative to the pavement edge, joint, or crack.

6. The service life of the pavement and the traffic history.

Interpretation of the NDT data has always been a complex and difficult
task. The data has traditionally been used as a tool to evaluate the structural
capacity and integrity of the pavements. One of the earliest uses of pavement
deflection (using the Benkelman beam) was that made in California in 1938 and
reported by Haveem (82). He stated that flexible pavements would have
satisfactory performance if the peak deflection under a 15000-pound single axle
load is less than 0.0200. Similarly, results of the WASHO Road Test
(conducted in Huba Valley on flexible pavements) indieated that a satisfactory
pavement performance can be achieved if the peak pavement deflection is less
than 0.030-inch for pavement located in cold regions and less than 0.040-inch for
those located in warm regions (83, 84). Recently, NDTs are conducted and the
measured deflection data are being used for the purposes of pavement evaluation
and management and for determining the required thicknesses of the asphalt
overlays. In this regard, various State Highway Agencies (SHAs) and other
organizations such as Utah DOT (85), California DOT (86), Oklahoma DOT
(87), Louisiana DOT (88), Texas DOT (89), and the Asphalt Institute (90) have
developed various procedures and protocols for the interpretation and use of the

200

NDT data.

Analysis of the measured pavement deflection data provides a quantitative
basis for evaluation of the pavement structural condition at any time during its
service life. Other important information relative to pavement rehabilitation and
maintenance requirements can also be inferred from the deflection profile
(deflection basin). Because the NDTs are nondestructive in nature and because
they are easily and quickly performed, the tests cause a minimum hindrance to
normal traffic flow and they are less hazardous and more economical to
undertake. In addition, the measured pavement deflections represent the direct
pavement response to the applied load.

To this end, a complementary component of this study involves the
development of a computer program (called MICHBACK) for the backcalculation
of the pavement layer moduli using NDT data (91). The pavement sections
selected for the NDT part of the study are the same as those selected in this part.
As noted in Chapter 4, 49 flexible and 15 composite pavement sections were
selected and each section was divided into several lOO-feet long test sites. At each
test site, at least five NDT tests (spaced at 20-feet intervals) were performed
using the MDOT FWD KUAB model. Additional NDT tests were also conducted
at each core location within the pavement sites. Several observations regarding
the NDT tests should be noted. These are:

1. The seven deflection sensors of the MDOT FWD were spaced as follows
0, 8, 12, 18, 24, 36, and 60 inch from the center of the load plate of the
FWD.

2. Each test consisted of three drops. For each drop, the weight and the
height of the drop was set such that the load delivered to the pavement is
about 9000-pounds. The actual measured load, however, varied slightly
from the target value of 9000-pounds.

201

3. All measured deflection data were normalized to the 9000-pound level and
for each deflection sensor, the average of the deflections obtained from the
three drops was calculated.

4. During each test, both the pavement and the air temperatures were
recorded directly on the deflection file.

5 . Each pavement section was tested once during each of the following
seasons fall of 1991, spring of 1992, summer of 1992, and spring of

1993.

In this study, the pavement deflection data measured during the summer
of 1991 , the pavement cross-section data, and the traffic volume in terms of the
number of l8-kip ESAL for the 13 cored sections (104 cored loeations) were used
to develop a second statistical rut-depth prediction model. This model is

presented and discussed in the next subsection.
5.5.3.2 Statistical Analysis

As noted above, in this study, a total of 49 flexible and 15 composite
pavement sections were selected and each section was divided into several 100-
feet long test sites. During the summer of 1991, at least five NDT tests (each test
consisted of three drops) were conducted along each pavement site (the test
locations were spaced at 20-feet intervals) and one test at each core location
within the site. For each test location and for each drop, the measured deflection
data were first normalized to the 9000-pound level and then the average deflection
of the three drops was calculated.

Table 5.24 provides the minimum, maximum, average, and standard
deviation of the pavement service life, cumulative 18-kips ESAL, layer

thicknesses, and the deflection of each of the seven sensors for the 563 NDT

202

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00.0 00.. .0... 00.. 00.. 00..0 00.0 00.0 .0.. 00.0 00.0 00.0 $00.30
00.. 00.0 00.0 00.0 05.0 00.0 00.0 00.0.05; 00.0. 00.0 00.0 .000
05.0 2.0 ...: 00.0. 00.0. ...0. 5.00 00.00 00.0 00.00 00.0. 8.0. .00..
05.0 00.. 05.. 2.0 00.0 00.0 05.0 00.. 2.0 8.0 00.0 00.0 .0...
A... 3.8. one.
50 00 00 00 00 00 .0 02$ 3.... 90 0000 00
0.... 0000
3.... 8:00:00 .0200 ...00 .50 28:00:20....

 

 

 

 

 

.500 2.. .0 83.0.0 02.0.88: . 00.0 0.00...

 

 

203

locations. The detailed data can be found in appendix "B" . Two very important

points should be noted herein are:

l.

Pavement cores were obtained from only 104 of the 563 NDT locations.

Hence, for these 104 locations, the AC thicknesses presented in appendix '3'
represent the actual thicknesses measured from the cores. The AC thicknesses

for the remaining 459 test locations are those obtained from the MDOT records

(the as designed thicknesses). Hence, for each non-cored test location, the actual

AC thickness varies from that listed in appendix "B".

2.

For each NDT location, whether the pavement was cored or not, the
thicknesses of the base and subbase layers were not easily identifiable.
The main reason is that the typical base and subbase materials used in the
State of Michigan are very similar. Consequently, it was almost
impossible to separate the two materials during coring. Therefore, the
thicknesses of the base and subbase layers listed in appendix "B" were
obtained from the MDOT file. For the cored section, the total thicknesses
of the base and subbase layers found in the MDOT files were verified
during pavement coring.

Nevertheless, prior to the commencement of the statistical analysis, several

engineering issues that are signifieant to the statistieol analysis should be noted.

These are:

1.

In general, the magnitude of the pavement deflection varies from time to
time and it depends on the existing pavement conditions, environmental
factors, and traffic load, volume, and speed. If one is to assume that the
traffic load and speed and the environmental conditions are constant with
time, then the magnitude of the present deflection of a pavement structure

is a function of the cumulative traffic volume since construction. Figure

5 .24 shows a generalized peak pavement deflection as a function of time.It

 

204

 

C

.9.

‘6

2

8 Initial Functicmall Failure
Phase PM“ Phase

 

 

--—--—~
)--—-——--—'

 

Time —>

Figure 5.24 : Pavement deflection as a function of time.

 

205
can be seen that the magnitude of the pavement deflection immediately
after construction is high, it decreases with increasing traffic volume due
to pavement consolidation and seating under traffic loading, and it
increases as the pavement deteriorates and loses its structural eapacity and
integrity with time. Pavement rutting is the direct consequences of
pavement consolidation and/or seating.

2. For any pavement structure, its rut depth measured at time 't" is a
function of the as-constructed pavement conditions (at time t) in terms of
structural capacity and integrity that corresponds to time "to", the number
of lS-ln'p ESAL trafficked that pavement during the time period 't - to”,
and the environmental conditions during that time period. The as-
constructed pavement structural capacity, on the other hand, can be
represented by the as-constructed deflection basin. That is, if the
deflection basin of a pavement structure is measured directly after
construction and prior to opening the pavement to traffic, then that
deflection basin expresses the structural capacity and integrity of that
pavement including the quality of construction and compaction. This
scenario implies that the pavement rut depth at time "t' is a function of
the as—constructed deflection basin. Unfortunately, the as-constructed
deflection basins of the pavement sections of this study were not measured
and they are not available.

3. The deflection basin of a pavement structure measured at time "t" is a
function of the existing rut depth of the pavement, the load magnitude, the
environmental factors such as moisture and temperature, and the other
pavement physical conditions such as the state of cracking and shoving.

The three issues presented above imply that the as-constructed pavement

deflection should be used to model the pavement rutting potential. Because of the

206
lack of such data at the present time, and in order to introduce an empirical
model relating the deflection basins and rut, the statistieal analyses below are
presented as an attempt to explain the variation in the measured rut depths as a
function of the present pavement deflections and the pavement cross-sections.

To this end, the scenario presented below, although it applies to the other
statistical analyses presented in this thesis, is very crucial to the development of
the rut distress model. The reason is that, none of the so called independent
variables can be truly identified as such. For example, a deflection basin consists
of seven deflection readings made at various lateral distances from the point of
load application. The value of each deflection reading is a function of the other
deflection readings, the pavement cross-section, the material properties (which are
not known), the magnitude of the applied load, the state of the pavement distress,
the moisture levels in the base subbase and roadbed soil, and the pavement
temperature. In addition, the pavement layer thicknesses are a function of the
traffic (thicker layers are used in pavements that are expected to carry higher
traffic load and volumes). Hence, the statistieal analysis must be conducted
carefully and in steps.

For any statistical analysis, the first essential step is the identification of
potential explanatory variables to be used in the development of the predictive!
correlation equation. In a statistical sense, these explanatory variables are
referred to as independent variables. In reality, various levels of dependency
exist between these variables and the pavement rut (the dependent variable) and
among the variables themselves. In some instances, the problem of collinearity
between the dependent variables can be minimized by combining them into
clusters based upon analytical and engineering backgrounds. In other situations
(such as large sample population), the variables may be stratified. Still in others,
the variables ean be included as polynomial terms of the same variables. For

207

example, the deflection measured at lateral distances of 8 and 12-inch from the

center of the loaded area can be thought of as two terms of a polynomial function

that is dependent on the deflection measured under the load and the pavement

cross-section. It is in this context (polynomial terms, and variable clusters), the

statistical analysis of the measured deflection and rut data was conducted. To

illustrate, consider the coefficient of correlations between the rut depth and the

measured deflections at the seven sensor loeations (D1 through D7) listed in

Table 5 .25. It can be seen that:

1.

As it was expected, the seven deflection values are highly collinear. The
deflection measured at any sensor location is strongly related to the other
deflection values.

The rut depth increases with an increase in the peak deflection. This
observation is reasonable. Weaker pavements deflect more under traffic
loading and are prone to higher rutting.

The outer sensor deflections (D2 through D7) are negatively correlated to
the rut depth. That is increasing deflections eause decreasing rut. This
observation was also expected because stiffer AC pavements distribute the
load over larger areas as compared to softer AC pavements. Hence,
stiffer AC courses cause a lower rut potential.

The highest value of the coefficient of correlation in the Table is ”-0.260”.
This should not be interpreted as an absence of significant correlation
between the various deflections and the pavement rut. The seven values
of the measured deflections represent only a few terms of the deflection
basin that affect rut. For example, the slope and the area of the deflection
basin (which affect the pavement rotting) can be calculated by clustering

various deflection terms which can be related to the rut depth.

Table 5.25 : Correlation matrix for rut and sensors deflection.

208

 

 

 

 

 

 

 

 

 

 

 

 

 

Sensor Deflection
Rut 01 DZ 03 04 05 06 07

Rut 1.000

01 .047 1.000

oz -.005 .975 1.000

03 -.051 .919 .977 1.000

04 -.137 .749 .860 .945 1.000

05 -.206 .536 .681 .809 .954 1.000

06 -.260 .183 .346 .507 .745 .907 1.000

07 -.213 .048 .194 .337 .576 .768 .950 1.000
D 0 Sensor deflection (1 to 7).

 

209

The second step in the statistical analysis is to observe the trends between
the dependent variable (rut depth) and the independent variables (polynomial
terms and variable clusters) to infer the proper variable transformation forms. To
this end, the polynomial terms and the variable clusters were plotted against the
rut depth. From the plots, the trend between the dependent and each of the
independent variable was observed. Based on the observations, several applicable
transformation forms were studied and the one that led to the lowest standard
error were selected. Analysis based on these variable strings and clusters are

presented in the next sections.

5.5.3.3 Regression Analysis

As noted above, the measured deflections at the seven sensor locations (0,

8, 12, 18, 24, 36, and 60-inch from the center of the loaded area) are given the

following symbols (D1, D2, D3, D4, D5, D6, and D7), respectively. The

deflections were used in a polynomial strings and they were clustered as to
calculate the various parameters of the deflection basins. These strings of
variables are presented below.

ESL = The cumulative l8-kip single axle load (ESAL) and the pavement
service life terms were clustered into one term by using the
following equation:

ESL = (LOG(1+CUM.ESAL”)/(1+Service Life))
The above cluster approximates the average yearly 18-kip ESAL
traveled the pavement section. This cluster combined two
collinear terms, the service life and the cumulative ESAL.

D1,“: = The deflection measured under the center of the load (D1) was
normalized relative to the thickness of the AC layer ('11.) using the

R61

R21

R12

R71

210

following equation:

D110 =(IOG(D1)/Ti"’)
The term D1 0c approximates the rate of deflection per inch of the
AC thickness. Higher AC thicknesses yield lower D1.
Expresses the ratio of the deflection (D6) measured at a lateral
distance of 36~inch from the center of the load normalized with
respect to the term D1Ac as follows:

R61 = LOG(ABS(D6/D1Ac))
The term is similar to the previous one (R61) except it normalizes
the deflection (D2) measured at a lateral distance of 8-inch from
the center of the loaded area as follows:

R21 = LOG(ABS(D2/D1Ac))
The term is similar to the previous two terms (R61 and R21)
except it normalizes the deflection (Dl) measured at the center of
the loaded area as follows:

R12 = (D1/(D1+D2))-”
The term is also similar to the previous terms except it normalizes
the deflection (D7) measured at a lateral distance of 60-inch from
the center of the loaded area as follows:

R71 ==LOG(ABS(D7/Dlm)
For each deflection basin, the slopes between adjacent deflection
sensor locations were ealculated. These include the following
terms and their definitions:

SS6 = (ABS(D5-D6)/12)°°”

S34 = (ABS(D3-D4)/6)""

S67 = (ABS (D6-D7)/24)

823 = LOG(ABS(D2-D3)/4)

21 1
S45 =(ABS(D4—D5)/6)".

Tas = This term represents the thicknesses of the base (T1) and subbase
(T,_) as follows:
TBS = (T2 + T32)
A = For each deflection basin, the area between adjacent deflection

sensor locations were calculated. These include the following

terms and their definitions:

A12 = (4*(D1+D2))

A23 = LOG(2*(ABS(D2)+ABS(D3)))

A45 = (3*(ABS(D4)+ABS(DS)))

A56 = (6*(ABS(D5)+ABS(D6)))

AA = ((D1+D2+D3+D4+D5+D6+D7)").

Based on the above definitions, variable strings and variable clusters were
formed and two statistieal analysis were conducted and are presented in the next

two subsections.

5.5.3.3.] Statistical Analysis Based on Strings of Variabla

The results of the regression analysis based on strings of variables are
listed in Table 5.26. It can be seen from the Table that all the variables in the
equation have a "T" significance values of less than 0.060. Hence, they are
significant variables. The results of the regression analysis listed in Table 5.26
indicate that the standard error (S.E.) of the resulting model is 0.093. The value
of the coefficient of determination (R’) is 0.591 and the adjusted R2 is 0.527.
The numbers listed under the column designated 'B" are the regression constants
for the indicated variables. Table 5.27 provides a list of the regression constants
and the values of the R2 and the standard error obtained from each step of the

212

Table 5.26 : Results of regression analysis.

 

 

REGRESSIOI *‘*

Hultlple It .76881
1! Square .59107
Adjusted it Square .52674
Standard Error .09325
Analysis of Variance
OF Sua of Squares
Regression 14 1.11850
animal 89 .77384
F 0 9.18852 Signif F 0 .0000
* * 9 9 l U L T l P l. 2

Mean Sqaare
.07989
.00869

 

Equation “whorl Dependent Variable.. P RUT
------------------ Variables in the Equation ------------------
Variable 8 828 Beta 1 Sin!
ESL .743214 .205337 .369246 3.619 .0005
1161 3016446 .664141 -6.653747 -4.409 .0000
res 4.9755706-04 9.604662-05 .566535 5.180 .0000
01,: 1.109569 .410916 .950740 2.700 .0083
A23 -24.o76327 4.347756 ~26.613294 -5.536 .0000
856 5.741293 1.129381 2.606077 5.064 .0000
M 16.586406 3.125505 34.256700 5.307 .0000
1112 -21.068777 4.240290 -1.615557 -4.969 .0000
A45 -.129160 .027572 -7.343351 -4.664 .0000
1121 3.255857 .721157 5.853058 4.515 .0000
A12 -.o37492 .009048 -7.366630 -4.144 .0001
:34 1.996104 .717777 2.304049 2.761 .0066
S67 8.008854 3.789590 .948452 2.113 .0374
S23 .155544 .082450 .563991 1.887 .0625
(Cmtant) 3.995250 1.667115 2.117 .0370
E81. . (Locrl+unl.esAL‘-‘)/r1+s«vlco L110»;
61.. - (moron/mu“):
s61 . Locussrouotscm
'I’IS - (Base-rslbbaae );
423 - Lootrtasswzmssron»:
S56 - rebates-661112)“;
A56 . <6*<Ass<05)+assw6m;
M - ((01+02+DS+D4+05+D6107)’);
1112 - (or/roman“;
A45 - (3*(ABS(D4)+ABS(DS))):
1121 0 Locraesrozmum
A12 - (momzm
534 - (euros-64ml";
:67 0 (assloo-ormu; and
523 0 Loomswz-onM).

 

213

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.8. .... a... 88.. ...... 2.8.. ...... i... 38.... 3.... ..x. a 8.3.. .8. _ n 88.. 3:... 5... a...
.8. .... 8.... 5.... ..8: as. 3.. .83.. ...... .8... n 8...... ...... a 388. 3.5. ...... al..
.8. 8.. .3... .8... .8... ...... 88... 8..... E... a I: .. .5.. n .88. 5.... ...... 8...
.8. .... a... :2... 2.8.. ...... ...... .85 n G .. 8.... .. 38.. 8.... 8.... «3..
.... .... =3. 88.. E5. ...... I... n .... 3.... a .88. ...... ..c. .3...
3.. 8.. 89. F... .....v ...... .. .... n 8.. . a... :8... .88. ...... :8. an...
8.. o... E... .3... 88.. 3... a on. v 8.... E. . .88. E... .8... ...!
8.. .... 38 :9... =8. 28. .88.. 38.7 2!. an . .88. :8. 8.... ......
.8.. E. 88.. i. .. .83 :8. 8..... a... 3:9 .88. ...... 8:. .5.
B... ...... 28.. 3.... =8. ...... a... 2.8.9 .88. a... 2.... 8....
...... .... ...... .8... ..8... 88.. .5... .88. E... 28. 80.
3.. .3. :8. a... a... ...... .88. a... 88. ......
«8.. 8.. .8... ...... 8..... ..88. ..R. ...... :8:
8.. .... .n... .5... .88.. 8.. ...... .8...
I: .... 38.. ....8. ...... It... :3.
.... 8.. 3.8... a... 8.... a...
.... a... .8... ...... .0..
5.. 8.. .5.. ......
... ...... .8 ..< .9. .2 u... << 0.. ..< §< 2:. S. we. .9. ...... ...»

dd 54. w .1. . ~ I . n e 28...

 

 

 

 

 

.95.... .8. .a...uE 5.889% u 56 0..—an.

 

214

stepwise method of the SPSS computer program. As it ean be seen that the
variable ESL is the most important variable and it alone explains about 16 percent
of the variation of the measured rut depth. This percentage increases, with the
inclusion of more variables in the model. The final form of the equation
modelling pavement rut as a function of the various sensor deflection, the
pavement cross-section, and the 18-kip ESAL is presented below:

RUT= 3.9952 + 0.7432 (ESL) - 3.0164 (R61) + 0.000498 (TBS) +1.1096 (DIM) - 24.0763

(A23) + 5.7413 (SS6) + 16.5864 (AA) - 21.0688 (R12) - 0.1292 (A45) + 3.2559 (R21)
- 0.0375 (A12) + 1.9961 (834) + 8.0089 (867) + 0.1555 (823) (5.6)

R2 = 0.591, SE = 0.093, F = 9.188, PM = 0.000

Where the terms are the same as before.

Based on the statistics of the model, the following observations were made.

1. The null hypothesis of no linear relationship between the independent
variables and RUT was rejected and it was concluded that at a probability
of F“, zero, 59 percent of the variation of the dependent variable is
explained by the above strings of variables.

2. The largest value of 'T' signifieance is .06. This implies that all the
variables in the model are statistieally significant. '

The Durbin-Watson statistics of equation 5.6 which is listed in Table 5 .28
signifies a satisfactory non autocorrelation between the residuals. Further, the
maximum, minimum, mean and standard deviation of the unstandardized and
standardized predicted values and the residuals are also listed in the Table. Based
on the values of the residuals and the standardized residuals, the ten worst
residuals cases are presented in Table 5.29.

Figure 5 .25 depicts the calculated and the observed rut depth values. As
it can be seen, most of the data points are located close to the line of equality.

215

Table 5 .28 : Residual statistics of equation 5 .6

 

 

 

 

 

 

 

 

Min Max lean Std Dev I
'PRED .0221 .4945 .2132 .1042 104
*RESlD -.2859 .2295 .0000 .0867 104
*ZPRED -1.8339 2.6989 .0000 1.0000 104
*ZRESID -3.0658 2.4612 .0000 .9296 104
Durbin-Bataan Test 8 2.06219

 

 

 

Table 5.29 : Ten worst residuals.

 

 

C686 9 *RESID *ZRESID
93 °.2859 -3.0658
87 .2295 2.4611
88 .2208 2.36745
70 -.1692 -1.81459

101 -.1644 -1.76338
74 -.1596 -1.71208
56 .1557 1.66963
45 .1473 1.57921
54 -.1471 -1.57766
77 -.1325 -1.42076

 

 

 

 

 

216

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

..
...
.. +
+ a $
+ .... +++
+ N + A .
...
+ ... ++
+ P? DD+P ’
.. 1.. J 11+.+M.
+. ...
+
... +
... +
+ ++ + ++++
++$+ + +3... to!
7. e. s 4. a 2 1.
O O 0 0 0 0 0
.865. £80 5.. 88.3...

0.3 0.4 0.5 0.6 0.7

Observed Rut Depth (inches)

0.2

0.1

figures.25:0bservedversuspredictedmtdeptbs.

217
The percent error between the calculated and the observed values are depicted in
Figure 5 .26. Examination of the Figure indicates that most of the ealculated rut
values are within 60 percent of the observed values. This indicates that the
statistical model is relatively accurate.

Equation 5.6 was extended to estimate the rut depth at other pavement
locations where the deflection data was available. Figure 5.. 27 shows the
predicted and the measured rut depths of 563 pavement locations (plus sign in the
Figure indicates the 104 core locations from which the equation was developed).
The variation between the predicted and the measured rut depths shown in Figure
5.27 are expected. The main reason for this variation is that (as it was mentioned
earlier) for the non-cored pavement sections the pavement cross-section data were
obtained from the MDOT files. Thus, the AC course, the base and the subbase
thicknesses were assumed to be constant for each non-cored section. However,
it was shown esrlier (see Figure 5.20) that variation in the AC layer thickness of
upto 40 percent were very common for the wearing and leveling courses. Further,
comments regarding the poor prediction are presented at the end

of next section.
5.5.3.3.2 Regression Analysis Based on Cluster of Variables

A second statistical analysis was conducted by using variable clusters. The
previously defined variable strings are clustered together and the resulting terms
are used as super single variables in this analysis. The variable clusters and their
definitions are listed below.

ESL = Traffic factor which is defined in the previous section.
D1AC = Normalized peak deflection which is also defined in the previous

section.

218

 

 

 
 

 

fIA

 

no”

  

l .... _.
9 x .x.

 

 

 

My
\

.\

§\\& 1

[A Q. ink

41% 61-80 81-100

\ \.

 

9'3 '6 .39.: 0

16971 '96 l..'lll"0|||'vlfdisr§ue 9'

elitesbilulfva ..5.. 611.7? .‘O‘Elgie 19 16191

      

 

 

 

 

 

 

 

 

/. /. V / V / / /. .
. m w .. M. . .. .. o
830 32030 .0 .3632

Percent Error
Figure 5 .26 : Percent error between the observed and the predicted rut depth values.

219

 

 

 

 

 

 

 

 

 

 

 

.3! +1.. I!!!
I...

... +53.
+ ......

n ... . ...

 

 

1.5

a. I . “a.
i ‘ ~ . l X a
.r 0
0
.85.... 5.8 5.. 86.8...

 

1.2

0.8

0.6
Observed Rut Depth (indies)

0.4

0.2

 

 

~1

W527:Observedversusprediaednndepthsforthe563pavanem10caflons.

220

SF = Slope factor defined by the sum of the slopes between all adjacent
pairs of deflection sensors. The slope factor is calculated as
follows:

SF= (l/ABS(823+S34+S45+SS6+867°))“”
where all terms are as previously defined.

DF = Deflection factor defined as the sum of the deflection ratios of all
adjacent sensor deflections. The deflection factor is calculated as
follows:

DF= D1,,¢/(D1,,¢+1?.21+R61-1-R71)2
where all terms are as previously defined.

61 Thickness factor defined as the sum of the thickness of the base

(1‘2) and subbase (T3) layers as follows:
‘ T881: (1122.5 +1323)

The results of the regression analysis are listed in Table 5 .30. It can be
seen that all clusters in the Table have a 'T" significance values of less than
0.050. Hence, they are signifieant variables. The results of the regression
analysis listed in Table 5.30 indieatc that the standard error of the resulting model
is 0.089. The value of coefficient of determination (R2) is 0.560 and the adjusted
R2 is 0.537. Table 5 .31 provides a list of the regression constants and the values
of the R2 and the standard error obtained from each step of the stepwise method
of the SPSS computer program. It can be noted that the traffic factor (ESL) is
the most important variable and it alone explains about 20 percent of the variation
of the pavement rut (the dependent variable). This percentage increases, with the
inclusion of more variable clusters in the model. The final form of the equation
expressing pavement rut as a function of the various variable clusters is presented
below.

Table 5.30 : Results of regression analysis.

221

 

 

 

 

 

 

 

Multiple R .74829

R Square .55994

Adjusted R Square .53702

Standard Error .08879

Analysis of Variance

0F Sun of Squares Mean Square

Regression 5 .96289 .19258

Residual 96 .75675 .00788

F I 24.43015 Signif F - .0000

' * * * I U L 1 i P L E I E 0 I E S S l 0 I * ' 8

Equation timber 1 Dependent Variable.. P 1101

------------------ Variables in the Equation ------------------

Variable 0 SE 8 Beta 1 Sin 1

ESL .870205 .172627 .476513 5.041 .0000

01 8.194847E-05 1.35422E-05 .428528 6.051 .0000

OF 24.974873 4.817170 2.052168 5.185 .0000

01 -2.006910 .453242 -1.796698 -4.428 .0000

SF .002031 7.089898-04 .243000 2.865 .0051

(Constant) .100403 .030668 3.274 .0015

Table 5.31 : Regresion matrix for rutting.
intercept R.Sq. 8.8.
ESL 61 0F 01 SF

.16526 .8190 .201 .117
.07741 .9479 7.6715E-05 .357 .105
.01373 1.2563 7.79388-05 4.3276 .455 .097
.08936 1.1357 7.3396E-05 21.9264 -1.6747 .522 .092
.10040 .8702 8.19488-05 24.9748 -2.0069 .0020 .560 .089

 

 

 

 

 

 

 

 

 

 

222

RUT = 0.1004 + 0.8702 (ESL) + 8.1948E-05 (G1) + 24.9749 (DE '-
2.0069 (DIAC) 0.0020 (SF)
(5.7)

R2 = 0.56, SE = 0.088, F = 24.43, F“, = 0.000

where all variable are previously defined.

Based on the various statistics of the model and the statistics of the residuals
presented in Tables 5.32 and 5.33, the following observations are made.

1. The null hypothesis of no linear relationship between the independent
variables and RUT was rejected and it was concluded that at a probability

of Fat) zero, 56 percent of the variation of the dependent variable is
explained by the variable clusters included in equation 5.7.
2. . The largest value of 'T" significance is .005. This implies that all the
variables in the model are significant.
Figure 5.28 displays a plot of the rut depth calculated by using equation 5.7 and
the measured rut depth values. As it can be seen, most of the calculated rut
values are located close to the 45 degree line (line of equality between calculated
and measured values). The percent error between the measured and the calculated
values are depicted in Figure 5.29. Examination of the Figure indicates that
about 75 percent of the predicted rut values are within 60 percent of the observed
values. .
Equation 5 .7 was also extended to calculate the rut values at other
pavement locations where the pavement deflection data are available but the exact
pavement cross-sections are not available. Figure 5 .30 shows the calculated and
the measured rut depths of 563 pavement core locations. As it can be seen, given
the lack of accurate information regarding the pavement cross-section data, the
statistical model (equation 5 .7) seems to be reasonable. Several observations

regarding both statistical analyses presented above are discussed in the next

223

Table 5.32 : Residual statistics of equation 5 .7.

 

 

 

 

 

 

 

Min flax Mean Std Dev I
*PRED .0487 .5027 .2076 .0976 104
*RESID -.2035 .2020 .0000 .0866 104
*ZPRED -1.6277 3.0222 .0000 1.0000 104
*ZRESlD -2.2922 2.2748 .0000 .9749 104

 

 

Durbin-Vatson Test 8

2.40685

 

 

 

 

Case 9 *RESID *ZRESID
99 -.2035 -2.29224
7 .2020 2.27403
54 -.1864 -2.09907
90 .1835 2.06709
47 -.1736 -1.95490
53 -.1706 °1.92135
94 .1605 1.80820
97 -.1504 -1.78461
81 .1575 1.77415
3 .1528 1.72052

 

 

 

 

Table 5.33 : Ten worst residuals.

 

224

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.7
0.6
0.5
A +
8
:5 A
5 0.4 +
S
Q +
5 +
C $ + + t ‘1' <1-
.8 0.3 _ r 2; 11'
E + + i 4h
3. + +
O. t + + +
on + I- 4'};
°‘ F; '; I
#i '1': 2 '1' if
u.- t 0 +
1: + + IF " *
0.1 t * 4
t i
+
0
0 0.1 0.2 0.3 0.4 0.5
Observed Rut Depth (inches)

figure5.28:0bservedversuspredictedrutdeptbs.

225

 

 

 

so«/

”‘1
15-/
1o-/ ’ . i .
5-V .

 

 

 

Number of Observed Cases
8
\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0..
0-20 21-40 41-60 60-80 61-100 >100
PercentError
Figure 5.29: Percent error betweenthe observed and the predictedrut depth

values.

226

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2
1
0.8
+
is? +
+
E + +
5 0.6- +
8‘ + E
0 7 +5 + + ... + *4-
+ ... +
g :: " I I
g 0.4‘ * Y : + f
- +
8 + + as +
i + + i is)- + + +
'3 + it
0.2‘ H g r} + *
1: 13+
0 a”: + +
r: +
c ¢
if
'0'
-0.2
0 0.2 0.4 0.6 0.8
Observed Rut Depth (inches)
Figure 5.30 : Observed versus predicted rut depths for the 563 pavement

locations.

 

1.2

227

section.
5.5.3.4 Observations and Discussion

The above presented statistical analyses present an attempt to model

pavement rut using nondestructive deflection testing data. Most available rut
prediction models are based on pavement layer properties and hence,
destructive tests need to be conducted to assess such properties. Several
attempts to predict pavement rut depths using NDT data were also made
in the past. The results can be considered as poor at best. The issues in
predicting rut depths by using NDT data can be divided into two
categories, statistical and physical.

The statistical issues are mainly related to the nature of the measured
deflection data. Since the pavement deflection measured at any lateral distance
from the applied load is a function of the pavement layer properties and
geometry, the magnitude of the applied load, the stress history (the number of 18-
kip ESAL traveled the pavement section), the environmental factors (moisture,
temperature, and time), and the state of the pavement distress, the various
deflection values are not truly independent. Further, various aspects of the
deflection basin are related to the material properties. For example, the slope of
the deflection basin between any pair of adjacent deflection sensor is mainly
related to the moduli ratio and thicknesses of the pavement layers. Hence, the
elimination of the slopes of the deflection basin from the string of variables to be
included in the statistical analysis is a problem related to the elimination of
valuable information. Likewise, the area of the deflection basin defined by any
two adjacent deflection sensor is a function of the amount of energy delivered to

one or more of the pavement layers due to the application of the load. The above

228
scenario implies that the elimination of one or more slopes, one or more aress,
and/or one or more deflection values will induce bias in the resulting model.

The physical issues are related to the available information regarding the
pavement geometry (layer tlnickrnesses). During this study, it was noticed that the
actual layer thickness mat vary by as much as 60 percent from the as-designed
values (A typical SHA record contains only the as-designed layer thickrnesses).
Since, layer tlnickrnesses have a major impact on pavement rut and deflection,
extending a statistical model to locations where such information are not
accurately available is problematic in nature. Indeed, even rut prediction models
developed on the basis of material properties cannot successfully be used to
predict pavement rut if accurate information regarding the material properties and
layer thickrnesses at the desirable points are not available.

The above issues indicate that the development of statistical models
relating a dependent variable to various independent but collinear variables is,
from the statistical view point, problematic. In addition, if a variable includes
more than one set of independent information that cannot be obtained by any
means other than using the variable in “two or more terms in the statistical model,
then such use should not be considered invalid. For example, if a real
mechanistic model expresses the value of ”Y” in terms of tlne values of 'x" as 'Y
= X + X‘-25 + X235 + X", and if the values of 'Y" and 'X" are krnown, then
the most correct model to predict 'Y" from 'X" must have the term 'X" as three
independent but collinear terms in the model.

Similarly, the method of variable clusters is very powerful in some
statistical analysis. To illustrate, consider a traffic congestion model for road
number 101, the number of vehicles to be used in the model is the cluster of
several independent but collinear variables that include the number of passenger
cars, trucks, and other vehicles traveling the pavement during the peak hours.

5.6

229
The reason that the various terms are collinear is that the number of each vehicle
class is a function of the same variables (road geometry, location, origination and
destination points, the number of traffic lights, availability of other routes, and
so forth). Now, for the same road 101, a rut or fatigue prediction model would
have the traffic data clustered in a different fashion. For these models, it is the
load placed and distributed by each vehicle axle is important. Hence, the traffic
data is assigned different weights (load equivalency factor) prior to clustering the
data. Another important point regarding the accuracy of the statistical analyses

relative to the various errors of the measured data is presented in the next section.

ERRORS

Several errors are typically associated with the measurements of any field and

laboratory types of data. These include systematic and random errors. Systematic errors

are defined as the error due to the inaccuracy of the measuring system whereas random

errors are variations due to the working of a number of uncontrolled variables, each of

which affects the outcome in a small quantity (92). The following systematic and random

errors can be identified in this study.

1.

The rut data was obtained by using a straight edge and two MDOT’s
prefabricated graduated gauges with accuracies of 0.0625 and 0.025 of an inch.
The rut depth measurement method consists of setting the straight edge on the
pavement across the rut channel and inserting the graduated rut gauge in tlne gap
between the pavement and the straight edge. The gauge was then moved in a
lateral direction until the maximum number of graduates are inserted. The total
rut depth was then recorded as the total number of graduate times the graduate
tlnickrness (0.0625 or 0.025-inch depending on the type of graduate being used).
This implies that the systematic error in the measured rut depths could be as high

230
as the thickness of one graduate. Although, the magnitude of this systematic error
is random in nature and is the same for all measurements, the percent error is
very high for the lower rut depths. For example, a measured rut depth of
”0.0625—inch” could in reality be any where from 0,0625 to 0.12-inch (about 100
percent error). On the other hand, a measured rut depth of l-inch could be any
where from 1 to 1.0624-inch (a 6.24 percent error). Hence, the percent error has
more bias toward the lower rut measurements than toward the higher ones.
The random error associated with the rut measurements is related to the pavement
texture and to the presence or absence of loose particles on the pavement surface.
Higher textured (rough as in open-graded asphalt mix) pavement surface would
yield higher error because the rut gauge could be setting on either the higher or
the lower ends of the aggregates. The presence of small soil particles on the
pavement surface also produce a random errors in the rut measurements. Both of
these random errors are very significant for shallow rut depth and are
insignificant for higher rut values.
Systematic error associated with the deflection measurements. The deflection
resolution of the MDOT Kuab 2-M FWd model is 0.04 mils and the relative
accuracy of the deflection measurements is 0.08 mils j: 2 percent (93). Which
implies that the outer deflection sensors ean be off by as much as 100 percent.
One point should be noted here is that this is the accuracy of the entire KUAB
system whereas more accurate gauges are used for the outer sensors to minimize
this error. In addition, the pavement surface texture and the presence of fine
particles on the pavement surface cause random errors in the measured
deflections.
A systematic error in the laboratory measurements of the thicknesses of the AC
layers for the cored pavement sections. The AC layer thicknesses were measured

by using a hand held scale with an accuracy of 0.0625-inch. The systematic error

231

is related to this measurement error as well as to the degree of the intrusion of
the base material into the AC layer. Both errors can be considered as random.
The error of the AC thicknesses of the non-cored pavement sections is related to
construction practices and the enforced quality control policy at the time of
construction. For any one pavement section constructed at the same time, this
error is random in nature. However, the magnitude and the percent of the error
varies from one section to another.

As noted earlier, pavement deflections represent the pavement system response
to load. Further, pavement deflection data and the various deflection basin
parameters provides a quantitative basis for the evaluation of the pavement
structural condition at any time during its service life. One of the objectives of
the above presented statistical analyses is to explore the potential of using the
NDT and other data to predict the pavement rutting. For these reasons, all
possible deflection basin parameter (deflections, slopes, and areas) were included
in the development of the regression models. Although the legitimacy of the high
number of variables included in the predictive equations can be argued, there are
' no formal rules regarding the minimum or maximum number of variables to be
included in an equation. However, it is known that various problems asSociated
with use of large number of collinear variables exist. The most important one of
these problems is that each variable in the final regression model has some input
error associated with it that causes an error in the estimates. The total error in the

estimates (due to various variables) can be additive in nature as it is expressed in

the following formula (94):

If Z= f( x1,....x,),

ei=£ifazex3 +2. 25f... fxiexiexirii (5.8)
where el = the error of z;

f,i = the partial derivative of f with respect to xi;

232
e,“ = the measurement error in the x,; and

p.

u = the correlation between x, and xj.

The second term on the right-hand side of equation 5 .8 indicates that the error in the
estimates can increase very rapidly when collinear variables are used to calculate the
estimates. Moreover, as the number of independent variables increases so does the error
of the estimates. .

Given the above scenario, the two regression equations relating pavement rut to
the deflection basin are exploratory in nature. The equations should not be used and/or
extended to predict rut depth of any pavement section without further study and

verification.

5.7 VERIFICATION OF THE SHIFT FACTORS OF THE FATIGUE LIFE

The sensitivity of the shifts factors of the fatigue life (presented in section 5.4.5)
to the variations in the values of the variables of the fatigue model (equation 5 .4) was
analyzed and is presented in this section. The purpose of the analysis is to determine
whether the values of the shifts factors are random in nature or they are pavement site
specific. The analysis was accomplished in three steps as follows:

1. For each pavement section, the average, maximum, and minimum values of the
measured material properties (angularity, percent AC and fine contents, and
specific gravity) were obtained. These values are listed in Table 5.34 such that,
for each pavement section, the first two lines in the table include the maximum
and minimum aggregate angularity and the average values of the other three
material properties (percent AC and fine contents and specific gravity). The
second set of two lines include the maximum and minimum of the percent AC
content and the average values of the other three properties. The third and fourth

sets of two lines include the maximum and minimum percent fine contents and

233

Table 5.34 : The maximum, minimum, and the average values of the shift factors
for the indicated pavement section.

7
7
7
7
7
7
7
7
7

““““

 

234

Table 5.34 : The maximum, minimum, and the average values of the shift factors
for the indicated pavement section (continued).

fiyVVflqqd

 

235
the maximum and minimum specific gravities, respectively. Finally, the data in
the last line includes the average material properties.
For each data line of Table 5.34, the fatigue model (equation 5.4) was then used
to predict two values of the fatigue life; one using the actual pavement service life
and the other for a zero service life.
The shift factor for each data line of each pavement section was then calculated
by dividing the cumulative l8-kip ESAL by the difference in the two values of
the fatigue life (the one calculated for the actual pavement service life and the one
for zero service life). For each pavement section, the last column of Table 5.34
provides a list of the maximum, minimum, and the average values of the shift
factor. It should be noted that, for the eight pavement section, the average value
of the shift factor corresponds to the average material properties.

Figure 5.31 depicts the maximum, minimum, and average values of the shift

factors of the eight pavement sections. Examination of figure 5.31 and the maximum,

minimum, and the average values of the shift factors listed in table 5.34 indicates that:

1.

‘3.

For five pavement sections (7F, 19F, 35F, 10F, and 13F), the maximum and
minimum values of the shift factor correspond to variations in the values of the
specific gravity of the asphalt mix of those sections. Higher values of the specific
gravity of the AC mix cause lower shift factors (low ratio of the field to the
laboratory fatigue lives).

For pavement section 29F, the maximum and minimum values of the shift factor
correspond to variations in the values of the aggregate angularity. Higher values
of aggregate angularity cause lower shift factors.

For pavement section 14F, the maximum and minimum values of the shift factor
correspond to variations in the values of the asphalt content of the AC mix.
Higher values of asphalt contents cause lower shift factors.

For pavement section 43F, the maximum and minimum values of the shift factor

236

 

            

      

 

 
    

 

 

 

12a
\.
\
t
10- \
\
x
\
\
\
a~ t
\i
§
a. A t
f: E x
u. 3 6~ :
5 g \
6 . \
\
\
\;
4~ \ t
x x:
\. \
\ \,
\ x
\ \:
\ \2
2- \ \; \t
x \ \
x \ \
\ \ii \
\ \; \
s \ § Q ‘.
01 . 05 .--\ .\'\ ‘\~, \5
13F 14F 10F 29F 35F 7F 19F 43F
Section Number
Figure 5.31 : 'lhe maxrm' urn, mmim’ um, and average values of the shift

factors of the fatigue life versus the indicated pavement section
nurhber. A

237

correspond to the lowest values of the specific gravity of the AC mix and to the

highest aggregate angularity, respectively.

The above observations indicate that the variation and the values of the shift factors are
a function of the variations of the various properties of the AC mix. Since the design of
the AC mix is site specific (different mix is typically used for different pavements), and
since the construction and quality control practices differ from one job to another, one
can conclude that the values of the shift factor relating the field and laboratory fatigue
lives are also pavement site specific.

One important point should be noted is that the fatigue model (equation 5.4)
predicts the number of load repetition to crack initiation. In the field, alligator cracks
may exist (at the bottom-side of the AC layer) in a pavement section for a long time
before they can be observed on the surface of the pavement. The time lapse between
crack initiation and crack observation on the pavement surface is a function of the
pavement layer thicknesses, the traffic volume and load, and the environmental
conditions. Given the above scenario, analysis of the relative accuracy of the shift factor
was conducted. First, the two pavement sections (13F and 7F) with existing fatigue
cracks were chosen and from each section, a pavement core was obtained from the
pavement area between the wheelpaths. Each core was then tested in the laboratory, and
the fatigue lives of the cores were determined and are listed in Table 5.35 along with the
corresponding average values of the shift factor. For each pavement section, the
predicted field fatigue life was then calculated by multiplying the laboratory fatigue life
by the corresponding shift factor. The results are listed in Table 5.35 along with the
cumulative 18-kip ESAL experienced by the two pavement sections. Examination of the
values of the predicted field fatigue life and the cumulative 18-kip ESAL indicates that,
for both pavement section, the predicted fatigue life is shorter that the observed 18-kip
ESAL. For example, for pavement section 13F, the predicted fatigue life is 840,000 18-
kip ESAL and the observed cumulative l8-kip ESAL is 1,510,000. The reason that the

238

 

 

 

 

 

 

 

 

 

 

 

can. 522,8 :3 3.. “3.. on 8.: 38:: t

3.8: 5:26. :3 3.. .3... a: 88 Twain. 5

.828. .5 .o «58:: 2:88 $2 . 333 3: 26:: 3: 262.: .2. .2.

2.2:: $0203.. of «c 57.26» .23 3:38 30: “.3059... .303 3.5 {39.33 5333.3 5303
5.8.6 9338

.53 «5:98 .5895.— e»; ..e 8.»: 2.33.. uotomee 6:: 38:92am u mad ~35.

 

239
observed number of ESAL is about twice as much as the predicted one is that the
1,510,000 ESAL is the cumulative ESAL from construction to the time where low
severity alligator cracks were observed along the entire pavement section. Hence the
number of ESAL to crack initiation is much smaller than the 1,510,000. Likewise, the
ratio between the observed (1,250,000) and the predicted (1,035,000) ESAL is about 1.2.
The section has low severity alligator cracks along 50 percent of its length. This implies
that the number of ESAL to crack initiation is lower than the observed one. In addition,
the data from the two pavement sections indicate that the ratio of the observed to the
predicted ESAL increases as the extent of the alligator cracking increases. This is

reasonable and consistent with the mechanism of the crack propagation.

CHAPTER 6

SUNIMARY, ACCOMPLISHMENTS, CONCLUSIONS AND
RECOMIVIENDATIONS

6.1 SUMMARY

The effects of the asphalt mix variables on the laboratory fatigue life and field
rutting were investigated in this study. Full depth AC cores were obtained from selected
pavement sections. The properties of the AC mixes were determined as described in
chapter 4. Indirect cyclic load tensile tests were conducted to determine the resilient and
plastic deformations and the fatigue lives of the core samples.

Prediction models of the laboratory fatigue life and field rutting were developed.
The laboratory fatigue life model is based on the AC mix properties and the pavement
service life. The field rutting model is based on the AC mix properties and the
cumulative 18-kip ESAL. Sensitivity analysis of the models were conducted to determine
the influence of each variable on pavement rutting and fatigue life. It is shown that the
aggregate angularity is the most significant variable affecting the fatigue life and that the
percent fine and sand contents in the AC mix are the most significant variables affecting
pavement rutting. Shift factors relating the laboratory and field fatigue lives were
developed and their variabilities were assessed. An exploratory statistical rut model
based on nondestructive deflection testing was also developed. It is shown that the NDT

data can be used to predict the pavement rut potential.

6.2 ACCOMPLISHNIENTS

The following accomplishments have been made in this study.
1. The factors affecting the rut and fatigue cracking potential of the AC mixes
presently being used in the State of Michigan were identified.

240

241

2. A test procedure to characterize aggregate angularity in terms of the number of
crushed faces, was developed.

3. The effect of coarse aggregate angularity (in terms of the weighted average
number of crushed faces) on rut and fatigue cracking potential of the AC mixes
were determined.

4. A field rut prediction model based on the 18-kip ESAL and the AC mix
properties was developed.

5. A laboratory fatigue life prediction model based on the AC mix properties and the
pavement service life was developed.

6. Sift factors relating the laboratory and field fatigue lives were developed and
verified.

7. An exploratory model relating pavement rut and NDT data was developed.

8. Several problems related to the asphalt mix design procedure and construction
practices were identified.

6.3 CONCLUSIONS
Based on the field and test data and on the analysis, the following conclusions

were drawn.

1. Coarse aggregate angularity is the most influential factor affecting the fatigue life.
Angular aggregate provides a better rut and fatigue cracking resistance.

2. The most beneficial aggregate angularity is that of aggregates crushed on all sides
(no flat particles).

3. Rut and fatigue cracking resistance of the AC mixes can be maximized by
specifying a maximum of 3 to 6 percent air voids.

4. The percent fine and sand contents in the AC mix are the most significant factors

affecting rut. A fine content of less than 5 percent and a sand content of less than

6.4

242
20 percent provide a better rut and fatigue cracking resistance.
For an AC pavement, the laboratory fatigue life of core samples tested in the
indirect cyclic load tensile test mode is related to the pavement fatigue life
through a shift factor.
Significant variation in the thicknesses of the various AC courses were observed
within one pavement section.
Significant variation in the AC mix properties were observed for the same AC
courses within one pavement section.
NDT data can be used to assess the strength of the pavement structure. A
preliminary model suggests that the data can be used to estimate the pavement rut
potential.
The model interaction between the various variables affecting pavement

performance can be minimized by using Proper normalization techniques.

RECOMMENDATIONS

Based on the findings and conclusions of this study the following

recommendations are made.

1.

For high traffic, when economically feasible, a high percentage of coarse angular
aggregates (crushed on all sides) should be used to maximize rut and fatigue
resistance of the AC mix.

To improve rut and fatigue resistance of the AC mix, air voids between 3 to 6
percent should be Specified.

Quality assurance /Quality control (QA/ QC) practices regarding pavement
construction and AC mix manufacturing operations should be modified and/or
enforced.

The rut and fatigue cracking models presented in this thesis should be extended

243

to include the effects of the base, subbase layers and the roadbed soil properties

on rut and fatigue potentials.

The results of this investigation have indicated that the as-constructed NDT data
should be collected and used:

a)

b)
c)
d)
e)
f)

To asses the uniformity or variability of the pavement along any given
project.

As a tool of quality control.

As a tool to determine the structural capacity of the pavement.

As a predictor of pavement rutting.

As a part of the pavement management database.

To backcalculate the as-constructed material properties.

10.

List of References

Yoder E. J. and M. W. Witczak, ”Principles of pavement design” . A Wiley-
Interscience Publication, John Wiley and Sons, Inc. , 1975 .

Santucci L. E., and R. J. Schmidt, ”The effect of asphalt properties on the
fatigue resistance of asphalt paving mixtures, " . Asphalt Paving Technology (APT)
Vol. 38, 1969.

Baladi G. Y. , "Integrated material and structural design method for flexible
pavements,” Vol. 1: Technieal Report, FHWA, 1988.

Report 5, Highway Research Board Special Report 61E, "The AASHO Road
Test, " 1962.

Morris J . , ”The predication of permanent deformation in asphalt concrete
pavement, " Department of Civil Engineering, University of Waterloo, Waterloo
Ontario Canada, 1973.

Morris 1., Ralph C. G. Hass, Park Reilly, and Edward T. Hignell, "Pemanent
deformation in asphalt pavement can be predicted, " APT Vol. 43, 1974.

Hughes C. S. and G. W. Maupin, Jr., ”Experimental bituminous mixes to
minimize pavement rutting,” APT Vol. 56, 1987.

Bonquist, R. , R. , "Effects of tire pressure on flexible pavement response and
performance, " Draft Report, Federal Highway Administration, Washington,
D.C. , 1989.

Harry A. Smith, ”Truck tire characteristics and asphalt concrete pavement
rutting, " Paper No. 910035, Transportation Research Board (TRB) 70th Annual
Meeting, 1991.

Hsien H. Chen, Kurt M. Marshek, and Chhotel L, Saraf, "Effect of truck tire
contact pressure distribution on the design of flexible pavement: A three
dimensional finite element approach, " Transportation Research Record (TRR),
,Transportation Research Board (TRB), 1095, 1986.

ll.
12.

13.

14.

15.

16.
17.

18.

«19.
20.
21.

.22.
23.

24.

245

Richard. D. Barksdale, "Practical application of fatigue and rutting tests on
bituminous based mixes," APT Vol. 47, 1978.

Robert N. Linden, Joe P. Mahoney, and Newton C. Jackson, "Effect of
compaction on asphalt concrete perfomance,” TRR. 1217, 1989.

Firm F. N. and J. A. Epps, ”Compaction of hot mix asphalt concrete,” Research
report 214-21 , Texas Transportation Institute, Texas A and M University,
College Station, 1980.

"Fatigue of asphalt concrete mixtures-Summary of existing information, " Special
technical publication 508. ASTM, Philadelphia, Pa, 1971.

Puangchit P., R. G. Hicks, 1. E. Wilson, and C. A. Bell, ”Impact of variation
in material properties on asphalt pavements life, " Report FHWA-OR-82-3.
Oregon Department of Transportation, 1982.

Miller C. Ford, Jr. , ”Pavement densification related to asphalt mix
characteristics," TR. 1178, 1988.

Jon A. Epps, and Carl L. Monismith, ”Influence of mixture variables on the
flexural fatigue properties of asphalt concrete, " APT Vol. 38, 1969 .

Brown E. R. , "Mix design and construction of asphalt concrete to support high
tire pressure," Presented at AASI-ITO/FHWA Symposium on high pressure truck
tires, Austin, Texas, 1987.

Huber G. A. and G. H. Heiman, ”Effect of asphalt concrete parameter on rutting
performance. A field investigation," APT Vol. 56, 1987.

Hani A. Lotfi, Charles W. Schwartz, and Matthew W. Witczak, "Compaction
specification for the control of pavement subgrade rutting," TR. 1196, 1988.

"Essential physical properties of sand, gravel, slag and broken stone for use in
bituminous pavements, " Better roads and streets. Vol 6, No 3.

“Mix design methods for asphalt concrete," Asphalt Institute Manual Series NO.

. 2(MS-2).

Hicks, R. G., and David C. Esch, " State of the art on rutting in asphalt
concrete,” Alaska DOT and PF Fairbanks, AK 99701, 1990.

Brown E. R., and Charles E. Bassett, ”Effects of maximum aggregate size on
rutting potential and other properties of asphalt aggregates mixtures,” TRR. 1259,
1990.

25.

26.

27.

28.

29.

30.

31.

932.

‘33.

34.

35.

36.

37.

38.

246

Kamyar Mahboub, and David L. Allen, "Characterization of rutting potential of
large-stone asphalt mixes in Kentucky,“ TRR. 1259, 1990. '

Moreland Herrin, and W. H. Goetz, "Effect of Aggregate Shape on Stability of
Bituminous Mixes, " Joint highway Research Project, Purdue University. HRB.
Proceedings 33th Anual Meeting 1954.

Moharnmed Osman Khalifa, and Moreland Herrin, "The behavior of asphaltic
concrete constructed with large-sized Aggregates,” APT Vol. 39, 1970.

Joe W. Button, Dario Perdomo, and Robert L. Lytton, ”Influence of aggregate
on rutting in asphalt concrete pavements,” TRR. 1259, 1990.

Mendenhall W. S. , Jr. , Chairman, " Ad hoc task force on asphalt pavement
rutting and stripping,” August 14, 1987.

Young M. A. and G. Y. Baladi, "Repeated load triaxial testing, state of the art,”
Michigan State University. Department of Civil Engineering, 1977.

Neil C. Kruts, Raj Siddharthan and Mary Stroup-Gradiner, ”Investigation of
rutting potential using static creep testing on polymer modified AC mixture, "
Paper # 910705, 70th meeting TRB, 1991.

Brown E. R., and Stephen A. Cross, "A study of in-place rutting of asphalt
pavements," APT Vol. 58, 1989.

Hensley M. J., and Rita B. Leahy, ”Asphalt concrete mixtures as related to
pavement rutting: Case study,” TRR. 1217, 1989.

Dale 8. Decker and Joseph L. Goodrich, ”Asphalt cement properties related to
pavement performance,” APT Vol. 58, 1989.

Kim Y. R., N. P. Khosla, and N. Kim, "Effect of temperature and mixture
variables on fatigue life predicted by diarnetral fatigue testing,” TRR 1317, 1991.

Vallerga B. A., F. N. Finn and R. G. Hicks, " Effect of asphalt aging on the
fatigue properties of asphalt concrete, " Proc. Second Int. Conf. on the Structural
Design of Asphalt Pavements, 1967.

William D. O. Paterson, ”Models for planning and management,” Road
deterioration and maintenance effects. A World Bank Publication, 1990.

Harold Von Quintus, and Thomas W. Kennedy, ”AAMAS mixture properties
related to pavement performance," APT Vol. 58, 1989.

39.

40.

41.

42.

43.

45.

46.

47.

48.

49.

50.

51.

247

James A. Scherocman, and Mike Acott, " Hot mix asphalt production, placement,
and compacu'on related to pavement performance, " APT Vol. 58, 1989.

Barksdale R. D. , ”Compressive Stress Pulse Time in Flexible Pavements for use
in Dynamic Testing, " Highway Research Board (I-IRB). Highway Research
Record (I-IRR), No. 345, 1971.

Barksdale R. D., ”Laboratory Evaluation of Rutting in Base course Materials,"
Pro. Third Int. Conf. on the Structural Design of Asphalt Pavements, London
1972.

Heukelom W. , and A. J. G. Klomp, ”Consideration of Calculated Strain at
Various Depths in Connection with the Stability of Asphalt Pavements, " Pro.
Second Int. Conf. on the Structural Design of Asphalt Pavements, Ann Arbor
1967. ,

Romain J. E., ”Rut Depth Prediction in Asphalt Pavement,” Pro. Third Int.
Conf. on the Structural Design of Asphalt Pavements, London 1972.

Barksdale R. D. , and Gerald A. Lenards, "Predicting performance of bituminous
surfaced pavements, " Pro. 2nd Int. Conf. on the Structural Design of Asphalt
Pavements, Ann Arbor 1967.

Soussou, J. E. , and Moavenzadeh, F. , ”Statistical characteristics of fatigue
damage accumulation in flexible pavements, " American Society for Testing and
Material. Special Technical Paper No. 561, 1973.

Rita B. Leahy, and Matthew W. Witczak, ”The influence of test conditions and
asphalt concrete mix parameters on permanent defamation coefficients Alpha and
MU, " APT Vol. 60, 1991.

Baladi G. Y. , “Fatigue life and permanent deformation characteristics of asphalt
concrete mixes,” TRR, TRB, 1227, 1989.

”Fatigue and dynamic testing of bituminous mixtures, " American Society for
Testing and Material (ASTM). STP 561, 1973.

Pell, P. S., and Cooper, K. 13., "The effect of testing and mix variables on the
fatigue performance of bituminous materials, " APT Vol. 44, 1975.

Prithvi S. Kandhal, "Design of large-stone asphalt mixes to minimize rutting,”
TRR. 1259, 1990.

"Technical information, " Michigan U.S.A, demonstration August 6 and 7, 1991.
Michigan Department of Transportation.

52.

53.

54.

55.

56.

57.

58.

59.

61.

62.

63.

248

Robert A. Romine, Maghsoud Tahmaressi, R. David Rowlett, and D. Fred
Martinez, " Survey of state highway authorities and asphalt modifier
manufacturers on the performance of asphalt modifiers, " Paper No 910242. TRB.
Meeting Washington, D.C., 1991.

Collins J. H., M. G. Boulddin, R. Gelles, and A.Berker, "Improved performance
of paving asphalt by polymer modification,“ APT Vol. 60, 1991.

Carpenter S. H. , and Tom Vandam, ”Laboratory performance comparisons of
polymer-modified and unmodified asphalt concrete mixtures,” TRR. 1115, 1987.

William A. Higgins, "Chemical modifiers to improve the strength and durability
of asphalt concrete," TRR. 1115, 1987.

Brown S. F. , and M. S. Snaith, "The pavement deformation characteristics of a
dense bitumen macadam subjected to repeated loading," APT Vol 43, 1974.

Monismith C. L. , and A. A. Tayebali, "Permanent deformation (rutting)
consideration in asphalt concrete pavement sections,” APT Vol. 57, 1988.

Wijeratne A. and M. Sargious, "Prediction of rutting in virgin and recycled
asphalt mixtures for pavement using triaxial tests,“ APT Vol. 56, 1987.

Dramawardene, M. W. W. , ”Permanent deformation characteristics of granular
base course materials subjected to highway loading, " Masters Thesis, University
of Waterloo, Canada, 1972.

Hass, R. , and Meyer, F., "Cyclic creep of bituminous materials under transient,
high volume loads,” TRR. No 549, 1975.

Vallejo, J., Kennedy, T. W., and Hass, R., "Permanent deformation
characteristics of asphalt mixtures by repeated load indirect tensile test, " Report
No CFHR 3-9-72-183-7, Transportation planning division , Texas state
department of highway and public transportation, Austin, Texas, 1976.

Reynaldo Roque, and William G. Buttlar, ”The development of a measurement
and analysis system to accurately determine asphalt concrete properties using the
indirect tensile mode,” Draft submitted to APT for the 1992 annual meeting.

Baladi G. Y. and Ronald S. Harichandran, "Asphalt mix design and the indirect
test. A new horizon. Asphalt Concrete Mix Design: Development of more
rational approaches,” ASTM SPT 1041, W. Gartner, Jr., Ed. American society
for testing and materials (ASTM), Philadelphia, 1989.

Barksdale, R. D. , ”Compressive stress pulse times in flexible pavements for use

65.

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

249
in dynamic testing,” HRB. 345, 1971.

Allen, J. J., and Thompson, M. R., ”Resilient response of granular
materials subjected to time-dependent lateral stresses," TRB. 510, 1974.

Bonnaure, F. P., Huibers, A. H. J. J., and Uge, P., ”A laboratory investigation
of the influence of rest periods on the fatigue characteristics of bituminous
mixes," APT Vol. 51, 1982.

Roque R. , and B. E. Ruth, "Material characterization and response of flexible
pavements at low temperatures,” APT Vol. 56, 1987.

Terrel, R. L., Awad, I. S., and Foss, L. R.,"Techniques for characterizing
bituminous material using a versatile triaxial testing system, " Fatigue and
dynamic testing of bituminous mixtures, ASTM STP 561, American society for
testing and materials 1974.

Monismith, C. L., Secor, K. E., and Blackmer, E. W., ”Asphalt mixture
behavior in repeated flexure,” APT Vol. 30, 1961.

Baladi G. Y., Ronald S. H., and Richard W. Lyles, “New relationships between
structural properties and asphalt mix parameters,” TRR,1171 1988.

Baladi G. Y., Richard W. L., and Ronald S. H., ”Asphalt mix design: An
innovative approach” TRR, 1171, 1988.

Lentz R.W. , ”Permanent deformation of cohesionless subgrade material under
cyclic loading,” Ph.D. Thesis Michigan State University, 1979.

Tresca, H. ”Memoire Sur L’ecoulement Des Corps Solides,” Mem. Pres. par div.
savants 18, 1868.

Venant, B. de Saint, "Memoire sur L’establishment des Equations Differentielles
des Mouvements Interieurs operes Dans les Corps Solids Ductiles au Dela des
Limites au L’elasticite Pourrait les Ramener a Leur Premier Etat,” C.R. Acad.
Sci. (Paris), 70, 1870.

Levy, M. , 'Memoires sue L’equations Generales des Mouvements interieurs des
Corps Solides Ductiles au Dela des Limits on L’elasticite Pourrait les Ramener
a Leur Premier Etat,” C.R. Acad. Sci. (Paris), 70, 1870.

Prager, W. , ”An Introduction to Plasticity, " Addison-Wesley Publishing
Company, Inc. , London, England, 1959.

ERES Consultants, Inc. , ”Pavement design principles and practices, " Champaign

78.

79.

80.

81.

82.

83..

85.

86.

87.

88.

89.

250
Illinois, National Highway Institute, Washington, D.C., 1987.

Majidzadeh, U. and G. Ilves, " Flexible pavement overlay design procedures,
volume I, Evaluation and modifieation of the design methods, " Final report
FHWA-RD—82a32. 1981.

John O. Rawlings, ”Applied regression analysis, a research tool, " Wadsworthand
Brooks/Cole, Statistics/ Probability Series, 1988.

David A. Belsley, Edwin Kuh, Roy E. Welsch, “Regression diagnostics,
identifying influential data and sources of collinearity, " Wiley series in probability
and mathematieal statistics, 1980.

Marija J. Norusis/SPSS Inc, "SPSS statistical data analysis ", 1990.

Haveem F. N. , ”Pavement deflections and fatigue failures, " Bulletin 114,
Highway Research Board, Washington, D. C.

Davies, G., T., and Marnlouk, S., M., ”Theoretical response of multilayer
pavement system to dynamic nondestructive testing, " TRR No. 1022. 1985.

Kausek, E., and Peek, R., "Dynamic loads in the interior of a layered stratum:
An explicit solution, " Bulletin of the Seismological Society of America, Vol. 72,
No. 5, October, 1982.

Molenaar, A. A. A., and Van Gurp, C. A. P. M., "Structural performance model
and overlay design for asphalt concrete pavements, " TRR No. 888, Highway
Research Board, National Research Council, Washington, D. C., 1982.

California Division of Highways, "Methods of test to determine overlay

requirements by pavement deflection measurements, " Test Method California
356, D, dated October 1973.

”AASHO,‘ American Association of State Highway Officials, 'AASHO interim
guide for design of pavement, structures,” Washington, D. C., 1972.

Kinchen, R. W. , and Temple, W. H. , ”Asphalt concrete overlays of rigid and
flexible pavements, " Report No. FHWA-LA-109, Federal Highway
Administration, Washington, D. C. , September 1977.

Brown, J. L., and Orellara, H. E., " Utilizing deflection measurements to
upgrade pavement structures, " Report No. 191-IF, Texas State Department of
Highways and Public Transportation, Austin, December, 1970.

" Pavement Rehabilitation: Proceedings of a Workshop, " Report No. FHWA-RD-

91.

92.

93.

94.

251

74-60, Transportation Research Board, Federal Highway Administration,
Washington, D. C., June 1974.

Ronald, S. Harichandran, Tariq Mahmood, A. Robert Raab, and Gilbert Y.
Baladi. , ”Modified Newton Algorithm for Backcalculation of Pavement Layer
Properties,” TRB, TR 1384, 1993.

Bright, E. Wilson, Jr. , ”An Introduction to Scientific Research," McGraw-Hill,
1975.

Crovetti, J. A., Shahin M. Y., and Touma B. B., ”Comparison of Two Falling
weight Deflectometer Devices, Dynatest 8000 and Kuab 2-M FWD, " ASTM STP
1026, A. J. Bush III, and G. Y. Baladi, Eds., American Society for testing and
Materials, 1989.

Alonso, William, ”Predicting Best With Imperfect Data, " Journal of the American
Institute of Planners 34, No. 4, 1968.

APPENDIX A

APPENDIX A

The data acquisition and reduction software for indirect cyclic load tensile test (six
inch diameter sample) is presented. The software was originally developed by the
Michigan Department of Transportation (MDOT) and was modified for the requirements
of this study.

252

2£i3

REM program revised March 6,1992, by Hamid
REM program to calibrate sensors and

REM perfore a constant cyclic load test

REM Program is Menu Driven

DIM DIOXIIS)

DIM A%(5000)

DIM DATAIXIIZODOI

COMMON SHARED DIOXt). DATA1%()

DECLARE SUB OBNRES (MDX, BYVAL DUMMYX, FLAGS)

IOADRX I ‘NSOO
C(18), V(18), PNT(100), XAXIS(100), DEV(18)

'I/D OBHRES base address

MEMBUFZITB), sxtrcst19). sxrpstta), EFV(18), rcvrta), rosrvr18), roerv1t1a), DEN(18)
vuru1r4, 18), vuruzck, 18), VMAX(4, 18), EFN(18), rcur18), roerutta)

vsanpxrt, 18), PMAbe, 18), PMIN(4, 18), AVGLOAD(18), dd(18), NN(18)

scurxrs, 18), anosxta, 18), RDELTA%(4, 18), VV(18), VV1(18), AA(18), TDD(18)
unaxrt, 18), unrutb, 18), NDELTAXl‘, 18), uuuc18), vvvr18), AAA(18)

DIM
DIM
DIM
DIM
DIM
DIM

NB(4, 18),
RB(4, 18).
vars, 18),
vnrusr18).
unaxstta).
RMAXSt18).

NC(4, 18), RMAth, 18), RMIN(4, 18), DERITB), EFR(18)

RC(4, 18), vnrurb, 18), VDELTAXI4, 18). FGRITB), TDEFR(18)

vets, 18), PMAXS(18), rurasrta), vnaxsr18), MRI18), MR1(18). EEIiO). EE1t18)
voersxr18), vasr18), vcsr18), Has<18). uur18), ruur18), EEN(18)

NMINS(18), HDELTSXIiB), ucst18), cccrta), urc1t18), urczr18)

RMINS(18), RoELrsx(18). RBS(18), RCS(18), orvr18)

NCSN(18), VAbe, 18), N1AB(4, 18), NZAB(4, 18), R1A8(6, 18), RZAB(‘, 18)
VABS(18), N1ABS(18), NZABSfTB), R1ABSf18), R2ABS(18), RFGI(18), RFGZ(18)
de(200)

DIM SLOPEXI3)

MEMBUFXII) ' &N4F00

MEMBUF%(2)
NEnsurxt3)
MEMBUFXf4)
MEMBUFXIS)
NENBUFxto)
MEMBUFXf7)
Renaurxra)
MEMBUFXIP)
MEMBUFNth) I CNEDOO
REM THIS IS A 3rd ORDER LON PAS BUTTERNORTN CASCADE FILTER
NC I .05
C I 1! I TAN(3.1415926# * NC)
a I 11 I (it + C) * 1| / (1! + C + C * 2)
A1 I 21: AA1 I 11
81 I (21 - 2! * C ‘ 2) I (1! + C + C ‘ 2)
02 I (ll - C + C ‘ 2) I (1| + C + C G 2)
881 I (1 - C) / (11 + C)
SCREEN 0, 0, 0: NIDTN 80
50 TYPE TRANSDUCER
CN AS INTEGER
UNIT AS STRING * 10
C AS SINGLE
DATEI AS STRING * 10
MPG as STRING * 16
SN AS STRING * 10
LOCATION AS STRING * 14
END TYPE
DIM DUCERITEM AS TRANSDUCER

99 REM CLS

'Memory Buffer address OBNRES - 128k
I GNSOOD
I GNSFOD
I lubOOO
GN6FOO
CNADDO
888000
I INCODD
I 8ND000

PRINT : PRINT : PRINT : PRINT : PRINT
100 PRINT "Constant Cyclic Load Program"

110 PRINT
120 PRINT
130 PRINT
140 PRINT
150 PRINT
160 PRINT

PRINT
170 PRINT
180 PRINT
200 PRINT
210 PRINT
215 INPUT

“Select Task"

“1.
'2.
'3.
'4.
'5.
“6.
'7.

Calibrate all Transducers“
View Transducer Calibretions"
Change Calibration"

Run Test"

Vieu Raw Data“

Process Date on Disk"

Exit Program”

“Select Task“

TS

TASK I VAL(T$)

254

IF TASK <I 0 THEN 215
IF TASK > 8 THEN 215
ON TASK GOSUB 1000, 2000, 3000, 4000, 4675, 15000, 9000
GOTO 99

1000 REM SUBROUTINE TO CALIBRATE TRANSDUCERS

1005 GOSUO 7010 'INIT AID

1010 CLS

1020 PRINT “Sensor Calibration"

1030 PRINT

1040 PRINT "Input Sensor Unit of Measurement - Load:Lbs, Displacement:Inches"

1050 INPUT UNITS

1060 PRINT "Input Sensor Manufacturer“

1070 INPUT MFGS

1080 PRINT “Input Sensor Serial Number?“

1090 INPUT SNS

1100 PRINT I‘Input Sensor Location?“

1110 INPUT LOCATIONS

1120 PRINT "Nhat channel will this sensor be connected to?"

1130 INPUT CH1: IF CH! >I 7 THEN 1120: IF CHX < 0 THEN 1120

1140 PRINT “Zero transducer and type any key“

1150 DUMS I INPUTS(1)

1160 GOSUB 1600 ' READ DATA ON CHANNEL (DAT1)

1165 DAT1 I val1x

1170 PRINT "Now apply load or move known distance"

1180 PRINT “Type any key when ready“

1190 DUMS I INPUTSt1)

1200 60808 1600 ' READ CAL SIGNAL GI CHANNEL (DATZ)

1205 DATZ I vallx

1210 PRINT "Type in “; UNITS; “ Applied“

1220 INPUT Cal .

1230 C(CHZ) I ABStDATZ - DAT1) I Cal 'VOLTS/UNIT

1235 C(CHX) I C(CHX) I 3276

12040 PRINT “SENSOR CALIBRATION IS: “; C(CHX); “ VOLTS/“; UNITS

1250 PRINT

1260 PRINT "If satisfactory type Y otherwise N '

1270 DUB I UCASES(INPUTS(1))

1280 IF DUMS I IN“ THEN 1140

1290 IF DUIS I 'Y" THEN 1350

1300 GOTO 1260

1310 REM STORE SENSOR DATA IN CAL FILE

1315 REM CALDAT IS PERMANENT FILE FOR DATA

1330 REM EACH SENSOR REQUIRES Tin LINES

1340 REM THEY ARE STmED IN NLMERICAL MOER

1350 CLOSE 2: OPEN “CALDAT” FOR RANDOM AS 2 LEN I LEN(DUCERITEM)

1352 DUCERITEM.CH I CH1: DUCERITEM.UNIT I LEFTStUNITS, 10): DUCERITEM.C I C(CHX)
DUCERITEM.DATE1 I DATES: DUCERITEM.MFG I LEFTS(MFGS, 14): DUCERITEM.SN I LEFTSISNS, 10)
DUCERITEM.LOCATION I LOCATIONS

1400 CH! I CH1 + 1

1420 PUT #2, CH2, DUCERITEM

1440 CLOSE 2

1450 PRINT I'Are there more sensors to calibrate? (Y-N)“

1460 DUMS I UCASEStINPUTSt1))

1470 IF DUMS I "N" THEN 1500

1480 IF DUMS I “Y“ THEN 1520

1490 GOTD 1450

1500 PRINT “Done with sensor calibration"

1510 CLS : GOTO 100

1520 GOTO 1010

1599 REM READ AID

1600 MD: I 1

1610 0102(0) I CH3: 0102(1) I CH!

1620 CALL asunesrmx, VARPrRroroxton. run)

1630 IF FLAGK > 0 THEN 7210

1640 val1 I 0

1650 M03 I 3

1660 FOR I I 1 TO 10

1670 CALL DBHREStMDX, VARPTRtDIOXt0)). FLAGS)

1671 LPRINT 0102(1). vali, 0102(0)

1672 velZ I 010%(0) / 1000

1680 vell I vall + val2

1690 NEXT I

255

1700 val1x I (val1 I 10) * 1000'AVERAGE

1701 LPRINT val1x

1710 RETURN

1990 REM VIEN CALIBRATION DATA

2000 CLOSE1: OPEN "CALDAT' FOR RANDOM AS 1 LEN I LENtDUCERITEM)
NuIberOfRecords I LOF(1) \ LENIDUCERITEM)

CLS

PRINT “CH UNITS CAL FACTOR DATE MFG S/N LOCATION"
PRINT ’

FMIS I "IN \ \#####.####f \ \ \ \ \ \ \

Fat .1 I 1 TO NurberOfRecords
GET #1, J, DUCERITEM

PRINT USING FMIS; DUCERITEM.CH: DUCERITEM.UNIT: DUCERITEM.C; DUCERITEM.UATE1; DUCERITEM.MFG:

DUCERITEM.SN; DUCERITEM.LOCATION
2090 NEXT J
2100 CLOSE 1
PRINT "STRIKE ANY KEY TO CONTINUE“: JUNKS I INPUTS(1)
2110 RETURN
2990 REM MODIFY EXISTING CALIBRATION VALUES
3000 CLS
3010 PRINT 'Uhat channel do you want to modify?I
3020 CHX I VAL(INPUTS(1)): CHx I CHX + 1
3030 CLOSE 1: OPEN "CALDAT' FOR RANDOM AS 1 LEN I LENfDUCERITEM)
NunberOfRecords I LOF(1) I LENCDUCERITEM)
IF CNX > NumberOfRecords THEN 3070
3050 GOTO 3100
3070 PRINT "NO DATA AVAILABLE FOR CHANNEL “; CHX - 1: GOTO 3010
3100 GET #1, CH3, DUCERITEM
PRINT DUCERITEM. CH; “ '; DUCERITEM. UNIT; “ '; DUCERITEM.C; ' ';
PRINT DUCERITEM.DATE1; I '; DUCERITEM. MFG; “ '; DUCERITEM.SN; ' “; DUCERITEM. LOCATION
3180 PRINT
3190 PRINT "TYPE IN NEH CALIBRATION VALUE "
3200 INPUT C(CNX): DUCERITEM.C I C(CNX)
3230 PUT #1, CHX, DUCERITEM
3350 CLOSE 1: RETURN
3990 REM RUN TEST
4000 CLOSE 1: OPEN 'CALDAT“ FOR RANDOM AS 1 LEN I LEN(DUCERITEM)
NCH I LOF(1) \ LENtDUCERITEM)
FOR I I 1 TO NCH
GET #1, I, DUCERITEM
CH1 I DUCERITEM.CH: UNITS I DUCERITEM.UNIT: C(I - 1) I DUCERITEM.C
DATE1S I DUCERITEM.DATE1: MFGS I DUCERITEM.MFG: SNS I DUCERITEM.SN
LOCATIONS I DUCERITEM.LOCATION
NEXT I
GOSUB 16000
CLS
4010 PRINT “CONSTANT CYCLIC LOAD TEST”
4020 PRINT
4025 DATE1S I DATES
4030 PRINT “INPUT SAMPLE NUMBER“I
4040 INPUT SAPNOS
4050 PRINT "PROJECT # 7'
4060 INPUT PROJS
4070 PRINT “MATERIAL DESCRIPTION 7“
4080 INPUT MATDS
PRINT "INPUT SPECIMEN LENGTH (inches)'
INPUT SPLNTH
PRINT "INPUT SPECIMEN DIAMETER finches)“
INPUT SPDIA
PRINT “INPUT CHAMBER TEMP..F 7'
INPUT TEMPF
4110 CLS
PRINT “HON MANY CREEP TESTS FOR SAMPLE ?(MAXI1O)“
INPUT SAPERX
PRINT “TYPE "; SAPERX; ' VALUES FOR NUMBER OF LOAD CYCLES BETNEEN CREEP MEASUREMENTS"
FOR I I 1 T0 SAPERX: INPUT SKIP8(I): NEXT I
REM ACCUMULATE COUNT FOR COUNTER
SAPERX I SAPERN + 1'ADD 1 FOR INITIAL CONDITIONS
SKIPC‘I1) I 20'INITIAL DELAY BEFORE COLLECTING DATA
SKIPCGfZ) I SKIP&(1)
FOR I I 3 TO SAPERX

256

SKIPC&(I) I SKIPC&(I - 1) I SKIP&(I - 1)
NEXT I
test I 0' INITIALIZE NUMBER OF CREEP TESTS
4180 PRINT “HON MANY CYCLES OF DATA IN EACH CREEP TEST 7“
4190 INPUT SP2
IF SP2 > 10 THEN 4195 ELSE 4200
4195 PRINT “MAXIMUN LOAD CYCLES IS 4“: GOTO 4180
4200 PRINT "NHAT IS THE LOAD THRESHOLD FOR DATA COLLECTION ?"
4210 INPUT thres
4215 thrs I three * C(O) * 3276
thrs2 I thrs
4220 CLS
4230 PRINT “INSURE THAT ALL SENSORS ARE OPERATIONAL"
4240 PRINT “INSURE THAT ALL SENSOR CALIBRATIONS ARE COMPLETE“
4250 PRINT "AND ON APPROPRIATE CHANNEL“
PRINT
PRINT “DO YOU NANT T0 VIEU DATA(Y-N) 7'
VIENS I UCASES(INPUTS(1))
IF VIENS I “Y“ THEN 4260
PRINT “PLACE A FORHATED DISK IN DRIVE 8“
PRINT “HIT ANY KEY TO CONTINUE“: DUMS I INPUTS(1)
4260 GOSUB 7010 'INITIALIZE AID MODULE
NXTCNT2 I -1 'COUNTI 65536
GOSUB 6500 'INITIALIZE COUNTER
0102(0) I 1
M02 I 12'READ COUNTER
CALL DBHRES(MD2, VARPTR(DIO2(0)), FLAG2)
IF FLA62 > 0 THEN 7210
FSTCT2 I DIO2(1)'COUNTER DOESN"T RESET UNTIL 1ST PULSE
CLS : LOCATE 2, 30: COLOR 0, 7: PRINT "PROCEED UITH TEST": COLOR 7, 0
LOCATE 5, 35: COLOR 0, 7: PRINT “START MTS“: COLOR 7, 0
4300 M02 I 12
0102(0) I 1 'READ COUNTER
CALL OBHRES(MD2, VARPTR(DIO2(0)), FLAG2)'sit here until 1st pulse
4500 IF FLAG2 > 0 THEN 7210
IF 0102(1) I FSTCT2 THEN 4300
FG CP I 1 TO SAPERX'SEE LINE 5410 Fm NEXT
CLS : LOCATE 2, 30: COLOR 0, 7: PRINT "PROCEED UITH TEST“: COLOR 7, 0
REM START TO COLLECT DATA
LOCATE 5, 35: COLOR 0, 7: PRINT I'START MTS“: COLOR 7, 0
4501 0102(0) I 1
M02 I 12
CALL OBHRES(MD2, VARPTR(DIO2(0)), FLAG2)
IF FLAG2 > 0 THEN 7210
IF CNTT < 65535 THEN
IF 0102(1) < 0 THEN
COUNT I 65536 + 0102(1)
ELSE
COUNT I 0102(1)
END IF
COUNT I 65536 - COUNT
END IF
IF CNTT >I 65535 AND CNTT < 131071 THEN
IF 0102(1) <I 0 THEN
COUNT I 65536 + 0102(1)
ELSE
COUNT I 0102(1)
END IF
COUNT I 131072 - COUNT
IF 0102(1) I 1 AND CNTT I 65535 THEN
COUNT I 65535
END IF
END IF
IF CNTT >I 131071 AND CNTT < 196607 THEN
IF 0102(1) <I 0 THEN
COUNT I 65536 + 0102(1)
ELSE
COUNT I 0102(1)
END IF
COUNT I 196608 - COUNT
IF 0102(1) I 1 AND CNTT I 131071 THEN

257

COUNT I 131071
END IF
END IF
IF CNTT >I 196607 AND CNTT < 262143 THEN
IF DI02(1) <3 0 THEN
COUNT I 65536 I DI02(1)
ELSE
COUNT I 0102(1)
END IF
CGJNT I 262144 - CGJNT
IF 0102(1) I 1 AND CNTT I 196607 THEN
COUNT I 196607
END IF
END IF
IF CNTT >I 262143 AND CNTT < 327679 THEN
IF DI02(1) <I 0 THEN
COUNT I 65536 + DI02(1)
ELSE
COUNT I DI02(1)
END IF
COUNT I 327680 - COUNT
IF 0102(1) I 1 AND CNTT I 262143 THEN
COUNT I 262143
END IF
END IF
IF CNTT >8 327679 AND CNTT < 393215 THEN
IF 0102(1) <I 0 THEN
COUNT I 65536 + DIO2(1)
ELSE
COUNT I 0102(1)
END IF
COUNT I 393216 . COUNT
IF 0102(1) I 1 AND CNTT I 327679 THEN
COUNT I 327679
END IF
END IF
IF CNTT >I 393215 AND CNTT < 458751 THEN
IF 0102(1) <I 0 THEN
COUNT I 65536 + 0102(1)
ELSE
COUNT I DI02(1)
END IF
COUNT I 458752 - COUNT
IF DIOX(1) I 1 AND CNTT I 393215 THEN
COUNT I 393215
END IF
END IF '
IF CNTT >I 458751 AND CNTT < 524287 THEN
IF DI02(1) <I 0 THEN
COUNT I 65536 + DI02(1)
ELSE
COUNT I DI02(1)
END IF
COUNT I 524288 - COUNT
IF 0102(1) I 1 AND CNTT I 458751 THEN
COUNT I 458751

IF CNTT >I 524287 AND CNTT < 589823 THEN
IF D102(1) <I 0 THEN
COUNT I 65536 + DI02(1)
ELSE
COUNT I 0102(1)
END IF
COUNT I 589824 - COUNT
IF DI02(1) I 1 AND CNTT = 524287 THEN
COUNT I 524287
END IF
END IF
IF CNTT >I 589823 AND CNTT < 655359 THEN
IF DIOX(1) <8 0 THEN

258

CGJNT I 65536 I 0102(1)
ELSE
CGINT I “02(1)
END IF
C(INIT I 655360 . CNNT
IF DI02(1) I 1 AND CNTT I 589823 THEN
C(IHIT I 589823
END IF
END IF
IF CNTT >I 655359 AND CNTT < 720895 THEN
IF DI02(1) <I 0 THEN
MINT I 65536 + 0102(1)
ELSE
CMT I DI02(1)
Ell) IF
CGINT I 720896 - CGJNT
IF DI02(1) I 1 AND CNTT I 655359 THEN
CGJNT I 655359
END IF
END IF
IF CNTT >I 720895 AND CNTT < 786431 THEN
IF 0102(1) <I 0 THEN
CGJNT I 65536 + 0102(1)
ELSE
C(IJNT I DI02(1)
END IF
C(IJNT I 786432 - COJNT
IF DI02(1) I 1 AND CNTT I 720895 THEN
C(IINT I 720895
END IF
END IF
IF CNTT >I 786431 AND CNTT < 851967 THEN
IF 0102(1) <I 0 THEN
CWNT I 65536 + DI02(1)
ELSE
C(IJNT I 0102(1)
END IF
CGNIT I 851968 - CGINT
IF DI02(1) I 1 AND CNTT I 786431 THEN
CGRIT I 786431
END IF
END IF
IF CNTT >I 851967 AND CNTT < 917503 THEN
IF 0102(1) <I 0 THEN
CGJNT I 65536 I DI02(1)
ELSE
CGJNT I DI02(1)
END IF
C(IJNT I 917504 - COJNT
IF 0102(1) I 1 AND CNTT I 851967 THEN
CON" I 851967
END IF
END IF
IF CNTT >I 917503 AND CNTT < 983039 THEN
IF 0102(1) <I 0 THEN
CGNIT I 65536 4' 0102(1)
ELSE
counr I DI02(1)
END IF
C(IJNT I 983040 - CWNT
IF 0102(1) I 1 AND CNTT I 917503 THEN
CONT I 917503
END IF
END IF
IF CNTT >I 983039 AND CNTT < 1048575 THEN
IF DI02(1) <I 0 THEN
MINT I 65536 + DI02(1)
ELSE
CENT I 0102(1)
EDD IF
CWNT I 1048576 - CWNT

4502
4503

4504
4505

4613

4615

4672
4673

4675

1255’

IF 0102(1) I 1 AND CNTT I 983039 THEN

CGINT I 983039

END IF

END IF

CNTT I COUNT

LOCATE 8, 30: PRINT 'PULSES COUNTED I '; CNTT

PRINT CP, CNTT, SKIPC&(CP)

IF CNTT < SKIPC&(CP) THEN 4501 'DID NOT REACH SKIP
REM DID REACH C(IINT

NXTCNT2 I 0102(1)'SAVE COUNT FOR NEXT CYCLE

N2 I SP2 * 6 * 200 'TOTAL NUMBER OF SAMPLES
Fm I I 1 TO SP2

M02 I 1: 0102(0) I 0: 0102(1) I 0

CALL DBHRES(MD2, VARPTR(DIO2(0)). FLAGE2)

M02 I 3

CALL OBHRES(MD2, VARPTR(0102(0)), FLAGE2)

BACK2(1) I DI02(0)

CALL DBHRES(M02, VARPTR(DIO2(0)). FLAGE2)

BACK2(2) I 0102(0)

CALL 08HRES(II)2, VARPTR(DIO2(0)), FLAGE2)

BACK2(3) I 0102(0)

PRINT BACK2(1); BACK2(2); BACK2(3)

IF BACK2(3) > BACK2(2) AND BACK2(2) > BACK2(1) AND BACK2(3) >I thrs2 THEN
GOTO 4504

ELSE

GOTO 4503

END IF

M02 I 1: 0102(0) I 0: 0102(1) I 5

CALL 08HRES(MD2, VARPTR(DIO2(0)), FLAGE2)

M02 I 6 'SET UP TO READ DATA”

DI02(0) I 1200

DI02(1) I MEMBUF2(I) '128K
DI02(2) I

DIO2(3) I 0

0102(4) I O'CHANNEL GAIN

CALL DBHRES(M02, VARPTR(DIO2(0)), FLAG2)

IF FLA02 > 0 THEN 7210

M02 I 8 'SEE IF DONE
CALL OBHRES(M02, VARPTR(0102(0)), FLAG2)

1F FLAGX > 0 THEN 7210

IF 0102(1) I 0 THEN 4615 ELSE 4613

NEXT 1

PRINT " now ready to transfer eenory to array“
GOSUB 7010 'INITIALIZE AID FOR NEXT CYCLE

REM NXTCNT2 ISTART COUNT

GOSUB 6500 'INITIALIZE COUNTER FOR NEXT

REM NON PROCESS DATA

Fat 1 I 1 T0 SP2

M02 I 9 'TRANSFER MEMORY TO ARRAY
0102(0) I 1200: 0102(1) I MEMBUF2(I): 0102(2) I 0
0102(3) I VARPTR(DATA12(0)) + (I - 1) * 2 * 1200
0102(4) I 0

CALL OBHRES(M02, VARPTR(0102(0)). FLAGX)

1F FLAG > 0 THEN 7210

NEXT 1

GOSUB 6000 'STORE DATA ON DISK

IF VIENS I "N“ THEN 4700

PRINT “ 00 YOU NANT TO VIEU DATA ?(Y-N)"

DUMS I UCASES(1NPUTS(1))

1F DUMS I "N“ THEN 4700

PRINT “THERE ARE “; SP2; " LOAD CYCLES“

PRINT "NHAT CYCLE DO YOU NANT TO DISPLAY ?"

INPUT SCN2: J I 1200 * (SCN2 - 1)

LPRINT C(0); 0(1); C(2); C(3); C(4); C(5)

FOR N I 0 TD 1080 STEP 120

CLS

PRINT ' LOAD LONGTL-I LONGTL-Z HORIZ-1 HORIZIZ VERT“
PRINT ' # INCHES INCHES INCHES INCHES INCHES “
FOR L I 0 T0 114 STEP 6

I I U + L + J

00 I DATA12(I) / (8(0) * 3276): 01 I 0ATA12(I I 1) I (C(1) * 3276)

260

02 I OATA12(I I 2) I (C(2) * 3276): 03 I DATA12(I I 3) I (C(3) * 3276)
04 I DATA12(I I 4) I (C(4) * 3276): 05 I DATA12(I I 5) I (C(5) * 3276)
PRINT USING ' 882*.28 '; 00; : PRINT USING ' ###*.#######“; D1; 02; D3; 04;
PRINT USING “822*.222828“; 05
NEXT L
DUMS I INPUTS(1)
NEXT U
4677 PRINT ' DO YOU HANT TO VIEN MORE DATA ?(Y-N)“
DUMS I UCASES(1NPUTS(1))
IF DUMS I “N“ THEN 4700
IF DUMS I “Y“ THEN 4675
GOTO 4677
4680 REM DETERMINE MIN-MAX LOAD FOR EACH LOAD CYCLE
4700 CLS
DIPY2 I CP
PRINT “PROCESSING CREEP PERIOD '; DIPY2
4710 IF VIEUS I “N“ THEN 4725
' F .......... LOAD APPLIED..........:'
’ “RESULTS FOR SAMPLE I '; SAPNOS
’ "RESULTS FOR CREEP MEASUREMENT C '; CP
CCC I SKIPC&(test I 1)
' “CYCLE COUNT I“; CCC
l

4725 J I 0: K I 0
FOR H I 1 TO SP2
GOSUB 14000
PMAX I LMAX2 I (C(O) ' 3276)
PMIN I LMIN2 / (C(O) * 3276)
IF CMAX2 I 1 THEN 4750'ONLY ONE PEAK VALUE
POSS2 I POSS2 I CMAX2 I 2
4750 LOPOS2 I POSS2 'SAMPLE I OF PEAK LOAD(RELATIVE TO 200)
4760 IF VIENS I "N“ THEN 4782
I
' "MINIMUM LOAD I '; PMIN; ' FOR THE I; H; ' CYCLE“
' “MAXIMUM LOAD I '; PMAX; ' AT THE I'; POSS2; ' SAMPLE“
' “THERE ARE '; CMAX2; “MAX VALUES“
RLAX2 I BCNT2 I 6 + 1
' “THE RELAXATION TIME OCCURED AT THE '; RLAX2; “SAMPLE“
4782 RLAX2 I BCNT2 I 6 I 1
REM STORE DATA FOR CREEP ANALYSIS
PMAX(H, CP) I PMAX
PM1N(H, CP) I PMIN
BCNT2(H, CP) I BCNT2 '(RELAX ADDRESS)
LOPOS2(H, CF) I LOPOS2
J I J I 1200
NEXT H
IF VIENS I “N" THEN 4830
PRINT
4830 REM CALC VERTICAL DEFLECTION CH #5
PRINT “ PROCESSING VERTICAL DEFLECTION“
4832 IF VIENS I "N“ THEN 4833
GOTD 4833
LPRINT : LPRINT : LPRINT
LPRINT '..........VERTICAL DEFLECTION .......... “
LPRINT I'RESULTS FOR SAMPLE I '; SAPNOS
LPRINT “RESULTS FOR CREEP MEASUREMENT # '; CP
CCC I SKIPC&(test I 1)
LPRINT “CYCLE COUNT I '; CCC
4833 J I 0: K I 5
FOR H I 1 T0 SP2
GOSUB 14000
MIN1 I LMIN12 I (C(S) * 3276) 'PRE-LOAD MIN
VMIN2 I LMIN22 I (C(S) * 3276) 'POST-LOAD MIN
VMAX I LMAX2 / (C(5) * 3276)
01F1 I VMAX - VMIN1: DIF2 I VMAX - VMINZ
VSAMP2 I (POSS2 I CMAX2 I 2) - 1
4834 IF VIENS I “N” THEN 4838
GOTD 4838
4835 LPRINT
LPRINT “MAXIMUM VERTICAL DEFLECTION“
LPRINT ' (before/after load)I"; 01F1; “I"; DIF2; “FOR“; H; “CYCLE“

4838

4950
4960

4970

4980

4990

5000

261

LPRINT “MAXIMUM DEFLECTION OCCURED AT THE '; VSAMP2; “SAMPLE“
LPRINT “THERE ARE I; CMAX2; “MAX VALUES”

LPRINT “THE MIN VALUES HERE“; VMIN1; “I": VMINZ

LPRINT "THERE ARE“; CMIN12; “I“; CMIN22; “MIN SAMPLES"

REM NON STORE DATA FOR CREEP ANALYSIS

VMAX(H, CP) I VMAX

VMIN(H, CP) I VMINZ

VDELTA2(H, CP) I VSAMP2 - LDPOS2(H, CP)

OFFSET2 I BCNT2(H, CP) I (VDELTA2(H, CP) - 1) * 6'GET DISPLACEMENT OB(ADDRESS)
tr OFFSET2 > 1194 THEN OFFSET2 I 1194

vstu, CP) I DATA12(OFFSET2 + K I J) / (C(S) I 3276)

VC(H, CP) I VMINZ 'POST-LOAD MIN

VAB(H, CP) I AAVG I (C(S) * 3276)'ABSOLUT POSITION OF SENSOR AFTER LOAD
J I J I 1200

NEXT H

IF VIEHS I 'N' THEN 4950

REM DETERMINE HORIZONTAL MOVEMENT

PRINT ' PROCESSING HORIZONTAL DEFLECTION"

IF VIENS I “N” THEN 4970

GOTO 4970

LPRINT : LPRINT : LPRINT

LPRINT “ .......... HORIZONTAL DEFLECTION .......... "

LPRINT “RESULTS FOR SAMPLE # I“; SAPNOS

CCC I SKIPC&(test I 1)

LPRINT “CYCLE COUNTI“; CCC

J I 0

FOR N I 1 10 SP2

K I 3 'FIRST XDUCER

GOSLB 14000

H1MAX I LMAX2 / (C(3) * 3276)

H1MIN I LMIN12 I (C(3) * 3276) 'PRE-LOAD MIN FOR 1ST XDUCER
H2MIN I LMIN22 / (C(3) * 3276) 'POST-LOAD MIN FOR 1ST XDUCER

H1A8 I AAVG / (C(3) * 3276)
P0512 I POSS2: C1MAK2 I CMAX2
C1MIN2 I CMIN12: C2MIN2 I CMIN22
K I 4 ’NOU SECOND XDUCER

GOSUB 14000

HZMAX I LMAX2 I (C(4) * 3276)

H12MIN I LMIN12 I (C(4) * 3276) ’PRE-LOAD MIN FOR 2ND XDUCER
N22MIN I LMIN22 I (C(4) * 3276) 'POST-LOAD MIN FOR 2ND XDUCER

HZAB I AAVG I (C(4) * 3276)

P0522 I POSS2: C2MAX2 I CMAX2

C12MIN2 I CMIN12: C22MIN2 I CMIN22

REM NON COMBINE THE THO XDUCER SIGNALS

HORI I H1MAX - H1MIN I H2MAX - H12MIN’PRELOAD

HOR2 I H1MAX - H2MIN I HZMAX - H22MIN'P05T L0AD'(DEIEF)

DIS3 I H1MAX - H1MIN 'Preload DISP SENSOR 3

DIS4 I H2MAK - H12MIN'PreLOAD DISP SENSOR 4

dis3p I H1MAX - H2MIN'postload disp sensor 3

dis4p I HZMAX - H22MIN'postload disp sensor 4

LPRINT "DIS3 '; DIS3; dis3p; "DIS4 '; DIS4; dis4p

IF VIENS I “N“ THEN 4990

GOTO 4990 '

LPRINT

LPRINT “MAXIMUM HOR...DISPI'; HOR1; “I“; HOR2; “FOR“; H; "CYCLE(before/after load)“
P0512 I P0512 I C1MAX2 / 2 - 1 'SHIFT T0 MIDDLE 0F PEAK
POS22 I P0522 I C2MAX2 I 2 - 1

POSS2 I (P0512 I P0522) I 2 'GET AVERAGE

IF VIEUS I “N“ THEN 5000

GOTO 5000

LPRINT “MAX HORZ DISP OCCURED AT '; P0512; “I“; P0522; “SAMPLES(SENSORl/SENSORZ)“
LPRINT ”THERE ARE“; C1MAX2; “I”; C2MAX2; “MAX SAMPLES“

LPRINT "THERE ARE"; C1MIN2; ”l“: C12MIN2; "MIN SAP BEFORE LOAD“
LPRINT "THERE ARE“; C2MlN2; “I“; C22MIN2; “MIN SAP AFTER LOAD"
REM NON STORE SAMPLES FOR CREEP ANALYSIS

HMAX(H, CP) I H1MAX I HZMAX

HMIN(H, CP) ' H2MIN I H22MIN 'KDUCER OUTPUT

HDELTA2(H, CP) I POSS2 - LDPOS2(H, CP)

0FFSET2 I BCNT2(H, CP) I (HDELTA2(H, CP) - 1) * 6'GET DISP a B
IF OFFSET2 > 1194 THEN 0FFSET2 I 1194

H81 I 0ATA12(0FFSET2 I 3 I J) I (C(3) * 3276)

5130
5140

5150

5160

5170

5180

5200

262

HBZ I DATA12(OFFSET2 I 4 I J) I (C(4) * 3276)

HB(H, CP) I H01 I H02 'POINT D XDUCER OUTPUT

NC(H, CP) I H2MIN I H22MIN 'POINT C XDUCER OUTPUT (TOTAL P05T-LOAD MIN)
M1AB(H, CP) I HIAB ’ABSOLUTE DISPLACEMENTS

H2AB(H, CP) I HZAB 'FOR PLASTIC MODULUS

J I J I 1200

NEXT N

REM GET LONGITUDINAL MOVEMENT

PRINT ' PROCESSING LONGITUDINAL DEFLECTION“

IF VIEHS I IN“ THEN 5150

GOTO 5150

LPRINT : LPRINT : LPRINT

LPRINT ' .......... LONGITUDINAL DEFLECTION .......... “

LPRINT IRESULTS FOR SAMPLE # I “; SAPNOS

CCC I SKIPC&(test I 1)

LPRINT “CYCLE COUNTI "; CCC

LPRINT

J I 0

FOR N I 1 TO SP2

K I 1 'FIRST XDUCER

GOSUB 14000

RTMAx I LMAX2 I (C(I) * 3276)

R1MIN I LMIN12 I (C(I) * 3276) 'PRE-LOAD MIN FOR 15T XDUCER
RZMIN I LMIN22 / (0(1) * 3276) 'POST-LOAD MIN FOR IST XDUCER
R1AB I AAVG I (C(1) * 3276)

P0512 I POSS2: C1MAX2 I CMAX2

C1MIN2 I CMIN12: C2MIN2 I CMIN22

K I 2 'NOU SECOND XDUCER

GOSUB 14000

RZMAX I LMAX2 I (C(2) ' 3276)

R12MIN I LMIN12 / (C(2) * 3276) 'PRE-LOAD MIN FOR 2ND XDUCER
R22MIN I LMIN22 I (C(2) * 3276) 'POSTILOAD MIN FOR 2ND XDUCER
RZAB I AAVG / (C(2) ' 3276)

P0522 I POSS2: C2MAX2 I CMAX2

C12MIN2 I CMIN12: C22MIN2 I CMIN22

REM NON COMBINE THE THO XDUCERS

RAD1 I R1MAX - R1MIN I RZMAX - RTZMIN 'PRE LOAD

RADZ I RTMAX - RZMIN I RZMAX - R22MIN 'POST LOAD(DEIEF)

IF VIEHS I “N“ THEN 5170

GOTO 5170

LPRINT “MAXIMUM RAD DISPI“; RADI; “I“; RADZ; “FOR"; H; "CYCLE(before/after load)”
P0512 I P0512 I C1MAX2 I 2 - 1 'SHIFT T0 MIDDLE 0F PEAK
POSZX I POSZX I CZHAxx I 2 - 1

P0552 I (P0512 I P0522) I 2

IF VIEUS I “N“ THEN 5180

GOTO 5180

LPRINT ”MAX LONGITUDINAL DISP OCCURED AT“; P0512; "I“; P0522; '5AMPLES(SENSORI/SENSORZ)“
LPRINT “THERE ARE”; C1MAX2: “I“; C2MAX2; “MAX SAMPLES“

LPRINT "THERE ARE“; C1MIN2; ”I“; CIZMIN2; “MIN 5AMP BEFORE LOAD“
LPRINT “THERE ARE“; C2MIN2; "I“; C22MIN2; “MIN 5AMP AFTER LOAD“
REM NON STORE SAMPLES FOR CREEP ANALYSIS

RNAX(H, CP) I R1MAX I RZMAX

mama, CP) I RZMIN I R22MIN

RDELTA2(H, CP) I P0552 - LDPOS2(H, CP)

OFFSET2 I BCNT2(H, CP) I (RDELTA2(H, CP) - 1) * 6

IF OFFSET2 > 1194 THEN OFFSET2 I 1194

RBI I DATA12(0FF5ET2 I 1 I J) I (C(I) ‘ 3276)

RBZ I DATA1%(0FFSETX I 2 I J) / (C(2) * 3276)

RB(H, CP) I R81 I RBZ

RC(H, CP) I RZMIN I R22MIN 'POINT C XDUCER OUTPUT (TOTAL P05T-LOAD MIN)
R1AB(H, CP) I RIAB 'ABSOLUTE LONGITUDINAL DISPLACEMENT

R2AB(H, CP) I RZAB 'FOR PLASTIC DEFORMATION

J I J I 1200

NEXT H

IF PLOTS I ”Y“ THEN 5500

REM DONE NITH TEST

REM DETERMINE IF ANY MORE CREEP TESTS TO 00

test I test I 1

IF test I SAPERX THEN 5415

IF P05T I 1 THEN 15150 'P05T PROCESS NEXT CREEP CYCLE

IF VIEN5 I “N“ THEN 5410

5410
5415

5420

5425

2fi3

PRINT

PRTNT “HIT ANY KEY TO START NEXT CREEP TEST“
PRTNT "AND START NTS-

DUMS I INPUTS(1)

NEXT CP

FOR K I 1 To 5

LOCATE 2‘, 30: COLOR o, 7

PRINT ICREEP TEST COMPLETE": COLOR 7, 0

FOR L I 1 TO 1000: NEXT L

LOCATE 24, 30: PRINT “CREEP TEST COMPLETE“

FOR L I 1 TO 1000: NEXT L

NEXT K

CLS

CLOSE 3 'DISK FILE CONPLETE

REM PROCESS CREEP DATA

DIM EL2(10)

CLS

PRINT ----- FINAL SPECTNEN RESULTS“

PRINT

FOR CP I 1 TO SAPER2 'SEE LINE 5426 IT FOR NEXT
PRTNT IAVERACES FOR i“; CP; “CREEP PERTODI

PRINT

PRINT INAX LOAD FOR EACH LOAD CYCLE FOLLOUS“

FOR N I 1 TO SP2

PRINT H, PMAX(H, CP)

NEXT N

FOR T I 1 TO SP2: EL2(I) I 0: NEXT I'ZERO ARRAY
PRTNT

PRINT IRON NANY CYCLES DO You NANT TO ELIMINATE?“
TNPuT R2

DTV I SP2 - R2'NUMB OF VAR IN AVG.

IF Rx . o TNEN 5425

PRTNT ITYPE IN THE“; R2; ICYCLE NUNEERS-

FOR I I 1 TO R2

INPUT EL2(I)'ARRAY INDEX FOR CYCLE TO BE ELIMINATED FROM AVERACE
NEXT T

REM NON CONPLETE RESULTS

REM COMPUTE AVERAGES OF LOAD CYCLE DATA FOR EACH CREEP TEST
FOR N I 1 TO SP2

FOR 2 I 1 TO SP2

TF EL2(Z) ' H THEN 5426

NEXT 2

PMAX5(CP) I PNAXS<CP> I PNAX<N, CP) I DTV
PMINS(CP) I PMINS(CP) I PMIN(H, CP) I DIV
VMAX5(CP) I VMAXS(CP) I VNAX(N, CP) I DTV
VMINS(CP) I VMINS(CP) I VMIN(H, CP) / DTV
VDELTS2(CP) I VDELTS2(CP) I VDELTA2(H, CP) / DTv
VBS(CP) I VBS<CP) I VBTN, CP) I DTV

VCS(CP) I VC5(CP) I VC(H, CP) 1 DIV

VABS(CP) I VABS(CP) I VA3(N, CP) I DIV
HMAXS(CP) I HMAX5(CP) I HMAX(H, CP) / DIV
HMINS(CP) I HMINS(CP) I HMIN(H, CP) / DTV
HDELTS2(CP) I HDELTS2(CP) I HDELTA2(H, CP) / DIV
HBS(CP) I HBS(CP) I HB(H, CP) I DTV

HCS(CP) I HC5(CP) I HC(H, CP) I DIV

H1ABS(CP) I H1ABS(CP) I H1AB(H, CP) / DIV
H2ABS(CP) I H2ABS(CP) I H2AB(H, CP) I DIV
RNAXS(CP) I RMAXS(CP) I RMAX(H, CP) I DIV
RMINS(CP) I RMINS(CP) I RMIN(H, CP) / DIV
RDELTSX(CP) I RDELT52(CP) I RDELTAxTN, CP) / DTV
RBS(CP) I RBS(CP) I RB(H, CP) I DIV

RCS(CP) I RCS(CP) I RC(H, CP) I DTV

R1ABS<CP) I R1ABS(CP) I R1AB(H, CP) I DIV
R2AES<CPT I RZADSTCP) I R2AB(H, CP) / DTV
DIV(CP) I ON

5426 NEXT H

NEXT CP

REM NON COMPLETE CREEP CALCULATIONS

CLS

LOCATE 14, 20: PRINT “PLACE PRINTER 0N -LINE.....FONT 8“
LOCATE 16, 20: PRINT "TYPE ANY KEY UHEN READY”

5427

5428

5430

5431

5437
5438

5439

5440
5441

5442

5443

264

DUM3 I INPUT3(1)

DIVX I DIV(I)

PLOAD I PMAXS(1) ‘ PMINS(1)

IF VIEU3 I “N“ THEN 5428

LPRINT : LPRINT : LPRINT : LPRINT

DIVX I DIV(1)

LPRINT "RESULTS OF CREEP TESTS“

LPRINT

PLOAD I PMAXSII) ’ PMINSII)

LPRINT "INITIAL CONDITIONS“

LPRINT ”AVG CYCLIC LOAD HAS“; PLOAD

LPRINT “PRELOAD HAS“; PMINS(1)

LPRINT I'NUMBER OF LOAD CYCLES FOR INITIAL DATAI 20“
LPRINT “NUMBER OF USEABLE LOAD CYCLES I“; DIVX

LPRINT

LPRINT

R13 I "VERTICAL DEFORMATION“

R23 I ' '''''' DELTAI“

R33 I ' ''''' RESILIENT DEFORMATION I“
R43 I ' ------ VISCOELASTIC DEFORMATION I“
R53 I ' ------ PLASTIC DEFORMATION I"

R63 I “HORIZONTAL DEFORMATION I“

R73 I "LONCITUDINAL DEFORMATION I“

R83 I “TOTAL DEFORMATION I “

FOR CP I 2 TO SAPERX

DIVK I DIV(CP): CRNX I CP - 1

CCC(CP) I SKIPC&(CP)

AVCLOAD(CP) I PMAXS(CP) ' PMINS(CP)

IF VIEU3 I “N” THEN 5431

LPRINT “RESULTS FOR CREEP TEST“; CRNK; ' CYCLE COUNTI“; CCC(CP)

LPRINT “NUMBER OF LOAD CYCLES IN AVGI“; DIVX

LPRINT “AVERAGE CYCLIC LOAD I '; AVGLOAD(CP)

LPRINT VHAXS(CP); VBS(CP); VCSCCP); VABS(1)

DEV(CP) I ABS(VMAXS(CP) ' VBS(CP)): VV(CP) I DEV(CP) * SPLNTH I AVGLOAD(CP)
VV1(CP) I AVGLOAD(CP) I (SPLNTH * DEV(CP)) 'FOR MR CALCULATION USING VERT SENSOR ONLY
EFV(CP) I ABS(VBS(CP) ‘ VCSICPII: VVV(CP) I EFV(CP) ‘ SPLNTH I AVGLOAD(CP)
TDEFV(CP) I DEV(CP) I EFV(CP)

TDEFV1(CP) I AVGLOAD(CP) I (SPLNTH * TDEFV(CP))

REM DETERMINE PLASTIC DEFOMATION

FCV(CP) I ABSCVABS(1) ' VABS(CP)) 'VERTICAL PLASTIC DEFORMATION

IF VIEUS I “N” THEN 5439

LPRINT R13

LPRINT R23; VDELTSN(CP); “SAMPLES"

LPRINT R33; DEV(CP)

LPRINT R63; EFV(CP)

LPRINT R53; FGV(CP)

LPRINT R83; TDEFV(CP)

LPRINT

REM PRINT “TYPE ANY KEY TO CONTINUE“

REM DUM3 I INPUT3(1)

CLS 'NON DO HORIZONTAL

DEHICP) I ABS(HMAXS(CP) ' HBS(CP)): HH(CP) I DEH(CP) * SPLNTH I AVGLOAD(CP)
EFH(CP) I ABS(HBS(CP) ' HCSICP)’: HHH(CP) I EFH(CP) * SPLNTH I AVCLOAD(CP)
REM DETERMINE HORIZONTAL PLASTIC DEFORMATION

HFG1(CP) I (H1ABS(1) ' H1ABS(CP))

HFGZCCP) I (HZABS(1) ' HZABS(CP))

FGH(CP) I ABS(HF61(CP) I HFCZ(CP)) 'TOTAL HORIZONTAL PLASTIC DEFORMATION
TDEFH(CP) I DEH(CP) I EFH(CP)

IF VIEN3 I “N" THEN 5443

LPRINT R63

LPRINT R23; HDELTSX(CP)

LPRINT HHAXS(CP); HBS(CP); HCS(CP)

LPRINT R33; DEH(CP)

LPRINT R43; EFH(CP)

LPRINT R53; FGH(CP)

LPRINT R83; TDEFH(CP)

LPRINT

REM PRINT ”TYPE ANY KEY TO CONTINUE“

REM DUM3 I INPUT3(1)

CLS 'NOU DO LONGITUDINAL

DER(CP) I ABS(RMAXS(CP) ' RBS(CP)): AA(CP) I DER(CP) I AVCLOAD(CP)

iZffiS

EFR<CP) I ABS(RBS(CP) - RCS(CP)): AAA(CP) I EFR(CP) I AVGLOAD(CP)

REN DETERNTNE LONCITUDTNAL PLASTIC DEFORNATION
5444 RFO1(CP) I (R1ABS(1) - R1ABS(CP))
5445 RFGZ(CP) I (R2ABS(1) - R2ABS(CP)) ~

FGR(CP) I ABS(RF61(CP) I RFOZICP)) 'TOTAL LONCITUDINAL DEFORNATTON

TDEFR<CP) I DER(CP) I EFR(CP)
5446 IF VIEUS I “N“ TNEN 5448

LPRINT R73

LPRINT R28; RDELTSX(CP)

LPRINT RHAXS(CP); RBS(CP); RCS(CP)

LPRINT R3S; DER(CP)

LPRINT R45; EFR(CP)

LPRINT R55; FGR(CP)

LPRINT R85; TDEFRICP)

LPRINT

GOTO 5448
5447 REN PRINT ITYPE ANY KEY TO CONTINUEI

REN DUNS I INPUT$(1)

dd(CP) I 1.105791 I (HH(CP) C 2 I VV(CP) C 2 I AA(CP) C 2) - (HH(CP) - 3.10979E-03 I VV(CP) I
.319145 I AA(CP)) C 2

TDD(CP) I 1.105791 I ((HH(CP) I HHH(CP)) C 2 I (VV(CP) I VVV(CP)) C 2 I (AAICP) I AAA(CP)) C 2)
' (HH(CP) I HHH(CP) . .0627461 * (VV(CP) I VVV(CP)) I .319145 * (AA(CP) I AAA(CP))) A 2

TUU(CP) I (.225127 I (HH(CP) I HHH(CP)) C 2 — .269895 I (VV(CP) I VVV(CP)) C 2 - .0447676 I
(AA(CP) I AAA(CP)) C 2 I 3.570975 I (HH(CP) I HHH(CP)) I (VV(CP) I VVV(CP)) I .086136 I (AA(CP) +
AAA(CP)) * (HH(CP) I HHH(CP)) I 1.145064 I (AA(CP) I
AAA(CP)) * (VV(CP) I VVV(CP))) I TDD(CP)

UUICP) I (.225127 I HH(CP) ‘ 2 . .269895 * VV(CP) ‘ 2 - .0447676 * AA(CP) ‘ 2 I 3.570975 ' HH(CP)
I VV(CP) I .086136 I HH(CP) I AA(CP) I 1.145064 I AA(CP) I VV(CP)) I dd(CP)

HR(CP) I (.25368 I HH(CP) I 3.9702876: I VV(CP) - .0142874 I AA(CP)) I dd(CP)

EE(CP) I (3.8949E-04 I (HH(CP) I HHH(CP)) I 3.9702876: I (VV(CP) I VVV(CP)) - .0142874 I (AA(CP)
I AAA(CP))) I TDD(CP)
5448 REN PRINT I TYPE ANY KEY TO CONTINUEI

REN DUNS I TNPUTSI1)

ddICP) I 1.046878 I (HH(CP) C 2 I VV(CP) C 2 I AA(CP) C 2) - (HH(CP) - .0417333 I VV(CP) I .212453
I AA(CP)) C 2

TDD(CP) I 1.046878 I ((HH(CP) I HHH(CP)) C 2 I (VV(CP) I VVV(CP)) C 2 I (AA(CP) I AAA(CP)) C 2)
° (HH(CP) I HHH(CP) - .0417333 * (VV(CP) I VVV(CP)) I .212453 * (AA(CP) I AAA(CP))) ‘ 2

TUU(CP) I (.170519 I (HH(CP) I HHH(CP)) C 2 - .271761 I (VV(CP) I VVV(CP)) C 2 - .101241 I (AA(CP)
I AAA(CP)) C 2 I 4.08595 I (HH(CP) I HHH(CP)) * (VV(CP) I VVV(CP)) I .057736 I (AA(CP) I AAAICPII I
(HH(CP) I HHH(CP)) I .868072 I (AA(CP) I AAA( _
CP)) * (WW?) I WV(CP))) / TDD(CP)

UU(CP) I (.170519 I NH(CP) C 2 - .271716 I VV(CP) C 2 - .101241 I AA(CP) C 2 I 4.08595 I HH(CP)
I VV(CP) I .057736 I HH(CP) I AA(CP) I .868072 I AA(CP) I VV(CP)) I dd(CP)

HR(CP) I (.1832585 I HH(CP) I 4.2817159: I VV(CP) - .0215089 I AA(CP)) I dd(CP)

EE(CP) I (.1832585 I (HH(CP) I HHH<CP)) I 4.2817159: I (VV<CP) I VVV(CP)) - .0215089 I (AA(CP) I
AAA(CP))) I TDDICP)

HR1(CP) I VV1(CP) I 4.07343'POSSION'S RATIO 0.3

EE1(CP) I TDEFV1(CP) I 4.07343'POSSION'S RATIO 0.3

EEH(CP) I ((AVGLOAD(CP)) I (SPLNTN I TDEFH(CP))) I .57176’ TOTAL NODULUS HOR.LVDT
5450 IF VIENS I IN" TNEN 5460

LPRINT IDDII; dd(CP); INNII; HH(CP); IVVII; VV(CP); IAAII; AA(CP)

LPRINT “RESILIENT HODULUS(PSI)I I; HR(CP); IRESILIENT NODULUS (VERT ONLYII“; HR(CP)

LPRINT ITOTAL HODULUS(PSI)I I; EE(CP); "TOTAL HODULUS(VERT ONLY)I I; HR1(CP)

LPRINT IRESILIENT POISSON'S RATIO I I; UU(CP); ""

LPRINT ITOTAL POISSON'S RATIO I I; TUU(CP)

LPRINT

REN PRINT ITYPE ANY KEY TO CONTINUEI

REN DUNS I INPUT$(1)

LPRINT : LPRINT

5460 NEXT CP

UIDTH LPRINT 132
LPRINT ”

DATE :“; DATE13
LPRINT “

SAMPLE NO. :“; SAPNOS
LPRINT '

PROJECT NO. :“; PROJS
LPRINT “

CHAMBER TEMP:“; TEMPF; “ F”
LPRINT : LPRINT : LPRINT

LPRINT “ NO. OF LOAD CYCLES “;

266

CP 8 SAPERX

FOR TP 8 2 TO CP

LPRINT USING “######### “; CCC(TP);
NEXT TP

LPRINT

LPRINT “ AVG. CYCLE LOAD ';
FOR TP 3 2 TO CP

LPRINT USING “###*.###N “; AVGLOAD(TP);
NEXT TP

LPRINT

LPRINT ' RESILIENT NODULUS ';
FOR TP 3 2 TO CP

LPRINT USING “######N.N '; HR(TP);
NEXT TP

LPRINT

LPRINT “ RESILIENT NODULUSV(P'.3D) ';
FOR TP I 2 TO CP

LPRINT USING “##‘NNNN.’ '; NR1(TP);
NEXT TP

LPRINT

LPRINT “ TOTAL NODULUS “;
FOR TP I 2 TO CP

LPRINT USING “N######.N “; EE(TP);
NEXT TP

LPRINT

LPRINT ' TOTAL NODULUSV(P8.30) ';
FOR TP I 2 TO CP

LPRINT USING 'fflNNNNN.’ '; EE1(TP):
NEXT TP

LPRINT

LPRINT “ TOTAL NODULUSN(PI.3D) “;
FOR TP 8 2 TO CP

LPRINT USING '#*####*.# “; EEN(TP);
NEXT TP

LPRINT

LPRINT “ RESILIENT POISSON'S RATIO “;
FOR TP 8 2 TO CP

LPRINT USING “##.#####* “3 UU(TP);
NEXT TP

LPRINT

LPRINT ' TOTAL POISSON'S RATIO ”;
FOR TP I 2 TO CP

LPRINT USING “##.###### '; TUUCTP);
NEXT TP

LPRINT

LPRINT : LPRINT
LPRINT ' VERTICAL DEFORMATION '
LPRINT " IIIIIIIIIIIIIIIIIIII "

'LPRINT ' TINE LAG “;
FOR TP I 2 TO CP
LPRINT USING “##Nflflliflfl '; VDELTSX(TP);
NEXT TP
LPRINT
LPRINT ' RESILIENT “;
FOR TP 8 2 TO CP
LPRINT USING “ ##.####i* “; DEV(TP);
NEXT TP
LPRINT
LPRINT ' VISCOELASTIC “;
FOR TP 8 2 TO CP
LPRINT USING “ ##.#####N “; EFV(TP);
NEXT TP
LPRINT
LPRINT ' PLASTIC “;
FOR TP I 2 TO CP

2(Y7

LPRINT USING I ::.#:###: I; FGV(TP):
NEXT TP

LPRINT

LPRINT I TOTAL I;
FOR TP I 2 TO 6?

LPRINT USING I ::.:###:: I; TDEFV(TP);
NEXT TP

LPRINT

: LPRINT
LPRINT “ HORIZONTAL DEFORMATION ”

FOR TP I 2 TO CP

LPRINT USING 'NNNNNNNN’ “; HDELTSX(TP);
NEXT TP

LPRINT

LPRINT “ RESILIENT “;

FOR TP 8 2 TO CP

LPRINT USING " #*.N####* “; DEN(TP);
NEXT TP

LPRINT

LPRINT “ VISCOELASTIC ";

FOR TP I 2 TO 6?

LPRINT USING I ##.#:###I I; EFH(TP);
NEXT TP

LPRINT

LPRINT I PLASTIC I;
FOR TP I 2 TO CP

LPRINT USING ' ##.###### “; FGN(TP);
NEXT TP

LPRINT

LPRINT ' TOTAL ':

FOR TP I 2 TO CP

LPRINT USING ' NC.‘NN#I# '; TDEFN(TP);
NEXT TP

LPRINT

LPRINT

LPRINT : LPRINT

LPRINT I LONGITUDINAL DEFORNATION I
LPRINT I ------------------ I

LPRINT I TINE LAG I;
FOR TP I 2 TO GP

LPRINT USING I:##::###: I; RDELTSxITP);
NEXT TP

LPRINT

LPRINT I RESILIENT I;
FOR TP I 2 TO CP

LPRINT USING I :9.::###: I; DER(TP):
NEXT TP

LPRINT

LPRINT I VISCOELASTIC I;
POR TP I 2 TO CP

LPRINT USING I #:.:##:#: I; EFR(TP);
NEXT TP

LPRINT

LPRINT I PLASTIc I;
FOR TP I 2 TO cP

LPRINT USING I ::.a####: I; FGR(TP);
NEXT TP

LPRINT

LPRINT I TOTAL I;
FOR TP I 2 TO CP

LPRINT USING I :0.:##:#: I; TDEFR(TP);
NEXT TP

LPRINT

GOTO TDD
REM DISPLAY SIGNAL DURING TEST
5500 SP5 I ' “
5550 CLS
SCREEN 2, D, D, D
LOCATE 1, 1: PRINT 'CYCLIC LOAD DATA FOR SAMPLE # “; SAPNOS
LOCATE 2, 1: PRINT “THERE ARE"; SPX; "CYCLES OF DATA“
LOCATE 3, 1: PRINT "UNION CYCLE DO YOU NANT?“
SCNX 8 VAL(INPUTS(1))
IF SCNX 8 0 THEN 5780
LOCATE 2 1: PRINT SPS

LOCATE 2, 1: PRINT ISUEEP PERIOD I I; DIPYx; I CYCLE COUNT II; SKIPC&(teSt I 1)
LOCATE 3, 1: PRINT SPS

LOCATE 3, 1:.PRINT IDATA CYCLE II; SCNX

LOCATE 4, 64: PRINT ILOAD(0)I

LOCATE 6, 64: PRINT IVERTICAL(5)I

LOCATE 8, 64: PRINT INORIzONTAL(3)I

LOCATE 10, 64: PRINT INORIzONTAL(4)I

LOCATE 12, 64: PRINT ILONGITUDINAL(1)I
LOCATE 14, 64: PRINT ILONGITUDINAL(2)I
I: I 1200 I (SCNx - 1) '200 SANPLES PER SCAN
5600 FOR pp1 I 0 TO 5'PLOT ALL SIX SIGNALS
PP2 I pp1 I 1 'NEED FOR CONPUTED GOTD STATENENT
v1 I 51 I C(pp1)
FOR I I 0 TO 1194 STEP 6
de(INT(I I 6)) I DATA1X(I I JX I pp1)
NEXT I
NAX I 0: NIN I 0 . NDRNALIzE AND SCALE PLOT
FOR T I 0 TO 199
IF dzx(T) > NAX TNEN NAX I dzx(T)
IF dzch) < NIN TNEN NIN I dzx(T)
NEXT T
RANGE I NAX - NIN
IF RANGE I 0 THEN RANGE I 1
deOC I 100 I RANGE
FOR T I 0 TO 199
X1 I INT(T I 3)
y1 I 190 - (INT(deOS I de(T)))
IF pp1 I 0 THEN y1 I 50 I lNT(8dpos I (dzch) - NIN I 150))‘FLOP LOAD SIGNAL
PSET (X1, y1). 2
IF T I 100 TNEN 5800' ORAN LINE
5710 NEXT T
NEXT pp1 'NEXT PLOT
5750 DUNS I INKEYS 'TEST IF DONE PLOTTING
IF LEN(DUNS) I 0 TNEN 5750
GOTO 5550
5780 SCREEN 0, 0, O, 0
GOTD 5200
5800 ON PP2 GOTO 5801, 5802, 5803, 5804, 5805, 5806
5801 LINE (X1, y1)-(465, 28): GOTO 5740
5802 LINE (X1, y1)-(465, 92): GOTO 5740
5803 LINE (X1, y1)-(665, 108): GDTD 5740
5804 LINE (X1, y1)-(465, 60): GOTO 5740
5805 LINE (X1, y1)-(465, 76): GOTD 5740
5806 LINE (X1, y1)-(465, 44): GOTO 5740
REN STORE DATA susROUTINE
6000 IF VIEUS I INI TNEN 6070
PRINT IDO YOU NANT TO STORE DATA 7(Y-N) I
DUNS I UCASES(1NPUTS(1))
IF DUNS I IYI TNEN 6040
RETURN
6040 PRINT INNEN TNERE Is A FORMATTED DISKI
PRINT IIN DRIVE 8 NIT ANY KEYI
DUNS I INPUTS(1)
6070 files I Ic:\data\I I SAPNOS I I.DATI
6080 OPEN fiIeS FOR APPEND AS 3
PRINT :3, PROJS
PRINT :3, NATDS

269

PRINT '3, SPLNTH
PRINT #3, TENPF
PRINT #3, DATE13
FOR I I 0 T0 5
PRINT #3, C(I) 'CAL FACTORS
NEXT I
PRINT #3, max; SPx; NX
FOR I I 1 TO SAPERX: PRINT #3, SKIPCCII); : NEXT I
FOR I I 0 TO NX
PRINT #3, DATA1%(I)'STORE RAN DATA ON DISK
NEXT I
CLOSE 3
RETURN
REN INITIALIZE COUNTER
6500 OUT IOADRX + 10, O'HRITE 0 TO ENABLE REG
0IOX(0) I 0: NDX I 10
CALL 08HRES<NDX, VARPTR(DIO%(0)). FLAGX)
IF FLAGX > 0 THEN 7210
010%(0) I NXTCNTX 'LOAD COUNTER VALUE
NDX I 11
CALL OBHRESINDX, VARPTR(DIOXIOII, FLAG!)
IF FLAGX > 0 THEN 7210
6520 RETURN
7000 REN INITIALIZE AID NODULE
7010 NDX I O'NODE
7015 FLAGX I 0
7020 0IOX(0) I IOADRX
7030 0101(1) I 7 ' INTERRUPT
7040 DIO%(2) I 3 'DNA LEVEL
7041 BACKXII) I 0
7042 BACKXIZI I 0
7043 BACKX(3) I 0
7060 CALL 08HRES(NDX, VARPTR(DIOXIO)), FLAGX)
7070 IF FLAG: > 0 THEN 7210
7080 REN SET CHANNELS
7090 NDX I 1
7091 0IOX(0) I 0
7092 0IOX(1) I 5
7100 CALL 08HRES¢NOX, VARPTR(0IOX(0)), FLAG!)
7110 IF FLACX > 0 THEN 7210
REN SET SAMPLE RATE FOR IKHZ (CLOCKI IONHZ)
0IOX(0) I 100: 0I0%(1) I 40
N01 I 17
CALL ODNRESOOX, VARPTR(Don(0)), FLAGX)
IF FLAG: > 0 THEN 7210
RETURN
7210 PRINT “DAS-HRES ERROR“; FLAGX; “MODE"; N01
7220 END
8990 REN ROUTINE TO EXIT PROGRAN
9000 CLS :
9005 LOCATE 10, 10:
9010 PRINT “TERMINATION OF CYCLIC LOAD TEST“
9020 'STOP
9030 END
REN ROUTINE TO NORNALIZE DATA AND DETERMINE NAX-NIN-COUNT
REN J,K ARE ARRAY OFFSETS
REN KISIG BEING PROCESSED
REN 0ILOAD,1ILONGTTUDINAL-1,ZILONGITUDINAL-2,3IHORZ-1,4IHORZ-2,SIVERTICAL DISP.
REN JIDATA OFFSET INDEX FOR BETNEEN EACH LOAD CYCLE
REN IIDATA OFFSET FOR EACH SIGNAL
14000 I I 0
FOR ID I 1 TO SO'INITIALIZE FILTER
X I 0ATA1X<I I K I J)
GOSUB 18000
NEXT ID
FOR I I 0 TO 1196 STEP 6'NON FILTER DATA
X I DATA1XII I X I J)
GOSUB 18000
0ATA1X(I I K I J) = y
NEXT I
REN DETERMINE ABSOLUTE POSITION OF SENSOR

14020

14030

14035
14040

14075
14100

14102
14104
14106

14108
14110

14111

14113

14115

14120
14130

14140

270

REM CALCULATE THE AVERAGE VALUE OF THE LAST 8 SAMPLES
REM USED TO CALCULATE THE PLASTIC DEFORMATION
ASUM I 0

FOR I I 1152 TO 1194 STEP 6

ASUM I ASUM I DATA1X(I I K I J)

NEXT I

AAVG I ASUM I O'AVERAGE VALUE

REM NOU PROCESS DATA FOR RELATIVE DISPLACEMENT
REM DO ALL DATA HAVE SAME SIGN

I I 0: NEGX I 0: POSSX I 0

IF K I 0 THEN 14190'TREAT LOAD SEPARATELY

FOR I I 0 TO 1194 STEP 6 ’look for neg
IF DATA1X<I I K I J) > NEGX THEN 14030

NEGX I DATA1X(I I K I J)’ MOST NEG VALUE

NEXT I

IF NEGX I 0 THEN 14075'N0 NEG VALUE

REM 'MUST BE SOME NEG N IN ARRAY

REM LOAD HILL NEVER HAVE POS ‘(COMPRESSION)

REM REMOVE NEG OFFSET

FOR I I 0 TO 1194 STEP 6

DATA1X(I I K I J) I DATA1X(I I K I J) I ABS(NEGX)
NEXT I

REM OFFSET REMOVED

REM SEE IF MIN VALUE IS ZERO IF NOT MAKE IT ZERO
LMAXX I -32768: LMINX I 32767

FOR I I 0 TO 1194 STEP 6

IF DATA1X<I I K I J) > LMAXX THEN 14102

IF DATA1X(I I K I J) < LMINX THEN 14104

0010 14106

LMAXX I DATA1X(I I K I J): GOTO 14106

LMINK I DATA1X(I I K I J)

NEXT I

IF LNINX I 0 THEN 14108

IF LMINX < 0 THEN 14106

FOR I I 0 TO 1194 STEP 6

DATA1X<I I K I J) I DATA1%(I I K I J) - LMINX
NEXT I

GOTO 14108

FOR I I 0 TO 1194 STEP 6

DATA1X(I I K I J) I DATA1X<I I K I J) I LMINX
NEXT I

OH K GOTO 14111, 14111, 14111, 14111, 14110

FOR I I 0 TO 1194 STEP 6

DATA1X(I I K I J) I LMAXX . DATA1X(I I K I J)
NEXT I

REM NON COMPUTE NAX-MIN-COUNT ETC

LMAXX I -32768: CMIN1X I 0

CMINZX I 0: CMAXX I 0: POSSX I 0: PEAKX I 0
LMIN1X I DATA1%(0 I K I J)

LHINZX I DATA1X(1194 I K I J)

REM ALL DATA VALUES ARE POSITIVE AND I SLOPE

REM FIND N 0F MAX VALUES AND CENTER SAMPLE COUNT
REM FIND I OF MIN VALUES (UITHINITOLERENCE)AND AVG VALUE
REM LMIN1IINITIAL NIN LMINZIMIN AFTER LOAD APPLIED
FOR I I 0 TO 1194 STEP 6

IF DATA1X(I I K I J) > LNAXX THEN 14170

IF DATA1X<I I K I J) I LMAXX THEN 14180

NEXT I

PEAKX I POSSX'LOCATION 0F 1ST MAX #

FOR I I 0 TO 1194 STEP 6

REM DEAL NITH DISP BEFORE-AFTER LOAD

IF I >I PEAKX THEN 14140' AFTER PEAK

IF DATAIXII I K I J) > LMINIX THEN 14130

IF DATA1X(I I K I J) I LMIN1K THEN 14120

LMINIX I DATA1X(I I K I J)'NEN PRELOAD MIN
CNIN1X I 1: MINP1X I I'MINIMUM POSITION BEFORE LOAD
GOTO 14130

CHIN1X I CMIN1X I 1

NEXT I

0010 14340

IF DATA1X(I I K I J) > LMINZX THEN 14142

271

IF DATA1!(I I K I J) < LMIN2! THEN 14144
14141 CMINZ! I CMINZ! I 1
GOTO 14130
14142 IF DATA1!(I I K I J) - 1 I LMIHZ! THEN 14141
GDTO 14130
14144 IF DATA1!(I I K I J) I 1 I LMIHZ! THEN 14141
LMIN2! I DATA1!(I I K I J)’NEN MIN
CMINZ! I 1: MINPZ! I I'MIN POSITION AFTER LOAD
GDTO 14130
14170 LMAX! I DATA1!(I I K I J)
POSS! I I: CMAX! I 1
14175 GOTO 14113
14180 CMAX! I CMAX! I 1
GDTO 14113
REM PROCESS LOAD SIGNAL° ALNAYS NEGATIVE-COMPRESSION
FOR ID I 1 TO 20'INITIALIZE FILTER
X I DATA1!(I I K I J)
NEXT ID
FOR I I 0 TO 1194' FILTER SIGNAL
X I DATA1!(I I K I J) 'FILTER INPUT
GOSUB 18000
DATA1!(I I K I J) I Y'FILTER OUTPUT
NEXT I
14190 LMIN! I 32767: LMAX! I 0
FOR I I 0 TO 1194 STEP 6
‘ IF ABS(DATA1!(I I J)) < LMIH! THEH 14192
14191 IF ABS(DATA1!(I I J)) > LMAX! THEH 14194
IF ABS<DATA1!(I I J)) I LMAX! THEH 14196
GOTO 14198
14192 LMIN! I ABS(DATA1!(I I J))'MIN NUMBER -MIN LOAD
VALLY! I I'ADDRESS OF MIN LOAD
EETO 14191
14194 LMAX! I ABS(DATA1!(I I J))‘MOST POS NUMBER -MAX LOAD
LPEAK! I I'ADDRESS OF PEAK LOAD
CMAX! I 1: GOTO 14198
14196 CMAX! I CMAX! I 1
14198 NEXT I
REM DETERMINE SAMPLE COUNT TO (B'DELTA ) TIME
REM MIN LOAD DEVIATIONIII'3R 1000*[32767I1/2#(II'6 COUNTS)
I I 1194
LMIN2! I ABS(DATA1!(I I J))’LAST VALUE
14310 IF ABS(ABS(DATA1!(I I J)) ' LMIN2!) > 6 THEN 14320’ TOLERENCE 3 LBS
IF I < 20 THEN 14320’THATS ENOUGH OF SIGNAL TO LOOK AT
I I I - 6: GOTO 14310
14320 BCNT! I I' SAMPLE ADDRESS FOR BEGINNING OF RELAXATION PERIOD OF LOAD
14330 POSS! I LPEAK! / 6 I 1 ' SAMPLE NUMB FOR MAX LOAD
RETURN
REM GET & STORE DATA FOR DEFORMATIONS
14340 POSS! I POSS! / 6 I I'LOCATION RELATIVE TO 200 SAMPLES
RETURN
15000 POST I 1'FLAG TO INDICATE POST PROCESSING DATA FROM DISK
PRINT "NHAT IS THE NAME OF THE DATA FILE“
INPUT fileS
REM SAPNOS I files
INPUT “DO YOU NANT TO DISPLAY DATA(Y-N)': DUMS
VIENS I UCASES(DUMSI
INPUT “DO YOU HANT TO PLOT DATA ON CRT SCREEN 7“; DUMS
PLOTS I UCASES(DUMS)
REM files I “ c:\data\“ I fileS I “.DAT“
CLS
CLS
OPEN files FOR INPUT As 3
GOSUB 15010
GOTO 15100
15010 INPUT #3, PROJS 'READ DISK FILE
INPUT #3, MATDS
INPUT #3, SPLNTH
mm #3, TEMPF
INPUT #3, DATE1S
FOR I I 0 TO 5
INPUT #3, C(I)'CAL FACTORS

15100

15150

15200
16000

17000

18000

272

NEXT I

INPUT #3, SAPER!, SP!, N!

FOR I I 1 To SAPER!

INPUT #3, SKIPC&(I)

NEXT I

FOR I I 1 TO SAPER!

PRINT SKIPC&(I)

NEXT I

FOR I I 0 TO N!

INPUT #3, DATA1!(I)

NEXT I

RETURN

PRINT “THERE ARE“; SAPER!; “CREEP CYCLES"
test I 0

CP I 1

6010 4672

FOR CN I 2 To SAPER!

60808 15010

CP I CP I 1 ' FOR CREEP TEST
60811816000

GOTO 4672 'PROCESS DATA

NEXT CN

CLOSE 3

FOR I I 1 To 10

PMAXS(I) I D

PMINS(I) I O

VMAXS(I) I 0

VMINS(I) I O

VDELTS!(I) I O

VBS(I) I 0

VCS(I) I D

VABS(I) I D

HMAXSII) I 0

HMINSII) I D

HDELTS!(I) I D

HBS(I) I D

RCS(I) I 0

H1ABS(I)
HZABSII)
RMAXS(I)
RMINS(I)
RDELTS!(I)
RBS(I) I D
RCS(I) I 0
R1ABS(I) I 0

RZABSII) I 0

DIVII) I 0

NEXT I

RETURN

END

FOR VH1 I 0 TO 1080 STEP 120

FOR LL1 I 0 TO 114 STEP 6

III-WIILLIIJ

DO! I DATA1!(II1): D1! I DATA1!(II1 I 1)

DZ! I DATA1!(II1 I 2): D3! I DATA1!(II1 I 3)
D4! I DATA1!(II1 I 4): DS! I DATA1!(II1 I 5)
PRINT 00!; 01!; 02!; D3!; D4!; 05!; K; J; NEG!
NEXT LL1

DUMS I INPUTSI1)

NEXT UU1

RETURN

H3 I X * 0 - B1 * V2 - 82 * U1

FILL I H3 I A1 * HZ I U1

N1 I 02

N2 I U3

NU2 I FILL - BB1 * NN1

y I NHZ I AA1 I NUT

UN1 I NNZ

RETURN

END

NOOOO

APPENDIX B

APPENDIX B

The layer thicknesses and deflection data for the indicated 563 pavement locations are

presented in this appendix.

273

 

 

 

 

 

 

 

 

 

 

 

274

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

»».. 6.» 6.» 3e ».... a»... »».» 8.» »».» 8.» 8.». 8.» »..v. .636» .»
»».» »».» »»... »».c »».» 6.» 6.» 8.» »».» 8.» 8.». 8.» »..v. ..»..».»» »»
6.. »».» »».» 8.» 6... 3e 8.» »..» »».» 8.» 8.». 8.» 6.». $2....» ».
»».. »».» »»... »».v »».» »».» »».» »..» »».» 8.» 8.». 8.» »..». ..6».»» ».
»».. »».» ...» »»... 2.... »».» »...» »..» »».» 8.» 8.». 8.» »»... 66.6» L.
»».» »».. 8.» »»... »...» »».» »..» »..» »».» 8.» 8.». 8.» »».». ..»»».»» ».
v». ...» »».» »...c »».» »».» 6.». »..» 6.. 8.». 8.». 8.» »».» .66.». ».
»... »..» »».» »»... »».» .».» 8.» »..» 6.. 8.». 8.». 8.» 8.» .66.». ...
»... »».. »».» »».» »»... »».» 6.» »..» 6.. 8.». 8.». 8.» »»... »»o»...». ».
»».. ....» »..» 3... 6.» 8.» »...». »».» 6.. 8.». 8.». 8.» »».» ..8».». ».
»... ....» »..» ».... 6.» ...» »».». »..» 6.. 8.». 8.». 8.» k... .».»..». ..
»».. 6.. »».» »».» 8+ 9.» »...» 6.» 6.. 8.». 8.». 8.» 3.» ..»»».». ».
»... »».. »».» 6.» 8... 3.» »».» »..» 6.. 8.». 8.». 8.» »»... .66.». o
8.. »».. »».» 6... »».» 6.» »».». »..» 6.. 8.». 8.». 8.» 8.» .88.». »
»... »».» ».... »».» »».» »».» c».». »».» »».. 8...» 8... 8.» »..» .66.» L.
8.. »».. »».» R.» v»... »».» »..» .».» »».. 8...» 8+ 8.» c».» ..».».» »
»».. 6.. »».» »».» »».» »...c »».» »».» »».. 8...» 86 8.» 6.» »»8»... »
»».» »».. 6.» 6.» »»... »».» »».» »..» »».. 8...» 8... 8.» »».» at»: v
»».. 6.» »»... 6.» »..» 6.» »».». 3..» »».. 8...» 8... 8.» »».» »»2»: »
»... »».» »...» »»... »».» »».» »».» »..» »».. 8+» 8... 8.» 8.» ....»».» »
»... »..» »».» »»... 6.» 6.» »».» »..» »».. 8..» 8... 8.» »».» ..»»..» .
B »» »o 3 »o »o .o A...» 93 »..».» .8» 2228 9. .3532 .o
3...» 88o...» .8...» SF .26» .85..» 82.on .98» .8,»

 

 

 

.isgfilu’ilaiggagghgj —.m .38.

 

275

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.» »»... »».» »».» »».» »».» 8.» 8.» 6.» 8.» 8.» »..» »...» .68». 9
....» ».... 6.» »».» »»... »».» »».» »..» »..» 8.» 8.». ».... ...» .6»»».. 6
»».» ».... »».» 6.» »..» 6.». ...». 8.» »..» 8.» 8.». »».» »».» ».»...».. ».
»...» »... 3..» »».» »... »»... 6.» ...» »..» 8.» 8.». »».» »».» »»o.»». . a»
3.» »»... »..» »».» »».. »».» »».» »».» »..» 8.» 8.». »».» »».» .6»»».. »»
»».» 8... 6.» »».» »».» 8.. 8.. 8.» »..» 8.» 8.». »».» ...» .89». . 6
3.» k... »».» ...» ....» »».» .... 8.» »..» 8.» 8.». »..» »...» .»»6».. »»
6.» 9.. »».» »».» »..» 6.» »..» »».» »».. 8.». 8.». 8.» »».» 66»... »»
6.» ».... »..» »...» 2.» 8... »».. »».» »».. 8.». 8.». 8.» »».. .666. 6
3.» ».... 8.» »..» 3.» »».» 8.. »».» »».. 8.». 8.». 8.» »..» 66...». »»
»».» »... »... »».» 9.» »»... »... »».» »».. 8.». 8.». 8.» »».» .966. »»
....» .... »... 6.» »».» 6... ».... »».» »».. 8.». 8.». 8.» »».» .»»»»6. 6
»».» »».. »... 3.» »».» »»... »»... »».» »».. 8.». 8.». 8.» »».» ..».»6. »»
»».» »... 6.. 9.» ....» »»... »..» »».» »».. 8.». 8.». 8.» »».» .6». 6. »»
»..» .... »... 6.» 6.» »».. »..» »».» »».. 8.». 8.». 8.» »».» ....»6. »»
»..» ».... 3.» »».» »».» ».... 6.. »».» »».. 8.». 8.». 8.» »..» ..8»... s»
6.» 6.. »».» »».» ...» »... 6.. »».» »».. 8.». 8.». 8.» »».» »»»»»6. »»
6.» 6.. »».» »».» ....» 8.. .... »».» »».. 8.». 8.». 8.» »..» .666. »»
R.» »».. »».. »».» »».» .... »».. »».» »».. 8.». 8.». 8.» »».» 68. 6. .»
.... »».» ...» »»... »».» 3.» »».» »..» »..» 8.» 8.». 8.» »».». .»»»»6» »»
»».» »».. 3.» »».» ».... »».» »».. »..» »..» 8.» 8.». 8.» 9.». 68.6» »»
B »o »o 3 »o »» .o 8.? »...... 3.».» .8» 3:28 9. .3522 .0
42.588...» .8...» Sal »..»» 6...»... 8.52% ......» .... 8m

 

 

 

.636»... .38.... Sign...» .... 3...»... .... ... ...» 8.8....» .8. 88.5....» ...»... ..» ......

276

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

»».. »q» »...» .6... 3.» »».» »».» »..» ...... 8.». 8.» 8.» »».. .696» 8
8.» 6.. »».» 6.» B.» 6.» »».. »..» 6.. 8.». 8.» 8.» »».» ..»»..»» »»
.... »... 6.» 6.» »».» k.» 6.» »..» 6.. 8.». 8.» 8.» »».» .686» .»
8.» 6.. »...» 6.» »»... »».» »».» »..» 6.. 8.». 8.» 8.» »».» .886» 8
6.» »».. »».» 6.» 6... »».» ».... »..» »».. 8.». 8.» 8.» »».» .686» o»
8.. 8.. »».» »...» »».. »».» »».» »..» 6.. 8.». 8.» 8.» »».» »»»....»» »»
.».. .... »».» 9.» »»... 6.» z... »..» 6.. 8.». 8.» 8.» 3.» 68.6» 6
»... »».. »».» »».» »..» »».» 8.» »».» 6.. 8.». 8.» 8.» »».» .»»»».»» »»
»..» 8.» »».» ».... 8.» »..» »».» »..» »..» 8.». 8.» 8.» »».». ......9 »»
8.» 8.. »».» 6... 8... ...» »».. 8.» »..» 8.». 8.» 8.» 8.». .».»»6.. 6
»».» »».» »».» »».. ...» 8.» 6.. »».» »..» 8.». 8.» 8.» »».» 68.6. »»
8.. 6.» 3..» 6.. ...» 3.» 6... »».» »..» 8.». 8.» 8.» 8... .966. »»
»..» 3.. »».» 6.» »».. 3.» »... »».» »...» 8.». 8.» 8.» »».». 88.6.. .»
3.» 8.» »..» »».» »».. ...» »».» »».» »..» 8.». 8.» 8.» »».». ..».».9 »»
»».. »..» ....» »..» ».... »».» »».» »..» »...» 8.». 8.» 8.» »».». ......9 ...
3.. »».» »».» 9... »».» »».» »»... »».» »».» 8.». 8.» 8.» »».» ..»»».9 9
3.» 3.» »».» ».... 8.» 3.» »... 8.» »...» 8.». 8.» 8.» »..». »..»...9 ...
8.» 8.» 8.» 8.» »».. »».» »».» »».» »...» 8.». 8.» 8.» 3.». .669 9
6.. »».» »..» 6.» »».. »..» »».» »».» »...» 8.». 8.» 8.» 6.». .66.». 9
6.» 8.» »..» »».» »».. ..».» »...» »».» »..» 8.». 8.» 8.» »».». .39.». 3.
»... »».» »».» »».» 6.» »».» »... 8.» 6.» 8.» 8.» 8.» »».» »»»..»». 9
E »o »o 3 »o »o .» ».... »...... 3.».» ...» ....ocoo o< .382 .o

4...... 88....» .8...» s... »..»» .88..» 8.5.0.5 ......» .... I.“

ll 11' I

 

.6288... .35.... 89.8....» .... ...-»...... .... ... a... 88...... u... 8.28.... ...»... ..» ......

277

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... »... 8.» 6.» »».» ....» »...» 9.» 6.» 8.» 8.» 8.. ».... .»»»»»» 3
8.. 3.» »».» 3.» »..» »».» 3.. »».» 6.» 8.» 8.» 8.. 8.» .»8»»» »»
»».. »».» »».» 8.» 8.» 6.» ».... 8.» z... 8.... 8.» »».» ».... ..»..»» »»
»».» »»... »..» »».» »».» »...» »».» »».» ...... 8.... 8.» 8.» »...» ..»..»» .»
6.» »..» 6... ».... 6... 8... 6.» 8.» 6.. 8... 8.» 8.» 8.» .668 »»
»..» 8... 6... »»... »».» »».» »..» »..» 6.. 8... 8.» »».» »».» .668 2.
»».» ...... 6.» 3.» »».» 8.» 6.» »..» ...... 8... 8.» »..» 6.» .668 2.
»».. 6.» 8.» »».» »...» »».» 3.. 8.» 6.. 8... 8.» »».» 9... »»».»»» t.
»».» »».» »..» »... 6... »»... 6... 8.» 6.. 8.... 8.» »».» »»... ..8»»» »h
3.. »...» »».» »».» »..» 8.» 9»... »».» ...... 8.... 8.» 8.» »»... 886» »»
».... 9.» 3... 9.» »»... »».» »».». »..» »».» 8.». 8.» 8.» »»... .86.». ...
8.. 8.» 6.. »..» »».» ...». 6.». »».» »».» 8.». 8.» 8.» »».» .62.». 2
9.. »».» »».» 6.» »..» »..» »...». »...» »».» 8.». 8.» 8.» »».» »»»»..». »..
8.. 3.» 6... »..» 6.. 6.. »».». 9.» »».» 8.». 8.» 8.» »».» 66.6. 6
»».. 8.» 6... R.» »».» »..» 8.». »».» »».» 8.». 8.» 8.» 6.. .68.». 2.
6.. »..» »»... »».» »»... »... ...». »..» »».» 8.». 8.» 8.» »».» 6.8.». 8
9.. 9.» »».. 9.» .... »».. 9.». »..» »».» 8.». 8.» 8.» 9.» .66.». 8
»».. »».» »..» 8... 8.» 9.. »».. »..» 6.. 8.». 8.» 8.» 8.» .866» 6
».... 6.» »».» »»... 6.» 9.» 6.» »..» 6.. 8.». 8.» 8.» »».» ....»6» 8
6.. »».» 9.» »»... »...» »».» ....» »».» 6.. 8.». 8.» 8.» »».» 6.86» »»
»... »..» »».» »»... 6.» ».... »».. »».» 6.. 8.». 8.» 8.» 8.» .686» 3
B »o »o v» »o »o .» ...... »...... 3.».» ...» ....»80 9. ..»..52 .oz
......» 88....» .0....» 5F .28 .88.... 88......» a...» .... L

 

 

 

.6888. ..»..5» 8..-8...» .... 3...»... .... 8. ...» 88....» »... 8.85....» ...... ..» ......

278

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

»».. »..» »».» 6.. ....» »».» »».». 6.. »...» » » » »».» ... 8.
»..» »..» 8.» 8.. 6.». 6.». 6.». »..» »..» 8.» 8.». 8.» »».» .69... 3.
»».» »».. 6.» »».» »»... ».... 8.». »..» »..» 8.» 8.». 8.» 9.» .86... 8.
»».. 6.» 8.» 8.» 8.». ...». 6.»» 9.» »..» 8.» 8.». 8.» »».» »»».»6. 8.
6.. »».» 3.» 8.» »..» 3... 8.». 8.» »..» 8.» 8.». 8.» 8.» »»»9.... 6.
6.. 6.» 8.. »».» 8.» ..».». »..». »».» »..» 8.» 8.». 8.» 8.» 88. .... 8.
...... »..» 8.. 6.. 6.». 6.». 6.... »..» »..» 8.» 8.». 8.» ..».» »...»... 8
»».. 6.» ».... »».» 6.» 8.». ...». 9.» »..» 8.» 8.». 8.» 8.» »».»»... 8
».... ....» »».. »».» »».» 8.». 6.... »..» »..» 8.» 8.». 8.» »..» ».».».... 6
6.. 8.» 9... »».» »..» 8... 8.». 9.» »..» 8.» 8.». 8.» »».» ».».».... 8
6.. 3.» 8.» ..».» 8.» 8.» 8... 6.» ...» 8.». 8.» 8.» »..». ....6. 8
».... 8.. »..» 6.» »...» 6.» 6.» »».» ...» 8.». 8.» 8.» »».». ..».»». 6
»».. ....» »...» 8.» 6.» »».» »».» »..» ...» 8.». 8.» »..» »».» .68». 8
».... ...» 3.» 8.» 3.» »».» 6.» »».» ...» 8.». 8.» 8.» 6.». .89». »»
8.. 6.» 9.» R.» 6.» ».... 6.» 6.» ...» 8.». 8.» »..» »».» ..»»6. 6
6.» »».» 8.» 6.» 8.» »... »».» 6.» ...» 8.». 8.» » ..» »».» . .98. 8
3.. »».» »...» 8.» ...» ....» 8.» ....» ...» 8.». 8.» »».» »..» ..».»». 8
8.. 8.» ..».» 8.» 6.» 6.. 8.» 8.» ...» 8.». 8.» 8.» 6.» ..».»». 8
»».. 8.. »..» 6.» 9.» 8.» 8.» »».» 6.» 8.» 8.» 8... 8.. 686» 6
»... »...» »».» ....» »».» 8.» 8.» »».» 6.» 8.» 8.» »».» 3.» »....»8 8
..... 8.. »».» »».» »».» 8.» »..» »..» 6.» 8.» 8.» 8.. 2..» ....9»» »»
..» »o »o 3 »» »o .» ....» »...... 3.».» ...» .....80 9. ..»...»z .o
3..... 88....» .8...» 5.. .28 88.... 8.5.2... ......» .... L
I I h I

 

 

 

 

6.2.58. ..».»... 888...» .... 8.8.»... .... ... a.» 88....» »... .85....» ...... ..» ......

 

 

 

 

 

 

 

 

 

 

 

 

279

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

»».» »...» ».... 8.» »»... »..» 8.». »».» 8.» .. 9 » »».» »» »».
»».» 8.» 6... »».» 8... »».» 8.». »».» 8.» .. c » »».» ».. 8.
8.» »».» »... »».» »».» 8.» 8... »...» 8.» .. .. » »».» o» v».
8.. 3.» »..» 3.. 8.» 8.. 6.». 9.» 8.» .. v » »».» 8 8.
8.. 8.» »..» 8... »».» 8.... 9.». »».» 8.» .. v » »».» 9 8.
8.. 3.» »».» »..... ....» »... 9.». »».» 8.» .. .. » »».» »» .».
»».. 6.» 8.» 8... »..» 6.. 8.». »».» 8.» v. .. » »».» .... o».
»».. ...» »..» »».. »...» »..» »..». »».. »...» » » » »».» 8 »..
6.. ...» 8.» »... »».» »».» »»... »».. »...» » » » »».» o» »..
9.. 9.» »».» »»... »... 8.» 8.... 6.. »..» » » » »».» ». »..
6.. ....» 6.» ».... 8.» 6.» »».». »... »..» » » » »».» »» »..
»».» 8.» ...» »»... ..».» »».» 6.». »... »..» » » » »».» ».. »..
»».. »».» »».» »»... 9.» 8.» »»... »».. »..» » » » »».» 8 ....
6.. ....» ...» »».. 8.» 8.» 2.... »».. »..» » » » »».» 8 »..
»».. 6.» 8.» 8.. »..» ....» »».». 8.» »..» » » » »».» ». »..
»».. »».» 8.» »».» »...» »..» 9.». »..» »..» » » » »».» »» ...
6.. 8.. »».» 8.» »».» »».» 6.». »».» »...» » » » »».» ».. »..
9.. »».» »».» 8... 6.. ...». ...». 6.» »..» » » » »».» 8 8.
»».. »».» 8.» 9.. 8.» 8.. 6.». k.» »...» » » » »».» 8 8.
»».. ....» »..» ...... »».» »..» »».». »».» »..» » » » »».» 9 6.
8.. »..» 6.» 9... 9.» »..» 6.». 6.. »..» » » » »».» a» 8.
B »» »o 3 »o »o .» ....» »...... 8.8.» .8» .....80 0.. ......»z ..z
3..... 88....» .8...» 5.. .8» .88.... 8.53... ......» .... ...
| II h I

 

 

 

..»..»»»... .85.... 888.83... 8.8.»... ..»... ...» 88....» »... 88.5....» ...... ..» ......

 

280

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

»9.» »».9 6.» 8.» »..». an». »».». ....» 9..» ». ». » »».» »9 6.
9.» 9.9 9».» t.» 9.». »...». »».». »..» 3.» ». ». » »».» o» »9.
»9.» »».9 »».» »».. »..». 9.». »».». »..» 9..» ». ». » »».» ».» »9.
»».» »».. .».» »... »».». 8.». 6.». »..» ..».» ». ». » »».» 8 9.
»».» »..9 »».» 8.. 8.» 9».». 8.». »..» 9..» ». ». » »».» »» 9.
»..» 6.» »..» »»... »...» 8... »..9. »..» 9».» ». ». » »».» »9 »9.
»».» 8.» 9..» »».. 6.. »..». »».». »..» 9..» ». ». » »».» o» .9.
»».» »».9 »..» ».... 8.». 9».». »».». »..» 3.» ». ». » »».» ».» »9.
»9.» 6.9 8.» 9.» »...». »..». 6.». »..» 9..» ». ». » »».» o» a».
»9.» 9.9 8.» »».» »».». »».». »».». »..» 3.» ». ». » »».» o» 8.
»...» 6.9 6.» »..» 9.». 8.». »».». »..» 3.» ». ». » »».» »9 6.
9.» 6.9 9..» .9.» 6.». ...». 6.». »».» 3.» ». ». » »».» »» o».
»9.» ..».9 8.» 9...» 6... 8.». »».». »».» 9..» ». ». » »».» ..» 8.
8.. »».» 9.» 9.9 8.» »»... »..». »».» 8.» 9. 9 » »».» o» 9».
9... 9».» »».» ...9 »».» 6.» 8.» »».» 8.» 9. 9 » »».» 8 8.
6.. »».» 8.» »..9 »».» .... 3.». 6.» 8.» 9. 9 » »».» »9 8.
8.. 8.» »».» »..9 »».» »».. 8.» »..» 8.» 9. 9 » »».» o» 6.
»... 6.» »9.» »..9 8.» 8.» »... »..» 8.» 9. 9 » »».» ».9 o».
8.. 6.» 6.» »..9 »».» 9.. 8.» »».» 8.» 9. 9 » »».» o» 6».
9». 6.» 9..» »».9 »..» »».. »».». »».» 8.» 9. 9 » »».» o» 8.
8.» ...» »».9 »..» »..» »w» 8.». »».» 8.» 9. 9 » »».» »9 6.
..» »» »» 9» »» »» .» ...... »...... 8.».» .8» .....80 9. ......»z .o
6...... 8.8....» ......» 5m ..5..» .88.... 8.5.2.... .o...» .... E
I II "

 

 

 

 

.828... .85.... 888...» .... 8.8.»... .... ... ...» 8......» »... 8.85....» ...»... ..» ......

281

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.. 8.. 8.9. 8.. ...... a... 8.. 8.0 o... 8 o o ...9 8 8.
8... 8.. 9m.“ 8.. 8... 8.. 8.. ....o o... 8 o o ...9 8 8.
8... 9m. .9.“ 99.. 8.» 8.. .8... 8... a... 8 o o ...9 8 8.
N... 8.. 8.. 8.9 8.... 8.. .... 8... o... 8 o o ....9 9... 8.
2... o... .o.~ 8... 8.9 8.. 2.. 8... c... on o o ...9 8 9o.
8... .... 8.. 8... 8.9 8.» 8... 8... o... 8 o o ...9 8 8.
2... m... 8.. 8.... .9.9 ...m 8... 8... o... 8 o o ...9 09 8.
8... .... 8.. 8.“ 8.9 9.... 8.. mu... o... 8 o o »..9 8 .o.
8... 8.. 8.. 8d 8.9 8.. 99... 8... o... 8 o o ...9 ...“. 8.
8... 8.. 9a.. 8.. .9.9 8... 8.» ...o o... 8 o o .....9 8 8.
9... 8.. 9... 8d .9.9 88 8... ...o o... 8 o o ...9 8 8.
8... o... 8.. 8.“ 8.9 8.» 8... 8.0 ...... 8 o o ...9 09 8.
...... .... 88 8.“ 8.9 9.... ...... 8... o... 8 o o ...9 8 8.
8.0 o... a... a... 8.9 3... 8.... 8... o... 8 o o ...9 a... 8.
8.. a... 8... o... 3.9 8.. 9.... 8.. o... 8 o o ....9 8 9m.
8.. m... «..u a... 9..9 8... 9o.» 8... ...... 8 o o ...9 8 8.
8... 8.. 84. B... 2.9 8.. ...... 9.... o... 8 o o ...9 8 «m.
...... 8.. 5.. 8.“ 8.9 9w... 8... ...o o... 8. o o ...9 8 .m.
.2. a... 8.. 8.. 8.9 88 99... ...o .... 8 o o ...9 ..u. 8.
8.“ .....9 8... «a... 99.... .3. 8d. a... 9... a. a. 0 m3 8 a9.
.9.“ 8.9 m... 8.. m3. 8.“. 8d. ...... 9.... m. u. o 8.“ 8 .9.
B 8 8 9o 8 «o .o ...... ....E. 388 ...m 3.880 0... .382 .o
3..... 8.8.80 8.8» 5m .28 .88.... 82.0.... ......o .... 2m
I \II \n‘ I

 

 

.6558. .88.. 8.29.... .... 38...... .... a. a... 88...... u... 8:88.... 8..... ..o ......

282

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.. .... «... 8.. 8.9 8.. .... o... 8.. 8 o o «9.. 8 8.
.... 8.. .... 8.. 8... ...... 8.. o... 8.. 8 o o N... 8 8.
8.. 8.. 8.. 8.. 8.. a... .... ...o 8.. 8 o o «9.. .9 ...
o9. .... ...... 8... 8.. 8.. o... «..o 8.. 8 o o «9.. 8 8.
8.. 8.. 8.. 8... 8... 8.. 8.. .... 8.. 8 o o a... a... 8.
o... 8.. 9...... 8.9 .... 8.. 8.. .... 8.. 8 o o «9.. 8 9..
8.. 9... 8.. n9... .... .... .... m... 8.. 8 o o a... 8 8.
8.. 8.. 8.. 89 8.. 8.. 8.. a... 8.. 8 o o 8.. .9 8.
.... .... 8.. 8.9 8.... o... a... «..o 8.. 8 o o «9.. 8 ...
«.... 8.. 8.. 8.. .... 8.. .9. «..o 8.. 8 o o «9.. a... 8.
...o .... 8.. .9... a... .... 9... ...o .... 8 o o ...9 8 ...
.... 8.. 8.. 8.. a... 8.. 8.. .... .... 8 o o ...9 8 ...
.... .... 9... 8.. 8.. .9... 8.. .... .... 8 o o ...9 .9 ...
.... .9. «.... .9... .... .... 8.. 8.. o... 8 o o ...9 8 ...
8.. 8.. 8.. 8.. .... a... .... 8.. .... 8 o o ...9 .... ...
.... «9.. 8.. 8.. 8.... 8.. .... ...o .... 8 o o ...9 8 9..
8.. 8.. 8.. 9... 8.. 8.. 8.. .... .... 8 o o ...9 8 0..
8.. .... 8.. .9... 8.. 8.. .... 8.. .... 8 o o ...9 .9 «..
.... 8.. .... 8.. 8.. 8.. 8.. 8.. .... 8 o o ...9 8 ...
8.. 8.. .... 8.. .... o... .... 8.. .... 8 o o ...9 m... ...
8.. 8.. 8.. 8..... 8.. 8.. 8.. 8.. .... 8 o o ...9 8 8.
.o 8 mo 3 8 «o .o ...... 9.... 88.... ...m 2.880 9. .882 .o
3..... 88...... 8.8m 5m .28 .888 3.5.2... .....o .... 2B
I J! ill 1

 

 

 

8.35:8. .35.... 8..-8..... .... 38...... .... ... a... 88...... .8 8.852... ...... ..o ......

283

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.. 8.. 9..9 .... 8.. 8.. .... 8.. .... .. 9 o 8.. .... ...
.... 8.. .9... 8.9 8.. 8.. ...... «... .... 8 o o ...9 8 .8
8.. 9... 8.. .9.9 8.. o... ...... «..o .... 8 o o ...9 8 .8
9... m... .... ...9 .... o... 9.... ...o .... 8 o o ...9 .9 .8
8.. .... .... 8.. .9. 8.. 8... ...o .... 8 o o ...9 8 .8
.... .... 8... 8.. 8.. 8.. 8... ...o .... 8 a o ...9 a... .8
8.. .... ...9 8.. 8.. 3.. .... ...o .... 8 o o ...... 8 8
8.. 8.. .... ...9 .... 8.. 8... ...o .... 8 o o ...9 8 .8
8.. 8.. 8... ...... 8.. .... 8... a... .... 8 o o ...9 .9 8
8.. 9... ...9 8... 8.. 8.. ... .. .... .... 8 o o ...9 8 .8
8.. .... .3. 8.. 8.. .... ...... a... .... 8 o o ...9 a... 8
8.. .... 9..9 8.. 9... 8.. 8... .... .... 8 o o ...9 8 8.
.... .... 9..9 .... .... .... ...... ...o .... 8 o o ...9 8 8.
.... 8.. 8.. ...9 .... .9... ...u. .... .... 8 o o ...9 8 ...
...... 8.. 8.. 9... 8.. .... 8... 8.. .... 8 o o ...9 8 8.
.... .98 .... 8.... .... 8.. ...... 8.. .... 8 o o ...9 .... 8.
.... 8.. .... .... 8... 8.. .... a... 8.. 8 o o «9.. 8 ...
.... 8.. .... .... ...9 8.. 8.. a... 8.. 8 o o «9.. 8 8.
.... 8.. 8.. 8.. .... 8.. 9... .... 8.. 8 o a «9.. .9 «..
8.. .... 3.. 8.. ...9 .... 8.. 8.. 8.. 8 o o N... 8 ...
8.. 9... .... 8.. 8.9 .... 9... 8.. 8.. 8 o o «9.. .... 8.
.o 8 mo 5 8 «a .o 8.7 9..... 88.... ...m .....80 9. .....52 .o
3..... 88...... .88... s... .28 .88.... 3.5.2... .....o .... hm
I II n \l

 

 

.2388 .0935: cos-.5.; .08 3.0.0:. 05 .0. 88. cog-cot u:- ooooocxowa ..o>3 .6 .3.»

284

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9... .... 8.. ...9 8.. .9.. .... .... 8.. 8 . . «9.. 8 .8
8... .... .... .... .... .... .... .... 8.. 8 . . 8.... 8... .8
.... .... .... ...9 .... .... .... .... .... 8 . . a... 8 .8
a... a... 8.. .... 8.. 8.. .... .... .... 8 . . 8.... 8 .8
8.. .... ...9 8.. .... 8.. .... .... .... 8 . . 89.. .9 .8
.... .... .... .... .... .... 3.. .... .... 8 . . «9.. 8 .8
.... 8.. 8.9 ...9 3.. 8.. .... .... .... 8 . . .... .... .8
8.. 8.. .... 8.9 .... .... 8.. .... .... .. 9 . 8.. 8 98
9... .... .... .... .... .... 8.. 8.. .... .. 9 . 8.. 8 .8
.... 8.. 8... 8.. 8.. .... .... .... .... .. 9 . 8.. .9 8.
.... .... .... ...9 .... .9. .... 8.. .... .. 9 . 8.. 8 .8
8.. .... .... 9... .... .... .... 8.. .... .. 9 . 8.. .... .8
.... .... .8... 8.. .... .... 8.. 9... .... .. 9 . 8.. 8 ...
.... 8.. ...9 .... .... .... 8.. 99.. .... .. 9 . 8.. 8 ...
.... .... ...9 8... .... .... .... .9. .... .. 9 . 8.. .9 ...
«9.. 8.. 8.9 .... .... .... 8.. .... .... .. 9 . 8.. 8 ...
.9.. 8.. 8.9 8.. .... .... .... 8.. .... .. 9 . 8.. 8... ...
.9. 8.. ...9 9... .... .... 9... 99.. .... .. 9 . 8.. 8 9..
.... 8.. 9... .... 8.. 8.. .... 99.. .... .. 9 . 8.. 8 ...
8.. 9... ...9 ...9 .... 8.. .9.. .9.. .... .. 9 . 8.. .9 8..
8.. .... .... ...9 .... .... 9... 8.. .... .. 9 . 8.. 8 ...
.o .o .o 5 .o a. .o 4% 9.... 3a... 8.. 3228 9 3.5.2 .o
is. 8.3.6 .8... Sal .2... was... 3.5.2» ...... 3?. 8m

 

 

.Goacacoov .0995: €09.53 «.8 3.0.3:. 05 .0. Jun c0901.... 93 00305.25 .0»... pd 03¢».

285

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.9.. ...8 .... ...9 .... 8.. ...8. .... 8... .8 .. . 8.. .. 8.8
8.. ...8 .... 8.. .... .9. 8.8. 8... 8... .8 .. . 8.. .8 ..8
...8 .... 8.. .... .... ..... 8.... 8... 8... .8 .. . 8.. . ..8
8.8 .... ...9 8.. 3.. 8... 8... .... 8... .8 .. . .... ..8 .8
...8 .... .... .... 8.. 8.8. 8... .... 8... .8 .. . 8.. 8 .8
.... ...8 .... .... 8.. .9.. ...... .... 8... .8 .. . 8... .9 .8
...8 ...8 .9.. .... 8... .8... ...... .... 8... .8 .. . 8.. .8 .8
9... ...8 ...9 .... .... .... ...8. .... 8... .8 .. . .8... 8.8 .8
...8 9... 8.. .... 8.. 8... 8... .... 8... .8 .. . 8.. 8 98
.... 8.. ...9 .8. 8... 8... ...8. .... 8... .8 .. . .... 8 .8
8... 88.. 8... 8.. .... 8... ...8. 8.. 8... .8 .. . 8.. .9 88
8... ...8 8.9 99.. 8.. 8... ...8. .... 8... .8 .. . .... 8 .98
8.. .... 9..9 .... .... .... ...8. .... 8... .8 .. . 8.. ...8 .8
.... 8.. ...9 9... 8... .... 8... .... .... .8 . . 8.... 8 .8
.... .... 8.9 8.. 8.. 8.. 8... .... .... .8 . . - 89.. 8 .8
...8 9... ...9 8.. .... .... .... .... .... .8 . . 8... .9 .8
..8 .... .9.. .... .8. 9... 8.8. .... 8.. .8 . . 8... 8 .8
...8 8.. ...9 8.. .... .... .... .... .... .8 . . 8... .... .8
8... 8.. 8... 8.. .... .... .... .... .... .8 . . 8... 8 88
.... .... .9.9 8.. .... 8.. 8... .... .... .8 . . 8.... 8 .8
8.. 8.8 .... ...9 9... 8.. 8.. 8... .... .8 . . 8... o. 88
.o .o .o 9. 8 8. .o ...... ...... .8... .8. 3228 o... 3.5.2 .o
...... 8.2% .8... ...I ...8 355 82E ...8 .8. 2M

 

 

.6888. 3...... 8..-...8. .8. .88.... .... .o. a... 8.2.... .5 882...... ...... ... ......

286

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.. 8.8 .... .... .99 .... .... .... .... 8 . . .... 8 ..8
.... 8..8 .... .... «.9 .... .... .... .... .8 . . ...9 o. 8..
.... .... 8.8 .... 8.. 8... .... 8... .... .8 . . ...9 .8 ..8
.... ...8 3.. 9... ...9 .... .... 8... .... .8 . . .... 9.8 ..8
.... 8.8 9.8 .9.. 8.. 9..9 8.. 8... .... .. . . .... 8 .8
9... ...8 .... .... 8.... ...9 .... 8... .... .. . o 8... 8 .8
8.. .... 3.. .... ...9 .... 8.. 8... .... .. o . .... .9 ..8
.... .... 8.8 .... ...9 .... .... 8... .... .. . . .... 8 .8
.... .... 8... ...... 8.. .... .... 8... .... o. . . .8... ..98 .8
8.. .... 8.. .8. .9.. .... .... .... .... .. . . .... 8 ...8
8.. 8.8 .... ...9 ...9 .... .... .... .... .. . . .... 8 ..8
8.. .... ...8 .... 8.. ...9 .... .... .... .. . . .... .9 8.8
.... ...8 ...8 8... 98.9 ...9 8.. .... .... .. . . .... 8 .8
.... .... ...8 .... 8.9 ...9 9... .... .... .. . . .... 8.98 88
.... 8.8 .... .... ...9 8... 8.. .... .... .. . . .... 8 .8
.... . ..8 3.. 8.. 8.. .... .... .... .... .. . . .... 8 .8
.... 8.8 .... ...9 ...9 .... 8... .... .... .. . o 8... .. .8
8... 8.8 8.. ...9 8... .... .... .... .... o. . . .... 8 .8
.... 88 .... .... .... 8.. 8.. .... .... .. . . .... ..98 .8
.... ...8 .... .... .... .... ...8. .... 8... .8 .. . .... 8 8.
.9.. ...8 .... ...9 8.. .... 8.8. .... 8... 8 .. . .... 8 .8
.o .o .o 8 .o 8. .o ...... ....5. .8... o... 2228 9. 3.5.2 .o
3.5. 5.82.6 .8... 5m... ...... ...8... 83......» ...8 .8. 2m

 

 

 

.6158.853§298§.8.23§§8888£8.§88§3.i§ ... 3...

287

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... .... ...8 .... .9... 8.. .8.. .9.. .... .. 9 . 8.. 8 ...8
.... .... ...8 .... .... .... .... .9.. .... .. v . 8.. 8 .8
8.. .... ...8 8.. 8.. 8.. .... 8.. .... .. c . 8.. .9 88
8... 8.. ...8 .... 8.. .... .... .9. .... .. 9 . 8.. 8 .8
.... 8.. ...8 .... 8... .... .... .... .... .. 9 . 8.. ...8 .8
.... ...8 8.. .... 8.. .9.. 8.. .... .... 8 . . .... 8 .8
3.. ...8 9... 8... .... .... .... .... .... 8 . . .... 8 .8
3.. ...8 .... .... .... 8.. .... .... .... .8 . . ...9 .9 .8
.... ...8 .... 9..9 9... .... 3.. .... .... .8 . . ...9 8 .8
.... ...8 .... ...9 8.. 8.. .... .... .... .8 . . .... ..8 ..8
.... .... .... .... .... .... .... .... .... .8 . . .... 8 .8
8... .... ...9 .... .... 8.. 8... 8.. .... .8 o . .... 8 .8
8... ...8 .... .... 8... .... .... .... .... 8 . . .... .. 8.8
9... ...8 .... 88.9 .... .8.. 8... . .... .8 . . .... 8 .8
.... 9.8 .... .... .... .... 8.. . .... 8 . . ...9 8.8 88
.... ...8 .... 8..9 .... .... 8.. .... .... 8 . . ...9 8 ..8
.... 8.8 8.. 8... .... 8.. 8.. .... .... .8 . . .... 8 ..8
.... ...8 .... .... .... .... 8... .... .... .8 . . .... .. ..8
8.. 8.8 .... .... .... .... .... 8... .... .8 . . .... 8 ..8
.... ...8 ...8 8.. .8. .... .... 8... .... .8 . . .... ..8 .8
8.. ...8 .... .... ...9 8.. .9.. .... .... .8 . . ...9 8 ...8
.o .o .o 5 8 8. .o .... 2.5. .8... 3.. 3288 3 8.5.2 .o
3.5. 5.8.3.... .8... ......l 2.. :22... 38.2% ...8. .8. 2%

 

 

€8.58. 3.5... 8..-...8. .8. .38.... .... ... ...... 8.8.... .5 882...... 8...... ... ......

 

 

 

 

 

 

 

 

 

 

 

288

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... .8.. 8.. .... .... .8. .... 8.. 8... 9 . . 8... .... ...
.... .Q. ...8 ...8 .8... 8.. .... 8.. 8... 9 . . 8... 8 9..
.... 89.. 8.8 .... ...9 8... .... 8.. 8... 9 . . 8.. 8 ...
.... .9.. 98.8 .... 8..9 9... 8.. .... 8... 9 . . 8... .. 8..
.... .... ...8 9.8 ...9 .9. 8.. .... 8... 9 . . 8... .8 ...
.... .... ...8 ...8 ...9 .... .... .... 8... 9 . . 8... 8... ...
.... .q. ...8 ...8 .... 8... .... .... 8... 9 . . 8... 8 8.
... 8.. ...8 8..8 ...9 .... .... .... 8... 9 . . 8... 8 .8
8... 8.. .... ...8 8... .... .... .... 8... v . . 8.. .9 ...
.... .... ...8 8.8 .... 8... 8.. .... 8... 9 . . 8... 8 ...
.... 8.. ...8 ...8 8..9 .... .... .... 8... c . . 8... .... ...
8.. 8.. 8..8 .... .9.9 .8. 8. 8.. 8.. ... 9 . .... 8 3.
.... .... .... .... 8.9 8.. .... 8.. .... .. 9 . 8.. 8 8.
.... .... .... 8... ...9 8.. .8. .... .... .. 9 . 8.. .9 8..
8. 8.. 8.8 .... .... .... .... .9. .... .. v . .... 8 .8
8... .... .... .... 8.9 8.. .... ... .... .. 9 . 8.. ...8 8.
.... .... .... .... 8... .... .... .... .... .. v . .... 8 .8
8.. .... ...8 .... ...9 8.. 8... 8.. .... .. 9 . 8.. 8 .8
8... .... ...8 .... .... .... .... .... .... .. 9 . 8.. .. .8
8... .... ...8 8.. ...9 .... 8.. ... .... .. 9 . 8.. 8 .8
8. .... ...8 99.. .9.9 .... .... 9.. .... .. 9 . .... 8..8 .8
.o .o .o .5 .o 8. .o ...... 9.5. S... 3.. 229.8 02 8.5.2 .o

3.5. 8..8... .8... ..F. .2... .88.... 8.5.0.... ...8. .8. 2.

L i I

 

 

.8358. .35... 8..-...8. .8. .38.... 2.... so. 8.2.... .5. 8.85.2... i... ... ......

 

 

 

 

 

 

 

 

 

 

 

 

 

289

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... 8.8 .... 8.9 .... .... 8.. .... .... .. 9 . 8.. .8 ...
8.. .8.. .... ...9 .... .... ... .... .... .. 9 . 8.. ...8 ...
.8.. 8.8 .9. 8... 8.. 8... 8.. .... .... .. 9 . 8.. 8 9..
.8.. 8.. .... 8.9 .... .... .9. .... .... .. 9 . .8.. 8 ...
8.. 8.. .... 8.. 8... .... 9... .... .... .. 9 . 8.. .9 ...
8.. 8.. .... 8.9 .... .... .... .... .... .. 9 . .8.. .8 ...
.8.. 8.8 .... ...9 .... 8... 8.. .... .... .. 9 . .8.. .... ...
8.. 99.8 .... ...9 ...9 .... .... ... .... .. v . .8.. 8 8.
.... .98 .... .... .... 8.. .9. ... .... .. 9 . 8.. 8 8.
.8.. .... .... ...9 .... .... .... ... .... .. 9 . 8.. .9 .8.
.8.. 8.8 .... ...9 .... 8.. .9. .... .... .. 9 . 8.. 8 8.
8.. 8... .... .... .... .... .... .... .... .. 9 . 8.. 8.8 8.
.9.. .9. .... ...9 .... .... 8... ... .... .. 9 . 8.. 8 8.
.... .9.8 .... 8..9 8... 8.. 3.. 8... .... .. 9 . 8.. 8 8.
8.. .... 8.. ...9 .... .9. .... 8... .... .. 9 . .8.. .. 8.
.... .9. .... .... .... .... 8.. 8... .... .. 9 . 8.. .8 .8.
.... .... .... ...9 .... 9... .... 8... .... .. 9 . .8.. .... 8.
.... .... 8..8 9.. ...9 .... .... ... .... 9 . . 8. 8 ...
.... .... .... .... .... 8.. 8.. 8... 8... 9 . . 8... 8 ...
.... .8.. ...8 .... 8.9 .... 8.. .... .... 9 . . 8. .. ...
.... 9... 8.8 .... 8... .... .... 8.. 8... 9 . . .... .8 ...
.o .o .o 9. .o 8. .o .... ...... 8.... .8. 2.6.8 02 3.5.2 .o
3:88.036 623. ... 2.. ...8... ......fi ...8. 3..

 

 

.6888. 3.5... 8..-...8. .8. .38.... a... a. so. 8.8.... .5. 88.5.0.5 3.... ... a...

 

290

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... ...8 .... .9.9 8.. .... .... .... .q. .. c . 8.. .9 .8
.9.. .9.. .... ...9 .... .n. .... .... .N. .. v . 8.. 8 ...
.9.. .9.. .... .... .... 8.. .... .... 8.. .. 9 . 8.. .... ...
.... 8.. .9.. .9.. .... 9... .... .... 8.. .. 9 . 8.. 8 9..
.... 88 .... ...9 8... .9.. .... .... .q. .. 9 . 8.. 8 .8
.... 8.8 8.. 8.9 .... .8.. 8... .... 8.. .. 9 . 8.. .. .8
.8.. 8.. .... .... 8.. .... 8.. 8.. 8.. .. c . 8.. 8 .8
.8.. 8.. .... ...9 .... 8.. 8. .8.. 8.. .. 9 . 8.. 9... ...
.... 8.. .... ...9 .... 8... .... .... 8.. .. 9 . 8.. 8 .8
.... ...8 8... ...9 .... 8... .... .... 8.. .. v . 8.. 8 .9.
.... 98.. 8... ...9 8.. .... .... .... .w. .. 9 . 8.. o. .8
.... .... .... .... .... .... .... ... 8.. .. 9 . 8.. 8 .9.
.... 8.. ...8 .... ...9 .... .... .... 8.. .. 9 . 8.. .... .8
.... ...8 8.. .... .... .... 8.. ... .... .. 9 . 8.. 8 98
8... .... .... 8.. .... 8.. .... ... .... .. v . 8.. 8 .9.
.... ...8 .... ...9 8... 8.. .... ... .... .. 9 . 8.. .9 89.
8... .... 8.. ...9 8.. 8. .... ... .... .. 9 . 8.. 8 .9.
.... .... .... .... .... ... .... ... .... .. . . .8.. ..8. .9.
.... .... .... .... .... .... .... 8... .... .. c . 8.. 8 ...
.... .... .... .9.. .... .... .... .... .... .. 9 . .8.. 8 .8
.... .... .... ...9 .... 9... 8.. ... .... .. 9 . 8.. .9 ...
.o .o .o 8 .o 8. .o a... 9.5. .8... 3.. 3228 02 3.5.2 .o
3.5. 8..8... ...... ... .2... ...8... 8.5.2... ...... 3.. L
I I h l

 

 

.6358. 3.5.. 8.38.... .8. .88.... 2:98... 8.8.3. .23 8.8.25.2... ... ......

291

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.... 9..9 .9... E... .9... a... 9..: .... .9.. . h . 8.. 8 ...
8.. .... .2 .... 9.... 2.9. ...: .8.. .9.. . h . 8.. .9 R.
.... ...9 .... 8.. ...... ...: 8... .... .9.. . s . 8.. 8 ...
8.. ...9 9... .... .9... .9.: 9..: .... .9.. . s . 8.. «.8 .8
.... .... kg 5... 8.... 3.9. 8... .... .3 3 9 . 8.. 8 9..
8.. .... .3 .... ...: 99... 8... .... .3 .3 9 . 8.. 8 2..
8.. 8.. 8.. .... 8... .....9. ...: .8.. .3 8 9 . 8.. .9 ...
2... ...9 9... .... «..: 9.... 8... .... .3 2 9 . 8.. 8 E.
.... 9..9 .9.. .... .8. ...9. .5: .... .3 3 9 . 8.. :8 8.
.... .9.. .... ...9 .... R. .9.. 8.. .3 3 9 . 8.. 8 ...
8.. 9... 9... .9.. .... .... 8.. 8.. .3 8 v . 8.. 8 ...
.3 2.. .... 8.9 .... .... .... 8.. .3 9 9 . 8.. .9 ...
8.. 8.. .... .9.9 .... .... 2.. 8.. .3 2 9 . 8.. 8 ...
.... .... .... .9.9 .... .... .... 8.. .3 .. 9 . 8.. .8. ...
.... .... .... ...9 8.. .... .... 8.. .3 2 9 . 8.. 8 9..
.3 .... 3.. 9..9 3.. .... .2. 8.. .3 .. 9 . .... 8 ...
.... .... .... ...9 .... 8.. 8.. 8.. .3 2 9 . 8.. .9 ...
.... .9.. .... 8.9 .... .... 9... 8.. .3 2 c . 8.. 8 ...
.... .... .... ...9 8.. 9... ...... 8.. .3 2 9 . 8.. .8. 8.
8.. 2.. .... .9.9 8.. 9.... .... 2.. .3 2 9 . 8.. 8 ...
.... 9... .... ...9 5.. P... 9... .... .3 2 9 . 8.. 8 ...
B .o .o 9. .o 3 E a... ...... .8... a... 222.8 o< 3.8.2 .o
3... 8.8.... .8... SF. 1.. 3.2... 32% ...8. .5. 2m

 

 

 

 

685:... .35.. .8228. .8. .83.... .5 ... a... 8.8.... .5 832...... i... ... ....»

 

 

 

 

 

 

 

 

 

 

 

 

292

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... 9... .... .... .... .... .... 8.. .... .. 9 . .... 8 ...
.... .... .... .... ...9 .... .... 8.. .... .. 9 . .... 8 ...
.... .... 9... ...9 .... .... .... 8.. .... .. 9 . .... .9 ...
.... .... 8.. 9..9 .... 8.. .... 8.. .... .. 9 . .... 8 ...
.... .... 9... ...9 .... 2.. k.» 8.. .... .. 9 . .... .... ...
.3 .... .... ...9 .... .... .... 8.. .... .. 9 . .... 8 ....
.... .... .... ...9 8.. .... 8.. 8.. .... .. v . .... 8 ...
.3 8.. .... v.9 .... .... .... ... .... .. 9 . .... .9 «..
.... .... 8.. ...9 ..9 .... .... .... .... .. 9 . .... 8 ...
.... .... .... .... 8.. .... .... .... .... .. 9 . .... .... ...
.... .... .... .... .... .... .... .... .... .. 9 . .... 8 ...
.... .... .... 9... 89 .... .... .... .... .. v . .... 8 ...
.... 8.. .... ..9 .... 9.. .... .... .... .. v . .... .9 ...
.... .... .... 8.. ..9 8.. .... .... .... .. 9 . .... 8 8.
.... .... 9... .... ...9 8.. 3.. .... .... .. 9 . .... 9... ...
8.. 8.. .... .... .... 2... .9... .... .... . s . 8.. 8 8.
2... ..9 .... .... .9... ...! .... .... 9.. . s . 8.. 8 ...
.... ...9 .... .... ...8. ...... .... .... .9.. . h . .... .9 ...
.... .... 8.. .... 8... .... .... .... 9.. . h . 8.. 8 ...
.... .... .... .... ...... ...... B... .... 9.. . h . 8.. ..8 ...
.... .... .2. .... ...8. ...9. 8... .... .9.. . s . 8.. 8 ...
B .o .o 9. .o u. .. .... as. .3... 8.. 222.0 9 3.5.2 .o

3.5 SEEM 52.. Sal .2... .8.... 82......» ...... .... 2

 

 

.§§.:.§c 8298833533§838888§§§£EJ ... ......

 

293

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.. .... 9n. 9... 8.9 ...9 .... .... 3. . .. . 8.. .... 89
.9.. .... 8.. ...9 .... .... .... .... .... 8 . . R... 8 ...
.9.. 9... .... ..9 .... 8.. .3 .... .... 8 . . R... 8 ...
.9.. R... .... 8.9 ..9 .... .9.. ... .... 8 . . R... .9 R9
8.. .... .... 8.. ..9 8.. .... .... .... 8 . . .... 8 ..9
.... 8.. .... ...9 ...9 .9.. .... .... .... 8 . . R... .... ..9
.3 .... .... .... ...9 .... .... ... .... 8 . . R... 8 9.9
.... .9.. .... ...9 .... 9... R... ... 8.. 8 . . R... 8 ..9
8.. 8.. 8.. .... ...9 .... 8.. ... .... 8 . . .... 8 ..9
8.. .... 9... ..9 z... .... .... ... .... 8 . . .... 8 ....
.3 .9.. .... ...9 .... .... R9,. ... 8.. 8 . . R... .... ..9
.3 .... .9.. 9..9 ..9 .... .... .... .... 8 . . R... 8 ..9
.... 9... .9.. ...9 .... R. 8.. .... 8.. 8 . . R... 8 ..9
.... 8.. 8.. ...9 ...9 .... 8.. .... .... 8 . . R... .9 ..9
.... .... 89 .... .... .... .... .... .... 8 . . .... 8 ..9
8.. .9.. .... ...9 9... .... 8.. .... .... 8 . . R... . R. ..9
R... 9... 8.. ...9 .... .R. 93. .... .... .. 9 . .... 8 ..9
.... .... .... 9..9 9... .9.. ...R .... .... .. 9 . .... 8 ..9
.3 .... .9.. ...9 8.. .... ...... N. .... .. 9 . .... .9 ...
.... .... 8.. ...9 ..9 .... .... 8.. .... .. 9 . .... 8 ..9
.... 9... .... 8.. 8.9 .9.. .... 8.. .... .. 9 . .... .... 89
.. .. .. 9. .. u. .. ...... ...... 8.... a... .33... o< 3.2.2 .o
..__%88.... 323. ... ...... .38.. 3.5.0.... ...... .8. 2m
I II [I I

 

 

 

€8.88. 3..... ...-...8. .8. 8.8.... .... 3. so. 8.2.... us. .8853... 3..... ... ......

294

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... .... .... ...9 .q. 8.. 9..R ... .... .. . . 8.. 8 .3
.... .... .... ...9 8.. 8.. ...R ... .... .. . . 8.. .... .99
.... 8.. .9.. ..9 .... 8.. .... ... .... .. . . 8.. 8 ....
.3 .... .... .... 8.. .... .... ... .... .. . . 8.. 8 ....
8.. .9.. 8.. ...9 .... .... .... .... .... .. . . 8.. 8 ..9
.... 8.. .... ...9 .... R. .... .... .... .. . . 8.. 8 ..9
.... .... .... 9.9 .... 8.. .... .... .... .. . . 8.. .... ..9
.... .... .... 8.. ..9 ...9 .... .... .... . .. . .3 8 8.
.... .... .... .... ...9 ...9 R... .... .... . .. . ...R 8 ...
.... .... .... 8.. ..9 9..9 .... 8... .... . .. . .3 .9 ..9
.... .... .... .... ...9 .R9 .... . .... . .. . .3 8 ....
.... .... .... .... ...9 ...9 8.. . .... . .. . .3 .... ..9
.... .... .... .... ...9 89 .... .... .... . .. . .3 8 ..9
.... 8.. 8.. .... ..9 ...9 .... .... .... . .. . .3 8 89
.... 8.. .... .... ...9 ...9 .... 8... .... . .. . .3 .9 ...
8.. .... 8.. .9.. ..9 ...9 .... .... .... . .. . .3 8 89
.... .... 9... .... 9... 8.. .3 .... 8.. . .. . .3 .... ...
8.. 8.. .... .... ..9 ..9 .... .... .... . .. . .3 8 9.9
8.. .... 9... .... ...9 8.9 .... .... 8.. . .. . .3 8 ..9
.... .... .9.. .... .... ..9 .... .... .... . .. . .3 .9 ..9
.... 8.. 9... .... ...9 ..9 8.. .... .... . .. . .3 8 ..9
R. .. .. ... .. .. .. ...... ...... .8... a... .3380 3 3.5.2 .o
3..... 8.02%“. 32.. Hm: ...... .38... 2353...“.n ...... .3: 8%

 

 

635:8. 89:5: c3392... 88 ...8-0.0:. .5 8. 8st 8309:... v... 33.5.0.5 .234 ..m 03-...

295

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R. .... 8.. 8.. .... ...9 .... . R... . . . .3 .. ..9
.... .3 8.. 8. 2... ...9 .... . R... . . . .3 8 ....
.... .... .... .... .... 8.9 .R.. . R... . . . .3 ...9 8.
9... .... .... 8.. 9.... 89 .... .... .... . . . .3 8 ..9
.... 8.. .... .... .... ...9 R. .... R... . . . .3 8 ..9
.... .... .... .... .... .... .... .... R... . . . .3 .9 ..9
.... .... .... .... .... ...9 9... .... .... . . . .3 8 ..9
.... .3 .... .... .9.. ...9 .... .... .... . . . .3 .... ...
.... .... .... .... .... .3 R... .... .... . . . .3 8 9..
.... .... .... .... 8. ...9 8.. .... .... . . . .3 8 ..9
9... .... .... .... .... ...9 .9.. .... .... . . . .3 .9 ..9
.... .... .... .... .... ..9 .... . .... . . . .3 8 ..9
.... .9.. .... .... .n. .... R. . R... . . . .3 .... 89
.9.. 8. .... 8.9 .... .... .9.. .... .... .. . . 8.. 8 .99
99.. .... .... ...9 .... .... .... .... .... .. . . 8.. 8 .99
9... R9. .... ...9 .... .... .3 ... .... .. . . 8.. .9 .99
.9.. .... .... ..9 8.. .... .3 ... .... .. . . .... 8 .3
.... .... .... ...9 .... .... .... ... .... .. . . 8.. .... .8
9... .... .... .... .... .... .3 ... .... .. . . .... 8 99..
8.. .... 8.. .... ...9 8.. ...R ... .... .. . . 8.. 8 ..9
.... 8.. 9... 9... ...9 .... .... ... .... .. . . 8.. .9 .99
B .. .. ... .. .. .. ...... ..5. .8... a... .3380 o... 3.5.2 .o

3..... .o.o._3m32.. 5m... .32... 32...... .85....» ...8. 3.. SB

 

 

.6358. 3..... 8..-...8. .8. .88.... 2.3. a... 8.2.3. .8. 8..-5...... 3.... ... ......

 

 

 

 

 

 

 

 

 

 

 

296

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... .... .... .9.. 89 8.. .... .... .... 8 9 . 8... 8 ..9
.... .... .... .... ..9 R... ...R .... .9.. 8 9 . 8... .. ...
9... .... .... .9.. 8.. ..9 .... .... .... 8 9 . 8... 8 ..9
.... 8.. 8. .... .R. ...9 9... .... .9.. 8 9 . 8... .... 89
.... .... .... 99.. ...9 .... 9... .... .... . . . .3 8 ..9
8.. .9.. .... .... .9.9 .9.. .3 .... .... . . . .3 8 .2.
R.. 99.. 8.. R... ...9 .9.. 93 .... .R.. . . . .3 .9 R9
.... .9.. 8.. .... 9N9 .... 8.. .... .... . . . .3 8 ..9
.... 8.. .... .... ..9 .... .3 .... .... . . . .3 ...9 ..9
8.. .... .... .... .... 8.9 8.. .... .... . . . .3 8 9...
.... .... .... 9... ...9 ...9 .... .... .... . . . .3 8 ..9
9... .... 9... .... .... ...9 .... .... .... . . . .3 .9 ..9
8.. .... 8.. ... .... ...9 .... .... .... . . . .3 8 ..9
.... .... .... .... 9... ...9 9... .... .... . . . .3 ...9 ..9
.... .... .... .... .... 9..9 .... .... .R.. . . . .3 8 ..9
R... .... 8.. R. .... ...9 .... .... .... . . . .3 8 ..9
.... .... 9... 8.. .... R9 .... .... .R.. . . . .3 .9 ...
.... 9... .... .... R. ...9 .... .... .... . o . .3 8 ..9
.... .... .... ... .... ..9 .... .... .... . . . .3 ...9 ..9
.... .... .... .R. .... ...9 .... . .... . . . .3 8 89
.... .... .... ... .... ...9 .... . .... . . . .3 8 ..9
.. .. .. 8 .. .. .. ...... ...... .8... 3.. .3380 o... 3.5.2 .o
...... 5.8.3. 32.. 5F. .2... ...8... 32...... ...8. 3..

 

 

33583.5 829.833.333.28... 8.888.882.3313 ... a...

 

297

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... .... 8.. .... ...9 ...9 .... ... R... . .. . .3 8 ....
9... .... 8.. .... ...9 ...9 .... ... .... . .. . .3 8 ...
.... .... ... .... ...9 ...9 .... ... .... . .. . .3 .9 ...
8.. .... 8.. .... ..9 ...9 .... ... .... . .. . .3 8 ...
.... 8.. 8.. .... 93 .... .... ... .... . .. . .3 ...9 8.
8.. .... .... .... R9 .... .... ... .... . .. . .3 8 ..9
.3 .... 8.. ...9 .... 8.. 8.. ... .... . .. . .3 8 ...
.... .... .... ..9 .... .... .... .... .... . .. . .3 .9 R...
8.. .... .... 89 .... .... .... .... .... . .. . .3 8 ..9
.9.. .9.. .... ..9 .... .... .... .... .... . .. . .3 ...9 ..9
.... 8.. .... 8.. ...9 .9.. R... .... .... 8 9 . 8... 8 9..
.... 9... .... .... .... ...9 .n. .... .9.. 8 9 . 8... 8 ....
.... .... .... .... R... ...9 .9.. .... .... 8 9 . 8... .9 ..9
.... .... .... .... ...9 .R9 .... .... .... 8 9 . 8... 8 ..9
.3 .... .... .9.. ...9 .... .... .... .... 8 9 . 8... .... ...
.... 8.. 8.. .... 9.9 R9 .... .... .... 8 9 . 8... 8 ...
8.. .... 8.. .9.. ..9 ...9 9... .... .9.. 8 9 . 8... 8 ..9
.... .... .... .... .9.9 .... .3 .... .... 8 9 . 8... .. R...
.... .... ... 8.. 8.9 8.. .... .... .... 8 9 . 8... 8 ..9
.... .... R... .... 9..9 .... .... .... .... 8 9 . 8... ...9 ..9
.... .... 8.. .... 8.9 8.. .... .... .... 8 9 . 8... 8 8.
.. .. .. 3 .. .. .. a... ...... S... 8.. 3.3.8 o... 3.5.2 .2

«...... 8.3.3. 38.. .... ...... 32...... 3.5.0.... ...8. .3. P...—

I i' n I

 

€35.80. 3..... 8..-...8. .8. .28.... 2.. 3. a... 8.333 ..5. $88.... 3..... ... ......

298

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... 9... .9.. 8.9 .... .... 8... .... .... .. .. . .... 9..9 ...
.... .... .... 8.9 .... .... 9.... .... .9.. .. .. . 8.. 8 9..
.... 8.. 9... ...9 .... .... .... .... .... .. .. . .... 8 ...
.... .... .... ..9 R... .... .... .... .... .. .. . .... .9 ...
.... .... .... .9.9 R... .... .... .... 8.. .. .. . .... 8 ...
8.. 8.. .... ...9 8.. .... 3... .... .... .. .. . 8.. ...9 8.
.... .... .... ..9 .... .... 8... .... .... .. .. . .... 8 ...
.... .... 9... .99 .... .... 8... .... .... .. .. . .... 8 ...
.... .... .... .99 .... .... ...... .... .... .. .. . .... .9 ...
.... .... .... ...9 .... 8.. .... .... .... .. .. . .... 8 ...
.... .... .... .... .... 8.. 8... .... .9.. .. .. . .... ..R. ...
.... R... .... .99 R... .... .... .... .9.. .. .. . .... 8 9..
.... .... .... .99 8.. .... 8... .... 8.. .. .. . .... 8 ...
9... .... .... ...9 .... .3 ...... .... .9.. .. .. . .... .9 ...
.... .R.. 9... .... .9.. 8. .... .... .... .. .. . .... 8 ...
.... 8.. ... .... .... .... .... .... .... .. .. . ... ...9 ...
.... .... .... ..9 .... 8.. 8.. .... R... . .. . .3 8 ...
.... .... .... .... ..9 .... .... .... .... . .. . .3 8 .8
...... 8.. R. .... ..9 8.9 .... ... .... . .. . .3 .9 ...
.... 8.. .... .... ..9 89 .... .... .... . .. . .3 8 ...
.... .... .... .... ..9 89 .... .... .... . .. . .3 ...9 ...
.. o. .. 9. .. .. .. .... ...... ...... .... .3380 9. 3.6.2 .o
3.... 8.8.6 3.8. .... ..<.. ...8... 88% ...... 3... ...

 

 

...3380. 3...... 8.29... .... .38.... .5 3. .... 8.8.... .... 8.8.8.... 3..... ... 2...

 

299

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9... 9... .... .... ...9 ...9 .... .... .... . . . .... 8 .9.
.... .9.. .... ..9 .... 9... .... .... .... . . . .... .... .9.
.... 9... .... ...9 ...9 .... .... .... .... . . . .... 8 99.
.R.. .... .... ...9 ..9 ...9 8.. .... .... . . . .... 8 .9.
.... .... 9... .... .... ...9 9... .... .... . . . .... .9 ...
9... 99.. 9... .9.. .... .... ...9 .... .... . . . .R.. 8 .9.
.... .... .... .... .... .... R... .... .... . . . .... .... .9.
.... R... .9.. ...9 .... .... 3.. .... .... . . . .R.. 8 ...
.... .... .... .... .... ...9 .... .... .... . . . .... 8 ...
.9.. .... .... R... 9... ...9 .... .... .... . . o .R.. .9 ...
.... .... .... .... .9.. .... 9... .... .... . . . .... 8 ...
.9.. .... .... .... .... .... ...9 .... .... . . . ...... .... ...
.... .... .... .... .... .... .... .... .9.. .. .. . .... 8 9..
.... .... .9.. 9..9 .... .... 9.... .... .9.. .. .. . .... .. ...
.... 9... R... ...9 .... .... .... .... .9.. .. .. . .... .9 ...
.... 9... .9.. ...9 .... .... 9.... .... .9.. .. .. . .... 8 ...
.... .... .9.. ...9 R... .... .... .... .9.. .. .. . .... ...9 ...
.... .... .... ...9 .... .... .... .... .9.. .. .. . .... 8 8.
.... .... .... ...9 .... .... .9... .... .9.. .. .. . .... 8 ...
9... 9... .... ...9 .... .9.. .... .... .9.. .. .. . .... .9 ...
.... .... .... k9 .... .... .... .... .9.. .. .. . .... 8 ...
B 3 .o 9. .o .o .o ..5. ...... ...... .... 3228 9. ...:52 .o
3.... 8.2%.“. .8... SF. .2... ...... 8.5.2..» .2... .... 2m

 

 

.8288. ....5. 8.89... .... 3...... .5 3. .... 8...... .8. 8.8.x... ..»... ... ......

300

 

 

.63....8. .35... 5.29... .... .38.... ... ... .... 5...... ... 88.5.0... i... ... ....»