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LIBRARY
Michigan State
University

 

 

 

 

PLACE IN RETURN BOX to remove this checkom from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

%EE,DUE

DATE DUE

DATE DUE

 

WE /

JUL 2 12062

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1100 W.“

 

 

-. _.__— ..-_.....——-

This is to certify that the

dissertation entitled -

BACKCALCULATION OF PAVEMENT LAYER PROPERTIES FROM
DEFLECTION DATA

presented by

Tariq Mahmood

has been accepted towards fulfillment
of the requirements for

Doctor of Philosophy degreein Civil Engineering

Ronald Harichandr nW‘CL'L

Gilbert BaladiMM‘
Majorprofes r

 

Date 11/17/93

man an Ajfmm‘w Action/Equal Opportunity Imitation 042771

BAC

 

BACKCALCULATION OF PAVEMENT LAYER PROPERTIES FROM
DEFLECTION DATA

By

Tariq Mahmood

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

‘X

ABSTRACT
BACKCALCULATION OF PAVEMENT LAYER PROPERTIES FROM

DEFLECTION DATA

BY

TARIQ MAI-IMOOD

A computer program named MICHBACK has been developed for the
backcalculation of pavement layer properties. The program uses a modified Newton
algorithm to backcalculate pavement layer moduli and thicknesses from measured
surface deflections. It is shown that the newly developed algorithm to predict the
roadbed soil modulus at the cost of only a single call to a mechanistic analysis
program is accurate. An iterative modified Newton method to calculate the stiff layer
depth from deflection data is presented and its accuracy is discussed. The ability of
MICHBACK to predict any one of the layer thicknesses along with layer moduli from
deflection data is presented. An extensive sensitivity analysis of the backcalculated
results to the initial seed moduli is included. Some of the user-friendly features of the
MICHBACK program are also presented.

The program has been extensively tested using theoretical deflection basins
generated by using a multilayer linear elastic program, as well as field data obtained
by using a falling weight deflectometer (FWD). The results of these tésts which
validate the accuracy and robustness of the program are included. The sensitivity of
the results to many factors known to affect the backcalculation results are also
explored. The capabilities of the program have been compared with other leading
backcalculation programs and the results indicate the superiority of the MICHBACK
program in many aspects. The effect of temperature on the backcalculated layer
moduli has also been examined.

 

TO MY PARENTS AND FAMILY

 

ACKNOWLEDGEMENTS

First of all I want to thank Allah Almighty for providing me with the
opportunity to undertake and complete this task. Thanks are also due to the Pakistan
Army Corps of Engineers for sponsoring my study program. I also want to thank the
Michigan Department of Transportation and the University of Michigan
Transportation Research Institute for sponsoring this study.

I want to express my gratitude and sincere thanks to my two co—chairpersons,
Dr. R.S. Harichandran and Dr. G.Y. Baladi for their continuous professional
guidance and moral support without which it would not have been possible to pursue
this study. Dr. Harichandran guided the development of the backcalculation algorithm
and the programming; Dr. Baladi guided the field data collection and validation, and
was the principal investigator for the project. Dr. W.C Taylor and Dr. R.V Erickson
deserve special thanks for serving on the advisory committee and for their comments
and interest.

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.

I acknowledge with gratitude the dedicated and professional assistance
provided by Cynthia Ramon and Weijun Wang in writing the MICHBACK program.
Hamid Mukhtar deserves special thanks for sharing the data prepared by him, and his
advise during the course of this study. Efforts of Stuart 8., Guy N., John A.,

iv

 

:4». l

well

Erich T., and others in data acquisition and reduction is appreciated.

The patience, understanding, and continuous prayers of my wife and my
family deserve a special mention and thanks. I am grateful to my elder brother
Mumtaz Ahmad Javaid for never letting my absence from home being felt. My
children Iqr'a and Umar deserve special thanks for their understanding and for
providing much needed moments of pleasure and relief.

. My wife deserves special thanks for her sacrifices, her help in data reduction,
proof reading, and preparation of the thesis. She prayed at difficult moments and was
a source of encouragement and inspiration. Finally, I am grateful to my late parents;

. their prayers and the strength of their education is felt every step of the way. May

Allah be happy with them.

TABLE OF CONTENTS

LIST OF TABLES ...................................... xii
LIST OF FIGURES .................................... xvii
CHAPTER 1
W ...................................... 1
1.1 GENERAL ...................................... 1
1.2 PROBLEM STATEMENT ............................ 2
1.3 RESEARCH OBJECTIVES ........................... 3
1.4 THESIS LAYOUT ................................. 3
CHAPTER 2
W ................................. 5
2.1 GENERAL ...................................... 5
2.2 NONDESTRUCTIVE DEFLECTION TESTING DEVICES ....... 8
2.3 SURFACE WAVE TESTING ........................... 10
2.3.1 Impulse Load Testing .......................... 11
2.3.2 Steady-State Vibration ......................... 12
2.3 .3 Advantages and Limitations ...................... 12
2.4 NONDESTRUCTIVE DEFLECTION TESTING .............. 13
2.4.1 Static Force-Deflection ......................... 14
2.4.2 Dynamic Steady State Vibrator .................... 15
2.4.3 ImmctLoading ........ 20
2.5 DEFLECTION RESPONSE OF PAVEMENTS ............... 21
2.6 INTERPRETATION OF DEFLECTION DATA .............. 23
2.6.1 Empirical Analysis ............................ 23
vi

 

 

 

 

W B.

2.6.2 Rational Methods .............. ' ............... 25

2.6.3 Mechanistic Analysis ........................... 25
2.7 SPECIAL PROPERTIES OF PAVING MATERIALS .......... 28
2.7.1 Material Non-Linearity ......................... 30
2.7.2 Temperature Dependency ....................... 35
2.8 MECHANISTIC ANALYSIS MODELS .................... 36
2.8.1 Layered Elastic Model ......................... 36
2.8.2 Hogg’s Model ............................... 40
2.8.3 Equivalent Thickness Model ...................... 41
2.8.4 Finite Element Method ......................... 42
2.8.5 Dynamic Analysis ............................ 42
2.8.6 Nonlinear Elasticity ........................... 46
2.8.7 Viscoelastic Model ............................ 49
2.8.8 Pavement Material Type and Choice of Analysis Model . . . . 50
2.9 BACKCALCULATION METHODS ..................... 51
2.9.1 Iterative Methods .............................. 51
2.9.2 Database Approach ............................ 58
2.9.3 Statistical Analysis ............................. 59
2.9.4 Conversion of Backcalculated Layer Moduli to Standard
Conditiom .................................. 60
2.9.5 Sources of Error In Backcalculated Layer Moduli ......... 68
2.9.6 Error Measures and Convergence Criteria ............. 7O
2.10 SUMMARY ...................................... 71
CHAPTER 3
W
W ....................... 74
3- 1 GENERAL ...................................... 74
3-2 IMPROVED ESTIMATION OF ROADBED MODULUS ......... 75
3-3 NEWTON’S METHOD .............................. 77
3-4 NEWTON’S METHOD WHEN THE DERIVATIVES OF THE
FUNCTION ARE NOT AVAILABLE ..................... 79
3-5 MUL'TI-DIMENSIONAL FORM OF NEW'TON’S METHOD ...... 81
3.6 USE OF NEWTON’S METHOD TO BACKCALCULATE

vii

3.7

3.8

3.10

 

4.3

4.4

PAVEMENT LAYER MODULI ......................... 82

LAYER THICKNESS ESTIMATION ..................... 85
THE MODIFIED NEWTON METHOD .................... 87
STIFF LAYER EFFECTS AND DEPTH TO STIFF LAYER ...... 87
LOGARITHMIC TRANSFORMATION ................... 90
3.10.1 Relationship between Surface Deflection and Layer
Moduli ............................... 90
3.10.2 Implementation of Logarithmic Transformation ...... 99

101

101
TYPICAL PAVEMENT SECTIONS AND TEST PARAMETERS
USED ......................................... 102
NUMERICAL ILLUSTRATION: IMPROVED ESTIMATION OF
ROADBED MODULUS ............................. 105
ESTIMATION OF LAYER THICKNESSES AND THEIR EFFECT
ON THE BACKCALCULATED LAYER MODULI ........... 105
4.4.1 AC Thicknom .............................. 107
4.4.2 Base Thickness ............................. 115
STIFF LAYER EFFECTS AND DEPTH ESTIMATION . ....... 121

4.5.1 Backcalculation of Layer Moduli and Stiff Layer Depth . . . 121
4.5.2 Sensitivity of Backcalculated Moduli to Stiff Layer

Characteristics .............................. 125
CONVERGENCE CHARACTERISTICS .................. 137
4.6.1 Three-Layer Flexible Pavements .................. 138
4.6.2 Four-Layer Flexible Pavement ................... 138
4.6.3 Four-Layer Composite Pavements ................. 140
4.6.4 Three-Layer Pavements Over a Stiff layer ............ 140
4.6.5 Five-Layer Flexible Pavement .................... 143
4.6.6 Performance Comparison ...................... 143
UNIQUENESS OF THE BACKCALCULATED RESULTS ...... 148

viii

4.8 EFFECT OF INACCURACIES IN DEFLECTIONS AT SIMULATED

 

SENSOR LOCATIONS ON BACKCALCULATED RESULTS . . . . 150
4.9 EFFECT OF POISSON’S RATIO ON THE BACKCALCULATED
LAYER MODULI ................................. 154
4.10 COMPARISON OF DEFLECTION OUTPUT OF DIFFERENT
ELASTIC LAYER PROGRAMS ....................... 158
4.10.1 Comparison of Deflection Output ................ 159
4.10.2 Comparison of Backcalcuiated Results ............. 162
4.11 COMPARISON OF MICHBACK RESULTS WITH SHRP
STUDY ....................................... 164
171
173
173
173
5.3 PROCESSING A FWD DEFLECTION DATA FILE .......... 174
5.3.1 Reviewing and Preprocessing the Deflection Data ....... 175
5.3.2 Data Analysk Options ......................... 178
5.4 PRIEENTATION OF THE BACKCALCULATED RESULTS . . . . 180
5-5 PROGRAM STRUCTURE ........................... 180
5-6 BACKCALCULATION OF LAYER PROPERTIES ........... 182
CHAPTER 6
........................ 187
6- 1 GENERAL ..................................... 187
6.2 PAVEMENT SELECTION ........................... 187
6-3 MARKING, CODING, CORING AND NDT ............... 195

5.4 BACKCALCULATION OF LAYER MODULI FOR SELECTED

ix

——*—__.—

 

 

6.4
6.4
6.4
6.4
6.4
6.4
4.6
4.6
6.4
6.4

6.4

”84

PAVEMENTSECTIONS............... ............. 197
6.4.1 Flexible Pavement Section MSU07F - Variable

Deflections ................................. 202
6.4.2 Flexible Pavement Section MSU19F - Uniform

Deflections ................................. 209
6.4.3 Flexible Pavement Section MSUIOF - Uniform

Deflections ................................. 215
6.4.4 Flexible Pavement Section MSU13F - Variable

Deflectiom ................................. 219
6.4.5 Flexible Pavement Section MSU14F - Variable

Deflection .................................. 219
6.4.6 Flexible Pavement Section MSU29F - Variable

Deflections ................................. 223
6.4.7 Flexible Pavement Section MSU35F - Variable

Deflections ................................. 226
4.6.8 Flexible Pavement Section MSU43F - Variable

Deflections ................................. 231
4.6.9 Composite Pavement Section MSU01C - Variable

Deflections ................................. 231
6.4.10 Composite Pavement Section MSU05C - Variable

Deflections ................................. 237
6.4.11 Composite Pavement Section MSU08C - Variable

Deflectiom ................................. 241
6.4.12 Composite Pavement Section MSU04C - Variable

Deflections ................................. 241

6.5 BACKCALCULATION OF LAYER MODULI AT DIFFERENT

LOAD LEVELS .................................. 246
6.5.1 Flexible Pavement Section MSU19F - Variable Load

Level ..................................... 249
6.5.2 Flexible Pavement Sections MSU35F - Variable Load

Level ..................................... 259
6.5.3 Composite Pavement Section MSU01C - Variable Load

Level ..................................... 265
6.5.4 Discussion ................................. 265

 

7.2 TEMPERATURE EFFECTS .......................... 278
7.2.1 Flexible Pavement Section MSU52F - Temperature

Variation .................................. 280
7.2.2 Flexible Pavement Section MSU13F - Temperature

Variation ................................. 288
7.2.3 flexible Pavement Section MSU19F - Temperature
Variation .................................. 292
7.3 THE ASPHALT INSTTTUTE TEMPERATURE CORRECTION
PROCEDURE .................................... 295
7.4 THE AASHTO TEMPERATURE CORRECTION PROCEDURE . . 299
7.5 SUMMARY AND CONCLUSIONS ._ ..................... 303
CHAPTER 8
W .............. 304
8.1 SUMMARY ..................................... 304
8.2 ACCOMPLISHMENTS ............................. 305
8.3 CONCLUSIONS .................................. 306
8.4 RECOMMENDATIONS FOR FUTURE RESEARCH .......... 308
xi

 

 

_‘—-—_—’

12662.1.

Table 2.2.

Table 2.1.
Table 2.2.

Table 4.1.
Table ‘4.2.
Table 4.3.
Table 4.4.

Table 4.5.
Table 4.6.
Table 4.7.
Table 4.8.
Table 4.9.
Table 4.10.
Table 4.11.

Table 4.12.

LIST OF TABLES

Summary of deflection basin parameters (Mahoney, et al.,

1991). ..................................... 27
Backcalculation programs compiled by SHRP as of November
1990 (modified afler ref. Mahoney, 1991). .............. 52
A typical three layer flexible pavement ................. 103
A typical four layer flexible pavement. ................ 103
Typical four layer composite pavements. ............... 103
A typical five layer flexible pavement. ................ 103
Improvement of the roadbed modulus for a three layer flexible
pavement. .................................. 106
Improvement of the roadbed modulus for a four layer flexible
pavement. .................................. 106
Improvement of the roadbed modulus for a five layer flexible
pavement. .................................. 106
The percent error in the backcalculated layer moduli due to percent
errors in the AC thickness. ....................... 108
Errors in the backcalculated layer moduli due to errors in the
specified AC thickness for different AC thicknesses. ........ 113
Errors in the backcalculated layer moduli due to errors in the
specified AC thickness for different AC modulus. ......... 116
The percent errors in the backcalculated layer moduli due to
percent errors in the base thickness. .................. 117
Backcalculation of stiff layer depth and moduli
for a three layer flexible pavement. .................. 122
xii

 

 

_———-———— —-—-——-'-—.

 

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Table 4.13.
Table 4.14.
Table 4.15.
Table 4.16.
Table 4.17.
Table 4.18.
Table 4.19.
Table 4.20.
Table 4.21.
Table 4.22.
Table 4.23.
Table 4.24.
Table 4.25.
Table 4.26.

Table 4.27.

Backealculation of stiff layer depth and moduli for a four
layer flexible pavement. .........................

Backcalculation of stiff layer depth and moduli
for a four layer composite pavement. .................

Error in the the backcalculated layer moduli due to percent
error in the depth to the stiff layer.

The effect of stiff layer modulus on the backcalculated layer
moduli (stiff layer depth fixed) ......................

Effect of stiff layer modulus on the backcalculated
layer moduli and stiff layer depth. ...................

Comparison of the results of three programs for a three layer
pavement. ..................................

Comparison of the results of three programs for a four layer
pavement. ._ .................................

Comparison of the backcalculated results for a composite pavement
section. 4

Comparison of the backcalculated results for a composite pavement
section consisting of a granular separation layer. ..........

Comparison of the results of three programs for a three layer
pavement over stiff layer. ........................

The MICHBACK backcalculation results for a five layer
pavement. ..................................

Comparison of the performance'of MICHBACK and
EVERCALC programs.

Uniqueness of the MICHBACK solution for a three layer flexible
pavement. ..................................

Uniqueness of the MICHBACK solution for a four layer flexible
pavement. ..................................

Uniqueness of the MICHBACK solution for a five layer flexible
pavement. ..................................

xiii

 

124

126

134

136

139

139

141

142

144

149

149

149

 

_—-——-.
_—.—
—_——
——
——-—-
_—————
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lab}: 4.
1: 114..
Table 4.1
M

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1111: 4.3

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1411 4.3

141216 4.31

Table 4.28.

Table 4.29.

Table 4.30.

Table 4.31.

Table 4.32.

Table 4.33.
Table 4.34.
Table 4.35.

Table 4.36.

Table 4.37.

Table 4.38.
Table 4.39.

Table 4.40.

Table 6.1.
Table 6.2.
Table 6.3.

Table 6.4.

Percent errors in the backcalculated layer moduli due to errors in

deflections - arithmetic scale. ...................... 152
Percent errors in the backcalculated layer moduli due to errors in
deflections - logarithmic scale. ..................... 153
Percent error in the backcalculated layer moduli

due to :l: 0.5 mil error in deflections - logarithmic scale. ..... 155
Percent errors in the backcalculated layer moduli

due to error in Poison’s ratio for flexible pavements. ....... 157
Percent errors in the backcalculated layer moduli

due to error in Poison’s ratio for composite pavement. ...... 157
Deflections from different elastic layer programs ........... 160
Percent differences in the deflections of elastic layer programs. . 161
Backealculated results of MICHBACK for deflection data generated

by different elastic layer programs. .................. 163
Deflection and cross sectional data for nine test sections

(after Rada, et al., 1992). ........................ 165
Comparison of the true and backcalculated moduli

values (after Rada, et al., 1992). .................... 166
MICHBACK results for nine pavement sections. .......... 167
Comparison of errors in the modulus values. ............ 168
Statistics of the maximum relative error for four

computer programs. ..... _ ....................... 170
Criteria for final section selection. ................... 189
Flexible pavement sections selected for study. ............ 191
Composite pavement sections selected for study. .......... 193
Summary of the layout and conditions of the cored flexible
pavement section. ............................. 199

xiv

Table 6.5.

Table 6.6.
Table 6.7.
Table 6.8.

Table 6.9.

Table 6.10.
Table 6.11.
Table 6.12.
Table 6.13.
Table 6.14.
Table 6.15.
Table 6.16.
Table 6.17.

Table 6.18.

Table 6.19.

Table 6.20.

Table 6.21.

Table 6.22.

Table 6.23.

Summary of the layout and condition of the cored composite
pavement sections ..............................

Backealculated moduli for pavement section MSU07F.

Backcalculated moduli for pavement section MSUl9F.

Backcalculated moduli for pavement section MSUIOF.

000000

Backcalculated moduli for pavement section MSU13F.

Backealculated moduli for pavement section MSUl4F.

Backcalculated modulus for pavement section MSU29F .......
Backcalculated modulus for pavement section MSU35F .......

Backcalculated moduli for pavement section MSU43F.

Backcalculated moduli for pavement section MSU01C.

Backcalculated moduli for pavement section MSUOSC.

Backcalculated moduli for pavement section MSU08C.

Roadbed characteristics of three pavement sections.

Backealculated moduli at various loads for pavement section
MSUl9F. ..................................

Differences between measured and linearly extrapolated deflection
basins for pavement section MSUl9F. ................
Backealculated moduli at various loads for pavement section

MSU35F. ..................................

Differences between measured and linearly extrapolated deflection

basins for pavement section MSU35F. ................
Backealculated moduli at various loads for pavement section
MSU01C. ..................................

Differences between measured and linearly extrapolated deflection
basins for pavement section MSU01C.

 

201

228
230

250

263

266

 

Table 6.24.

Table 6.25.

Table 7.1.

Table 7.2.

Table 7.3.

Table 7.4.

Table 7.5.

Table 7.6.

Table 7.7.

Table 7.8.

Table 7.9.

Backcalculation of layer moduli at different Poisson’s ratios for
pavement section MSU19F (test No. 19113011). ..........

Backcalculation of layer moduli at different Poisson’s ratios for
pavement section MSU35F (test No. 35114211). ..........

Deflection variation with temperature for pavement section
MSU52F. ..................................

Percent variation in deflection from lowest temperature recorded
for pavement section MSU52F. .....................

Backealculate layer moduli for selected sections. ..........

Deflection variation with temperature for pavement section
MSU13F. ..................................

Percent variation in deflections from lowest temperature recorded
for pavement section MSUl3F. .....................

Deflection variation with temperature for pavement section
MSU019F. .................................

Percent variation in deflections from lowest temperature recorded
for pavement section MSUl9F. .....................

Observed and Asphalt Institute AC modulus temperature correction
factor. ....................................

Observed and AASHTO temperature correction factors for Do.

xvi

272

273

282

282
285

289

289

293

 

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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.

Figure 2.13.

Figure 2.14.

LIST OF FIGURES

Typical output of a vibrating steady state force generator
(Moore, et al., 1978). ........................... 16

Typical load-deflection curves for frequencies of 10, 15, and 40
Hz. (Green, et al., 1974). ......................... 17

Mass-spring-dashpot representation of a pavement structure
subjected to a forced dynamic vibration (Lorenz, et al., 1953). . . l9

Well-designed pavement deflection history curve (Moore, et al.,
1978). ..................................... 22

Influence of season on pavement deflections (Izada, 1966). ..... 24

Use of deflection basin parameters to analyze pavement structural
layers, from Utah overlay design procedure (Molenaar, et

al.,1982). ................................... 26
Component versus system analysis of pavement structures. ..... 29
Typical variation of resilient modulus with repeated stress

for cohesive roadbed soil (Ming-Shah, 1989). ............. 33
Multi-layered elastic system (Yoder, et al., 1975). .......... 37
Assumed periodicity of FWD impulses (Sebaaly, et al.,

1986). ..................................... 45
Schematic showing measured and predicted surface

deflection basins (Stolle, et al., 1989). ................. 47
Typieal flow chart for an iterative program (Lytton, 1989) ...... 54
Basic process for matching deflection basins

(Van Cauwelaert, 1989). .......................... 57
Predicted pavement temperatures (Asphalt Institute, 1977). ..... 62

 

 

 

Figure 2.15.

Figure 2.16.

Figure 3.1.

Figure 3.2.
Figure 3.3.

Figure 3.4.

Figure 3.5.

Figure 3.6.

Figure 3.7.

Figure 3.8.

Figure 3.9.

Figure 3.10.

Figure 3.11.

Figure 4.1.

Figure 4.2.

Figure 4.3.

Temperature prediction graphs for pavements equal to or less than

2 inches thick (Asphalt Institute, 1977) .................. 63
General hyperbolic stress-strain curve for base, subbase, and
roadbed materials (Richard, et al., 1975). ............... 66
General illustration of Newton’s method (Dennis, 1983). ...... 78
Seeant approximation of Newton’s method (Dennis, 1983). ..... 80
Graphieal illustration of Newton’s method iteration

to find pavement layer moduli. ...................... 83
Effect of AC layer modulus on pavement surface deflections. . . . 91
Effect of AC layer modulus on pavement surface deflections
(logarithmic scale). ............................. 92
Effect of base layer modulus on pavement surface deflections. . . . 93

Effect of base layer modulus on pavement surface deflections
(logarithmic scale). ............................. 94

Effect of roadbed layer modulus on pavement
surface deflections. ............................. 95

Effect of roadbed layer modulus on pavement surface deflections
(logarithmic scale). ............................. 96

Graphic illustration of surface deflection variation with AC and
roadbed modulus. .............................. 97

Graphic illustration of surface deflection variation with AC
and roadbed modulus (logarithmic scale) ................. 98

Errors in the backealculated AC modulus due to incorrect
AC thickness specification. ....................... 109

Errors in the backcalculated base modulus due to incorrect
AC thickness specification. ....................... 110

Errors in the backealculated roabed modulus due to
incorrect AC thickness specifieation. ................. 111

xviii

Figure 4.4.
Figure 4.5.
Figure 4.6.

Figure 4.7.

Figure. 4.8.

Figure 4.9.

Figure 4.10.
Figure 4.11.
Figure 4.12.

Figure 4.13.

Figure 5.1.

Figure 5.2.

Figure 5.3.
Figure 5.4.
Figure 5.5.
Figure 5.6.

Figure 6.1.

Errors in the vertical stress at the top of the base layer due
to incorrect AC thickness specification. ................

Errors in the backcalculated AC modulus due to incorrect base
thickness specifieation. ..........................

Errors in the backealculated base modulus due to incorrect
base thickness specification. .......................

Errors in the backcalculated roadbed modulus due to
incorrect base thickness specification. .................

Effect of the depth to stiff layer on surface deflections. ......

Errors in backcalculated AC modulus due to incorrect stiff layer
depth specification. ............................

Errors in the backcalculated base modulus due to incorrect
stiff layer depth specification. ......................

Errors in the backcalculated roadbed modulus due to
incorrect stiff layer depth specification. ................

Comparison of the performance of MlCI-IBACK and EVERCALC
programs. ..................................

Maximum absolute relative percent error in layer moduli for
different programs. ............................

Deflection profile for pavement section MSU07F. .........

Zoom-in function between stations 10 and 15 of pavement section
MSU07F. ..................................

Flow chart for MICHBACK program. ................
Details of backcalculataion procedure for cases A & B. ......
Details of backealculataion procedure for cases C & D. ......
Details of backcalculataion procedure for case B. ..........

Distribution of selected pavement sections across the State of
Michigan. ..................................

114

118

119

120

128

130

131

132

146

169

183
185

186

194

 

II 1‘ t .V
.. w. .b... we... .w. .3. a; .r a... ......
P y b .7 D 5 .' .. a Z.
fin E El. F :1 E .5 2% a a .t the CUR.

 

Figure 6.2.
Figure 6.3.

Figure 6.4.

Figure 6.5.

Figure 6.6.

Figure 6.7.

Figure 6.8.

Figure 6.9.

Figure 6.10.
Figure 6.11.
Figure 6.12.

Figure 6.13.

Figure 6.14.
Figure 6.15.
Figure 6.16.

Figure 6.17.

Figure 6.18.

Figure 6.19.

Deflection profile for pavement section MSU07F. ......... 203

Variation of backcalculated layer moduli, the AC thickness, and
the deflection of sensor 1 and 7 along pavement section

MSU07F. .................................. 206
Variation of deflections for all seven sensors along pavement

section MSUO7F. ............................. 208
Deflection profile for pavement section MSUl9F. ......... 210

Variation of backcalculated layer moduli, the AC thickness, and
the deflection of sensor 1 and 7 along pavement section MSUlQF. 213

Variation of deflections for all seven sensors along pavement

section MSUl9F.. ............................. 214
Deflection profile for pavement section MSUlOF. ......... 216
A typical deflection basin at test location No.2 of pavement section

MSUlOF. .................................. 217
Deflection profile for pavement section MSU13F. ......... 220
Deflection profile for pavement section MSUl4F. ......... 222
Deflection profile for pavement section MSU29F. ......... 225
Typical deflection basins at test loeations 18, 27, 41, 44, and 52

for pavement section MSUZ9F. ..................... 227
Deflection profile for pavement section MSU35F. ......... 229
Deflection profile for pavement section MSU43F. ......... 232
Deflection profile for pavement section MSU01C. ......... 234
Typieal deflection basins at test locations 4, 35, and 37 for

pavement section MSU01C. ....................... 235
Deflection profile for pavement section MSUOSC. ......... 238
Typical deflection basins at test locations 28, 43, 45, and 46 for

pavement section MSUOSC. ....................... 240

xx

 

 

 

11,411 4

figure 1

1111: 1

12m 6

111116

11441: 6.

.
71444 6.

64426.:

F
*l

‘43? 6.2

141*: 6.2

Figure 6.20.

Figure 6.21.

Figure 6.22.

Figure 6.23.

Figure 6.24.

Figure 6.25.

Figure 6.26.

Figure 6.27.

Figure 6.28.

Figure 6.29.

Figure 6.30.

Figure 6.31.

Figure 6.32.

Deflection profile for pavement section MSU08C. ......... 242

Typieal deflection basins at test locations 2, 7, 9, and 33 for
pavement section MSU08C. ....................... 244

Deflection profile for pavement section MSU04C. .........
Typical deflection basins at test locations 4, 10, 11, and 12 for
pavement section MSU04C. ....................... 247
Comparison of measured and expected linear response deflection
basins for pavement section MSU19F (FWD test code

19113011). ................................. 252
Comparison of measured and expected linear response deflection
basins for pavement section MSU19F (FWD test code
191 1831 1). ................................. 253
Comparison of measured and expected linear response deflection
basins for pavement section MSU19F (FWD test code
19121611). ................................. 254
Comparison of measured and expected linear response deflection
basins for pavement section MSU19F (FWD test code
19128221). ................................. 255
Variation of backealculated layer moduli and the deflection of
sensor 1, 2, and 7 along pavement section MSU19F at low load
level. ..................................... 257
Variation of backcalculated layer moduli and the deflection of
sensor 1, 2, and 7 along pavement section MSU19F at high load
level. ..................................... 258
Comparison of measured and expected linear response deflection
basins for pavement section MSU35F (FWD test code
35118931). ................................. 260
Comparison of measured and expected linear response deflection
basins for pavement section MSU35F (FWD test code
351 14222). ................................. 261
Comparison of measured and expected linear response deflection

basins for pavement section MSU35F (FWD test code
35123311). .................................. 262

xxi

 

 

 

figure 1

115118 1

Figure 6.33.

Figure 6.34.

Figure 6.35.

Figure 7.1.

Figure 7.2.

Figure 7.3.

Figure 7.4.

Figure 7.5.

Figure 7.6.

Figure 7.7.

Figure 7.8.

Figure 7.9.

Figure 7.10.

Comparison of measured and expected linear response deflection
basins for pavement section MSU01C (FWD test code
01284611). .................................

Comparison of measured and expected linear response deflection
basins for pavement section MSU01C (FWD test code
01272411). .................................

Comparison of measured and expected linear response deflection
basins for pavement section MSU01C (FWD test code
01261611). .................................

Variation of maximum deflection with temperature observed for
pavement section MSU52F. .......................

Percent variation in deflections with temperature for pavement
section MSU52F. .............................

Variation of backealculated AC modulus with temperature for
pavement section MSUS2F. .......................

Variation of backcalculated base and roadbed moduli with
temperature for pavement section MSU52F. .............

Percent variation in deflections with temperature for pavement
section MSU13F. . . ...........................

Variation of backcalculated AC modulus with temperature for
selected pavement sections. .......................

Percent variation in deflections with temperature for pavement
section MSUl9F. .............................

Comparison of observed and Asphalt Institute for selected
pavement sections ..............................

Variation of peak deflections with temperature for selected
pavement sections ..............................

Comparison of observed and AASHTO temperature conversion
factors for peak deflections. .......................

mi

268

269

270

281

286

287

301

301

302

CHAPTER 1

INTRODUCTION

1.1 GENERAL

A pavement system subjected to a vehicular or other load input produces a
measurable output response in the form of surface deflections. Hence, pavement
deflections represent an overall "system response" of the paving layers and the
roadbed soil to an applied load. Pavement surface deflections have traditionally been
used as an indicator of its structural capacity. Emphasis on mechanistic design and
analysis led to the search for efficient schemes to backcalculate layer properties
needed for the analysis. The assessment of layer properties and their variation along
the road is essential for accurate evaluation of existing pavements and for the design
of the asphalt overlays.

A review of existing backcalculation schemes and their characteristics suggest
that, in general, they can be grouped into one of three categories: those based on
regression equations, those based on pre-calculated database of deflections basins, and
those based on iterative methods. The accuracy of the methods based on statistical
equations is generally low and problem dependent. Methods based on a database of
deflection basins received a better acceptance because of the MODULUS program
(Scullion, et al. , 1990). However the accuracy of the backcalculated results are
affected by the seed values of the layer moduli especially that of the roadbed soil.
Another shortcoming is that the estimation of the stiff layer depth is not very accurate
which in turn can contribute considerable error to the backcalculated results. Existing
iterative methods are relatively slow, share the disadvantage of dependence on seed
modulus values, and are unable to mechanistically predict the stiff layer depth. In

many cases the accuracy of these methods decreases with the increasing number of

pavement layers.

Most existing iterative programs seek to minimize an objective function for the
estimation of layer moduli. The objective function is normally the weighted sum of
squares of the difference between calculated and measured surface deflections (Uzan,
et al., 1989). One of the problems of this approach is that the multi-dimensional
surface represented by the objective function may have many local minima. The
minimum to which a numerical solution may converge depends on the seed moduli
supplied by the analyst and may yield unacceptable results. Also, for many cases, the
method may fail to converge on a solution within a reasonable time.

The exact layer thicknesses at the point of FWD testing are seldom known.
Pavement coring is one direct method of measuring the layer thicknesses. A typical
core, however, yields layer thickness information at a point. The FWD test provides
deflection information over much wider distance (60 - inch for the MDOT FWD).
Unfortunately, variation in construction and terrain make the variation in layer
thicknesses inevitable. lnaccuracies in the layer thicknesses can contribute a
signifieant error in the backcalculated layer properties. Therefore, backcalculation
methods which can compute layer thicknesses along with the layer moduli from the
deflection data will have the advantage of increased accuracy.

Detection of the depth to the stiff layer is also essential for accuracy in the
backcalculated layer moduli. Estimation of stiff layer depth by existing methods is not
very accurate and ean induce considerable error in the backcalculated properties.

Improvement of this estimate would represent a major contribution to this profession.

1.2 PROBLEM STATEMENT
Most existing backcalculation of pavement layer moduli methods seek to
minimize an objective function for the estimation of layer moduli. This approach

makes the backcalculated results dependent on the values of the seed modulus. None

.1

3
of the existing programs appear to determine the stiff layer depth mechanistically,
they are capable of only providing a rough estimate which can adversely affect the
backcalculated layer moduli. Hence, there is a need to produce a backcalculation
algorithm such that its outputs are not affected by the values of the seed moduli, and
is able to provide a mechanistic estimate to the stiff layer depth along with the layer

moduli.

1.3 RESEARCH OBJECTIVES

The main objective of this research is to develop a robust backcalculation
program whose results are not sensitive to the seed values of the layer moduli. Also,
the algorithm should have the capability to accurately compute the stiff layer depth.

The program should be user-friendly, provide various options to the user to
view and pre-process the deflection basins if necessary, to be of benefit to local State
Highway Agencies (SHA) and able to directly process the format of the deflection
output files of the Michigan Department of Transportation (MDOT) operated version
of the KUAB Falling Weight Deflectometer.

1.4 THESIS LAYOUT

This thesis is organized in eight chapters as follows:

Chapter 2 - Literature review - Nondestructive deflection testing (NDT)
methods and related equipment along with their limitatiOns and capabilities are briefly
discussed. Various uses of the deflection data, backcalculation of layer moduli
methods and their merits and limitations, and pavement material properties are
introduced. Also some of the difficulties related to the backcalculation process, error
sources, and various methods for converting the backcalculated properties to standard
load and temperature conditions are presented.

Chapter 3 - Efficient iterative methods for backcalculation of pavement layer

 

BTU:

a

3‘s

.3!

4
properties - The Newton method and its application to the backcalculation of
pavement layer properties is presented. A new method to estimate the modulus of the
roadbed sail in a single call to an elastic layer program is introduced. Also, the
modified Newton method and a logarithmic transformation to spwd up convergence is
discussed.

Chapter 4 - Verification of MICHBACK algorithm using theoretical deflection
basins - Verification of the MICHBACK backcalculation algorithm using theoretical
deflection basins are presented. The backcalculated results are compared to those
obtained from MODULUS 4.0 and EVERCALC 3.0 computer programs. Important
aspects of convergence characteristics and uniqueness of the solutions are tested.
Sensitivity of backcalculated results to Poisson’s ratios, inaccuracies in deflections at
different sensor locations and accuracy of elastic layer programs is also examined.

Chapter 5 - Michback program structure and features - The features and the
structure of the MICHBACK program are presented.

Chapter 6 - Validation using field data - Validation of the MICHBACK
program using FWD test data from pavements across the State of Michigan is
presented.

Chapter 7 - Temperature effects on the backcalculated layer moduli - The
effects of the pavement temperature on the AC modulus are discussed.

Chapter 8 - Summary, conclusions, and recommendations.

 

CHAPTER 2

LITERATURE REVIEW

2.1 GENERAL

A pavement system subjected to a vehicular or other load input produces an
output response in the form of deflection. Hence, pavement deflections represent an
overall ”system response" of the paving layers and the roadbed soil to an applied
load. A load applied at a point (or an area) on the pavement surface will attenuate
with depths and radial distances thereby, causing all pavement layers to deflect as a
consequence of the introduced stresses and the resulting strains. The amount of
deflection in each layer will generally decrease with depth and radial distance and will
vary depending on the layer properties. Beyond a certain depth and radial distance,
the induced stresses become negligible and the materials are not affected by the
applied load. Further, stronger pavements (i.c., those with good quality materials and
thick layers) deflect less under a given load than do weaker pavements. Hence,
pavement deflections are being used as indieators of pavement quality and as inputs
(along with the layer thicknesses) to a mechanistic analysis routine to backcalculate
the properties of the various pavement layers.

Pavement deflection can be measured by using nondestructive deflection tests
(NDT). An NDT consists of applying a known force to a pavement surface and
measuring its response (deflection). In some test methods (e.g., the Benkelman
beam), the pavement deflection (or more precisely pavement rebound) is typically
measured at a point loeated between the two tires of the back axle of a single axle
truck. In other methods (e. g. , dynaflect, falling weight deflectometer (FWD), road
rater), the pavement deflection profile (deflection at several points located under, and

at various radial distances away from the center of the loaded area) is typically

6
measured. Analysis of the measured pavement deflection provides a quantitative basis
for evaluation of the pavement structural conditions at any time during its service life.
In addition, important information regarding rehabilitation and maintenance
requirements can be inferred from the deflection profile (deflection basin). Because
they are nondestructive in nature, NDT are easily and quickly performed, the tests
cause minimal hindrance to the normal flow of traffic, and they are less hazardous
and more economical to perform. In addition, the measured deflections are
representative of the actual pavement response to the applied load.

As stated earlier, pavement surface deflection has traditionally been used as an
indieator of the structural capacity of pavements. One of the earliest uses of pavement
deflection was that made in California in 1938 and reported by Haveem (1938). He
concluded that flexible pavements would have satisfactory performance if they deflect
less than 20 mils under a 15000 lb axle load. The WASHO Road Test (conducted in
Huba Valley on flexible pavements) results showed that for a satisfactory pavement
performance, pavement deflections should be limited to 30 to 40 mils for pavements
located in cold and warm regions, respectively (WASHO, 1954; WASHO, 1955).

Presently, NDT data are being used in conjunction with the pavement distress
survey for evaluation, rehabilitation, and pavement management purposes. A proper
analysis of the NDT data can provide information regarding:

l. The need of a particular pavement section for an overlay and perhaps, the
required thickness of the overlay.

The degree of variability of the materials along the roadway.

Potential locations of voids beneath the surface layer.

The load transfer efficiency across joints in concrete pavements.

The elastic properties of the various pavement layersand the roadbed soil.

am???"

The ability of the pavement structure to support traffic loads at the
posted speed limits.

7
7. The effect of seasonal variations on the load carrying capacity of the
pavements.
8. The need for, and perhaps the type of rehabilitation activities.
9. The in situ stress sensitivity of the paving materials.

10. The effectiveness and benefits of various rehabilitation techniques.

The mechanistic analysis of pavement deflections to infer the structural
properties (moduli and Poisson’s ratios) of the various layers is referred to as
"backcalculation of layer moduli". The task of backcalculation of layer moduli,
however, is a difficult one. This difficulty is related to several reasons including:
1. The variability of the pavement materials along a given stretch of roadway.
2. The changing characteristics of the pavement materials due to seasonal

changes, time, and temperature.

3. The nonlinear behavior of the paving materials.

4. The lack of accurate information concerning layer thicknesses and depth to
stiff layer (e.g., bedrock).

5. The existence (in some cases) of a very thin layer (e.g., a one-inch debonding

layer between an original pavement and an overlay).

Nevertheless, backcalclation of layer moduli techniques have been developed
and have been successfully applied to both flexible and rigid pavements. Most of
these techniques are based on elastic layered concepts and are directed at the
incorporation of NDT data collected on flexible pavements and at mid-slabs of rigid
pavements. Elastic layered analysis does not adequately model discontinuities such as
joints and cracks in rigid pavements.

The NDT equipment used to measure pavement deflections differ in the

methods used in applying loads to pavement and in the number and location of

8

sensors needed for measuring the pavement response. The various types of NDT

equipment can generally be divided into five categories as presented in the next

section.

2.2

NONDESTRUCTIVE DEFLECTION TESTING DEVICES

NDT devices can be categorized as follows:

Static Deflection Equipment - Static deflection equipment measure pavement

deflections or rebound due to the application of a gradually increasing or

decreasing load. This type of equipment includes the Benkelman Beam

(Moore, et al., 1978; Asphalt Institute, 1977; Epps, et al., 1986), Plate

bearing test (Moore, et al., 1978; Nazarian, et al.,. 1989), Dehlen Curvature

Meter (Guozheng, 1982), Pavement Deflection Logging Machine (Keneddy, et

al., 1978), and C.E.B.T.P. Curviameter (Paquet, 1978). Several technical

problems are associated with this type of equipment including:

a) ' it is time consuming and laborious.

b) The test requires closing the pavement section to traffic.

c) Deflection can be measured only at one point (special arrangements
need to be made to measure the deflection profile).

(1) The test presents hazardous conditions to both the traveling public and

the test operators.

Automated Deflection Equipment - Automated deflection equipment delivers
a gradually applied load to the pavement structure in an automated mechanism.
This type of equipment includes the La Croix Deflectograph (Hoffman, et al.,
1982; Keneddy, 1978) and the California Travelling Deflectometer (Roberts,
1977). The technical problems associated with this type of equipment are

9

similar to those associated with the static deflection equipment.

Steady-State Dynamic Deflection Equipment - Steady-state dynamic
deflection equipment (also called vibrators) produce a sinusoidal vibration in
the pavement with a dynamic force generator (typically rotating eccentric
load). The most popular devices include the Dynaflect, the Road Rater, the
Cox Device, the Waterways Experiment Station (WES) Heavy Vibrator, and
the Federal Highway Administration (FHWA) Thumper (Scrivner, et al.,
1969; Smith, et al., 1984, Moore, et al., 1978). Each of these devices has
some limitations and advantages that are addressed elsewhere (Bush, 1980;

May, 1981).

Impulse Deflection Equipment - Impulse deflection equipment delivers a
transient force impulse to the pavement surface by means of dropping a
weight. The most popular devices include the Dynatest Falling Weight
Deflectometer (FWD), the KUAB Falling Weight Deflectometer, and the
Phoenix Falling weight Deflectometer (Nazarian, et al., 1989; Hoffman, et al.,
1981; Bohn, et al., 1972; Crovetti, et al., 1989; Claessan, et al., 1976).
Recently, FWD devices have become popular and they are being used by an

increasing number of State Highway Agencies (SHA).

Wave Propagation Equipment/Method - The wave propagation method (also
called surface wave testing) has been used with some success to backcalculate
the layer moduli of pavements. The method is not very widely used because of
the complex data analysis procedures associated with it (Thomas, 1977).

A study carried out by Lytton et a1. (1990) lists in detail the characteristics,

10

operational costs, and data analysis techniques associated with different types of NDT
equipment. The NDT equipment have been rated after assigning weights to various
important factors associated with the use of the equipment. The study concluded that
the FWD is the best equipment available for simulating the actual traffic loading and
further ranked the Dynatest Model 8000 as the best FWD equipment available.

Since the backcalculation technique presented in this thesis is based on NDT,
only a brief summary of the wave propagation method is presented in the next
section. The concepts regarding deflection testing and backcalculation of layer moduli,

on the other hand, are presented in greater detail in subsequent sections.

2.3 SURFACE WAVE TESTING

The surface wave testing technique involves the measurement of the velocity
and length of the surface waves propagating away from the point of application of an
impact load (Nazarian, et al., 1983; Nazarian, et al., 1984; Robert, et al., 1986).
This technique was pioneered by the German Society of Soil Mechanics in the late
1930’s (Bernhard, 1939). The wave propagation theory is based upon the fact that
wave velocities in a homogeneous and isotropic half space subjected to external

impact load can be expressed by the following equation:

v = . rm (24>
where E = modulus of elasticity;
p = mass density; and
a = a coefficient that is a function of Poisson’s ratio of
the medium.

Upon excitation by an impact or a vibratory load, three types of waves are generally

transmitted through and along the pavement. The three wave types and the percent of

 

a“? -
r...

r3)

I1."

124'

in"

I!"

1 1
the applied energy that is dissipated by each type are tabulated below (Miller, et al. ,
1955).

 

 

 

 

 

Have type Energy dissipation
(X of applied energy)

Culpression (P) 7

Shear (S) 26

Rayleigh (R) 67

 

 

 

For a multi-laycr pavement structure, analysis of these waves is a complex
proposition. Extensive mathematical analysis of these waves can be found elsewhere
(Thomas, 1977). The remaining part of this section summarizes two techniques that
can be used to induce the three types of waves in a pavement structure and the

advantages and disadvantages of the surface wave method.

2.3.1 Impulse Load Testing

. In this technique, an impulse (impact) load is applied at a point (called the
source) on the surface of the pavement section. Any impact device (e.g., sledge
hammer or impact hammer) can be used for this purpose. Upon impact, the three
types of waves will propagate away from the source either along the pavement surface
or with depth. At an interface between two pavement layers, the wave fronts undergo
both, reflection and refraction. During the test, the time of arrival of several wave
fronts at different points along the pavement surface is recorded in order to measure
the travel paths of these waves through different layers and to deduce their velocities
in each layer. This method is not applieable when high-velocity stiff layers, as is the
ease for flexible pavements, are encountered at the top and the layers grow

progressively weaker with depth (Moore, et al., 1978). As such the method cannot be

12

applied to backcalculate the layer moduli of pavements.

2.3.2 Steady-State Vibration

In the steady-state vibration technique, a vibratory source is placed at an
arbitrary point on the pavement surface and a vibrating load (typically sinusoidal) is
applied at the source. In this technique, the phase lag (the time delay which occurs
between the motion of the pavement and that of the source as the waves travel away
from the source) is measured. High frequency waves have shorter wave lengths and
hence can penetrate only the surface layer. On the other hand, if low frequency waves
are used they will have lengths several times that of the pavement thickness and their
speed will be determined by the properties of the roadbed soils. Intermediate wave
lengths can be used and their speeds can be related to the elastic properties and
thicknesses of the underlaying layers (Jones, 1960).

2.3.3 Advantages and Limitations
The surface wave test method has several advantages over other NDT

methods. These include:

1. Layer thicknesses of the various pavement layers can be calculated and as such
no assumptions or approximations are required (Nazarian, et al., 1989).
Therefore, the method is more pertinent when the dimensions of the structure
is not known (Robert, 1986).

2. The depth to bedrock as well as the bedrock modulus can be accurately
calculated. These two factors represent a major source of error for the
deflection based backcalculation technique (l-Ieukelom, et al., 1962).

3. The elastic modulus of a thin or a thick asphalt concrete (AC) layers can be
estimated. Variations of the modulus within, any paving layer can also be

estimated. The method has the potential of being fully automated at a later

 

l
-.4

5'"

13
time (Hiltunen, et al., 1989).
4. The test method and equipment are simple to operate, but sophisticated
data analysis is required (Robert, et al., 1986). The test result pertain
to a wide area and not necessarily to the local pavement properties in

the vicinity of the applied load (Watkins, et al., 1974).

The major disadvantage of this method is that the testing and data reduction
cannot be performed rapidly. It takes about 20 minutes to perform one test whereas a
deflection test can be performed in less than 2 minutes (Wang, et al., 1989). Also the
moduli obtained are for low strain levels which may not be an accurate estimate of
the moduli under actual traffic loading (large load may cause the pavement materials
to exhibit stress-dependent behavior). At best, the method is presently suited for
project level surveys only (Nazarian, et al., 1989). Interpretation of the data is an
extremely complex process which can only be undertaken by experts. The test results

are not necessarily unique and the method works only for a few special structures

(Thomas, 1977).

2.4 NONDESTRUCTIVE DEFLECTION TESTING

Applying a known force to measure the deflection response of a pavement
structure is the essence of NDT. The earliest device used in the United States (U .S.)
for measuring pavement deflection is the General Electric Travel Gage in 1938
(Moore, et al., 1978). The tests showed that the pavement deflection can be measured
to a depth of 21 feet and that the main contribution to the total deflection comes from
the upper 3 feet of the structural section (Haveem, 1938).

During the WASHO Road Test (1954; 1955) an improved version of the
General Electric Travel Gage, incorporating a Linear Variable Differential
Transformer (LVDT), was used. In 1952, A.C. Benkelman developed a simple and

14
easy to use instrument for measuring pavement deflections called the Benkelman
Beam. The Benkelman Beam is still widely used in many countries across the world
for measuring pavement deflections. Recent years have witnessed the development of
equipment with better capabilities than the Benkelman Beam and as a result new NDT
methods have been developed. Currently used techniques can be placed into one of
the following categories based on the method by which the deflections are induced:
1. static force-deflection
2. dynamic steady-state vibrations

3. dynamic impulse force-deflection

2.4.1 Static Force-Deflection

In this procedure, the response of a pavement structure to gradually applied or
gradually removed loads is measured. The force may be applied by a slow moving
vehicle of known weight or through a rigid plate of specified diameter that is part of a
stationary loading frame. Static or quasi-dynamic measurements of either rebound or
loading deflection are made by making the load vehicle pass a point located on the
pavement surface at a creep speed. Deflection and rebound deflection testing
procedures have been published by AASHTO (1982) and the Asphalt Institute (1977),

respectively.

2.4.1-l W

The basic advantage of the static deflection method can be attributed to its
simplicity, cheaper equipment, and low maintenance costs. The disadvantages are:
1. It is difficult to obtain an immovable reference point for making deflection

measurements.

2. All the devices measure only a single deflection making it difficult to obtain

valuable information regarding the shape and size of the deflection basin.

15
Moreover, no information on the critical strain in the upper layer is obtained.
3. The automated beam equipment is further handicapped by the fact that it is
difficult to test a specific point on the pavement. Further if the deflection basin
is large, the reference point may be located within the basin itself.
4. The method is suitable only for use with static analysis and dynamic effects

cannot be analyzed.

2.4.2 Dynamic Steady-State Vibrator

Essentially all steady-state vibrator equipment induce a steady state sinusoidal
vibration in the pavement using a dynamic force generator. The dynamic force is
superimposed on the static force exerted by the weight of the force generator (Figure
2.1). The dynamic load causes the pavement system to vibrate at the same frequency
as the load. The deflection response of the pavement is usually measured with inertial
sensors. Velocity sensors (called geophones) are commonly used, although some
equipment make use of accelerometers as well. Many of the devices can vary both the

amplitude and the frequency of the excitation (Moore, et al., 1978).

2.4.2.1 - mi R f v

Under static loads, pavement deflection is normally proportional to the applied
forces, and substantial recovery is obtained when the load is removed. Dynamic
response is no different in that, at any specific driving frequency, the amplitude of the
dynamic deflection is approximately proportional to the amplitude of the applied force
(Moore, et al., 1978). Green and Hall (1974) obtained results using a 16 kip vibrator
at three different driving frequencies (Figure 2.2). The test results showed that the
deflection is almost proportional to the loads at 15 Hz and 40 Hz and somewhat non
linear at 10 Hz.

The overall rigidity of road construction, S, defined by Van der Poel (1951)

16

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18
as the amplitude of the dynamic force required to produce a unit amplitude in the
deflection of the pavement surface. He pointed out that S is not constant, it depends
upon the driving frequency.

The Kelvin model has been used to represent the pavement response to.
dynamic loading as shown in Figure 2.3 (Lorenz, et al., 1953; Van der Poel, 1953).
The equation of the motion and significance of different parameters involved in the
model can be found elsewhere (Baladi, 1976; Baladi, 1979; Taylor, 1978; Thompson,
1972; Heukelom, et al., 1960; Heukelom, 1961; Szendirei, et al., 1970).

2.4.2.2 v n n Lirn i
The advantages of NDT are:
l. Accurate deflection basin measurements can be made with respect to an inertial
reference.
2. Steady state dynamic deflection devices correlate well with the static
deflection measurements. Many agencies make use of these correlations

for pavement evaluation.

The disadvantages are:

1. These types of measurements represent the stiffness of an entire pavement
structure. The separation of the effects of all the pavement components with
measurement of the deflection basin has not yet been accomplished (Nazarian,
et al., 1989).

2. The commercially available machines operate at light loads and hence the
pavement is not stressed to traffic loads. As a result, the effect of any non-
linearity in the paving materials is neglected (Fell, et al., 1972).

3. The steady state deflections are observed to be greater in magnitude than
rebound deflections for Bankelman Beam (Hoffman, et al., 1981), while

l9

Force generated

  
   

Fer-ea exerted on pave-en: (1')

Pennant S '- ~-

 

 
 
 

Effective Haas (K)

   

 

helping (C)

 

nut! Supper:

'""i"?;’%§‘/71’2’47?“ Z/.”////////// // 7W / ’/ 144/w

Figure 2.3. Mass-spring-dashpot representation of a pavement structure subjected
to a forced dynamic vibration (Lorenz, et al., 1953).

 

20
the deflections under moving vehicle are found to be smaller than those for

equivalent static loads (Lister, 1967).

2.4.3 Impact Loading

Impact loading devices deliver an impulse force to the pavement surface and
measure the transient response. Force impulses are normally generated by dropping a
known weight from a known height on a plate placed on the pavement surface.
Inertial motion sensors are normally used to record the pavement response. In the
U.S. , the Cornell Aeronautical Laboratory (CAL) was the first agency to use a trailer
mounted force generator for impulse loading (Moore, et al., 1978).

The pavement properties can be investigated by using the classical Kelvin
single degree of freedom (SDOF) system. Fourier transform of an instantaneous
impulse response deflection can provide complete information regarding the steady-
state frequency response. Practically, however, it is impossible to generate an
instantaneous impulse. Based on their test results, Szendrei and Freeme (1970) and
Moore et al. (1978) concluded that a load pulse duration must be less than 1 msec to
be considered instantaneous. Longer force impulses do not contain all the steady-state
frequency response. Analytical treatment of the instantaneous force impulse of the
classical model can be found in the literature (Richart, 1970; Tayabji, et al., 1976;
Hansen, et al., 1956).

2-4-3-1 W
The advantages of the impact load test include:

1. The loading most closely resembles actual traffic loading (Hoffman, et al.,
1982). Therefore the shape of the deflection basin and hence the developed
strains closely reflect those due to actual traffic load.

2. The actual duration of the test is only a few minutes and the measured data

 

2.5

21
gives sufficient information regarding the deflection basin to investigate the
layer properties (Moore, et al., 1978).
Results can easily be correlated with those of the static load test.
The test equipment is simple to operate and can be maintained at reasonable

costs.

The disadvantages are:

Complex analysis is required to model the response because of the

difficulty of producing an instantaneous impulse (Taylor, 1978).

Analysis of longer force impulses are even more complex.

It is a problem to obtain the response in the low frequency range because of

the low output characteristics of the motion sensors.

DEFLECTION RESPONSE OF PAVEMENTS

Based on review of the literature, certain concepts regarding the deflection

response of the pavements can be expressed (Moore et al., 1978; Taylor, 1978):

l.

A maximum tolerable deflection level can be assigned to each pavement

structure. This level is typically a function of the layer thicknesses and

properties and the traffic load and volume.

Overlaying a pavement will reduce its deflections.

The deflection history of a well designed pavement can be traced through three

phases (Figure 2.4):

a. 111mm: Just after construction, the pavement undergoes
consolidation and the deflections show a slight decrease.

b. W: The deflections remain constant or increase
slightly.

c.«Eajlu1e_phase: The deflections increase rapidly.

22

Dellactlon —e

—-"""""""1

Functional
Phase

Initial
Phase

Failure
Phase

 

 

 

Time ——>

Figure 2.4. Well-designed pavement deflection history curve (Moore, et a1. , 1978).

23

4. The deflections of a flexible pavement increase with the increase in
temperature of the bituminous surface depending upon the thickness of the
bituminous layer.

5. The deflection history of the pavement varies throughout the year depending
upon the environmental factors (Izada, 1966). A typical annual deflection
history of a pavement subjected to frost and spring-thaw actions can be divided
into four periods (Figure 2.5):

a. A deep frost period when the pavement is frozen.

b. A spring-thaw period during which the pavement deflections rise
rapidly.

c. A rapid strength recovery period during which water from
melting frost starts draining and evaporating from the pavement.

d. A relatively dry period during which the pavement deflections

level off.

2.6 INTERPRETATION OF DEFLECTION DATA

Interpretation of NDT deflection data is a complex and difficult task. The
techniques used to extract useful information from deflection data can be divided into
three basic groups
1. Empirical Analysis
2. Rational Analysis

3. Mechanistic Analysis

2.6.] Empirical Analysis
In the past most pavement design procedures were empirical in nature. An
empirical approach relies upon the results of past experiments and experience.

Generally, deflections are directly related to the pavement conditions and other

24

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25

variables such as traffic, pavement type, and environment factors. Results of a
number of experiments are used to obtain a relationship between the variables and the
outcomes. The relationship is typically not supported by theory. Statistics rather than
the phenomena shaping the results are given more importance.

The Utah Department of Transportation (UDOT) procedure (Molenaar, et al.,
1982) is one such example. The maximum deflection (DMD), the Surface Curvature
Index (SCI), and the Base Curvature Index (BCI) are compared to the acceptable
values of these parameters which are inferred from a long term pavement
performance (LTPP) (Figure 2.6; Table 2.1). The California DOT (1973), Asphalt
Institute (1974), Oklahoma DOT (AASHTO, 1972), Louisiana DOT (Kinchen, et al.,
1977), and Texas DOT (Brown, et al. , 1970) methods are other such examples where
the pavement deflections have been utilized directly to infer information regarding the

pavement condition and its capability to carry projected future traffic.

2.6.2 Rational Methods

Rational methods utilize basin properties such as spreadability or representative
structural properties to describe the pavement strength (Lytton, et a1. , 1990). The
representative structural properties of a pavement are normally taken as the effective
thickness of the pavement (McComb, et al., 1974; Kinchen, et al., 1980), effective
thickness of the asphalt concrete and base courses (Vaswani, 1971), or the effective

modulus of the pavement (Asphalt Institute, 1977; Lytton, et al., 1990).

2.6.3 Mechanlstlc Analysis

A mechanistic approach refers to the calculation of induced stresses and strains
to determine the response of the pavement structure to applied load. In order to
calculate the response of the pavement structure, certain fundamental material

properties along with the layer thicknesses must be known. The results obtained can

 

 

 

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28
thus be explained by theory and changes in response due to changes in any variables
can be predicted more rationally. The advantages of such an approach include

(Mahoney, et al., 1991):

l. The accommodation of changing loads.

2. The ability to account for changes in materials and environmental
conditions.

3. Improvement in the reliability of performance prediction models.

4. Better assessment of the performance of various paving materials.

The aim of backcalculation methods based on mechanistic analysis, is to
backcalculate the layer moduli of different paving layers. Which in turn are used to
calculate stresses and strains induced in the pavement structure due to a given load.
Mechanistic properties can be used for both the design and evaluation of pavement
structures. The mechanistic design procedures use laboratory determined material
properties to calculate a layered system response to an applied load. The mechanistic
evaluation procedures, on the other hand, uses the measured pavement response under
a known load to backcalculate the layer properties (Robert, et a1. , 1986). The two
procedures are illustrated in Figure 2.7.

In general mechanistic-based backcalculation procedures require computer
based solution. Some of the better known mechanistic models are discussed in

detail in Section 2.8.

2.7 SPECIAL PROPERTIES OF PAVING MATERIALS
Stress sensitivity of unbound materials and temperature dependency of asphalt
concrete have considerable affects on the backcalculated layer moduli. These two

properties of paving materials are discussed next.

29

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2.7.1 Material Non-Linearity

The response of common highway materials to traffic loading typically
includes elastic, viscoelastic, and plastic components. During the initial cycles of
stress, at slow loading rates or high stress levels, the viscous and plastic components
may be dominant (Dehken, 1978).

The stress-strain response of different highway materials is different under
changing stress conditions depending upon their properties and is discussed separately
for each material type.

2.7.1.1 W

The resilient modulus of sands andgravel is reported to increase with
confining pressure. The magnitude of repeated deviator stress, unless high enough to
induce shear failure, has no effect on the resilient modulus (Dehken, 1978). Biarez
(1962) suggested a relation for the resilient modulus (MR) after performing tests on

uniform sand in a triaxial apparatus:

MR 3 K1 (6)9 (2.2)

where K, and k, are material constants, and 0 is the sum of the principal stresses
(identical to the stress invariant 1,). If 0 is increased in a manner that (a, - 0,) are
constant essentially there will be no change in the modulus but the model fails to
address this condition.

Trollope, et al. (1963) observed that the rebound modulus increased with
confining pressure and also confirmed earlier observation that as long as failure
conditions are not approached the modulus was not affected by the axial stress.
Morgan (1966) performed repeated load triaxial tests on two sands and observed
marked increase in resilient modulus with increasing confining pressure and a slight

decrease with increasing deviator stress. He also stated that the resilient Poisson’s

 

31
ratio remained unaffected by both the deviator stress and the confining pressure.
Mitray and Seed, et a1. (1964; 1969) found the M, of sand subjected to triaxial
repetitive load tests can be expressed as:

M, = [(3.039 (2.3)

where a, is the confining pressure and K3 and K4 are material constants. Equations
2.2 and 2.3 were also found to apply to gravel with changed values of exponents K2
and K,. Jones (1960) observed stress-dependency of the modulus of sand subjected to
dynamic (vibratory) tests. Hardin and Black (1966) found that the shear modulus, G,

could be represented by:

G = KS (6)“ (2.4)
where 0 is the sum of normal stresses. The exponent K,5 was 0.6 for 0 < 42 psi. and

0.5 for greater values. Stress sensitivity of cohesionless roadbed soils of Michigan

was confirmed by Baker (1978).

2.7.1.2 iv i

Resilient modulus of cohesive soils is reported to decrease with increasing
deviator stress and is little affected by the transverse stresses (George, 1969). Seed, et
a1. (1972) reported results of repeated load triaxial tests on silty clay. The resilient
modulus was found to decrease rapidly with increase in the deviator stress up to 15 or
20 psi, any further increase in deviator stress resulted in an increase of the modulus.
The variation in modulus between deviator stress values of 3 and 15 psi was found to
be about 400 %. _

Kallas and Rilley (1977) found that in repeated compression tests on silty clay,
the values of MR increase slightly with increasing confining pressure and decrease

more markedly with increasing deviator stress. Sparrow and Tory (1966) performed

H

32
in-situ tests on medium plastic clay and reported an increase in modulus with increase
in depth and offset radius. The secant modulus was found to decrease with increase of
the major principal stresses, the effect being more pronounced at lower stresses.
These results were confirmed by Brown and Pell (1967).
The most commonly used model representing the stress dependency of fine

grained soils is reported by Young and Baladi (1977) as follows:

Mn = Klarogc’ (2'5)
where on = deviator stress; and
K, , K, = material constants.
Some mechanistic pavement design procedures use non-linear models. For
example, MICI—IPAVE and ILLIPAVE computer programs use a bilinear model for

cohesive soils. The relationship is expressed as:

M = ‘2 + kslkr - (01 - 03)] for k1> ((11-03) (2.6)
' k2 + 4““: ' 0,) ' k1] for ki‘ (or-03)
where (a, - a3) = deviator stress; and
k,, k2, k,, and k, = material constants.

The relationship is illustrated in Figure 2.8.

2.7.1.3 W
Fossberg (1969) conducted tests on highly plastic clay stabilized with lime and

concluded that the resilient modulus increased with increasing confining pressure and
decreased with increasing deviator stress. Mitchel, et al. (1977) observed a decrease
in MR of cement stabilized sand with increase in deviator stress. Wang (1968) found
that the resilient modulus of a silty clay stabilized with cement increase with
increasing confining pressure and decreased with increasing deviator stress. Both

researchers concluded that cement stabilized materials behave essentially linearly

33

 

The Resilient Modulus (pal)

 

 

,.._ 1:1

The Deviacor stress («71 - 03. ps1)

Figure 2.8. Typical variation of resilient modulus with repeated stress
for cohesive roadbed soil (Ming-Shan, 1989).

ll

 

in

inns
Chat
T3116“

J

Bot.

34

under repeated flexure, but non-linearly under compression.

2.7-1.4 mm

Asphalt cement exhibits a linear viscoelastic response, but asphalt aggregate
mixtures were found to display non-linear viscoelastic behavior, or even behavior
which was not viscoelastic (Krokosky, et al., 1963). Based on uniaxial creep tests,
Monismith, et al. (1966) concluded that for uniaxial strain of less than 0.1%, asphalt
aggregate mixes behavior is linear.

Terrel (1967) observed that the MR of asphalt mixtures increases slightly with
increase in lateral pressure and it decreases as the deviator stress was increased.
Chatti (1987) and Baladi (1988) also found similar trends in another study. Through
repetitive triaxial confining tests Trollope, et al. (1962) found that the rebound

modulus increased almost linearly with increase in the confining pressure.

2.7-1.5 W
Sparrow, et al. (1966) performed plate bearing tests on a roadbed soil

consisted of a homogeneous silty clay of medium plasticity in a test pit. Tire test
results showed stress-softening material non-linearity. This observation was also
confirmed by others through independent tests on silty clay (Mitray, 1964; Wang,
1968; Terrel, 1967). The most marked non-linear effects were observed at pressures
below 3 to 6 psi, at higher pressures a linear behavior was observed.

Mitray (1964) observed stress hardening behavior for pavement structures
consisting of a gravel base over a highly plastic roadbed soil. The response of the
roadbed soil was observed to be of the stress softening type but the overall results
were controlled by the over riding stress hardening behavior of the base material.
Shifley (1967) performed similar test on an actual pavement structure. During its

construction, different paving layers were subjected to plate bearing tests. The clay

 

 

35
roadbed was found to be of the highly stress softening type, but an addition of 11 in.
thick crushed base aggregates changed the behavior to a stress hardening type, and the
subsequent addition of a 2.4 in. thick asphalt concrete (AC) layer rendered the
pavement response almost linear. The pavement when completed with a further
addition of 4.8 in. AC layer showed markedly stress softening behavior.

The test results at the AASHO road test (1962) confirmed the pattern of non-
linearity described above under actual traffic loading. The non-linearity of the
measured pavement deflections was found to be much less pronounced than those of
the constituent materials in the laboratory. This phenomenon can be explained by the
fact that in a layered system consisting of stress-hardening and stress-softening
materials, the opposite effects counter each other, reducing the overall effect of

material non-linearity.

2.7.2 Temperature Dependency

Asphalt cement and asphalt-aggregate mixes are known to behave elastically at
low temperatures, whereas the behavior tends to be viscoelastic at higher
temperatures. Temperature dependency of the asphalt cement behavior was related to
its stiffness characteristics (Heukelom, 1969; Mcleod, 1969). Van der Poel (1954)
devised the Shell nomograph for estimating the asphalt layer stiffness with changing
temperatures. Heukelom (1969) modified the Shell method to make it applicable to
North American asphalts. Further, modification was suggested by McLeod (1969),
who proposed the Penetration-Viscosity-Number (PVN) as a means of characterizing
the asphalt. As a result of a study conducted at the state of Washington (Bubusait, et
al., 1974), an empirical relationship was suggested for temperature adjustment of the
asphalt cement modulus. The results of the study also indicated that the sensitivity of
the backcalculated asphalt layer modulus to temperature depends on the condition of

the pavement. New pavements being affected more than distressed ones.

 

.‘EF J -.. -vn .
9 . "

36
The problem of temperature measurement and application of temperature

correction to the asphalt layer modulus is discussed in more detail in section 2.9.1.

2.8 MECHANISTIC ANALYSIS MODELS

The load-carrying capacity of a flexible pavement is enhanced by the load-
distribution characteristics of its layered system. The system consists of various
paving layers with the highest quality material placed at the top (Yoder, et al., 1975).
The load distribution over the roadbed soil is achieved by building up thick layers of
paving materials. Early calculations of stresses in flexible pavements were based on
linear elastic theory. Since then efforts have been made to improve the basic models
to incorporate non-linear and material damping effects under traffic loads. Although
more complicated techniques to model the pavement response are now available,
(e. g., dynamic, viscoelastic) layered elastic analysis is still widely used because of its
simplicity and ease with which the required input data can be acquired in practice.
Elastic layer analysis and some other models which have traditionally been used are

reviewed in this section.

2.8.1 Layered Elastic Model
Multi-layered elastic theory has been extensively used to model the stresses
and strains in flexible pavements. The basic multi-layered system as pictured by
Yoder, et al. (1975) is shown in Figure 2.9. The analytical solution based on elastic
theory has several inherent assumptions including:
1. The material properties of each layer are homogeneous and isotropic.
2. Each layer has finite thickness except the roadbed soil, and all are infinitely
wide in the lateral directions.

3. Full friction between the paving layers is developed at each interface .

37

 

 

 

 

hr.£r.ur ' .MQl
as.» ’3‘ 8‘
. W2
Ila-Esau
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Figure 2.9. Multi-layered elastic system (Yoder, et al., 1975).

38

4. There are no shearing forces at the pavement surface.

Early calculations of stresses and strains in flexible pavements were based on
Boussinesq’s equations originally developed for a homogeneous, isotropic, and elastic
half-space subjected to a point load. The vertical stress at any point below the earth’s
surface due to a point load at the surface is given by Boussinesq’s formula as

a = k I— (2.7)
22

Z

k = —3— ———1— (2.8)
2" [1+(r/z)2]”z

where r = radial distance from the point load; and
= depth.

According to the above equation the vertical stress is independent of the
properties of the medium and depends only on the vertical depth and radial distance
from the load. By treating the whole pavement as a homogeneous and isotropic half-
space, it is assumed that the contribution of pavement layers above the subgrade
towards the total surface deflection is negligible (Yoder, et al., 1975).

Burmister (1943; 1958) developed a solution for a two-layered elastic system.
The materials in both layers are assumed to be homogeneous, isotropic and elastic.
The surface layer has finite depth and is assumed to be infinite in the lateral direction,
whereas the lower layer is infinite in both the lateral and vertical directions. Both
layers are assumed to have a full contact and the surface layer is free of shear and
normal stresses outside the loaded area. This model takes into account the properties
of the materials above the subgrade. It also accounts for a uniformly distributed
circular load which is a better representation of the wheel load than a point load.

Further, the high stiffness of the surface layer has a pronounced effect on the vertical

 

w
2.8

 

1‘

39
stresses and strains. In contrast to Boussinesq’s solution, the stress gradients obtained
by two layer theory are appreciably different from those obtained using a
homogeneous half-space.

Burmister and other researchers (Acum, et al., 1951; Jones, 1962; Peattie,
1962) expanded the solutions to three layer systems and presented the radial and
vertical stresses in tabular and graphical forms.

The advent of microcomputers made it possible to extend the linear elastic
layer analysis to systems with more than three layers. Many computer programs are
now available which can handle up to ten paving layers. Mathematical derivations and
comprehensive explanation of concepts and assumptions pertaining to the elastic layer
theory can be found elsewhere (Higdon, 1967; Westergaard, 1964; Timoshenko,
1987). Despite the availability of more advanced and complicated analysis models, the
elastic layer solution is still widely employed for pavement analysis because of its

practicality and simplicity.

 

The basic advantages of elastic layer theory are:

1. It satisfies the laws of mechanics and is thus capable of making consistent
calculations.

2. It is a relatively simple method and the calculation effort and capabilities
required of computers are small.

3. Iterative variations of elastic layer theory that can approximately account for
the non-linear variation of material properties in the vertical direction have
also been developed, but for highly stress sensitive materials these may be
inadequate.

4- Only two parameters, resilient modulus E and Poisson’s ratio ,1, are required

in elastic layer theory. The results are not too sensitive to the value of

40
Poisson’s ratios and reasonable values are assumed in most cases. This leaves
E as the only required material property, along with the layer thicknesses, as

an input to perform the analysis.

The limitations and inconsistencies related to the elastic layer assumptions are:

1. The behavior of the paving materials is not purely elastic. It has plastic, and
visco-elastic components.

2. The stress-strain relationships for the materials are not linear for the range of
stress levels encountered in pavements. Linear elastic theory may be
inadequate to model highly stress sensitive materials when encountered.

3. Most paving materials are particulate in nature, hence, they are neither

homogenous nor isotropic.

4. The stress-strain characteristics of most materials vary over time in all three
dimensions.
5. Boundary conditions are quite complex and different from those assumed by

elastic layer theory.
6. Actual traffic and the FWD apply dynamic loads to the pavement, elastic layer
analysis is typically used with static loading.

2.8.2 Hogg’s Model

Hogg (1938; 1944) modeled the pavement as a thin plate resting on an elastic
subgrade. This model assumes that the vertical stresses. within the pavement structure
are small and ean be neglected. The model has yielded good results for the
backcalculation of roadbed modulus values. A major advantage of this model is that
the roadbed modulus can be estimated without a prior knowledge of the characteristics
of the pavement layers (Wiseman, et al., 1985). The model was used to evaluate three
layer pavements using deflection data obtained by the La Crox-L.C.P.C.

 

 

mu

41
Deflectograph. The results were satisfactory (I-oninck, 1982). Details about the model
have been presented elsewhere (Wiseman, 1975; Wiseman, 1983).

2.8.3 Equivalent Thickness Model

All equivalent layer models developed for estimating deflections of
multilayered pavements share Odemark’s assumption (Odemark, 1949). Odemark’s
assumption is used to convert a multilayered elastic system to a single layer elastic
model. He suggested that deflections of multilayered pavement with moduli E., and
layer thicknesses hi, can be approximated by a single layer thickness, H, and a single

modulus E,, if the thickness H is calculated as;

2.9
H = 21‘ Ch, (E, / 5y” ( )

f
i?
3
:2
II

the equivalent thickness;
hi = actual thicloiess of the ith layer;
Ei = the elastic modulus of the ith layer;
1?.0 = the modulus of a single layer to which the multilayered
system has been converted; and
C = constant.

The equivalent thickness method has limitations in its application and for
certain types of pavements is known to give erroneous results (Kuo, 1979; Lytton, et
al., 1979; Hung, et al., 1982). The method has the advantage of simplicity and speed
of computation.

Ulliditz (1978) used the equivalent layer model successfully for pavements
with all linear elastic materials and also for pavements with non-linear roadbed soils.

Lytton (1989) also used the model with some modifications for the analysis of flexible

pavements.

42
2.8.4 Finite Element Method

This is the only method which theoretically can adjust the stiffness of each
element according to its own stress state. The method recognizes that for a nonlinear
material the modulus is not characteristic of the whole layer but instead pertains to a
point within that layer.

MICHPAVE (Ming-Shen, 1989) is one such program which uses finite
element method for linear and non-linear elastic analysis of layered system. In this
program the limitation of modeling an infinite subgrade by deep fixed boundary has
successfully been overcome by the incorporation of a flexible boundary concept.

There are no known backcalculation programs directly based on finite element
analysis because of computational time required. Instead, the data generated from
finite element programs has been used to generate regression equations in order to
account for the non-linearity of the paving materials (Hoffman, et al., 1982). Such an
approach requires lesser time for backcalculation but all the limitations of regression

type analysis of deflection data are applicable.

2.8.5 Dynamic Analysis
Static analysis are generally used to backcalculate the layer moduli of

pavements regardless of the load application mode. A load applied dynamically is not
equivalent to the static loading and so should not be the stress and strain fields
induced by each loading mode (Wiseman, et al., 1972; Stolle, et al., 1989). However,
conflicting views regarding the magnitude of the error induced by the inertial response
of pavements to dynamic loading can be found in the literature. Some researchers
have reported significant error (Davies, et al., 1985), while others found the error to
be insignificant (Roesset, et al., 1985).

Davies and Mamlouk (1985) argued that the single-degree of freedom (SDF)

models employed by most researchers are inadequate. They stressed the need to use

43
elastodynamic solution for the analysis of pavement deflection data, which can
account for loading from multi-directions. In elastodynamics, Helmholtz equation for

steady-state harmonic motion is used (Erigen, et al., 1975):

C,2 grade(dive u) - Cf curl(curl u) + p20.)2 a = 0 (2.10)
where c, and c, = the pressure and shear wave velocities, respectively;
u = displacement vector; and
a: = the circular frequency of the excitation.

The displacement vector u can be expressed in the form:

u(t) = u ‘e“’" (2'11)

where u' = complex amplitudes of the displacement vector;
t = time; and
i = unit imaginary number.

The wave velocities are related to the stiffness and mass density of the material by:

 

r
c = [ E(l-u) J3 (2.12)
’ (1+n)(l-2u)p
1
c = [ E J 2 (2.13)
’ 2(l+u)P
where E, u and p are Young’s Modulus , Poisson’s Ratio, and mass density,

respectively.
A closed form solution for equation 2.12 is available only for a point load

excitation on a homogeneous half-space. Numerical solutions, must be obtained for a
multi-layered system. The usual assumptions of linear elastic material and isotropy are
invoked. The soil and pavement layers are assumed to be unbounded laterally,

bedrock is assumed at a finite depth and full bonding is assumed at all layer interfaces
(Davies, et al., 1985).

44
Using the numerical solution technique presented by Kausel and Peek (1982)
the in—phase and out-of-phase displacements at any location throughout the pavement
can be obtained (Sebally, et al., 1986). Davies, et al. (1985), however, have stressed
the complexity and difficulties associated with the analysis despite making a number

of simplifying assumptions.

2.8.5.1 i D mi n l

Loads applied by the FWD are transient in nature and not harmonic. The ‘
Fourier transform is used to represent the transient load by the sum of the harmonic
load over different frequencies and amplitudes (Roesset, et al., 1985). Sebaaly et al.
(1986) assumed a periodic loading impulse with period T, which they divided into a
loading pulse-width, t,, and a rest period, TR, (Figure 2.10). The loading pulse width
is a function of the loading device and pavement system properties, with typical
values ranging between 25 and 60 msec for most FWD devices. The rest period Ta is
chosen to be large enough such that the pavement fully recovers from deformation
and hence the response of every drop is independent of the earlier one.

The Fourier coefficients for the load impulse expansion are analyzed and then
the phase lag, frequency, and amplitude of each harmonic response component are
obtained. The harmonic responses are summed in the time domain to obtain the
complete response due to the impulse. Similar solution was sought by Roesset and

Young (1985).

2.8.5.2 gamma} 9n 9! Static and Dynamic Analyses

1. Static analysis of dynamically loaded pavements result in a significant error if
the frequency of the applied load is approximately equal to the resonant
frequency of the pavement system, or if the resonant frequency is so high that

the inertial forces become dominant (Davies, et al., 1985).

 

45

 

 

[DAD

 

 

 

 

 

TIME

Figure 2.10. Assumed periodicity of FWD impulses (Sebaaly, et al., 1986).

 

 

2.8.6

46
Static interpretation of the deflections measured by an FWD test is reasonable
when the depth of the bed rock is more than 60 feet. The resulting error
increases when the subbase material is not homogeneous and/or when its
stiffness increases with depth (Roesset, et al., 1985).
Dynamic effects are less important for FWD loading because its load covers a
wide band of frequencies. The results obtained by Roesset, et al. (1985) using
dynamic and static analysis of FWD deflections showed that the difference in
backcalculated moduli using two methods was small. In an independent
study conducted on three different pavement structures in the United
Kingdom, Tam, et al. ( 1989) concluded that the differences in the
results of backcalculated moduli, for static and dynamic analysis using
FWD deflection basins, were insignificant.
Stolle and Hein ( 1989) observed from the results obtained by Sebaaly, et al.
(1986) that better agreement exists between the deflection basins measured by
FWD and that predicted by static analysis, than between that predicted by
dynamic analysis (Figure 2.11). They also pointed out from a previous study
(McCullough, et al., 1982) that while the accuracy of the measured deflection
values is important to evaluate the roadbed modulus, the shape of the
deflection basin is more important to accurately evaluate the pavement layer

moduli. '

Nonlinear Elasticity

Stress-strain curve for many paving materials are nonlinear. One simple

method of dealing with such materials is to replace the elastic constants in the linear

stress-strain relations with tangent moduli dependent upon stress or strain. The elastic

constants can be obtained by using piece wise linear models. Such an approach is

called a Cauchy elastic formulation (Chen, et al., 1985).

 

47

 

 

 

 

 

sunrace onseuceueur

 

 

RADIAL DISTANCE

Figure 2.11 Schematic showing measured and predicted surface deflection basins
(Stolle, et al., 1989)

48

The Cauchy type of elastic models may generate energy for certain types of
loading-unloading cycles. Hyperelastic models do not suffer from this drawback. Both
of these models suffer from the disadvantage that they are independent of the stress or
strain path, which is not true for soils in general.

A more realistic and rational description is provided by the hypoelastic
formulation in which the incremental stress and strain tensors are linearly related
through variable material response moduli that are functions of the current state of
stress or strain. Details of the three formulations and their respective characteristics
can be found elsewhere (Chen, et al., 1985). Here, only the second order stress-strain
relationships are reproduced (Uzan, 1993).

The constitutive relationship for the Cauchy model is of the form
a” = (C,I,+Czl,2+C,lz)bv + (C‘+C,I,)eu + Cseueu (2°14)
while for the hyperelastic model it is

o” = (2C111+3C2112+C312)50 + (c,+c,l,)eu + cseueu' (2.15)

In the hypoelastic model, the stress rate is expressed in terms of the stresses and

strain rates by:
60 == Coéuby + Clé,j + Czouéubu + 030.3.” + gave",
+ C,(oméw+éhow) + Csoflémby. (2-16)
where ”v , 5,,- = components of stress and strain tensor;
0", , a", = components of stress and strain rate
tensor;
1,, I2 = stress invariants; and

C0, to C, = material parameters.

49
These formulations, while having a strong mechanistic basis, are not widely
used beeause the material constants have little or no physical interpretation (Uzan,
1993). Uzan (1985) presented a simplified and general model for the secant resilient

modulus of paving materials as:

 

MR = klp‘ [3]“ [Ear (2.17)
P. Pa
Where p, = atmospheric pressure;
rm, = octahedral shear stress;
0 = bulk stress; and
kI , k2 , and k3 = material constants.

This model is a simplified form of the non-linear Cauchy model, and though
appealing, violates the laws of thermodynamics. In a recent paper Uzan (1993)
presented a modification of this model where two more material constants have been
added to account for the non-liner behavior of Poisson’s ratio and are derived by
imposing the path independence of the strain energy density function.

The five parameters for each paving layer cannot be directly backcalculated
from the set of deflection data measured by FWD equipment. Hence, Uzan suggests
that only k, be backcalculated, while k2 - k, be estimated from laboratory testing or
existing data banks. This partially defeats the purpose of backcalculation, making non-

linear models unappealing at present.

2.8.7 Viscoelastic Model

Asphalt displays viscoelastic behavior, and since FWD loadings are essentially
dynamic, some researchers have used viscoelastic models to obtain a more accurate
representation. In general, even granular and cohesive material can be modeled as

being viscoelastic. Viscoelastic material can be easily modeled by using a complex-

 

50
valued modulus (Wolf, 1985) as:

E*(c->) = 5’0») + iE”(w)=E’(w)[l+i25] (2.18)
where E', E', E" = complex-valued modulus and its real
and imaginary parts;
to = circular frequency; and

= damping ratio.

Granular materials are normally assumed to have a constant damping ratio
(Uzan, 1993). Nonlinear viscoelastic models are used more and more for dynamic
backcalculation but are relatively complex and hence have not been used widely in

practice. The increased number of parameters makes it difficult to backcalculate all of

them solely from FWD measurements.

2.8.8 Pavement Material Type and Choice of Analysis Model

Differences in opinion regarding the degree of non-linearity of pavement
materials can be found throughout the literature. Uzan (1993) recommended the use of
complex moduli to model the viscoelastic behavior of pavements and recommended
that data of the last few deflection sensors not be used in the backcalculation if the
complex moduli tended to increase away from the applied load. He further
emphasized the importance of using linear dynamic analysis when the bedrock is
present at a shallow depth. For deep bedrock Uzan recommends the use of the static
non-linear backcalculation as the state-of-the—art improves. Presently the use of non-
linear or viscoelastic models require some of the material properties to be inferred
from existing data banks or from laboratory tests. As a result, they have not found

much use in practice, and backcalculation based on simple linear elastic models are

still the most popular.

51
2.9 BACKCALCULATION METHODS
Existing backcalculation routines can be classified into three major groups
depending on the techniques used to reach the solution. These three techniques may
have any of the forward analysis methods, discussed earlier, embedded in them. The
first group is based on iteration techniques, which repeatedly use a forward analysis
method within an iterative process. The layer moduli are repeatedly adjusted until a
suitable match between the calculated and measured deflection basins is obtained. The
second group, is based on searching a database of deflection basins. A forward
calculating scheme is used to generate a data base which is then searched to find a
best'match for the observed deflection basin. The third group is based on the use of
regression equations fitted to a database of deflection basins generated by a forward
calculation scheme. Some of the known backcalculation computer programs and their

characteristics (adopted from Mahoney, et al., 1991) are presented in Table 2.2.

2.9.1 Iterative Methods

The ultimate objective of most backcalculation methods is to find a set of
moduli such that the calculated deflection basin match the measured one within a
specified tolerance. This is usually achieved by minimizing an objective function

which is commonly defined as the weighted sum of squares of the differences between

calculated and measured surface deflections (Uzan, et al., 1989) i.e.,

minimize f = 2:1 “ltmlfwiy (2.19)
where win = the measured deflection at sensor j;
wjc = the calculated deflection at sensor j; and
a,- = a weighing factor for sensor j.

The flow chart (Lytton, 1989) presented in Figure 2.12, illustrates this

process. The main steps of the iteration process are:

52

 

 

 

 

 

 

 

 

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54

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measured ..... Seed Moduli ..... Controls on the
Doflecfiom Range 01 Moduli
$ :
I
, I
l
Layer Dcflecuon '
Masses. Calculation
Loads , .
‘ ‘ Search for New
Moduli
Not OK T
Error Check

 

 

 

OK

 

m 1

 

Figure 2.12. Typical flow chart for an iterative program (Lytton, 1989).

l I
1 _,
~I’ '. > _

 

Step I.

Step 2.

Step 3.

Step 4.

Step 5.

j 55 .
Surface deflections at known distances away from the applied
load are measured.
Layer thicknesses, load application characteristics, and Poisson’s
ratios for each layer are required to be input by the user. In
almost all programs constant values of Poisson’s ratios are used.
In order to start the forward calculation process, approximate
layer modulus values (seed moduli) are required as input. Seed
moduli are sometimes generated by the program using measured
deflections and regression equations, or else they must be
specified by the user. Some programs use a database approach at
this stage to obtain seed moduli.
The data specified in step 2 and the latest set of layer moduli are
used to calculate surface deflections at the same radial offsets at
which the deflections were measured.
An error check is performed to assess if the measured and
calculated surface deflections are within a specified tolerance
limit. Different techniques are used at this stage to adjust the set
of layer moduli so that the new set of moduli reduces the error
quantified by the objective function. The method by which the
moduli are adjusted is the main differentiating factor between
most iterative procedure based programs. Steps 4 and 5 are
repeated until the value of the objective function is sufficiently

small or the adjustments to the layer moduli are very small.

One of the problems faced with this approach is that the multi-dimensional

surface represented by the objective function may have many local minima. As a

“33““ the program may converge to different solutions for a different set of seed

56
moduli. Some programs overcome this problem by automated assignment of the seed
moduli. Another problem is that the convergence can be very slow, requiring
numerous calls to a mechanistic analysis program. ‘

An example of an iterative program is EVERCALC (Sivaneswaran, et al.,
1991), which uses an efficient and general minimization method (Levenberg—
Marquardt algorithm). The program seeks to minimize an objective function formed
as the sum of squared relative difference between the calculated and measured surface
deflections. EVERCALC is a robust, efficient, and accurate program, and uses the
CHEVRON computer program for forward calculations.

The "---DEF" series of programs use an assumed linear variation in _
logarithmic space to revise the layer moduli after each iteration. These programs
employ a gradient search technique and the correct set of moduli is searched in an
iterative manner. The CHEVDEF program (Bush, 1980) is one such example in
which the CHEVRON program (Michelow, 1963) is used for forward calculations. A
set of seed moduli are required to be input by the user in this program to start the
iteration process. The simplified description of the process to find new layer modulus
from an initial guess for one layer and one deflection is shown in Figure 2.13. For
multiple deflections and layers a set of equations defining the slope and intercept for
each deflection and each unknown layer modulus is developed as follows (Van

Cauwelaert, et al. , 1989):

log (deflection) = A}: + Sfi (logEi) (2.20)
where A5, = intercepts;
Sis = slope;
j = 1,2,...ND (ND=No. of deflections); and

i = 1,2,...NL (NL=N0. of layers with unknown moduli).

57

mm FROM LAYERED
can»:

  

 

 

 

I
g I
.- I
a
_, I I
e I I
g I I maceration-“suns:
.. g 2 I

- I

I i I |

l 3 l I

I w I |

I I I

I I I

l I

I I '

I I I

l V l l

emu emu em
LOG mom

Figure 2.13. Basic process for matching deflection basins (Van Cauwelaert, 1989)-

 

 

58 p

The linearization of the model in logarithmic space simplifies the search for
new set of moduli. However the results obtained by these programs are highly
dependent on the initial seed moduli.

Some programs such as ELMOD (Ullidtz, et al., 1985) use an equivalent layer
thickness concept along with Bousinesq’s equation in an iterative program to
backcalculate the layer moduli. There are some other programs which are based on
the elastic layer concept but which first estimate the subgrade modulus based on the
deflections measured by the outermost senors. The subgrade modulus is then fixed
and intermediate layer moduli are estimated using the middle sensor deflections and
finally the AC modulus is inferred from the set of inner-most sensor deflections. The
error in the estimated moduli of lower layers thus contribute to the errors in the

moduli of the upper layers.

2.9.2 Database Approach

In this method, a forward calculation program is used to generate a data base
of deflection basins for different combinations of layer moduli, and specified layer
thicknesses, material properties, pavement types, and loading conditions. The
measured deflection basin is compared with the deflection basins in the database using
a search algorithm, and a set of moduli are interpolated from the layer moduli which
produced the closest calculated deflection basins in the database.

The MODULUS backcalculation program (Uzan, 1985) is one such example
which uses databases generated by WESLEA (Van Cauwelaert, 1989) program. The
number of basins required to obtain a suitable database depends upon the number of
layers and the expected moduli ranges provided by the user. Wide ranges require a
greater number of basins to be generated than narrow ones. The generated deflection
basins are then searched using the Hookes-Jeeves algorithm and a three-point

Lagrangian method is used to interpolate the moduli. The program seeks to obtain a

59 _
set of moduli which will minimize an objective function defined as the relative sum of
squared differences between the measured and calculated surface deflections. The
program is known to converge always, although the chances of converging to a local
minimum cannot be ruled out (Scullion, et al., 1990). The program performs a
convexity test to determine the likelihood of having converged to a local minimum
and the user is warned if this test is not satisfied.

. Backcalculation based on a database search is especially suited when a large
number of pavements with similar configuration are to be tested in continuation. For
these situan'ons the data bank once generated can be used repeatedly to backcalculate
moduli for all similar pavements, and the time required to generate the database can
be minimized. This technique can be used with database generated from any linear or
nonlinear program (Chua, et al., 1984). The results obtained are modemme accurate,
but the accuracy of the results is sensitive to the expertise of the user and his or her
knowledge of pavement materials.

The COMPDEF (Chua, 1989) program also uses a database approach to
backcalculate the layer moduli. The program uses a precalculated database of
composite pavement deflection basins stored in a matrix, which is searched by an

interpolation technique to find the layer moduli.

2.9.3 Statistical Analysis

This method is similar to the database technique, the only difference being in
how the database is used. The database is created by using any forward calculation
routines, and then statistical analysis is performed to generate regression equations.
These equations take the deflections as independent variables and attempt to predict
the values of the layer moduli. Pavements of different configuration can be grouped
separately to yield different equations for more accurate predictions. Different

prediction equations are required for each pavement layer and pavements with a

60
different number of layers have to be treated separately.

The LOADRATE program (Chua, 1989) belongs to this category and uses
regression equations generated from a database obtained by using the ILLIPAVE non—
linear finite element program (1982). This technique is best suited for agencies which
deal with a limited and known type and configuration of pavements. Data bank
generation to include all the expected combinations of pavement layers in the initial
stages can offset this disadvantage to a large extent. Proper statistical interpretation of
data can give reasonably accurate results. Once the regression equations are obtained
this technique is simple, and extremely quick. The results on the other hand vary in
accuracy depending on how well the database which was used to generate the

statistical equations represents the pavement being analyzed.

2.9.4 Conversion of Backealculated Layer Moduli to
Standard Conditions

The modulus of the asphalt concrete surface course is significantly affected by
the temperature and frequency of loading. On the other hand, the base, subbase and
roadbed soil moduli are more affected by confining pressure, moisture, and stress
levels. For a better interpretation of the modulus values, the backcalculated moduli
should be converted to some standard conditions (moisture and temperature). The
conversion to standard conditions is referred to as corrections to backcalculated

moduli.

2.9.4.1 n n i

The temperature correction procedure suggested by the Asphalt Institute is
most commonly used for pavements with more than 2 in. thick AC layer (1977). The
mean temperature of the pavement must be calculated for the same time when the

pavement deflections are measured. This procedure requires exhaustive data

61

including: .

l. The maximum and minimum temperatures for five days prior to the day the
test is performed.

2. The pavement surface temperature at the time of NDT is conducted.

3. The frequency of loading or in case of FWD loading the time duration of the
load impulse .

4. The percent asphalt cement content by weight.

The chart in Figure 2.14 is used to determine the temperature at the top,
middle, and bottom of the asphalt layer. The data in steps 1, 2, and 3 described above
are required to use the figure. The mean of the three temperatures is considered as the
mean temperature of the pavement.

Southgate (1968) presented a slightly different procedure than the one
described above to find the mean temperature of pavements having an asphaltic
concrete layer thickness of less than or equal to 2 in. This procedure stresses that for
thin asphaltic layer pavements, the hour of the day and the amount of heat absorption
is more important than the maximum and minimum temperatures used in the Asphalt
Institute method. Figure 2.15 is used to find the temperature on the underside of a
thin asphaltic concrete layer. This temperature and that of the surface of the layer at
the time of testing are then averaged.

The frequency of loading is also required to use the Asphalt Institute equation
(1982). The frequency in the case of a cyclic loading device, such as the Dynaflect or
Road Rater, is the actual frequency of loading. In the case of a FWD device the

frequency is obtained as:

62

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64
__1_
f 2t

where t = time duration of the impulse load in seconds.

The frequency and temperature corrected modulus is then calculated using the

following equation:

1 l r
logE, =IogE +P [— -—] +0.000005 P“[(t '-(t)’]
200 (,0), (”I J— 0)

 

—.00189‘/P—“[ (1,): -LZ'1]+.9317[—1_-.L] (2.21)
(0' (0' (f.)" (0"
where I = 0.17033;
)1 = 0.02774; ‘
E = backcalculated uncorrected modulus;
At, = test and reference temperatures in °F;
ff, = loading and reference frequency in Hz;
P, = percentage of asphalt cement in the mix;
E, = the corrected modulus;
r, = 1.3 + 0.49825 log (fn);
r = 1.3 + 0.49825 log (t); and

P,» = the percent passing the No. 200 sieve.

Germann and Lytton (1989) evaluated the accuracy of this correction
procedure. They concluded that the procedure gives better results when correcting a
modulus measured at a low temperature to a higher standard temperature, than vice

V6138.

 

 

 

65
2.9-4-2 W

Load level corrections are necessary only when the applied load, under which
the modulus is required to be calculated is outside the elastic range for any of the
paving layers. Also the load level correction is only required for base and roadbed
materials since the AC layer behaves almost linearly. Basically two corrections are
required (1) for confining pressure level, and (2) for the strain level (Germann, et al.,
1989).

All the layered elastic analysis methods make some assumptions regarding the
use of an average modulus for the entire paving layer, which technically is incorrect.
The FHWA-ARE method assumptions (1975) have been found to provide a suitable
basis to apply load level corrections to the average modulus values.

Richard and Abbot (1975) proposed the following equation for the general

stress-strain curve (Figure 2.16) for the base, subbase, and roadbed soils:

 

 

E's
o=E e+
' Ere a 1 (2.22)
[l+[ ] 1"
0,
where 0,5 = any stress and its corresponding strain levels;

E, = initial tangent modulus;
E, = plastic modulus;
E. = E. - E. ;
a, = maximum plastic yield stress; and
m = a material constant.

Germann and Lytton (1989), used this equation and assumed that the resilient
modulus is a secant modulus of the curve shown in Figure 2.16, proposed a relation

between the secant modulus, E, and the initial modulus, E, as:

‘I

66

Stress

 

 

 

 

Strain

Figure 2.16. General hyperbolic stress-strain curve for base, subbase, and roadbed ‘
materials (Richard, et al., 1975).

The unknowns of equation 2.23, a, b, m, and E can be found through

67

[_l_-a_],,,_[_(_l—_a)£],,=l

Epl Es;
0, / Ea;
initial tangent modulus; and

a material constant.

(2.23)

regression analysis. The final correction equation is of the form (Lytton, et al., 1990)

where E, / E5

E,

E,

Err
a,b,m
5k

‘1

 

 

 

 

I (l-a) 11m.
(I-a)e, "
E, _ (ol+oz+03) k '2 1+ b
E} [(014-024-03) j] (l -a) ll»:

 

 

 

(1-a)e,] "

 

l

 

= correction factor to convert backcalculated moduli;

 

= resilient (secant) modulus at a standard load level;
= initial tangent modulus at the standard load;

= initial tangent modulus at the NDT load level;

= dimensionless constants;

= strain under standard load level; and

= strain under NDT load level.

(2.24)

Equation 2.24 is used in an iterative process. A mechanistic program is used

to calculate the principal stresses and strains for standard and NDT load levels.

Stresses are calculated at mid.depth for the paving layers and at one foot depth for the

roadbed soil.

68

The iterative procedure is initiated by assuming a modulus for each layer
under the standard load, the secant modulus for the non-standard load being known
for each layer from the analysis of the NDT data. The confining pressure and strains
are then calculated for both loading conditions. From known properties of the
materials, the modulus for each layer under standard loading conditions are then
calculated. If these calculated moduli are significantly different from those initially
assumed, the procedure is repeated using the new values until all values are close
enough to the values from which they were calculated.

2.9.5 Sources of Error In Backcalculated Layer Moduli

The sources of errors in the backcalculated layer moduli can be classified into
two main groups: random errors that are mainly associated with the measuring
devices and pavement structural geometry and condition; and the systematic errors
associated with the load representation, theoretical model, and the analysis process

(Uzan, et al., 1989).

2.9-5.1 121mm

Load cell and deflection sensors have manufacturer’s accuracy specifications
which for deflection sensors is 12% of their full range. This error may be larger
depending upon the pavement condition and the way the sensors rest on the pavement.
The load cell error seemingly renders error of similar magnitude and nature to the
backcalculated moduli. The overall error due to measuring devices may lead to
inadmissible errors in the backcalculation. Being random in nature, this error can only
be minimized by making a greater number of measurements at each test site and

averaging the results.

69

2.9.5.2 W

The relative rigidity of the pavement and the loading plate affects the pressure
distribution on the loaded area. The pressure concentration will be higher at the edge
when the pavement is relatively flexible while a relatively rigid pavement will result
in pressure concentrations near the middle of the loading plate.

Replaceable ribbed rubber pads of different rigidities can be used to overcome
this problem which has been discussed in detail elsewhere (Uzan, et al., 1989). Also
the presence of a hole at the center of the plate is a source of error. Both of these

errors are systematic in nature.

2.9-5.3 BamLdelflanandflmm

Pavement condition, such as the presence of voids, cracks, surface texture of
the loaded area and variable layer thicknesses all effect the backcalculated moduli.

The thickness of the upper layer has the maximum effect on the backcalculated
moduli (Rwebangira, et al., 1987). Using average values from the cores or from
design data may yield a random error. The effect of layer thickness accuracy has been
discussed by Irwin, et a1. (1989). Similarly the seating of the loading plate may be
affected by the rough surface texture of the pavement which again will result in a
random error. Seating errors can be minimized by dropping the weight at least two

times before the data is recorded.

2.9.5-4 Matedalflmlel
Use of different material models affects the backcalculated results in a

systematic way. The assumption of linear, homogeneous, isotropic materials can give
rise to errors in the backcalculated moduli if the actual materials do not satisfy such

assumptions.

70
2.9.5.5 AaalxsisMetlmd
The analysis method must conform to the mode of loading. Most NDT devices
impart a dynamic load to the pavement, while the analysis methods used are typically
static (Mamlouk, 1987). This discrepancy introduces a systematic error in the
backcalculated moduli.

2.9.6 Error Measures and Convergence Criteria

In order to assess how well the layer moduli are backcalculated, some measure
of the error between measured and calculated surface deflections is required. In
iterative methods, this error can be used as a criterion to determine convergence.

Most programs use one of three most frequently used error measures. These
are the sum of absolute differences, the sum of squared differences and the sum of
squared relative errors between the measured and calculated deflections.

The absolute arithmetic error (AAE) is defined as:

" l100*(dd-d~)|

 

ME, % = 2 (2.25)
I d» l
where n = number of measured deflections;
d,, = ealculated surface deflection at sensor i; and
dmi = measured surface deflection at sensor i.
The root mean square (RMS) error is expressed as:
In
RMS, 95 2(3— d'" (23‘)
n l-1(

 

Irwin, et al. (1989) suggested that the RMS is a better measure of the

goodness of fit because its magnitude is unconstrained by the number of sensors,

71
while the AAE is directly proportional to the number of sensors.
Uzan, et al. (1989) also argued that since the accuracy of the sensors, a major
contributor to random errors, is normally specified in relative terms, the objective
function to minimize the deflections at respective sensors should also be expressed in

relative terms. The error measure they suggested takes the form:

 

 

I d dll-dc 2
e2 = 22 V U w, (2.27)
M j-l d;
where d5", d,,-° = measured and calculated deflections at ith sensor and jth drop;
wi = weight assigned to the ith sensor;
n = number of sensors; and
j = number of drops with approximately the same drop height.

This function has been used in the MODULUS program, and differs from the
RMS only slightly.
The third measure, the average of AAE, is obtained by dividing the AAE by

the number of sensors.

2.10 SUMMARY
Deflection testing is the most widely accepted and used method for evaluating

pavement performance. The load applied by the FWD is considered to resemble
actual traffic loading. The test is simple to perform and is automated. Dynatest is
rated as the most efficient FWD equipment available.

Deflections are affected by season and temperature at the time of testing, the
condition of the pavement and the moisture in the roadbed soil. Seasonal correction
factors developed for a general geographic area must be used.

Paving material response to traffic loading is non-linear. Most studies,

72
however, have highlighted the fact that in a layered system, the overall non-linear
effect is reduced because of the interaction of different paving materials.

The linear layered elastic model is used most widely to analyze FWD data
despite its shortcomings. A number of more complex models have been presented
recently with claims of having overcome some of the limitations of the elastic layer
model. However these models have not been tested extensively, they are quite
complex to use, and may even require expert users. Further, the various material
parameters required in these complex methods often cannot be inferred from the
present NDT equipment. Hence, they must be inferred either from existing databases
or from laboratory testing. As such the advantages associated with these models
mostly come from their theoretical soundness.

Existing backcalculation programs are mostly engineered to minimize an
objective function, which is constructed from the observed and measured surface
deflections. These programs suffer from the disadvantage that the backcalculated
results may be a consequence of convergence to a local minima rather than a global
one. Some of these programs have incorporated some measures to guard against such
a convergence, but the effectiveness of these measures vary from one program to
another. Existing methods of predicting the stiff layer depth from FWD deflection
data are restricted to using regression equations or trial and error methods. Further,
no program can practically estimate layer thicknesses from measured deflection data.

There are no truly non-linear backcalculation programs, and most programs
require deflection data from at least three load levels to infer non-linear response.
Finally, the backcalculated results are affected by a variety of complex factors making
backcalculation of layer moduli a difficult undertaking.

In light of the shortcomings of the existing backcalculation programs, some of
the objectives that will be persued in the course of this research to offer enhanced

capabilities in a new computer program include:

73 p
The ability to mechanistically estimate stiff layer depth from FWD deflection
data.
The capability to predict the thickness of any layer other than the
roadbed soil.
Eliminate or reduce the sensitivity of the backcalculated results to the
seed values.
Enhance the user interaction in a manner not only to facilitate and
simplify the use of the program but also to enhance the understanding
of the backcalculation process and results.
Finally, since the project is sponsored by MDOT, verify the
applicability of the existing temperature conversion factors to the

pavements in the state of Michigan.

CHAPTER 3

EFFICIENT ITERATIVE METHODS FOR BACKCALCULATION OF
PAVEMENT LAYER PROPERTIES

3.1 GENERAL

Elastic layer analysis of pavements is used to calculate the load induced strains
and stresses in different regions of a pavement system whose properties are already
known. Backcalculation, on the other hand, is the inverse problem related to elastic
layer analysis in which some of the unknown layer properties are estimated from the
measured pavement response (deflections) due to a known load. The two problems are
depicted in Figure 2.7. The deflections are typically measured at various lateral
distances away from the load and the number of deflection measurements must be
greater than or at least equal to the number of parameters to be backcalculated.

For three or more layers, the inverse problem cannot be solved exactly and a
numerical solution scheme must be used. A review of backcalculation methods that
use elastic layer analysis has been presented in section 2.9, and most of them are
based on the minimization of an objective function formulated in terms of the error
between the measured and the calculated surface deflections.

In this study, a new and efficient method to substantially improve the predicted
value of the roadbed modulus with a single call to a forward calculation program is
developed. Along with this a backcalculation procedure based on the Newton method
for the solution of non-linear equations is developed, and this method is known for its
fast convergence (Dennis, et al., 1983). In addition the Newton method is extended to
estimate layer thicknesses and the depth to the stiff layer along with the layer moduli.
Finally a logarithmic transformation of the data to improve the speed of convergence

is implemented.

74

75
3.2 IMPROVED ESTIMATION OF ROADBED MODULUS
It is well known that the roadbed soil often contributes up to 90% of the
pavement peak surface deflection (Yoder, et al., 1978). Deflections measured by all
sensors are affected substantially by the roadbed modulus with the farthest sensor
from the applied load being affected the most. Hence, accurate estimation of the
roadbed modulus is essential for the over all accuracy of the backcalculation results.

For an iterative backcalculation program, an early accurate estimate of the
roadbed modulus will not only reduce the analysis time but will also reduce the
possibility of divergence for complex problems. The algorithm developed below has
been incorporated in the MICHBACK program in order to substantially improve the
roadbed modulus at the beginning of the backcalculation. Further improvement to the
roadbed modulus is carried out simultaneously along with the backcalculation of the
other layer properties.

Recognizing that the roadbed soil contributes strongly to the deflection
measured by all sensors, a technique is developed to improve the roadbed modulus
using a single eall to a mechanistic analysis program. This estimation at the beginning
of the backcalculation procedure facilitates convergence.

Consider a pavement with n layers for which m surface deflections are
measured ( m 2 n ). Let the vector { W, } contain the m deflections computed at the
top of the jth layer using current estimates of the layer moduli (E ). The vertical
compression under the sensors in the jth layer is { I9, } - { 191+ , }. For the last layer,
one can take { W", } = { O }. The vertical compression in any layer is a result of the
accumulated vertical strain (éj), which is inversely proportional to the layer modulus
(i.e., proportional to é, = l/Ej ). By scaling the compression in each layer by the

layer modulus, one can obtain the following vector:

76

{‘31} = E'j( {raj} — {em} ) (3.1)
The collection of all such vectors will be an n x m matrix of the form:
(3 . 2)

A = [ {all {a2}. . .(a,)]

The sum of the compressions in each layer must add to the total surface deflection.

that is:
n
2 ( {oil-{91,1} ) = {:91} (3.3)
j-r
or equivalently
Ala} =l011 (3.4)
Equation 3.4 can be used as the basis to the following iterative scheme
A‘ (all+1 = {w} (3.5)

in which [A]‘ is computed using the current moduli estimates {E}‘, and {w} are the
measured surface deflections. The over—determined system of equations (n equations
and m unknowns) can then be solved using the method of least squares to obtain the
revised inverse moduli {é}”'.

It may appear that Equation 3.5 can be used to improve the estimates of all
layer moduli. Unfortunately, the technique is very unstable for estimating all the
unknown moduli. The method was found to be very sensitive to the ratios of the md
moduli (e.g., ratio of each layer moduli to the roadbed modulus). When the ratios of
the seed moduli are close to the actual ones (even though the initial moduli estimates
may be substantially different from the actual ones) the results for all the unknown
moduli are predicted very well even after a single iteration. However, the sensitivity

0f the method to the ratios of the seed moduli often results in a negative modulus

 

77
value of one of the layers other than the roadbed. Therefore, the method has been
adopted to improve only the roadbed modulus. The values obtained for the other layer

moduli are disregarded.

3.3 NEWTON’S METHOD
Consider the example of finding the roots of a nonlinear equation in one

unknown

f(x) = x2-3 (3-6)

Suppose an initial estimate of the answer is xo=2, a better estimate i, can be obtained
by drawing the line that is tangent to fix) at (2,f(2))=(2,l) and finding the point 'ri,

where the line crosses the x axis as shown in Figure 3.1.

 

21 = filo-Ax (3-7)
It can be readily verified that -
fl}? )
2 = - O 308
1 ° r’Iso) ( ’

for this particular case

x, = 2 -l/4 = 1.75

If two more additional iterations are performed in a similar manner, the result
will be 1.7320508 which is accurate to the eight significant digits. This method is
called the Nemon-Raphson method, or simply Newton ’5 method. The use of Newton’s
method for backcalculating layer moduli in flexible pavements was first suggested by
Thomas Hou (1977), but the method has not been pursued since until recently (Wang,

5‘ al., 1 993; Van Cauwelaert, et at., 1989).
Newton’s method is a useful tool for solving nonlinear problems. It is an

78

flat) 'x2 -3

 

 

 

Figure 3.1. General illustration of Newton’s method (Dennis, 1983).

 

 

Iterz
SOIU

itsei

layer

3.4

explic:

araflat

ltlues

79 p
iterative method which generates a sequence of points that rapidly approach the true
solution. The convergence of the method depends upon the nature of the problem
itself. Given a good initial estimate, the method is known to converge quadratically
for most problems but for some ill-behaved functions with poor initial estimates, it
may not converge at all. Also local convergence for certain types of problems cannot

be ruled out. The characteristics of Newton’s method when used to backcalculate the

layer moduli are highlighted in Chapter 4.

3.4 NEWTON’S METHOD WHEN THE DERIVATIVES OF THE

FUNCTION ARE NOT AVAILABLE

In many practical problems, the closed-form of the function f(x) is not known
explicitly and is obtained as an output from some numerical or experimental
Procedure, as is the case in FWD testing. In such cases the derivatives are also not
available in a closed-form and Newton’s method must be modified to make use of the
Values of f(x) only.

In the classic Newton’s method the values of f (x) are used to model f(x) near
the current solution estimate xo by the line tangent to f(x) at x0 as shown in Figure
3.1 . When the derivative of the function is not available, the model can be replaced
by the secant line that passes through fat x. and some nearby point x, + h, as
dcDicted in Figure 3.2. The slope of this line is given by the following equation:

= f(x°+h°) - f(xa) (3.”

a0 )1
RePlacing f'(x°) by a, in Equation 3.8 yields.

(3.10)

 

 

80

 

 

 

 

Figure 3.2. Secant approximation of Newton’s method (Dennis, 1983).

 

 

81 g
It is apparent that in the limit as h, _. O, a, will converge to f'(x,,). When h, is chosen
to be small, a, is called a finite-difference approximation to f' (x). This modified
quasi-Newton’s method is known to work as well as the Newton’s method and
sometimes is referred to as the Secant Method. The characteristics of the quasi-

Newton method is similar to the standard Newton’s method, but convergence is

usually slow.

3.5 MULTI—DIMENSIONAL FORM OF NEWTON’S METHOD
Newton’s method can be easily expanded to accommodate the solution of a set

of nonlinear equations to solve for more than one unknown. Consider the set of

equations

f1(x1,x2,...,xn)= 0

f2 (x1,x2,...,xn) = 0

(3 . 11)
fn(x1,x2,...,xn) = O
or in the vector form
fix) =0 (3. 12)
Given an estimate
2, = [23,2;,...,2f,]’ (3.13)
an improved estimate is obtained by
21,1 = 21 - Ax
(3.14)

= 2,. - crl fled)

where

1“ general, rather then inverting G, it is more efficient to solve the set of linear

82

 

 

 

 

 

 

 

 

’arl at, ar,‘
6x1 Er: 6xn
a: ._. [%S = 5 s (3.15)
x ‘3’ ' W at“ at, atn
_ax, 3x2 axnI (xi-(21)
equations as follows:
a A: =:I2,) (3.16)

3.6 USE OF THE NEWTON ’8 METHOD TO BACKCALCULATE

PAVEMENT LAYER MODULI

Consider a pavement with n layers for which m surface deflections are
measured (m 2 n). Let the vector w represents the measured surface deflections due
to applied FWD load. The non-linear deflection versus modulus curve is
approximated by a straight line which is tangent to it at the estimate 19‘. The slope of
the straight line, (dw / dE)| E . 3,, is used to obtain the increment, AE‘, which is added
to I? to obtain the improved modulus estimate 1?” as shown in Figure 3.3.

Since the slope is not known analytically, it is obtained numerically, as

discussed in section 3.4, by using the following equation:

 

dw ,_ w((1+r) £1) — ww‘)

FélE-E“ .. :3" (3.17)
in which r is sufficiently small. This requires additional deflections arising from
moduli values of (l -+-r)Ei to be computed.

For the described system of n layers and m sensors, the slope is represented by

the following gradient matrix:

83

Deflection»!

\, ME)

 

 

 

 

 

 

 

5" 5"“ E Modulus,E

Figure 3.3. Graphical illustration of Newton’s method iteration
to find pavement layer moduli. ‘

84

r aw1 6w1 6w;

613, as; 6E

n

(a) - (Is-)1
awm aw, awm
. 6E1 6E2 6E". (a) - (3)1

 

 

oi=[%

 

 

 

 

The element of the jth row and kth column of the matrix can be estimated numerically

 

as follows:
aw w ( [R] (Ell) - w ((31))
—1 1 z j j 0
aEkIB-E IE: (3 19’

in which [R] is a diagonal matrix with kth diagonal element being (1+r) and all other
elements being 1. Thus the partial derivative is estimated numerically by taking the
difference in the jth deflection arising from the use of a set of moduli

1?“ 3‘2, ..., (1 + r)E‘,, ..., E‘, and the moduli L5,, 5",, ..., I?” ..., 3,. Hence, a
separate call to the mechanistic analysis routine is required to compute the partial
derivatives in each column of the gradient matrix. The increments to the moduli,

{AER can then be obtained by solving the m equations in n unknowns:
9i + GI AE" = at (3-20)

The method of least-square may be used at this stage to solve the over-
determined system of equations (m equations in n unknowns) to determine AB. If
desired, weights can be used for each sensor measurement to emphasize some

mmUI‘ements over others. The revised moduli are obtained through

{2}“1 = (31+(AEI‘ (3-21)

The itel‘Eltion is terminated when the changes in layer moduli are smaller than a

tolerance or. specified by the analyst. That is,

 

 

85

3.1 +1 _ E31
——“ “ se1 , K=1,2,3...n (3-22)
.. .i
Er:
When the computed and measured deflection basin match closely, the following root-

mean-square (RMS) error criterion can also be used to terminate the iteration:

 

1 2
_ 1 “j " W 3 23)
RMS .. _ (___l) 55 (-
Jm Elia-1 w, 2

The iteration will end if either of the two criteria is met at any stage of the process. It
should be noted that the RMS error criterion will usually be met only if the model
used for the forward calculation accurately represents the pavement system that
produced the measured surface deflections. Equation 3.22, on the other hand will

always be satisfied if the numerical algorithm converges.

3.7 LAYER THICKNESS ESTIMATION

The layer thicknesses at the locations of the FWD tests are seldom known
exactly- One direct method of measuring the layer thicknesses is coring. But selective
or random coring provides only a better estimate of the average layer thicknesses in
the section of interest, since it will never be possible to core all the FWD test
locations. Variation in construction and terrain make the variation in layer thicknesses
inevitable. Estimation of layer thicknesses along with the layer moduli from the
deflection data can enhance the accuracy of the backcalculated results.

Newton’s method can be extended to backcalculate pavement layer thicknesses
along with layer moduli. The restriction remains that the total number of unknown

moduli and layer thicknesses together must not exceed the number of deflection

mmurernents.

F or improving I layer thicknesses in addition to n layer moduli Equation 3.8 is
extendad as follows:

86

 

aei

in which AI is the vector of thickness increments and the augmented gradient matrix

6' is given by

 

 

 

’aw, .. 6w1 aw1 6w;

6M 6M 55—1 . BE; 7t: a:

”32h .3“... ..= «ms»
a__w. 3w, 6w, 8w.
‘63, E; 37:: TC, (SI-(8)1

Ia - (E P
A column of the gradient matrix corresponding to a partial derivative with respect to a
thickness is estimated numerically by computing the surface deflections due to a slight
increase in that thickness. The number of forward calculations during each iteration
now increases to (n + I + 1).

During extensive testing of the method to backcalculate layer thicknesses and
moduli it was observed that a better overall convergence is achieved if only the layer
moduli are improvediin the first few iterations. Additional iterations are then
performed to improve both the layer moduli and thicknesses as outlined in this
section.

Theoretically it should be possible to backcalculate the thicknesses of any
number of layers simultaneously, provided the total number of unknowns do not
exceed the number of deflection measurements. In practice however, backcalculating
layer thicknesses for more than one layer often causes the scheme to diverge. Further
investigations indicated that if the deflections calculated by the forward analysis
program are used in the backcalculation without any truncation, then up to two layer
thicknesses can be backcalculated simultaneously. However, if the deflections are
truncabd to imitate field measurements, then the scheme often diverges if more than

one layer thickness is backcalculated.

87 _
Theoretically speaking, the technique outlined above can be extended to predict
any layer property, including Poisson’s ratio, as long as the number of unknown
quantities does not exceed the number of sensors. However, convergence of the

method must be studied rigorously to validate such a claim.

3.8 THE MODIFIED NEWTON METHOD

In the Newton method, the number of calls made to a mechanistic analysis
program for each iteration is (n + I +1). In the modified Newton method the total
number of calls to a forward calculation program can often be reduced. In the
modified method several iterations are performed with a gradient matrix before it is
revised. Although, the convergence in the modified approach is slower than the
normal method, the n forward calculations required to calculate the gradient matrix
during each iteration can be reduced. The total number of iterations required to reach
a desired level of accuracy will become higher in the modified method but the total
number of calls made to the forward analysis program may be reduced. Experience
has shown that performing n iterations before revising the gradient matrix yields

better results with fewer calls to the mechanistic analysis program.

3.9 STIFF LAYER EFFECTS AND ESTIMATION OF DEPTH TO STIFF

LAYER

In elastic layer modeling of pavements the roadbed materials are assumed to be
uniformly stiff and infinitely thick. However, in most real pavements, the roadbed
stiffness increases with depth. This increase is mainly due to the increasing lateral
stress with depth and is influenced by changes in the material or even the presence of
a stiff layer (e.g., bedrock) within the zone influencing the FWD measurements.

Many researchers have acknowledged the need to incorporate a stiff layer at an
appropriate depth since this can significantly affect the backcalculated results(Bush,

 

met
mor
sift

Ch;1

Elle

The I

88
1980; Chou, 1989). Various methods of estimating the depth to the stiff layer have
been suggested.

In a layered elastic analysis the rigid layer can be incorporated by assigning a
very high modulus to the lowest layer, but the depth to this layer may be unknown.
Bush (1980) recommended the use of a rigid layer at 20 feet depth for all FWD
analysis. Uddin, et al. (1986) suggested that the roadbed depth can be inferred from
the velocity of compression waves in the roadbed and frequency of loading. Chou
(1989) suggested an iterative approach based on a trial and error method. The depth
which results in the least RMS error can be found which will presumably be the true
depth. The method apart from being tedious is prone to error owing to the non¢
uniqueness of the solution.

Recently, Brown (1990) presented a set of regression equations to estimate the
depth to stiff layer using the measured deflections and layer thicknesses. These
equations have been incorporated in the MODULUS and EVERCALC programs to
estimate the depth to the stiff layer (Rohde and Scullion, 1990; Mahoney, et al.,
1993). The regression equations yield relatively inaccurate depth estimates for
medium to deep stiff layer locations. EVERCALC allows the user to input the
modulus of the stiff layer, while the MODULUS program assigns the modulus of the
stiff layer automatically. The accuracy of the regression equations has been tested in
Chapter 4. .

The estimation of stiff layer depth based solely on regression equations can
give rise to significant errors in the backcalculated moduli. In MICHBACK program
the initial estimate of the stiff layer depth is obtained using regression model
developed by Baladi (1994). Unlike the other two programs, however, an iterative
process has been developed and is implemented in MICHBACK to improve the stiff
layer depth, or equivalently the roadbed thickness. The iterative process is carried out

in two distinct steps as follows:

89
In this step only the values of the layer moduli are improved until they
show some stability.
In this step two distinct schemes are used to find the-roadbed thickness.
The first scheme is identical to the one explained in section 3.7.1. The
roadbed thickness is included as an unknown in the gradient matrix
along with the layer moduli (Equation 3.25). As reported earlier, this
method can estimate the unknown thickness of any layer other than the
roadbed along with the layer moduli. However, this method alone was
insufficient in predicting the roadbed thickness accurately. When this
method is used, the moduli are estimated much better and faster,
compared with the method in which only the moduli are kept as
unknowns. This method also works well in providing fine corrections to
the roadbed thickness when some other method has been used to bring
the estimate reasonably close to the actual one. The shortcoming of this
method is overcome by adding another scheme to this step, involving
iteration to derive the layer thickness of the roadbed solely based upon
the deflections. The gradient matrix is constructed for one variable
alone and then a least squares solution is sought. This method makes
the estimation of the roadbed thickness fast and accurate. These two
schemes are used iteratively until one of the convergence criterion
specified by the user is met. It is ensured that the scheme where the
layer moduli and roadbed thickness are both treated as unknowns,
always occurs last. This guarantees the revision of layer moduli after an
accurate estimate of the stiff layer thickness has finally been obtained

using the scheme which only estimates the stiff layer depth.

90
3.10 LOGARITHMIC TRANSFORMATION
It has been reported (Bush, 1980) that the relationship between surface
deflections and layer moduli display less non-linearity if the deflections and layer
moduli are transformed to a logarithmic scale. This section explores this

transformation.

3.10.1 Relationship between Surface Deflection and Layer Moduli

The relationship between surface deflections and layer moduli was probed
extensively. The layer moduli of an arbitrary three—layer flexible pavement section of
medium AC thickness were varied, one at a time, and their effects on the calculated
surface deflections were analyzed. Figures 3.4 through 3.9 depict the pavement
surface deflections plotted against the layer moduli using both arithmetic and
logarithmic scales. To avoid clutter in the plots, only the deflections at three locations
are shown. It can be seen that the relationship between the layer moduli and the
surface deflections are non-linear for both the AC layer and the roadbed soil and
nearly linear for the base layer. The logarithmic transformations substantially decrease
these non-linearities.

Arithmetic and logarithmic plots of the pavement surface deflection as a
function of the moduli of the AC and roadbed soil are shown in Figure 3.10 and 3.11
respectively. It can be seen that the use of logarithmic scale transformed an otherwise
curved surface to a much flatter one. The analysis of such a flat surface results in

computational savings that are highlighted in Chapter 4.

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3.10.2 Implementation of Logarithmic Transformation
In order to shorten the computational time, logarithmic transformation was
implemented to calculate the gradient matrix and the moduli increments in the

logarithmic space by using the following equation:

 

d(log w) z log(w(10‘1“"1°9‘1)) ‘ 109(“é1” (3.26)
d(log E) 3.31 , I log (91)

It this case the additional deflections arising from a modulus of

10 “‘*""°“E” have to be computed, where r is a sufficiently small number.

The set up of the gradient matrix 6", representing the slope for a system of n
layers and m sensors is essentially the same as in Equation 3.25. The difference in the
formulation of this matrix in the logarithmic space is that the element in the jth row
and kth column of the matrix is estimated numerically for columns related to the

moduli as follows:

aw

E1 , 109(wj(1o(tal{m§:}))) — log (wj{§:}) (3,27,

5.31 r 109%,?)

 

 

For columns related to layer thicknesses, since the thicknesses are not transformed to

the logarithmic’s scale, the following equation is used:

 

tn) 1°“ .3: 31
ac, t _ E, r “,5

For these cases, the following equation is set up for Optimum least square solution

109 (0") + a1 {1°g (35)} = 109 (v) (3-29)

100
Finally, the revised moduli and thickness are calculated using the following equations:

{am

1
tin {Eli ,., {10mg )} (3.30,

t1+At1

After this step is performed the deflections and the revised moduli are both converted
back to the arithmetic scale. Then the usual convergence checks as given by
Equations 3.22 and 3.23 are performed to determine whether the iteration has
converged.

. For very shallow stiff layer depths (e. g., 36 in. or less), negative deflections
may be measured by the outer sensors. Almost all existing backcalculation programs,
do not accept negative deflections at any of the sensors. For such cases, a solution
that ignores the deflections of the outer sensors is used. The MICHBACK program
can analyze deflection basins containing negative measured deflections. However,
since negative deflections cannot be transformed to the logarithmic scale the

arithmetic scale is automatically used by the program.

CHAPTER 4

VERIFICATION OF THE MICHBACK ALGORITHM USING THEORETICAL
DEFLECTION BASINS

4.1 GENERAL

In the previous chapter, a mechanistic based gradient method to backcalculate
the layer moduli of a pavement structure using FWD data was described. The
algorithm for improved estimation of the roadbed modulus, layer thickness and stiff
layer depth were also introduced. This algorithm has been incorporated into a
microcomputer based backcalculation program named MICHBACK. The MICHBACK
program uses an enhanced version of the CHEVRON program (named CHEVRONX)
to perform multilayer linear elastic analysis. The modification to the original
CHEVRON program was done by Dr. Lynne Irwin of Cornell University. The
structure of the MICHBACK program and its different components are illustrated in
Chapter 5.

The theoretical aspects of the backcalculation program presented in Chapter 3
are validated in this chapter using theoretical deflection basins generated by
CHEVRON X. Numerical examples have been incorporated to highlight the effects of
incorrect layer thicknesses and stiff layer depth specifications on the backcalculated
layer moduli. Two important properties of the program, the convergence
characteristics and the uniqueness of the results are also examined. Analyses of the
effect of errors in the deflections measured at different sensor locations on the
backcalculated layer properties are presented. Sensitivity analysis of the
backcalculated results is conducted and presented in both arithmetic and logarithmic
scales. The sensitivity of the backcalculated moduli to Poisson’s ratios is also

highlighted.

101

102

Existing backcalculation programs use different analysis routines, as indicated
in Table 2.2. Most of these routines are based on multilayer elastic analysis schemes.
However, the deflections computed by these programs differ from each other. The
difference in some cases is substantial. Consequently the backcalculated properties are
affected not only by the backcalculation technique used but also by the analysis
scheme.

In addition, the results of the MICHBACK program have been compared with

those of two leading backcalculation programs, MODULUS 4.0 and EVERCALC
3.0.

4.2 TYPICAL PAVEMENT SECTIONS AND TEST PARAMETERS USED ‘
The effectiveness of the MICHBACK program was studied by using four
hypothetical pavement sections with known layer thicknesses and properties as shown
in Tables 4.1 through 4.4. For each pavement section, its layer thicknesses and
properties were used as inputs to the CHEVRONX computer program and the
theoretical deflections at lateral distances of O-, 8-, 12-, 18-, 24-, 36, and 60-inch

from the center of the loaded area were calculated. The other input factors to the
' CHEVRONX were as follows:

1. 9000-lb load.

2. A 5.9l-inch radius of a circular contact area.

3. When incorporated, a stiff layer modulus of 5000 ksi, Poisson’s ratio of 0.25,

and depths from the pavement surface of 36, 144, and 240-inch.

The calculated theoretical deflection basins and the layer thicknesses were then used
as inputs to the MICHBACK program and the layer moduli were calculated. A match
between the backcalculated layer moduli and those listed in Tables 4.1 through 4.4
imply a perfect accuracy of the backcalculation routine.

The same calculated theoretical deflection basins and layer thicknesses were

103

Table 4.1. A typical three layer flexible pavement.

P ' ’ 1
Layer . . raqigson s M503“ us

 

Table 4.2. A typical four layer flexible pavement.

9

 

Table 4.3. Typical four layer composite pavements.
Layer
AC

Base

 

Table 4.4. A typical five layer flexible pavement.

 

104
also used in two other leading backcalculation routines; MODULUS 4.0 and
EVERCALC 3.0. The values of the seed moduli (the range for MODULUS) used in

the three programs are provided below.

Computer . Pavement Seed moduli (ksi)

”gram Subbase Roadbed
soil

 

3-layers
flexible

 

4-layers

MICHBACK ‘ flefible

and ‘ 4-layers
EVERCALC . composite

 

 

3-layers
flexible

 

I 4-layers
MODULUS flexible

 

4-layers
composite

 

 

 

 

 

 

It should be noted that the above ranges in the md moduli for the MODULUS
program were expanded whenever the program had indicated that one of the limiting
value had been reached. For the examples involving the stiff layer there was no
change in the seed moduli or in the moduli ranges specified for the MODULUS
program.

The MICHBACK and EVERCALC programs essentially require similar types
of input parameters. The convergence criterion for the moduli for the two programs
was specified as e = .001 (.196) (see Section 3.6). Further, the MODULUS program
requires, as an input, the most expected value of the roadbed modulus, a value of 7
ksi (compared to the actual one of 7.5 ksi) was provided for all examples to make the

105
comparison favorable to MODULUS. With the exception of problems involving a stiff
layer at finite depths, a semi-infinite roadbed thickness was assumed for all other
examples. The MODULUS program assigns the stiff layer modulus internally, but for
the other two programs the actual value of the stiff layer modulus of 5000 ksi was
specified. The MODULUS program was allowed to automatically assign weight
factors to the different deflection locations and the "RUN A FULL ANALYSIS"

- option was used for all examples, so that material types were not required as input.

4.3 NUMERICAL ILLUSTRATION: IMPROVED ESTIMATION OF

ROADBED MODULUS

An improved technique to accurately estimate the roadbed modulus at the onset
of the analysis was presented in Chapter 3. The effectiveness of the method is
illustrated in this section by using the pavement sections of Tables 4.1, 4.2, and 4.4.

The improved estimates of the roadbed moduli after the first iteratibn with a
single call to the mechanistic analysis program (CHEVRONX) are presented in Tables
4.5 through 4.7. lt can be seen that after only one call to the CHEVRONX program,
the maximum error in the estimated roadbed value is 5 %. The importance of this
improvement in the roadbed modulus after the very first iteration can be explained by
the fact that the deflections at all locations are affected by the roadbed soil modulus.
The accurate estimate of these effects at the onset of the analysis increases the
accuracy and efficiency of the estimates of the moduli of the other pavement layers in

the consequent iterations.

4.4 ESTIMATION OF LAYER THICKNESSES AND THEIR EFFECT ON
THE BACKCALCULATED LAYER MODULI
The effect of incorrectly specified layer thicknesses on the backcalculated layer
moduli is investigated using the MICHBACK, EVERCALC, and MODULUS

106

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.5. Improvement of the roadbed modulus for a three layer flexible pavement.
Pavement Actual modulus (ksi) Seed modulus (ksi) Improved roadbed modulus II
type AC Base Roadbed AC Base Roadbed Modulus (ksi) Error (95) II
100 10 1 7.88 5.07
Thin 500 45 7.5
1000 70 20 7.44 -0.8
100 10 l 7.54 0.53
Medium 500 45 7.5
1000 70 20 7 .5 0.0
100 10 l 7.38 -1.6
Thick 500 45 7.5
1000 70 20 7.47 -0. 13
Table 4.6. Improvement of the roadbed modulus for a four layer flexible pavement.
: _
[ Actual modulus (ksi) Seed modulus (ksi) Improved roadbed
modulus
AC Base Subbase Roadbed AC Base Subbase Roadbed [Modulus (ksi) Error (96)
100 25 7 l I 7.83 -l.6
500 45 25
1000 100 45 30 I 7.37 -l.7
Table 4.7. Improvement of the roadbed modulus for a five layer flexible pavement.
Actual modulus (ksi) Seed modulus (ksi) llmproved roadbed modulus"
AC Base Base Subbssa Roadbed AC Base Base Subbase Roadbed Modulus (ksi) Error (5)
100 so l5 7 l 7.7 2.67
500 100 45 is 7.5
1000 300 70 so 20 7.33 .2.27

 

o

 

 

 

 

 

 

 

 

 

 

 

 

 

107
programs. The performance of the Newton’s method to predict the actual layer
thicknesses from incorrectly specified values is highlighted in this section.

The three layer flexible pavement with medium AC thickness (Table 4.1) was
used to study the effect of incorrectly specified layer thicknesses on the backcalculated
layer moduli. Either the AC or the base layer thickness was specified with an error
range of i 40 % relative to the true thickness. Two types of backcalculations were
performed using MICHBACK: one with automatic correction of the incorrectly
specified thickness (MICHBACKI), and the other with the thickness held fixed at the
incorrect value as done by the other two programs (MICHBACKZ). The percent
errors in the estimated modulus values relative to the actual ones are calculated and

presented below.

4.4.1 AC Thickness
The percent errors in the backcalculated layer moduli due to an incorrectly
specified AC layer thickness are presented in Table 4.8 and Figures 4.1 through 4.3.

Examination of the figures indicate that for all three pavements:

l. The effect of the errors in the AC thickness is most pronounced on the AC
modulus.

2. i The roadbed modulus is relatively insensitive to inaccuracies in the AC layer
thickness.

3. A positive error in the AC layer thickness results in a lower prediction of the

AC and base moduli and a negative error results in stiffening of the two
moduli.

4. When the option to correct the erroneous AC thickness was used,
MICHBACK produced accurate prediction of all layer moduli along with the
AC thickness.

108

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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112
Eff fA Thikn Errr anemen wihDiff nA

mm

The effect of incorrectly specified AC thicknesses on the layer moduli of

pavements with different AC thickness was studied using three typical three-layer

flexible pavements listed in Table 4.1. The AC thickness was varied between j; 10 %

for all three programs. The results obtained from the programs are presented in

Table 4.9. Examination of the results of the three programs indicate:

1.

lnaccuracies in the AC thickness affect the AC modulus of thin AC layer
pavements the most and thick pavements the least.

The base modulus was affected the most for thick pavements and the least for
thin ones. This observation was further investigated by Studying the change in
the vertical stresses at the top of the base layer with inaccuracies in the AC
layer thickness. The study reveals that owing to an inaccuracy of —10% in the
AC thickness of the thin pavement, the increase in the vertical stress at the top
of the base layer is about 6% , compared to about 20% for the thick pavement
as shown in Figure 4.4.

For EVERCALC, it can be noted that for the thick pavement, even for cases
in which the error in the AC thickness is negative, the predicted AC modulus

is always smaller than the actual. This is because of the relative inaccuracy of

the older version of CHEVRON (used in EVERCALC 3.0), which becomes
more significant for stiffer pavements. This discrepancy is highlighted in
Section 4.10 where the results of different elastic layer programs are

compared.

113

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4.4.1.2 E1131 of AC Thickness Eggpr 9n Eavgmgngs with Different AQ
Stiffngs

The medium thickness pavement listed in Table 4.1 was used to study the
effect of error in the AC thickness for pavements having different AC stiffness. The
AC moduli of 300, 500, and 800 ksi was used to simulate soft, medium and stiff
pavements. The resulting errors in the different layer moduli due to the error in the
AC thickness are presented in Table 4.10.

As it was expected, for the same inaccuracy in the AC layer thickness, the
error in the backcalculated AC layer modulus is higher for stiffer pavements for all
three programs. The MICHBACK and EVERCALC programs have similar trends for
the base modulus also (i.e., having greater error for stiffer pavements), but the
MODULUS program gave erratic results not indicating any trends.

The roadbed modulus remained insensitive to inaccuracies in the AC thickness

for all three programs as observed earlier.

4.4.2 Base Thickness
The percent errors in the backcalculated layer moduli due to an incorrectly

specified base layer thickness are presented in Table 4.11, and Figures 4.5 through

4.7. The observations from these results for all three programs are:

1. The roadbed modulus is relatively insensitive to errors in the base thickness.

2. Both the AC and the base layer moduli are significantly affected by
inaccuracies in the base layer thickness. With the base layer being affected the
most.

3. The base layer modulus shows stiffening effect due to negative errors in the
base layer thickness and vice versa-

4. The AC modulus was found to be positively related to the errors in the base

layer thickness (i.e., negative errors in the specified thickness produce

116

 

 

 

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negative errors in the AC modulus). This is probably because of the
sensitivity of the base modulus to the errors in base thickness. Small
errors in the base thickness result in higher errors in the base modulus
which are compensated by corresponding errors in the AC layer
moduli.
5. Again, the results of MICHBACKI (where layer thickness option was used)

indicate excellent prediction of all layer moduli and the base layer thickness.

4.5 STIFF LAYER EFFECTS AND DEPTH ESTIMATION

The effect of the stiff layer depth may be observed either by the presence of a
stiff layer under the roadbed soil or even by the soil overburden and stress hardening.
The need to incorporate the stiff layer at an appropriate depth has been recognized
and various methods have been developed and discussed in Section 3.9. A mechanistic
based method introduced in Chapter 3 has been incorporated in the MICHBACK
program.

The capability of the three programs to estimate the stiff layer depth along
with pavement layer moduli was tested using the three-layer medium thick flexible the
four layer flexible, and the composite pavement sections listed in Tables 4.1, 4.2, and
4.5 respectively. The deflection data was generated using the CHEVRONX program.
For the stiff layer, a modulus of 5000 ksi was used for the MICHBACK and
EVERCALC programs, whereas the MODULUS program assigns the modulus
internally. The stiff layer depth was varied between 36 and 240 inch. The results are

presented below.

4.5.1 Backcalculation of Layer Moduli and Stiff Layer Depth
For the three layer pavements, the results are presented in Table 4.12, the

salient points observed are:

Table 4.12.

 
 

Backcalculation of stiff layer depth and moduli

122

for a three layer flexible pavement.

 

 

 

 

 

 

 

 

 

 

 

 

I Percentage error in backcalculated properties I
I Stiff layer AC Base I
l modulus modulus modulus I
IR MICHBACK -0.3 -0.5 0.7 -0.6 I
$2112"; EVERCALC 5.6 23.6 -19.7 15.2 I
MODULUS 5.6 10.5 -20.4 21.3 I
I Medium MICHBACK -0. 1 0.5 -0.6 0. 1
I (144 in.) EVERCALC .41.7 -56.2 179.7 -42.8
. MODULUS 41.6 ~23.7 59.6 -32.0
I MICHBACK 0.3 1.0 -1. l 0.15
I (223111.) EVERCALC -56.6 -53.9 144.3 -36.7
I, _ MODULUS -52.5 {39.6“II 118.9 -33.3

 

 

 

 

 

123
The regression equations used by MODULUS and EVERCALC yield quite
accurate results for the shallow stiff layer cases, but as the depth to the stiff
layer increases so does the error. However, as shown in the following section
the backcalculated layer moduli are more sensitive to the inaccuracies in the
depth for a shallow stiff layer.
For the MODULUS and EVERCALC programs the error in the predicted stiff
layer depth ranges from about 6% to 50% for the shallow and deep stiff layer
cases.
MICHBACK on the other hand, with an initial start from the regression
equations (Baladi, 1993) can converge to accurate results by refining the stiff
layer depth as discussed in Section 3.9.1. The maximum error in the
backcalculated depth to stiff layer remained below 0.5 % for all examples.
Hence, incorporation of the stiff layer had no impact on the results
backcalculated by MICHBACK, whereas the results of other two programs are

significantly affected.

For the four layer flexible pavement the results presented in Table 4.13

indicate:

1.

The regression equations yield results quite similar to those of the three layer
pavement. Hence, the errors in the backcalculated moduli for the MODULUS
and EVERCALC programs are about the same as they were for the three layer
pavement.

Results from MICHBACK program are way better than the other two
programs.

The stiff composite pavement listed in Table 4.4 was used to study the

capability of the three programs to predict the layer properties of composite

pavements with a stiff layer present at a finite depth. The highlights of the results

124

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.13. Backcalculation of stiff layer depth and moduli
for a four layer flexibile pavement.
Percent Error in Backcalculated Properties
Stiff layer Program .
('er Stiff layer AC Base Subbase Roadbed
depth modulus modulus modulus modulus L
QI
MICHBACK 2.5 0.8 -2.6 3.3 6.4
Shallow
(48 in.) EVERCALC 6.7 0.37 20.4 -80.6 139.9
MODULUS 6.9 4.3 18.2 72.7 9.3
MICHBACK -5 .3 0.04 0.1 1.4 —0.7 il
Medium
(144 in.) EVERCALC -31.5 -31.6 ~37.0 565.1 41.9
MODULUS -31.3 2.6 -20.4 221.3 -36.0
MICHBACK 2.2 -0.2 1.1 -3.9 0.4
Dec
(240 1:.) EVERCALC -3s.2 12.8 -50.3 464.7 -29.3
MODULUS -35.0 -3.9 -4.7 118.7 -24.0

 

 

 

 

 

 

 

 

125

presented in Table 4.14 are:

l. The regression equations were probably not designed to account for composite
pavements. The errors in the stiff layer depth prediction for the EVERCALC
and MODULUS programs are over 300% and induce errors higher than 400%
in the backcalculated moduli.

2. For the shallow stiff layer depth the prediction error for the two programs was
almost the same, the depth being over predicted by about 130%. But for
medium and deep stiff layer cases the MODULUS program predicted the
depths as 300 inch. and EVERCALC as 600 inch. for both cases. This
suggests that MODULUS has 300 inch. and EVERCALC 600 inch. as the
maximum allowed depth to a stiff layer. The regression equations must have
predicted values higher than these and the programs must have fixed the depth
to the stiff layer at the arbittarily set maximum limit. As a result the error in
the predicted depths to the stiff layer for the two programs is different for
these two cases.

3. It is highly recommended that whenever a stiff layer is used with composite ‘
pavements, the results from MODULUS and EVERCALC programs should be
scrutinized carefully.

4. Results from MICHBACK, however, were comparable to those of the four
layer flexible pavement and consistently better than those of the two leading

programs.

4.5.2 Sensitivity of Backcalculated Moduli to Stiff Layer Characteristics

Having established the ranges of error in the stiff layer depth estimation by the
three programs, the effect of inaccuracies in the depth to stiff layer on the
backcalculated moduli was studied. Coupled with depth, the sensitivity of the

backcalculated results to the stiffness of the stiff layer is also studied.

126

 

 

 

 

 

 

 

 

 

 

 

Table 4.14. Backcalculation of stiff layer depth and moduli
for a four layer composite pavement.
Percent Error in Backcalculated Properties
Stiff Layer Program .
depth Stiff layer AC Base Subbase Roadbed
depth modulus modulus modulus modulus
MICHBACK -3.1 -1.6 1.9 -13.7 5.9
Shallow
(48 in.) EVERCALC 172.95 -15.78 -28.55 -18.21 661.8
MODULUS 172.3 -14.92 -24.45 35.96 353.3
MICHBACK 0.5 -1 .1 0.5 6.8 0.1
Medium
(144 in.) EVERCALC 329.0 40.9 -17.38 -9S.75 201.0
MODULUS 108.3 26.97 -36.33 15.28 83.03
MICHBACK -0.7 0.2 -2.0 54.6 -1.0
Deep
(240 in.) EVERCALC 150.0 198.8 -37.5 -96.0 78.8
MODULUS 25.1 17.36 -25 .7 279.8 12.4

 

 

 

 

 

 

 

 

 

127
4.5.2.1 ff f h iffl h n the B I 1 111
MM

The backcalculation was performed with an incorrectly specified depth to the
stiff layer depth. As discussed in the previous section, many researchers have
advocated the use of a stiff layer at an arbitrarily fixed depth. The medium pavement
listed in Table 4.1 was used to study the effect of the depth to stiff layer. With all
other parameters kept constant, the depth of the stiff layer with a modulus of 5000 ksi
was varied between 36 and 600 inch.

The results are presented in Figure 4.8. It can be seen that the deflections
obtained by an elastic layer program are affected even by a stiff layer located as deep
as 600 inch. However, as the stiff layer depth increases, the effect of the stiff layer
becomes smaller relative to the solutions where presence of the stiff layer was
ignored.

The effect of using an incorrect stiff layer location on the backcalculated
moduli was studied by using all three programs. Here the stiff layer was deliberately
specified incorrectly. The stiff layer at medium depth (144 inch.) along with the
medium three layer flexible pavement (Table 4.1) was used, and the error in the stiff
layer depth was varied between 1: 40 %. The errors in the backcalculated moduli are
presented in Table 4.15 and Figures 4.9 through 4.11.

The trends observed for all three programs are:

l. The roadbed modulus backcalculated by all three programs is sensitive to
errors in the stiff layer depth, since‘the error directly affects the roadbed
thickness and hence its stiffness.

2. When the roadbed thickness is over-estimated, the roadbed modulus is also
over-predicted as to reduce the total compression of the roadbed soil, and vice
versa.

3. In general, the backcalculated moduli for the AC and the base layers interact

128

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Table 4.15. Error in the backcalculated layer moduli due to percent
error in the depth to the stiff layer.

 

   
 

Percent error in the backcalculated results for the indicated programs
(’1 AC I 7 Base I Roadbed

 

    

 

 

 

 

 

 

 

MOD MB EC MOD
57.1 ~33.4 41.8 -30.7
-20 ~14.2 -55.8 -11.3 27.8 82.5 22.2 -13.4 -16.6 -12.0 I
-10 -7.02 45.0 -3.6 12.7 - 43.1 8.0 -6.1
-5 -3.22 -34.9 -0.4 5.8 24.2 2.0 -2.9
0 0.4 -21.6 ' 2.8 -.4 6.6 -3.3 0.1
5 3.92 -6.0 4.6 -6.1 -9.6 -7.1 2.8

 

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133
with each other, and the over-estimation of one results in the under—estimation
of the other.

4. For all three programs the roadbed modulus was found to be very sensitive to
error in the stiff layer depth. Therefore, the base modulus always showed an
opposite trend than that of the roadbed compensating for the sensitivity of the
adjacent layer. Thus, an over-estimation of the roadbed thickness resulted in
the base modulus being under-predicted and the AC modulus being over-

predicted, respectively.

4.5.2.2 ’ff 1 M I
W

Generally, the stiff layer modulus is more difficult to predict than the depth.
This is especially true when the stiff layer effect is being observed not due to the
presence of a hard layer but because of the soil overburden or stress stiffening
characteristics of the roadbed soil. In the latter case the roadbed modulus gradually
increases with depth, making the prediction of its modulus difficult.

The effect of the modulus of the stiff layer on the backcalculated layer moduli
are illustrated in this section. The three layer medium thick pavement (Table 4.1) was
used to study this effect, and the depth to stiff layer was varied between 36 and 240-
inch. 1n the first case the correct depth to the stiff layer (i.e. the same as that used to
generate the deflection data using CHEVRONX) was used. The data was generated
using a value of 1000 ksi for the modulus of the stiff layer, while for the purposes of
backcalculation, the modulus was varied between 500 and 7000 ksi (error range of -
600% to 50%). The results presented in Table 4.16 indicate that:

1. Within the wide range of error in the stiff layer modulus, the observed error in
the backcalculated layer moduli was reasonably small for the shallow stiff

layer and almost insignificant for the medium and deep stiff layers.

134

Table 4.16. The effect of stiff layer modulus on the backcalculated layer moduli
(stiff layer depth fixed).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stiff layer Stiff layer Error in stiff layer Error in backcalculated moduli (%) ll
1h modulus i. modulus % RMS
dc” 0“ ) ( ) AC Base Roadbed
7000 -600 3.7 -5.3 8.3 4.9
Shallow
(36 in.) 5000 400 3.5 4.9 7.7 4.6
1000 0 0.03 0.0 0.0 0.0
500 50 4.5 6.8 ~10.1 6.5
7000 -600 0.1 -3.2 3.8 -0.8
Medium
(144 in.) 5000 400 0.1 -3.0 3.6 -0.7
1000 0 0.0 ~2.7 0.7 -0.1
500 50 0.1 2.4 -2.8 0.7
7000 -600 0.1 -1.8 2.0 -0.4
(240 in.) 5000 400 0.1 -1.7 1.9 -0.3
1000 0 0.1 -0.6 0.6 0.0
500 50 0.03 0.7 -1.0 0.4
.— E=

 

 

 

 

 

2.

135

The RMS error decreases as the stiff layer depth increased for the same degree

of error in the stiff layer modulus.

The example above was repeated for all cases, but this time instead of

providing the actual stiff layer depth and fixing it MICHBACK was allowed to find

the stiff layer depth iteratively along with the layer moduli. The stiff layer modulus

was deliberately varied between the above mentioned limits, and the seed value for

the stiff layer depth was provided by the regression equations.

The results presented in Table 4.17 indicate:

1.

The MICHBACK program compensates for higher values of the stiff layer
modulus by reducing its depth keeping the stiffness of the other layers almost
the same.

In the case of an incorrectly specified stiff layer depth, the backcalculated
moduli have a slightly larger error than that when the true depth is specified.
This observation is more pertinent to the shallow stiff layer. The reason for
this is that as the stiff layer depth decreases, the backcalculated results become
more sensitive to the stiff layer pr0perties. At shallow depths, small errors in
the backcalculated thickness coupled with the error in the stiff layer modulus
can produce moderate errors in the backcalculated layer moduli.

The above exercise indicates that the stiff layer modulus has a negligible effect
on the backcalculated layer properties, especially when the stiff layer depth is
not very shallow.

It is further emphasized that the error range for the stiff layer modulus tested
in the above exercise was extremely wide. Hence, making a reasonable guess
regarding the stiff layer modulus will not have a significant effect on the
backcalculated layer moduli. Also interaction between the stiff layer depth and

modulus will only make the iterative process more complicated and prone to

136

Table 4.17. Effect of stiff layer modulus on the backcalculated
layer moduli and stiff layer depth.

Stiff layer Stiff layer Error in RMS Stiff la er
depth modulus(ksi) modulus (%) dept

88'133’

1‘1” ‘35

(2983.)

 

137
enon
5. Based on the above observations, no effort has been made in the MICHBACK
program to include the stiff layer modulus as an unknown in the

backcalculation process.

4.6 CONVERGENCE CHARACTERISTICS

Newton’s method is a rapidly convergent and accurate optimization technique.
The speed of convergence, in MICHBACK, has been enhanced by the logarithmic
transformation of the gradient matrix as explained in Chapter 3. The convergence
characteristics have been tested in this section using the deflection data generated by
CHEVRON X.

The MODULUS and EVERCALC programs being used for comparison are
limited to a maximum of four pavement layers, and therefore no comparison could be
made for the five layer example. The EVERCALC program uses the original version
of the CHEVRON program for forward calculations, which being less accurate affects
the backcalculated results. In order to make the comparison fair for EVERCALC
program, the backcalculation was conducted by using theoretical deflection basins
generated by both CHEVRONX and CHEVRON. The results where, CHEVRON
generated data was used in the backcalculation, are denoted by EC-ALT.

For all examples, surface deflections were rounded to the nearest hundredth of
a mil. An improved accuracy was obtained for MICHBACK when the surface
deflections were input to a greater precision, especially for the composite pavements.
The other two programs do not allow the surface deflections to be input to a precision
greater than hundredth of a mil. Although, such a precision is unrealizable in the
field, this observation with MICHBACK indicates the sensitivity of the backcalculated

results for composite pavements to even small changes in the measured deflections.

138
4.6.1 Three—Layer Flexible Pavements

The properties of the three layer flexible pavements used in the analysis are
listed in Table 4.1. The backcalculated results along with the maximum error in the
moduli and the RMS error specified by Equation 3.23 are given in Table 4.18.

The MICHBACK program yields accurate results for all three layers.
MODULUS. on the other hand, has comparatively larger error for the base modulus,
4% being the largest. For other layers, the errors are smaller. The EVERCALC
program has the largest error of the three programs, mainly because the CHEVRON
program is used in the backcalculation algorithm. Also it can be seen that
EVERCALC progressively calculates poorer results as the pavement becomes stiffer.
This indicates that the difference between the modified and older versions of the
CHEVRON program increase for the stiffer pavements. When the deflections
generated by the old version of the CHEVRON program is analyzed EVERCALC
(EC-ALT) also yields excellent results for three layer pavements (similar to

MICHBAC K).

4.6.2 F our-Layer Flexible Pavement .

The actual properties of the pavement are given in Table 4.2. The
backcalculated results (Table 4.19) indicate that as the number of layers in the
pavement increases MICHBACK clearly produces better results than the other two
programs. EC-ALT results are comparable to those of MICHBACK but the largest
error is more than 4% compared to less than 1% for MICHBACK. For pavements
with more than three layers the MODULUS program yields a poorer result at least
for one of the layers. MICHBACK produced consistently accurate results for all other

four layerpavements tested as well.

139

Table 4.18. Comparison of the results of three programs for a three layer pavement.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pavement Backcalculated modulus (ksi) Max. error RMS
Program type AC Base Roadbed 1n mggull error (%)
Thin 497.9 45.0 7.5 0.42 .02
MICHBACK Medium 499.9 45.0 7.5 0.02 .03
Thick 501.2 44.6 7.5 0.84 .01
Thin 485.4 45.9 7.5 2.92 .37
MODULUS Medium 503.1 44.6 7.5 0.89 .11
Thick 485.4 46.8 7.5 4.00 .14
Thin 503.6 44.9 7.5 0.73 .02
EVERCALC Medium 477.7 46.0 7.5 4.45 .06
Thick 439.6 58.0 7.5 28.87 .13
Thin 500.2 44.9 7.5 0.11 , .02
EGALT Medium 502.9 44.8 7.5 0.57 .02
’ Thick 500.5 45.8 7.5 0.17 .15

 

 

 

 

 

 

 

 

 

Table 4.19. Comparison of the results of three programs for a four layer pavement.

 

 

 

 

 

 

 

Backcalculated modulus (psi) Max. error RMS error in
Program in moduli deflections
AC Base Subase Roadbed (%) (g)
MICHBACK 500.1 45.1 14.9 7.5 0.6 .01
MODULUS 544.9 36.0 22.3 7.6 48.7 .16
EVERCALC 476.2 46.3 14.7 7.5 4.8 .09
EC-ALT 495.0 46.3 14.3 7.5 4.6 .06

 

 

 

 

 

 

 

 

140
4.6.3 Four-Layer Composite Pavements

The properties of the two composite pavements analyzed are listed in Table
4.3. One composite pavement (composite 1) had a separation layer between the AC
overlay and the PCC slab, whereas the other pavement (composite 2) had no such
layer.

The results shown in (Tables 4.20 and 4.21) indicate that while MICHBACK
converges reasonably well for both composite pavements, the other two programs
yielded considerable errors especially for the composite 2. It has been pointed by
various researchers that for composite pavements, the modulus of the layer
immediately under the slab is the most difficult to predict unless the lower layer is the
roadbed soil. For this pavement the maximum error for MICHBACK is 8%
compared to about 61% for MODULUS and 131% for EVERCALC (using the data
generated by old CHEVRON (EC-ALT». This indicates that MODULUS and
EVERCALC do not produce accurate results for composite pavements. MICHBACK
has also shown some problems in predicting the modulus of the layer immediately
under the slab. However the magnitude of the error is comparatively smaller. For all
other composite pavement examples, the MICHBACK produced better results than
both EVERCALC and MODULUS programs.

4.6.4 Three-Layer Pavements Over a Stiff layer

The medium thickness three layer flexible pavement (Table 4.1) was underlain
by a stiff layer at two different depths, 36 and 240 inch. All other parameters were
the same as for the three layer flexible medium thickness pavement analyzed without
the stiff layer. The results are presented in Table 4.22. It can be seen that the results
of MICHBACK and EVERCALC (EC-ALT) are comparable and better than those of
MODULUS.

141

Table 4.20. Comparison of the backcalculated results for a composite pavement

 

 

 

 

 

 

section.
Backcalculated modulus (ksi) Max. error RMS error
Program in moduli (%) (%)
AC Slab Base Roadbed
MICHBACK 499.4 4516.3 23.0 7.5 8.0 0.01
MODULUS 527.7 4471.1 9.8 7.6 60.8 0.07
EVERCALC 1582.2 2297.1 13.2 7.5 216.4 1.53
EC-ALT 494.7 4217.1 57.8 7.4 131.1 0.06

 

 

 

 

 

 

 

 

 

Table 4.21. Comparison of the backcalculated results for a composite pavement
section consisting of a granular separation layer.

 

 

 

 

 

 

Backcalculated modulus (psi) Max. error RMS error
Program in moduli (%) (95)
AC Base PCC Slab Roadbed
MICHBACK 499.4 24.8 4472.9 7.5 0.6 0.03
MODULUS 492.1 25.4 4402.5 7.5 2.2 0.08
EVERCALC 622.7 27.7 3959.7 7.5 24.5 0.75
EC-ALT 491.5 25.5 4412.6 7.5 2.1 0.11

 

 

 

 

 

 

 

 

 

142

Table 4.22. Comparison of the results of three programs for a three layer pavement
over stiff layer.

 

 

 

 

 

 

 

 

 

 

Stiff layer Backcalculated modulus (psi) Max. error RMS error in
Program location in moduli deflections
AC Base Roadbed (%) (95)
Deep 501.7 44.9 7.5 0.34 0.04
MICHBACK
Shallow 499.8 44.9 7.5 0.19 0.09
Deep 502.0 44.8 7.5 0.44 0.19
MODULUS
Shallow 508.9 43.9 7.7 3.55 0.07
Deep 796.8 31.2 7.5 59.36 1.15
EVERCALC
Shallow 598.0 40.3 7.6 19.60 0.60
Deep 498.3 45.2 7.5 0.41 0.02
EC-ALT
Shallow 501.4 44. 8 7.5 0.34 0.04

 

 

 

 

 

 

 

 

 

143

4.6.5 F ive-Layer Flexible Pavement

For the five layer pavement, the results of MICHBACK are presented in Table
4.23. The other two programs cannot analyze a five layer pavement. The five layer
pavement configuration used for the analysis is specified in Table 4.4. It can be seen
that the maximum error produced by MICHBACK for the modulus of any layer is
less than 1%. It indicates that, unlike the other programs, there is no decrease in the
accuracy of the backcalculated results with the increase in the number of pavement

layers for MICHBACK.

4.6.6 Performance Comparison

Performance comparison has mostly been restricted to the examples presented
in this section only and to MICHBACK and EVERCALC programs because
MODULUS is not an iterative program. For MODULUS, the number of deflection
bowls generated depends upon the number of layers in the pavement as well as on the
range of the moduli provided by the analyst. The range in turn affects the
backcalculated results and a closer range was provided to keep the convergence
performance of the program compatible. The MODULUS program has, therefore, not
been included in the performance comparison.

The results of the comparison are provided in Table 4.24 and Figure 4.12.
The number of calls for EVERCALC are based on deflections generated by the old
CHEVRON (the number of calls for data generated .by CHEVRONX were a little
higher). The designation MICHBACK(N) refers to the use of arithmetic scale,
MICHBACK(M) represents the results for the modified Newton method and
MICHBACK(L) refers to the use of the logarithmic scale together with the modified
Newton method, respectively. ‘

The results indicate that after logarithmic transformation, the performance of

MICHBACK is somewhat better than that of EVERCALC. The effect of logarithmic

144

Table 4.23. The MICHBACK backcalculation results for a five layer pavement.

 

 

 

 

  

 

 

 
 
  
 

Backcalculated modulus (psi) Max. error RMS error in
in moduli deflections
Subbase I Roadbed (%) (%)

 

 

AC I Treated base Base

 

0.02

 

 

 

 

  

497.0 I 100.4 45.1 14.9 I 7.5 -0.96 £

145

Table 4. 24. Cgm gall-{son of the performance of MICHBACK and EVERCALC
P 8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Program Number of times ogretion was performed
,2 CHEVRON called __ _ _W

MICHBACK(N) 22 5 5

Three layer
(min) MICHBACK(M) 19 3 8
MICHBACK(L) 14 2 6
EVERCALC 17 4 4
MICHBACK(N) 26 6 6

Three layer
(Medium) MICHBACKOVI) 24 4 10
MICHBACK(L) 13 2 5
EVERCALC l7 4 4
MICHBACK(N) 25 5 5

1a er
midi) MICHBACK(M) 20 3 5
' MICHBACK(L) 14 2 6
EVERCALC l7 4 4
MICHBACKm) 37 7 7
Four layer MICHBACKM) 23 3 9
MICHBACK(L 16 2 6
EVERCALC 21 4 4
. MICHBACKm) 32 6 6
W” MICHBACK(M) 28 4 10
MICHBACKG.) 14 2 4

EVERCALC 21 4

. MICHBACK(N) 32 6 6
(with grantlzlar MICHBACKGQ 28 4 10
mm 1"“) MICHBACKG.) 21 3 7
JWRCALC 21 4 4
MICHBACK(N) 32 5 5

Five Layer
MICHBACK(M) 26 3 9
MICHBACK(LL 18 2 6
MICHBACKm) 36 7 7
(Deep Stiff uhyer) MICHABCK(M) 24 4 10
MICHBACK(L) 12 2 5

EVEALCRC ,_ __ _ 17 4

146

 

 

 

 

 

 

 

 

 

 

 

 

 

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Pavement Type

 

I- MICHBACK(N) - MICHBACK(MN) m MICHBACKLOG [mm EVERCALC

 

Figure 4.12. Comparison of the performance of MICHBACK and EVERCALC programs.

147

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148
transformation becomes more significant as the nature of the problem becomes more

complicated.

4.7 UNIQUENESS OF THE BACKCALCULATED RESULTS

Many backcalculation programs suffer from the disadvantage that the
backcalculated results are highly dependent on the md modulus values provided by
the user. The farther the guess is from the true values, the higher are the chances of
converging to a wrong solution. This is especially true for the methods which seek the
minimization of an objective function where the chances of converging to a local
minimum are higher. The convergence of Newton’s method in general is also not
global, but is problem dependent. For many complicated problems, the solutions are
reported to be governed by the starting values. However, backcalculation of layer
properties from FWD deflection data appears to be a well behaved problem,
especially for flexible pavements, and the results obtained using Newton’s method
seem to be independent of the starting values. Many researchers (Sivaneswaran, 1991)
have also pointed out, though not with absolute certainty, that the criterion function
constructed by minimizing the squared difference between measured and calculated
deflections is convex in shape and hence will have a unique minimum.

For the flexible pavement examples, it was observed that the results obtained
by MICHBACK are independent of the seed values. The results for three, four, and
five layer pavements are presented in Tables 4.25 through 4.27, respectively. The
deflection data was generated by using the pavement cross sections introduced earlier
but the layer moduli were changed as shown in the respective tables. The seed moduli
were chosen randomly but far from the true values to test the capability of the
program to converge to the correct solution even for unreasonable seed values.

It can be seen from these tables that the results obtained by MICHBACK are
not affected by the seed moduli at all. The only difference is in the number of

149

Table 4.25. Uniqueness of the MICHBACK solution for a three layer flexible
pavement.

 

Ex. Actual modulus (ksi) Seed modulus (ksi) Bbackcalculated modulus (ksi) II

 

El E2 E3

 

 

 

1000 500 100 499.2 75.10 15.0
1 1 1 499.2 75.10 15.0

 

 

2000 100 100 801.3 44.91 7.5

3 800 45 7.5
l 1 1 801.3 44.91 7.5 II
j——————+_‘*

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.26. Uniqueness of the MICHBACK solution for a four layer flexible

 

 

  
  

 

 

 

 

 

pavement.
Ex. Actual modulus Seed modulus Backcalculated
(ksi) (ksi) modulus (ksi)
E2 E3 E4 El E2 E3 E4 1 El E2 E3
2000 100 100 100 500.1 45.1 14.9
45 15 7.5
1 1 1 1 500.1 55.1 14.9
2000 500 50 50 803.0 74.6 25.3 15.0
75 25 15

 

 

 

 

 

 

 

 

 

 

 

 

 

1 l l 1 803.1 74.6 25.3 15.0

 

Table 4.27. Uniqueness of the MICHBACK solution for a five layer flexible

 

 

 

pavement.
II Seed Modulus (ksi) Backcalculated Modulus (ksi)
El E2 E3 E4 E5 E1 E2 E3 E4 E5

 

 

1 l 1 1 1 511.0 I 96.1 48.1 ' 13.3 7.52

100 1000 15 5 1.5 510.8 I 96.2 48.0 13.3 7.52

 

 

 

 

 

 

 

 

150
iterations required to meet the given convergence criterion. The upper and lower
limits for all the layer moduli were set at 10,000,000 and 1 psi respectively. This
capability has been provided in the MICHBACK program so that the analyst can
specify bounds for the backcalculated moduli. This further ensures that the solution
should remain within the expected or even known moduli ranges for the pavement
materials. In the case of flexible pavements this capability was not invoked.

For the composite pavements convergence to the correct results from
excessively erroneous seed values can only be achieved by intelligent use of the
bounding values. However, even for composite pavements, convergence from
reasonable seed values (expected even from a novice) is not a problem. Unreasonable
seed values were used only to check the robustness of the program. This problem has
been partially addressed in the program by automatically setting a lower bound of 1
million on the backcalculated results whenever the analyst recognizes the pavement to
be composite and not built on a rubbled slab. No upper bound is required to be set.
The pre-specified lower limit assures convergence to the correct results even from

unrealistic seed values.

4.8 EFFECT OF INACCURACIES IN DEFLECTIONS AT SIMULATED

SENSOR LOCATIONS ON BACKCALCULATED RESULTS

The accuracy of each sensor of FWD is about :1; 2% of the sensor’s range.
Hence, similar range in the accuracy of the backcalculated results should also be
expected. Also it is a general belief that since the deflections at the outer sensors are
comparatively smaller, inaccuracies at these sensors have a larger contribution
towards the overall error especially for the lower layers. In this section, the effect of
inaccuracies in deflections at different sensor locations on the backcalculated layer
moduli are examined. It was feared that logarithmic transformation may make the

backcalculated results more sensitive to the inaccuracies in the measured deflections.

151

Therefore, a comparison has also been made between the sensitivity of the

backcalculated results to the surface deflection for both arithmetic and logarithmic

scales.

The thin, medium, and thick three layer flexible pavements (Table 4.1) were
used to study the sensitivity of the backcalculated results to the surface deflections.
The medium three layer pavement was used to examine and compare the sensitivity of
the backcalculated results when working in logarithmic scale. The surface deflections
were generated using the CHEVRONX program. An error of i 2% was deliberately
introduced in each sensor deflection individually.

The results for the arithmetic and logarithmic scales are presented in Tables
4.28 and 4.29, respectively. The results indicate:

1. lnaccuracies in the deflections of these locations close to the load (for fixed
percent error) induce larger error in the backcalculated layer moduli than the
other locations.

2. For the same absolute magnitude of the error, negative errors induce greater
errors in the backcalculated results than the positive ones.-

3. For almost all locations, the AC modulus is the most affected followed by the
base modulus. The roadbed modulus is least affected by inaccuracies in the
surface deflections at any locations. Although errors in the last few locations
do affect the roadbed modulus slightly more than errors in the others, the
maximum error in the roadbed modulus remains well below 1.5%.

4. The AC modulus of thin layers is affected the most by deflection inaccuracies.
This is because pavements with a thick AC layer can compensate for the
erroneous deflections by smaller changes in the AC modulus, whereas to
redress the same amount of error, the AC modulus must undergo a bigger
change for pavements with a thin AC layer.

5. The base modulus of a pavement with a thick AC layer is affected more than

152

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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154
that of a pavement with a thin AC layer. This is probably because the
inaccuracies in the AC modulus for a pavement with a thick AC layer affects
the overall strength of the pavement more than for a thin pavement. Therefore,
in trying to adjust the overall stiffness the base modulus for thick AC

pavement is affected more.

Results of a similar test for the medium thick pavement performed after the
logarithmic transformation are presented in Table 4.29. It can be observed that this
change does not significantly affect the sensitivity of the backcalculated results to the
surface deflections. Except for the last deflection location, for most other sensors the
error in the backcalculated layer moduli is slightly less than those arising from the
arithmetic scale.

The above exercise was repeated by fixing the induced difference in the
measured deflections at :1: 0.5 mils for all the sensors. The results are presented in
‘ Table 4.30. The errors in the backcalculated moduli are a little higher than in the case
where the errors were induced as percentages of the measured deflections. This is

because of the fact that the 1: 0.5 mil error is larger than the 2% error.

4.9 EFFECT OF POISSON ’S RATIO ON THE BACKCALCULATED

LAYER MODULI

Several studies were conducted to assess the effects of Poisson’s ratios of the
various pavement layers on the calculated deflections. Pichumani (1972) concluded
that Poisson’s ratio of only the roadbed soil has some appreciable effect on the
surface deflections. Variations in the Poisson’s ratios of the other layers were found
to have little effect on the surface deflections. Another study, conducted at the
University of Utah (Hou, 1977), suggested that for three-layer pavements, variations

in Poisson’s ratio of each layer including the roadbed soil from 0.25 to 0.45 have no

155

Table 4.30. Percentage error in backcalculated layer moduli
due to i 0.5 mil error in deflections-log scale.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Samar Error AC Base
No.
+0.5 -25.8 17.7
1 -0.5 32.7 -18.6
+0.5 19.5 -19.3
2 -0.5 -21.7 25.3
+0.5 12.4 -10.9
3 -0.5 -11.7 . 11.2
+0.5 9.9 -7.1
4 -0.5 ~8.3 5.9
+0.5 3.6 -0.2
5 -0.5 ~3.0 -0.5
+0.5 7.2 12.4
-12.2
24.9
-29.6

 

 

 

 

   

 

 

156

significant effect on the surface deflections. These and other similar findings have led

to a general consensus that since Poisson’s ratios of the paving layers have little

influence on the surface deflections, their effect on. the backcalculated layer moduli
must also be negligible. No study appears to have investigated the direct effect of

Poisson’s ratios on the backcalculated layer moduli. In this study, this issue was

investigated and the results are presented in this section.

The deflection basins used in the previous sections were generated by using
constant Poisson’s ratios of 0.35, 0.4, 0.45, and 0.45 for the AC, base, and subbase
layers and for the roadbed soil, respectively. To assess the effect of Poisson’s ratio on
the backcalculated layer moduli, the value of Poisson’s ratio of one layer at a time
was varied by i 0.05 from the true value. The results of this analysis for the medium
thick flexible pavement of Table 4.1 an listed in Table 4.31. Results of similar tests
for composit pavement (Table 4.3) are presented in Table 4.32. Examination of the
results indicate that:

1. An error of i .05 in Poisson’s ratio of the AC layer introduces about a 4%
error in the backcalculated modulus of the AC layer. The errors in the moduli
of the other two layers are comparatively small and the roadbed soil modulus
is the least affected.

2. As the stiffness of the AC layer increases so does the effect of Poisson’s ratio.

3. Poisson’s ratio of the base layer has some impact on its modulus and the least
effect on the backcalculated results of the other layers.

4. An error of i 0.05 in Poisson’s ratio of the roadbed soil has the largest
effects on the backcalculated results. It introduces a 10 % error in the AC
modulus, a 9 % error in the base modulus, and a small error in the roadbed
soil modulus.

5. For composite pavements, the backcalculated layer moduli appear to be very

sensitive to errors in the value of Poisson’s ratio. For example, an error of

 

157

Table 4.31. Percent errors in the backcalculated layer moduli
due to error in Poison’s ratio for flexible pavements.

Layer Error in Error in backcalculated moduli (%)
Poiszon’s
ra 0

AC Base Roadbed

 

Table 4.32. Percent errors in the backcalculated layer moduli
due to error in Poison’s ratio for composite pavement.

Layer Error in
Porsson,s

 

 

158
300 % in the subbase layer modulus (the layer immediately beneath the PCC
slab) was observed. The errors in the modulus values of the other layers were
less than 20 %.

6. The effects of Poisson’s ratios on the calculated deflection basins is negligible.

The above observations do not negate the past findings, they only emphasize
that small changes in the deflection basins can significantly affect the values of the
backcalculated layer moduli. I

It should be noted that the results presented above are pertinent to the
MICHBACK program (which uses the CHEVRONX as the forward analysis
program). The sensitivity of the various backcalculation techniques to Poisson’s ratios
or to small changes in the deflection basins may vary. One point can be made here is
that, given the present state of the equipment (deflections at only seven sensor
locations are measured), and the number of unknowns that need to be estimated, the
inclusion of Poisson’s ratios of the various layers in the pool of unknown to be
calculated will only make the backcalculation more complicated and prone to higher
errors. Furthermore, the intention of the analysis presented above is to warn the
analyst that reasonable ranges of Poisson’s ratios of the different paving materials

must be known and must be used cautiously.

4.10 COMPARISON OF DEFLECTION OUTPUT OF DIFFERENT ELASTIC
LAYER PROGRAMS
The advent of fast micro-computers, made automated backcalculation of layer
moduli possible. Most backcalculation programs make use of a multi-layer elastic
routine as a forward analysis programs in one way or another. Hence, the
backcalculated results are not only affected by the backcalculation technique, but also

by the precision of the forward analysis routine. Surface deflections are the common

 

 

159
output used from these routines in the backcalculation process. The accuracy of the
multi-layer elastic routines is generally established by comparing the deflection results
to those of an established and reputed one such as the "BISAR".

MICHBACK initially used CHEVRON as the forward analysis program. At
the onset of this study, the analysis of deflection data received from various agencies
have indicated that differences between the deflections obtained from the CHEVRON
program and those from the BISAR program exist. Consequently, a corrected version
"CHEVRONX“ of the CHEVRON program was obtained from Dr. Lynne Irwin at
Cornell University and it was embedded in the current version of MICHBACK. It
should be noted that, originally, results of the CHEVRON program was validated by
Lee, et. al. (1988). They concluded that the output of the CHEVRON program differs
slightly from that of the BISAR program for flexible pavements and that the program
should not be used for the analysis of stiff flexible and composite pavements.

In this section surface deflections from four elastic layer programs,
(CHEVRON . ELSYMS, WESLEA, and CHEVRONX) have been compared with
those of BISAR. Once again, CHEVRONX is the enhanced version of the
CHEVRON program and it is used in MICHBACK. The five pavement sections listed
in Tables 4.1 through 4.4 are used in this comparison. Further, an AC modulus of
800 ksi (instead of 500 ksi) was used for the medium thick three-layer flexible
pavement. The stiff layer depth for the pavements was set at 144-inch to represent the

presence of bedrock.

4.10.1 Comparison of Deflection Output

The deflections from all the five programs are presented in Table 4.33. The
deflections were rounded to the nearest hundredth of a mils to represent the FWD
readings. It can be seen that the outputs of BISAR, WESLEA and CHEVRONX are

essentially the same. Table 4.34 provides a list of the percent differences in the

 

160

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.33. Deflections from different elastic layer programs.
Pavement Deflections (mils)
Type Program d0 d1 d2 d3 d4 d5 d6
BISAR 24.400 20.900 18.600 15.600 13.100 9.500 5.530
Three CHEVRONX 24.370 20.870.18.570 15.580 13.120 9.498 5.534
Layer CHEVRON 24.260 20.870 18.570 15.580 13.120 9.498 5.534
Medium ELSYM5 24.260 20.870 18.570 15.580 13.120 9.497 5.534
WESLEA 24.369 20.872 18.570 15.578 13.123 9.498 5.533
BISAR 22.200 19.600 17.700 15.100 12.900 9.500 5.600
Three CHEVRONX 22.200 19.570 17.700 15.120 12.900 9.497 5.595
Layer CHEVRON 22.070 19.560 17.700 15.120 12.900 9.497 5.595
Medium ELSYM5 22.070 19.560 17.700 15.120 12.900 9.497 5.595
Stiff WESLEA 22.203 19.572 17.700 15.121 12.905 9.497 5.599
BISAR 16.600 14.900 13.900 12.500 11.200 8.980 5.810
Three CHEVRONX 16.650 14.900 13.910 12.530 11.230 8.977 5.813
Layer CHEVRON 16.470 14.790 13.920 12.530 11.230 8.977 5.813
Thick ELSYM5 16.470 14.790 13.920 12.530 11.230 8.977 5.813
WESLEA 16.649 14.899 13.913 12.530 11.234 8.978 5.813
BISAR 19.600 17.000 15.400 13.300 11.600 8.930 5.660
Four CHEVRONX 19.630 17.030 15.420 13.330 11.590 8.929 5.662
Layer CHEVRON 19.530 16.960 15.420 13.330 11.590 8.929 5.662
ELSYM5 19.530 16.960 15.420 13.330 11.590 8.929 5.662
WESLEA 19.634 17.032 15.421 13.331 11.593 8.929 5.658
BISAR 20.900 17.400 15.100 12.100 9.710 6.140 2.340
Three CHEVRONX 20.910 17.420 15.120 12.150 9.709 6.140 2.345
Layer CHEVRON 20.310 16.700 14.950 12.240 9.739 6.134 2.345
With ELSYM5 20.310 16.700 14.950 12.240 9.739 6.134 2.345
StiflLayer WESLEA 20.910 17.420 15.120 12.150 9.709 6.140 2.345
BISAR 9.480 8.800 8.600 8.270 7.890 7.080 5.520
Composite CHEVRONX 9.479 8.800 8.599 8.268 7.890 7.080 5.521
81111 CHEVRON 10.040 8.766 8.479 8.272 7.896 7.090 5.520
ELSYM5 10.040 8.766 8.479 8.272 7.896 7.090 5.520
WESLEA 9.479 8.800 8.599 8.268 7.890 7.080 5.521

 

 

 

 

 

 

 

 

 

 

Tab|e4.34. Perceritdlflereneeinfiiedeflectionaofdiflemntelasfielayerprograma.

161

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pavement Diflerance in Deflections (96)
Type Program d0 d1 d2 d3 d4 d5 d6
BISAR 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Three CHEVRONX 0.123 0.144 0.161 0.128 0.153 0.021 0.072
Layer CHEVRON 0.574 0.144 -0.161 0.128 0.153 0.021 0.072
Modlum ELSYM5 0.574 0.144 -0.161 0.128 0.158 0.032 0.072
WESLEA 0.128 0.133 0.182 0.140 0.173 0.026 0.060
BISAR 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Three CHEVRONX 0.000 0.153 0.000 0.132 0.000 0.032 0.089
Layer CHEVRON 0.588 0.204 0.000 0.132 0.000 0.032 0.089
Medium ELSYM5 0.586 0.204 0.000 0.132 0.000 0.032 0.089
61111 WESLEA 0.013 0.141 0.000 0.139 0.036 0.028 0.010
BISAR 0.000 0.000 0.000 0.000 0.000 0.000 0.000
nine CHEVRONX 0.301 0.000 0.072 0.240 0.268 0.033 0.052
Layer CHEVRON 0.783 0.738 0.144 0.240 0.268 0.033 0.052
Thick ELSYM5 0.783 0.738 0.144 0.240 0.268 0.033 0.052
WESLEA 0.293 0.008 0.094 0.238 0299 0.023 0.049
BISAR 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Four CHEVRONX 0.153 0.176 0.130 0226 0.086 0.011 0.035
Layer CHEVRON 0.357 0235 0.130 0.226 0.086 0.011 0.035
ELSYM5 0.357 0.235 0.130 0.226 0.086 0.011 0.035
WESLEA 0.172 0.191 0.135 0232 0.057 0.007 0.028
BISAR 0.000 0.000 0.000 0.000 0.000 0.000 0.000
111m CHEVRONX 0.048 0.115 0.132 0.413 0.010 0.000 0214
Layer CHEVRON .2823 4.023 0.993 1.157 0299 0.098 0.214
With ELSYM5 -2.823 4.023 0.993 1.157 0.299 0.098 0214
Stll'fLayer WES-LEA 0.048 0.115 0.132 0.413 0.010 0.000 0.214
BISAR 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Composite-CHEVRONX 0.000 0.000 0.000 0.000 0.000 0.000 0.000
8011 [CHEVRON 5.907 0.386 -1407 0.024 0.076 0.141 0.000
ELSYM5 5.907 0.386 -1.407 0.024 0.076 0.141 0.000
[WESLEA 0.000 0.000 0.000 0.000 0.000 0.000 0.000

 

 

 

 

 

 

 

 

162

deflection at each sensor location relative to the BISAR calculated deflection. It can

be seen that:

1. Except for rounding-off precision, there are no significant differences in the
outputs of the CHEVRONX, WESLEA, and BISAR programs.

2. The deflection outputs of the CHEVRON and ELSYM5 programs are the
same. However, the following observations can be made relative to the
differences between these two outputs and that of the BISAR program:

a) The differences are more pronounced at the first two sensor locations
and negligible at the outer sensors.

b) The differences increase as the stiffness of the pavement increases. For
the medium thick pavements with a stiff layer, the differences at all
sensor locations are higher than those for the same pavement without a
stiff layer. The maximum difference of 4% is observed at the second
sensor location. For flexible pavements, the CHEVRON deflections are
generally lower than those of BISAR.

c) For the composite pavements, significant differences were found

between the CHEVRON and the BISAR deflections.

4.10.2 Comparison of Backcalculated Results
The deflections from the CHEVRONX and CHEVRON programs were used in

MICHBACK to backcalculate the layer moduli. The results are presented in Table

4.35. It can be seen that:

l. The backcalculated results are appreciably different for the two sets of
generated data. The difference increases as the overall stiffness of the
pavement increases.

2. For the flexible pavement with a stiff layer, the maximum error is about 34%.

3. For the composite pavement, the results are quite erroneous, with a maximum

163

Table 4.35. Backcalculated results of MICHBACK for deflection data generated
by different elastic layer programs.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pavement Error in backcalculated layer moduli (%)
I
ype AC Base Subbase Roadbed
Three layer CHEVRON 5.39 3.05 - 0.05 ’ 0.05
medium
CHEVRONX -.02 -0.07 - 0.0 0.03
Three layer CHEVRON 11.48 -16.1 - 0.2 0.15
thick
CHEVRONX .25 -0.84 - 0.04 0.0]
Three layer CHEVRON 5.74 -3.71 - -0.01 0.09
medium stiff
CHEVRONX -.28 0.69 - -0.06 0.02
Three layer CHEVRON 34.05 42.01 - 0.2 1.04
with stiff layer
(144 in.) CHEVRONX .43 044 - 0.04 0.03
CHEVRON 4.26 -O.48 -2.83 0.09 0.08
Four layer
‘ CHEVRONX .02 0.22 -.05 0.03 0.03
Composite CHEVRON 66.1 77. 13 -99.4 231.7 0.01
CHEVRONX -.14 0.34 -7.9 0.07 0. 89

 

 

 

 

 

 

 

 

 

 

164

error of about 231%.

The scenario presented in this and in the previous section demonstrates that the
results of the backcalculation are, in general, affected by the accuracy of the
employed forward analysis program. Based on these results, the use of the
CHEVRON and the ELSYM5 programs for the backcalculation of layer moduli of

any pavement type is not recommended.

4.11 COMPARISON OF MICHBACK RESULTS WITH SHRP STUDY

In the previous section, the backcalculated results of MICHBACK were
compared with two leading programs and various performance aspects were
highlighted. In this section, additional comparison of the MICHBACK results with
three programs (MODCOMP, MODULUS, and WESDEF) is presented. In this
comparison, the pavement cross sections and the deflection basins that reported by
Rada, et al., 1992 and listed in Table 4.36 were used. The true values of the layer
moduli and those backcalculated by using the three programs are listed in Table 4.37
(Rada, et al., 1992). Table 4.38 provides a list of the layer moduli of the first six
pavement sections of Table 4.37 that were obtained by using the MICHBACK
program. Table 4.39 provides a summary of the error in each layer modulus as well
as the accumulated absolute error in the backcalculated results for all four programs.

It should be noted that the errors the MODCOMP, MODULUS, and WESDEF
programs were obtained from Rada et al. study (1992). The accumulated absolute
errors of the four programs for the six pavement sections are shown in Figure 4.13. It
can be seen that the MICHBACK results have consistently the lower cumulative error.

Table 4.40 provides a list of minimum, maximum, average, and standard -
deviations of the accumulated absolute errors in the moduli values of the six pavement
sections for the four programs. It can be clearly seen that the results of MICHBACK

are much more consistent than those of the other programs. This comparison of the

165

Table 4.36. Deflection and cross sectional data for nine test sections
(after Rada, et al., 1992).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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ID Layer 5“ nua-
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1 PC1281» 12

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168

Table 4.39. Comparison of errors in the modulus values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E o 1 1 1 no ('1 [51%)
. :....--.-. RMS(%)
W .025 3.17 - .0-24 -11
. _MODCOMP 10-62 -96 - 0-14 2- .
WHEEL—1&6 -22 - 0.0 .16
. WESDEF 3.87 -20.74 - 6.39 2.32
W 2.2 1-91 - .003 -17
MODCOMP 3-72 -8-71 - 1-46 3
. LMODULUS -3.67 1.5 - 0.0 -17
‘ WESDEF 15.13 -25.77 - 6.41 1.12
JIIQHBACK L06 .2-67 - 0.02 -04
MODCOMP -10-04 19.5 - 0-87 -81
440001.113 3.03 -6.54 - .0-5 .22
WESDEF 3.92 -21.83 - 7.74 .26
W -359 -65 - .14 -03 I
, MODCOMP 10-69 J'I-Sl - 0.96 .81
I mums 22.03 -295.5 - L5 .52
WESDEF 8.87 494.92 - 8.66 .23 l
W 437 - ~ 0-0 -03 I
I W]? 12-59 - - .3-3 3-. E
I loom-us .97 - - -O-67 .2 I
WESDEF -§.57 - - 6.81 -91 l
..MICHBACK -5-6 -05 - -0-18 -03 ‘
JODCOMP 0 10-27 - 0-93 6- ; I
44113111113 -6-16 8.52 - 0.0 -12 }
WESDEF 6.07 .20-31 - 14.06 .21
‘ mum—.24 4-1 - -03 -03
. _MODCOMP 51 18.99 - -4-6 3-24
i 440001.115 -1.33 2.91 - -1.0 -15
1 WESDEF 14.116 22.5 - 10.57 1.47
! W .167 8-23 .33-74 -1-1 -03
410130081? .57-75 44-41 -13455 3.73 .37
l _MODULUS -8.22 30.89 .1549 1.2 .37
_3NESDEF 1.34 3.22 44.14 8.96 -58
W .215 12-49 -15-0 --21 -01
MP 0 0 5-96 1.36 5-
JEDULUS 10.42 47.42 63.27 -.67 .19
[ A . . . - 01‘. q . "J

 

 

 

 

 

 

 

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170

Table 4.40. Statistics of the maximum relative error for four
computer programs.

 

   
   
  
  
   
 

 

 

 

 

 

 

 

 

 

Statistics of maximum error
Program
Minimum Maximum Average Standard
Deviation
MODCOMP 5.96 134.55 35.44 44.1
MODULUS 0.97 295.5 59.3 94.23
WESDEF 8.57 194.9 46.51 55.23
MICHBACK 2.06 33.74

 

 

171

resulting observations confirm once more the accuracy and consistency of the

MICHBACK program relative to those programs.

4.12 SUMMARY

Several analysis for the validation of a new technique to assess the roadbed

modulus, and to compare the effects of several factors on the backcalculated results

are presented. Based on the analysis, the following conclusions were drawn:

1.

The new technique to estimates the roadbed soil modulus effectively and, at
the cost of only one call to CHEVRONX program, it yields a relatively
accurate prediction.

The Newton’s algorithm is incorporated in the MICHBACK program in a
manner that can predict layer moduli accurately.

For flexible pavements without stiff layer, the accuracy of the MICHBACK
results relative to other programs increases with increasing number of
pavement layers.

For composite pavements, the MICHBACK results are significantly better than
the other leading programs.

lnaccuracies in the layer thicknesses can induce large errors in the

. backcalculated layer moduli. The MICHBACK program, at the desire of the

user, can correct any one layer thicknesses while estimating the layer moduli.
lnaccuracies in the stiff layer depth can induce large errors in the
backcalculated results. The advantage of the MICHBACK program is its
ability to accurately predict the stiff layer depth using mechanistic analysis.
The modulus of the Stiff layer has an insignificant effect on the backcalculated
results.

The values of Poisson’s ratios of the various pavement affect the accuracy of

the backcalculated layer moduli.

172
The deflection outputs of the CHEVRON, ELSYM5, and EVERCALC
programs differ from that of the BISAR (the accuracy of the BISAR output has
been well established). The difference increases with the stiffness of the

pavements.

CHAPTER 5

NIICHBACK PROGRAM STRUCTURE AND FEATURES

5.1 GENERAL

The MICHBACK program has been written in Fortran 77. The structure and
the user friendly features have been designed to facilitate the use of the program even
by amateurs. The program can read the output files of the MDOT operated Falling
Weight Deflectometer (KUAB), and minor changes in one of the subroutines can
enable it to read the output of any other type of FWD. When processing the data from
an FWD output file the program provides a wide range of options to the user to view
and process the deflection data before it is analyzed.

In this chapter, the general structure and some of the features of the program
are described. The function of each of the program subroutine is briefly introduced in
Appendix A (Mahmood, 1993). Detailed explanation of the inputs required in each

window would be available in a User’s Manual (Harichandran, et al., 1994).

5.2 , DATA INPUT

Deflection data can be entered using the keyboard or if the deflection output
file format is that Of the MDOT operated KUAB FWD, the file can be read and
processed by the program automatically. The cross-sectional data, Poisson’s ratios,
type of the pavement being analyzed, the desired convergence criteria, expected
ranges of the layer moduli, pavement temperature, and information regarding load
application arrangement must be entered using the keyboard. Two options of the more
frequently encountered deflection sensor layout schemes are provided. Other layouts
can be specified by the users by the keyboard input. The default weight allocated to
each sensor is 1.0, but can be changed by the user if desired. The input information is

stored in a data file which can be edited on the interactive screen at any stage.

173

174

When entering the deflection data using the keyboard, a total of 4 deflection
basins can be entered and processed by the program simultaneously. These basins
must pertain to the same pavement cross section, although the test load may be
different. The deflection basins are displayed on the screen in graphical form for the
user to view and subsequently edit if an incorrect input is detected. Analyst can view
the entered deflection basins one at a time or even can choose to look at all four
basins simultaneously. All the deflection basins are analyzed without interruption and
the backcalculated results of one basin are taken as seed moduli for the next basin.
When processing the deflection data from a file, comprehensive keyboard input is
required only at the start of the analysis. All the essential information required to
operate the program is stored in easily accessible data files. When changes in the
pavement cross section are encountered, required changes in the data file can be made
by editing the existing data file. The various options provided to view, process, and

analyze the deflection data from FWD files are discussed in the next section

5.3 PROCESSING FWD DEFLECTION DATA FILE

The MICHBACK program can read output files containing deflection data
generated by the MDOT operated FWD (KUAB). The system is flexible and only
minor changes would be required in one of the subroutines to customize the program
to read other formats. The FWD output files normally contain deflection data for tests
conducted over long pavement sections. Hence, a wide range of variability in the
deflection data is expected. Even if the section length is small it will be beneficial to
the user to view and understand the variability of the deflection data before starting
the backcalculation process. The analyst should be able to identify and if necessary
remove any outliers indicative of erroneous sensor measurements. Also, sub-dividing
a long test section can be done in a more effective manner after reviewing the data.

The MICHBACK program provides features which make the pre-processing of the

175
deflection data very easy and efficient. The highlights of these features are covered in

the next section.

5.3.1 Reviewing and Preprocwsing the Deflection Data

Most backcalculation programs can read the FWD deflection output files of the
agencies for which they were developed. Some of the programs use statistical methods
to subdivide the pavement test section into uniform subsections, mostly based on the
variations in the pavement peak deflections. The MODULUS program allows the user
to review the measured surface deflections at each sensor location along the length of
the section. But the program does not allow more than one sensOr readings to be
viewed simultaneously. Review of all the sensor readings along the pavement length
of interest allows the user to observe the deflection trends and identify outliers. The
analyst is not required to remember the deflection trends at all the stations for
previously viewed sensors. The ability to drop an entire set of deflection readings at
any station or even only few readings at some of the sensors, identified as outliers, is
also essential for the accuracy and dependability of the backcalculated results.

In the MICHBACK program, deflections at all the sensors are plotted
simultaneously along the length of the pavement section being analyzed (Figure 5.1).
For a long pavement section the user can zoom-in on a smaller section for a more
detailed viewing of the data (Figure 5.2).

Coupled with this feature is a "deletion" option which can be used while
viewing the deflection data without having to exit the view mode. For each deflection
basin, if the deflection at one or more sensor locations are identified as outliers, they
can be deleted prior to performing the backcalculation at that location. Likewise, a
deflection basin can be deleted if the user identifies such a basin as an outlier.
Further, an option is provided so that the analyst can quit the system without

implementing/ saving the deleted data.

176

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178
5.3.2 Data Analysis Options

Most backcalculation programs provide the option, to either analyze deflection
data at all the test stations or to backcalculate the layer moduli values based on
averaged data for similar test sections. Sections that are similar are normally chosen
by the programs internally without any user interaction. In MICHBACK the data
analysis can be undertaken in a variety of possible methods, ensuring maximum user
interaction.

Like most programs, for a test section where the cross section of the pavement
does not change, the data can be analyzed at all the test locations. The user can view
and process the FWD data that is read from a file and is required to enter the cross
sectional data through the keyboard. The program can analyze the required data
without any interference after this stage. To improve the program efficiency the
results of previous location are taken as seed values for backcalculation at the next
location. All the backcalculated results are saved in two different files, one file
contains the summary of the results and the other contains a more detailed output.

The second available option is to choose a section with relatively uniform
deflection measurements after visual inspection, and then backcalculate the results on
the averaged deflection basin over the length of the chosen section. In this option, the
average values of the cross section should normally be used for backcalculation. The
results represent the average values of layer moduli for the section. This option may
yield inaccurate results when the variation in the deflection data along the section is
considerable. If the variability in the deflection data along the length of the section is
moderate, this option may provide stability to the backcalculated results by reducing
the random errors in the deflection measurements.

In the third option the program automatically selects the most representative
deflection basin for analysis, from the uniform section chosen by the user. The

concept of choosing the representative basin was first presented by Alexander et al.

179

(1989). The method has been adopted with some modification in MICHBACK. If all
the test locations cannot be individually analyzed then a representative basin for the
section being analyzed can be chosen. In this way an actual basin, which was
physically measured, is selected to represent the section rather than an artificially
computed basin, as would be the case if an averaged basin is analyzed. In
MICHBACK the representative basin of a pavement section is chosen in four steps:
1. SELL Average of the peak deflections is computed (PKD).
2. Step;- Average of measured deflections for respective sensors is

computed (DF).
3. SEED—3- Average of the area for all deflection basins is computed

(AREA). The area is computed as the area under the

measured portion of the deflection basin. The area

between two sensors is assumed to be trapezoidal.
4. 31:93. An error function (A) is computed for each basin in the

section as follows:

 

 

A g [PIED-PKDT + " [BF-BF]: + [AREA-AREA):
X

PEI) .1 07V AR-EA
where PKD = peak deflection;
DF = measured deflection;
AREA = computed area; and
n = number of sensors.

The measured deflection basin with the least error is then chosen as the representative
basin.

Extensive study by Anderson (1989), showed that the use of the representative
basin concept for flexible pavements yields good results. But for composite

pavements, due to the wide variability in the backcalculated moduli, the use of a

180
representative basin to estimate the moduli for an entire section is not recommended.
In MICHBACK all three options have been provided. After gaining some experience
with the deflection data pertaining to pavements in their area the users may choose the

method best suited to their needs.

5.4 PRESENTATION OF THE BACKCALCULATED RESULTS

The backcalculated results are saved in a file which can be printed, or can be
viewed on the screen. Results can also be seen graphically to observe the variation
along the desired section length. The backcalculated layer moduli for all layers are
plotted separately to present the variation clearly. The test locations for which the
backcalculated results have touched either of the higher or lower bounds, specified by

the user, are posted by a warning in the output for the user to consider.

5.5 PROGRAM STRUCTURE

The flow diagram of the program is presented in Figure 5 .3. Some of the
features related to the diagram have already been explained. Seed values for the layer
moduli and the stiff layer depth are furnished by regression equations. The user is
required to provide a set of seed values for the layer moduli as well. Just prior to the
start of the backcalculation the two sets of seed moduli values are displayed and the
user may select one or the other, or enter new values altogether.

Similarly, the seed value for the stiff layer depth estimated by the regression
equations is displayed so that the user may decide whether or not to incorporate a stiff
layer. If a stiff layer is desired the user can choose the seed value suggested by the
program or can enter the most probable depth if known. When the stiff layer is
incorporated, the program also requires its modulus and Poisson’s ratio to be entered.
Finally the user decides if estimation of the stiff layer depth along with layer moduli
is also desired or the stiff layer depth may be fixed. Backcalculation is performed as

181

 

 

Read initial data or open existing file

 

 

l"—

[ Keyboard input

1

View/process data

 

 

 

 

 

 

¢ N° Read FWD Yes +

file?

1
Convert FWD file

I

Graphics: vlew/precess/
select analysis section

 

 

 

 

 

 

 

 

 

 

a

 

Input seed values for moduli
8: stiff layer depth

_._|

 

 

 
   
  
   

 

 

 

 

Input stiff layer properties

 

thickness
correction 7

 

 

Case E Case 8 Case D

   
 

Incorporate

 

No

 

 
      
   
 

Perform
thickness
correction 7

No

  

 

Case C Case A

 

 

Poe-form backcalculatlon

 

 

1L

 

Graphics: view results

 

 

 

Figure 5.3.

l

Print results

 

 

 

 

Flow chart for MICHBACK program.

182
desired by the user and the results are saved in a file. These backcalculated results
can be viewed graphically as explained earlier. Finally the summary or the detailed

results can be printed as desired.

5.6 BACKCALCULATION OF LAYER PROPERTIES
The backcalculation tasks performed by the program can be divided into three
major groups: C
l. Backcalculation of layer moduli without incorporation of stiff layer
(Case A), or with stiff layer depth fixed at the probable value chosen
by the user(Case B).
2. Backcalculation of layer moduli and the layer thicloress of one of the
layers when a stiff layer is not incorporated (Case C), or with the stiff
layer depth fixed at the seed value (Case D).
3. Simultaneous backcalculation of layer moduli and the stiff layer depth
(Case E).

5.6.1 Cases A and B

For cases A and B the layer moduli are backcalculated with or without a stiff
layer (Figure 5 .4), and if a stiff layer is incorporated then its depth is fixed at the
user-specified value. A three layer pavement being analyzed as Case A (without stiff
layer) will be treated as a four layer pavement under case B (with the stiff layer at a
fixed depth). But the properties of fourth stiff layer are assumed to be known. This is

the only capability available with existing backcalculation programs.

5.6.2 Cases C and D
These two problems require one of the layer thicknesses to be backcalculated

along with the layer moduli. Like Case B above, Case D has a stiff layer incorporated

183

1 Cases A818

 

Calculate deflections & RMS error

.L

Improved roadbed modulus
i «
Compute gradient matrix 87'

 

 

 

 

 

 

 

 

 

revise moduli

1

Calculate deflections & RMS error

 

 

 

 

 

 

Converged

   
    
 

Yes

 

Iteration < N

 

 

WARNING
No convergence

 

 

 

Graph and print output

 

 

 

 

Figure 5.4. Details of backcalculataion procedure for cases A & B.

184
at a fixed depth for this option (Figure 5 .5).
Initially the layer moduli estimates are improved. When the RMS error falls
below 10% or when the number of iterations exceeds 2, only then is the improvement

of the layer thickness undertaken along with the layer moduli.

5.6.3 Case E

Like Cases A and D, the backcalculation of layer moduli is the only desired
objective. But for this case the depth to the stiff layer is not known and must be
estimated by the program from the deflection data. The same criteria as outlined for
Cases C and D is used to switch between the improvement of layer moduli alone to
the improvement of layer moduli along with the stiff layer depth (Figure 5.6).

This option works like Cases C and D with a minor change. Each time after
layer moduli and stiff layer depth are improved simultaneously the stiff layer depth is
improved by itself. This alternating scheme has the best convergence characteristics.

For all the cases described the backcalculation is terminated with a warning if
at any time during the backcalculation process the number of iterations equals the
maximum number of iterations specified by the user. In such an event, the layer
properties for which the RMS error was lowest during the entire backcalculation
process is assumed to be the closest to the actual value and are printed as the
backcalculated results along with a warning. When any of the specified convergence
criteria is met, the results along with the convergence criteria are recorded. Various

options to examine the backcalculated results have been presented in Section 5.4.

185

T Cases C&D

Calculate deflections 81 RMS error

1

Improve roadbed modulus

[L ,
Compute gradient matrix &

revise moduli

Y

Calculate deflections 81 RMS error

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Compute gradient matrix &
revise moduli & thickness

T

Calculate deflections & RMS error

 

 

 

 

 

 

 

    

Yes

 

Converged

 

 

 

Graph and print output WARN'NG
No convergence

 

 

 

 

 

 

Figure 5 .5. Details of backcalculataion procedure for cases C & D.

186

T Case E

Calculate deflections & RMS error
‘_—_f f;

I

 

 

 

 

 

 

 

Improve roadbed modulus

Y
Compute gradient matrix 8:
revise moduli

Y
Calculate deflections 8: RMS error

 

 

 

 

 

 

 

 

 

 

No

 

 

 

 

 

revise moduli & thickness

1

Compute gradient matrix 81

revise stiff layer depth
+

Calculate deflections 81 RMS error

I Compute gradient matrix &

 

 

 

 

 

 

 

 

 

 

Yes

 
   
 

Converged

 

 

 

 

Graph and print output WARNING
No convergence

 

 

 

 

 

Figure 5.6. Details of backcalculataion procedure for case B.

 

CHAPTER 6

VALIDATION USING FIELD DATA

6.1 GENERAL

As stated earlier a comprehensive FWD testing plan was undertaken by
MDOT as a part of this study. The FWD test data were analyzed to evaluate the
capabilities and characteristics of the MICHBACK computer program. The analyses
include the backcalculation of layer moduli values for various pavement sections

tested by using varying load levels.

6.2 PAVEMENT SELECTION
The selection of the pavement test sections was accomplished in consultation
with personnel from the Michigan Department of Transportation (MDOT). The main
criterion used in this selection is that the pavement sections be representative of the
spectrum of pavement cross-sections, paving materials, and traffic volume and load
found throughout the State of Michigan. Also, the selected pavement sections should
serve the needs of another separate but concurrent study (Mukhtar, 1993). 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-inches), moderately thick (3- to
6-inches), and thick (more than 6-inches) asphalt surfaces.
2. Traffic Volume and Load - Heavy, moderate, and light traffic load and volume
in terms of 18-kips equivalent single axle load (ESAL).
3. Pavement Types - Flexible pavements without overlays, flexible pavements
with overlays, and PCC pavements with asphalt overlays.
4. Cross-Sections - One layer (AC only), two layers (AC and base), and three

layers (AC, base and subbase).

187

188
5. AC Mixes - Stability based and standard type mixes.
6. Roadbed Type - Cohesive and cohesionless soils.
7. Pavement Surface Age - Newly constructed and/or rehabilitated (less than 3-
year old) and older pavement sections.

8. Distress Types - Rut and fatigue cracking.

Table 6.1 provides a list of the combination of variables used to prioritize the
various flexible and composite pavement sections and the weights assigned to each
variable. The weights are based on the importance of the variable in question. For
example, a heavy traffic load (high percent commercial vehicles travelling the
pavement section) was assigned a weight of 4 while a light traffic load was assigned a
weight of 3. Likewise, a weight of 2 was assigned to each of two types of distress,
fatigue cracking and rut. That is, the weight assigned to pavement section showing
either rut or fatigue cracking was 2, the weight for a pavement showing both fatigue
cracking and rut was 4, and the weight for a pavement section with no fatigue cracks
and/or rut was 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 weights) was then calculated. A pavement

189

Table 6.1. Criteria for finial section selection.

    
  
  
    
    
  
 
   
   
 
  
    

 

 

 

 

 

 

 

 

 

Flexible Pavemerna Composite
Pavements
Factor Weight Factor Weight 1
raffle (ESAL) Traffic (FSAL)
Light 3 Light 3
Heavy 4 Heavy 4
' knees (rnchea) Thickness (inches)
Thin < 3' 3 11in < 3' 2
Medium 3 To 6' 2 Medium 3 To 6" 3
Thick > 6' 2 Thick > 6' 4
Cross Section AC Overlay
2 Layer: 3 1 Course 2
3 layers 2 2 Couree 2
4 layers 2 3 or more 3
Courses
AC Cour-ea (no Number of Overlays
overlay). l Overlay 2
Lean than 3 I 2 or more 2
More than 3 1 Overlays
AC (overlay) l lava-lay Age (years)
Lesa than 3 2
. New Mix 2
Roadbed 8011
Sand 2 Old Mix 2
Clay 2
Pavcmcrn Age (yeare)L
Lear than 3

 

 

 

 

 

190
score consists of the sum of the weights 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 6.2 and 6.3 provide
lists of these flexible and composite pavement sections. Other information 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 are also listed in the tables. Figure 6.1 shows the distribution of the selected
pavement sections across the State of Michigan.

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
eategory. Rather, it identifies the severity and extent of cracking which includes
various types of cracks. Therefore, only the rut data in the MDOT data bank were
considered.

Each pavement section was divided into several lOO-feet long test sites. For
some 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 of
the sites.

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.

 

191

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6.2 Flexible pavement sections selected for study.
Section Route Dir. District Control Mile Post
NO. I =11 N=1 Sectio FROM TO Remarks
us=22 s=2
M =33 E=3
w=4
IMSUOlF 3355 1 3 40031 200 13.00
[fisuo2r 3350 3 3 23052 1.30 14.00
[rusuoer 3334 3 3 46041 1.50 11.20
[MSUO4F 3372 3 3 40023 0.00 3.00
[usuosr 3323 3 1 66022 3.00 14.40
[MSUOGF 3350 4 5 34021 4.50 3.00
Wsuwr: 22131 1 ' 5 54014 3.00 11.10 Cored
[msuoer 33133 3 5 79011 15.70 19.90
IMSUOQF 3320 4 5 54022 0.00 0.50
[MSUlOF 3323 3 1 31021 4.60 9.50 Cored
[fisunr 3344 3 5 41051 4.20 5.20
[MSU12F 1195 3 5 61152 1.20 5.40
@sumr 2227 1 3 13034 1.31 1.30 Cored
[MSU14F 3377 1 2 75052 3.00 10.00 Cored
5150156 2227 2 4 20016 0.00 6.30
[MSU16F 22131 1 3 33031 2.50 3.00
wsum= 22131 1 5 54013 0.50 3.41
flaswer 2227 1 4 20016 0.00 5.30
“161.11% 1175 1 4 59013 0.00 5.00 cored
Wsuzor 3365 1 5 59051 11.90 13.20
6490211: 3319 1 5 74032 0.00 10.00
lstuzzF 3332 4 5 52041 0.00 5.90
[MSU23F 3323 3 1 66023 6.60 11.00
flusuz41= 3399 1 3 33011 4.30 4.60
5450255 22131 2 3 33031 3.00 2.00
[MSUZGF 3357 3 6 25102 2.35 2.95
[MSU27F 1175 1 4 72061 7.00 13.40
[msuzer 1 175 1 4 15093 0.00 5.90
[MSU29F 3399 1 3 23092 2.20 7.30 cored
[We-0305 1175 1 4 69013 5.00 7.00
[NTSU31F 3325 4 1 66051 0.00 4.00
[rTsust 22131 1 5 59012 11.00 11.10

 

 

 

 

 

 

 

 

 

192

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6.2 Flexible pavement sections selected for study (continued).
Section Route Dir. District Control Mile Post
Designation l=11 N=1 Section FROM TO Remarks
03-22 3:2
M =33 E=3
W=4
[MSUSSF 22131 2 5 54014 3.50 3.50
[Ms034r= 33129 1 2 17072 12.10 19.30
[MSU35F 1175 1 4 16091 0.00 1.50
[MSU36F 1175 2 4 72061 13.30 7.00
[Ms037F 1175 1 4 72061 19.00 23.66
[Ms033F 3365 1 3 57013 3.20 12.71
[Ms039F 222 3 2 21024 4.30 14.30 cored
[MSU40F 1175 1 4 20015 4.10 9.10
[MSU41F 1175 1 4 20015 9.10 14.20
[MSU42F 1194 3 7 11015 13.00 15.00
[MSU43F 1194 3 7 11015 3.00 7.00 cored
[M5044F 2223 1 4 71073 24.70 26.71
[M50451= 1175 1 4 20015 0.00 1.00
[MSU46F 3366 1 3 40031 0.00 1.22
[MSU47F 3351 3 3 13041 3.65 3.92
[MSU48F 3349 1 3 30011 11.00 17.00
[M5049F 1175 2 4 72051 15.30 17.50

 

 

 

 

 

 

 

 

 

193

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6.3 Composite pavement sections selected for study.
Section Route Dir. District Control Mile Post
Designation l =1 1 N=1 Section FROM TO Remarks
US= 22 S=2
M =33 E=3
W=4
MSU01 C 1194 4 8 81104 5.60 7.90 cored
MSUOZC 1194 4 8 81104 1.90 5.60
MSU030 3350 3 8 46081 1 .10 3.00
MSU04C 22127 1 8 30071 0.00 4.90 cored
MSU050 2241 1 1 7023 8.48 14.01 cored
MSU06C 22223 3 8 46061 2.80 3.60
MSU07C 22127 1 8 46011 4.50 5.18
MSU08C 3350 3 8 46081 8.30 13.20 cored
MSUOQC 2241 1 1 7013 0.00 3.10
MSU1OC 3350 3 8 46081 3.00 8.30
MSU11C 3325 3 6 32012 12.00 19.90 cored
MSU1ZC 3325 3 6 32012 19.90 27.90
MSU130 22127 1 8 30071 9.80 10.30
MSU14C 22127 1 8 30071 4.90 9.80
MSU15C 1 175 1 9 63173 9.25 9.50

 

 

194

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6.1. Distribution of selected pavement sections across the State of Michigan.

195
All sites were visited again during the summers of 1992 and 1993. During each visit,
the rut and fatigue cracking data were collected and the general conditions of the sites
were recorded. The rut depth was measured by using a six feet straight-edge leveling
rod and a graduated triangular wedge with an accuracy of 0.025-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 condition was recorded in terms of
severity and the percent of the lOO-feet long test site showing alligator cracking.
Further, a total of 106 locations 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.

6.3 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. 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
location from the beginning of the site; and the seventh digit indicates the core
number within that site. For example, a core location designation of 2712402

indicates (left to right) that the c0re is obtained from section 27, flexible pavement,

196

test site number 2, at 40 feet from the beginning of the site, and the second core of

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 undisturbed
samples from unbound bases, subbases and roadbed soils so that different layers could
be easily identified. Inspite of this, for most pavement sections, separate and accurate
identification of the base and subbase layer thicknesses was not possible because of
the type of materials encountered (cohesionless and moist).

Non-destructive deflection tests (NDT) using a falling weight deflectometer
(FWD) were conducted at several locations along each test site. The NDT tests were
divided into two categories as follows.

1. Regular tests - Each test site ( 100-feet long) was subjected to five FWD tests
(a test is 3 drops). The tests were conducted at equal intervals of 20-feet
starting at the beginning of the test site.

2. Additional tests - For cored test sites, additional FWD tests were conducted
over the core locations.

The NDT were performed during various seasons as follows:

1. Summer 1991 - All test sections at about 9000 lb load.

Fall 1991 - All test sections at about 9000 lb load.

Spring 1992 - All test sections at about 9000 lb load.

PP.“

Summer 1992 - All test sections excluding core locations were tested at
about 9000 lb load. For the cored pavement sections the FWD test
were conducted at three load levels 4500, 9000, and 15000 lb.
5. Spring 1993 - Cored sections only at about 9000 lb load.

Each FWD test and the resulting deflection files were 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

197 .
for composite); the fourth digit designates the site number; the fifth and sixth digits
indicate the distance of the test location from the beginning of the site; the seventh
digit indicates the sequential drop number (drop number 1, 2 or 3); and the eighth
(right most) digit indicates test location (0 for 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 feet from the beginning of the

site, and the second drop of a regular test in the wheel path.

6.4 BACKCALCULATION or LAYER MODULI FOR SELECTED

PAVEMENT SECTIONS

As noted earlier, during the Summer of 1991, NDTs were conducted on all
cored and uncored flexible and composite pavement sections. The measured deflection
basins are tabulated in Appendix C and the pavement layer thicknesses are included in
Appendix B of a research report (Mahmood, 1993). It should be noted that for the
uncored pavement sections, the thicknesses of the pavement layers were obtained from
the proper MDOT files. For the cored pavement sections, the layer thicknesses were
measured from the cores. Since the layer thicknesses of the uncored pavement
sections are not accurately known, the results of only typical cored flexible and
composite pavement sections are presented and discussed in this section. Recall that
each NDT test consisted of three drops. The target load for each drop was set at 9000
pounds. The actual load delivered to the pavement section and measured by the load
cell of the FWD however, varied slightly from the target load. Therefore, the average
of the three deflection basins and the average load of the three drops were used to

perform the backcalculation of the layer moduli using the MICHBACK computer program.

198

For most flexible pavement sections there are no significant differences
between the base and subbase layer materials (Chapter 4, Field Manual of Soil
Engineering, MDOT). In addition, as stated earlier, the similarity in the texture of the
base and subbase materials made it very difficult to identify the thickness of each
layer (the materials were soaked by water during the coring). Because of this
similarity and due to the lack of accurate base and subbase thickness data, the two
layers were combined into a single layer and all flexible pavements were analyzed as
three-layer systems (AC, base, and roadbed).

All of the composite pavement sections included in the study are listed in the
MDOT proposed cross-section file as a three layer system. The construction
procedure, however, recommends the inclusion of a 3-inch base layer under the PCC
slab (Chapter 4, Field Manual of Soil Engineering, MDOT). During coring, a base
layer of various thicknesses was detected under some of the PCC slabs. However,
these thicknesses could not be accurately measured during coring. Therefore, all the
composite pavements are also analyzed as three layer systems.

A second peculiarity of the composite pavement sections is that the history of
the pavement was not available from the MDOT records. All sections were originally
constructed as PCC pavements. Only after their deterioration were they overlaid by an
AC layer. The conditions of the pavement or the treatment given to the pavement
before the overlay (joint repair, crack seating, etc.), could not be verified. During the
visual inspection, only the distresses that could be observed on the AC surface were
recorded. The condition of the slab after the overlay has a significant influence on the
backcalculated moduli. Hence, major factors that can be used for interpreting the
deflection data and backcalculated moduli are missing from the pool of explanatory
variables.

Tables 6.4 and 6.5 provide a summary of the general conditions (fatigue

cracking, rut depth, and other types of distress) and layout (section and site numbers,

199

Table 6.4. Summary of the layout and conditions of the cored flexible
pavement sections.

Pavement Pavement site Distance Fatigue Rut variation Other distress Deflection
section No. between sites cracking (in.) type along the
desi '00 miles % vement

 

Transverse
Adjacent sites 50-100 0.19-0.50 cracking Variable

   

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSUO7F ..
4
5 Adjacent sites 0-15 0.19-0.50 Variable
6
1 High severity .
MSUIOF Adjacent sites 0.05-0.42 transverse Unrform
2 cracking,
l
Adjacent sites 50-100 0.12-0.25 Lane shouler Moderate
_3__- Variation
MSU13F 3
' 0.30 «4 ..
4
Adjacent sites 0.12025 Lane shouler Moderate
5 separation Variation
6
1 High severity
transverse
__2__ cracks, lane
MSU14F 3 Ad' t ' 100 0 10-0 50 shoulder High
acen srtes . . tron,
J and bad local
4 “993°
5 conditions
6
1
. . Uniform to
__L__ Adjacent sites 0.20-0.28 ' d variati
MSUI9F
1.0 .-
Uniform to
Adjacent sites 0.20028 ' d variati

 

 

 

 

 

 

 

 

 

 

200

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6.4. Summary of the layout and conditions of the cored flexible
pavement sections (continued).
Pavement Pavement Distance Fatigue Rut Other Deflection
section site No. between cracking variation distress along the
designation sites (miles) (%) (in.) type pavement
1 Block and _
transverse High
2 Adjacent 100 0.06-0.12 cracking, vanation
3 srtes and
stnppmg
4
~ MSU29F
5 Block and .
. transverse Hrgh
6 Adjacent 100 0.06-0. 12 craclnng, vanatron
7 srtes and
stripping
8
1 Block and
Adjacent 100 0.12-0.30 transverse High
2 srtes crackmg
MSU35F 3
4 . Block and .
Adjacent 100 0.12-0.20 transverse ngh
5 srtes cracking
6
1
Adjacent 0.25-0.35 Medium
2 srtes
0.30 '< -
4
Adjacent 0. 38-1 .0 Medium
5 srtes
MSU43F 6
1.0
7
Adjacent 0. 12—0. 19 Medium
8 srtes

 

Summary of the layout and condition of the cored composite

 

 

 

 

 

 

 

 

201

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6.5.
pavement sections.
Pavement Pavement site Distance Distress type Rut variation Deflection
section No. between sites (in.) along the
dedgnation (miles) pavement
I _
1 . . Edse cracking. high awed HES?!
Adjacent srtes lane shoulder separation an 0.25-0.31 variation
2 transverse cracking
3
MSU01C 1.0
4 Edge cracking, high severi High
Adjacent sites lane shoulder separation 0.25-0.31 variation
5 transverse cracking
6
1 Edge crackin , transverse Very high
Adjacent sites cracks and ongitudinal 0.25-0.56 var-ration
2 cracks
3
MSUOSC 1.0
4 Edge crackin , transverse Very high
Adjacent sites cracks and ongitudinal 0.25-0.56 var-ration
5 cracks
6
l 5 to 7 even] spaced hi Hi
Adjacent sites severity transir'erse cracksshin 0.25-0.56 vana‘trhon
2 each site
3
MSU08C 2.0
4 5 to 7 even] spaced hr h Hi
Adjacent sites severity transzerse crackg rn 0.25-0.56 variagtrhon
5 each site
6
1 High
MSU04C 2 Adjacent sites Pavement in good condition variation
3

 

 

 

 

 

202
and distances between the test sites) of eight cored flexible and four cored composite
pavement sections, respectively. Descriptive terms relative to the variability of the
deflection data along the various pavement sites are also listed in the right-most
column of the tables. It should be noted that the location of any FWD test (a test
consists of three drops) is designated by a location/station number. Location or station
number 1 is always located at the beginning of the first test site of each pavement
section. For any given pavement section, regardless of whether the test sites are
adjacent to each others or not, a continuous numbering system (e.g., l, 2, ..., 8) is
used to designate the location/station numbers. In the next subsections, examples of
the actual variations of the various deflection values along the sites are presented.
Further, typical deflection basins measured at various location/station numbers along

various pavement sites are also presented.

6.4.1 Flexible Pavement Section MSUO7F - Variable Deflections

There are a total of six test sites in this section, the first three and the last
three sites are grouped together with a distance of 1.5 miles between the two groups.
The first three sites have low severity fatigue cracking extending over 50 to 100
percent over each site, while the extent of cracking along the last three sites is
between 0 to 15 percent. The second group of sites is located on a fill section. The
variations of the deflections (measured bythe seven FWD sensors) along the length of
the entire pavement section is shown in Figure 6.2. The backcalculated layer moduli
are presented in Table 6.6 and they are discussed below in detail as an example of
typical results for pavements with a relatively high variation in the measured
deflections. 2

Examination of the values of the backcalculated layer moduli listed in Table
6.6 indicates that:

1. The AC modulus varies from a low value of 711,248 psi at test location

203

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204

Table 6.6. Backcalculated moduli for pavement section MSU07F.

 

VET 2‘ "_ ‘ 2' if i 2 E Cl T 2‘ ‘ if 'L Ti
‘1 FWD test Test location Backcalculated moduli (psi) RMS Error 1
P code No. AC R oadbed (%) +

 

 

 

 

 

 

; 07112011 3 711248 33538 30701 1.04 41

3 07122411 12 1106757 34646 29804 0.72

" 07127721 15 1131439 33336 36455 1.25
07128332 17 1320628 54731 34356 1.55
07131211 19 1028024 43254 32759 1.46
07137022 24 767833 21714 27864 0.36

g 07141211 26 909228 20197 27628 0.79

 

 

 

 

 

 

205
number 3 to a high value of 1,320,628 psi at test location number 17 (a factor
of about 1.86).
The base modulus varies from a low value of 20,197 psi at test location
number 26 to a high value of 54,731 psi at test location number 17 (a factor of
about 2.71).
The roadde modulus varies from a low value of 27,628 psi at test location
number 26 to a high value of 36,455 psi at test location number 15 (a factor of
about 1.32).
The maximum values of the root-mean—square of the errors between the seven

calculated and measured deflection values is 1.55 %.

In order to discuss the variations in the values of the backcalculated layer

moduli provided in Table 6.6, the measured pavement deflections at sensors 1 (the

inner-most sensor) and 7 (the outer-most sensor) and the AC thickness for test

location number 3 were designated as datum values and the percent differences

between the datum values and the corresponding values at other test locations were

calculated and are depicted in Figure 6.3. Examination of the figure indicates that:

l.

The relatively high AC modulus values at test locations. 12, 15, and 19 can be
related to lower measured deflections (sensor 1) and AC thicknesses at these
locations. Thin AC layers should lead to higher deflections. The low measured
deflection values at these locations relative to those at test location number 3,
imply that the AC layer is stiffer and hence its modulus is higher.

For test location number 17, the measured deflection at sensor 1 is lower than
that at test location number 3, yet the AC thickness is almost the same
(slightly higher). Again, the stiffer (higher modulus) of the AC is the main
contributing factor to lower deflection.

For test locations 24 and 26, the measured deflections at sensor 1 are higher

206

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than those at test location number 3 and yet the backcalculated layer moduli
are higher. One may expect that higher deflection values imply softer materials
and lower moduli. Although this is true, the thicknesses of the AC layer at
these two test locations are substantially lower than the AC thickness at
test location number 3. Lower AC thicknesses cause higher deflections.
The above scenario implies, as expected, that the deflection of a
pavement structure is a function of both the modulus and the thickness
of the AC layer. Variations in any one variable lead to variation in the
measured deflection. At test location number 24 and 26, the thickness
of the AC is the main cause of higher deflections.
The variation in the values of the roadbed modulus is well explained by the
variation in the measured deflection at sensor 7 (located at a lateral distance of
60-inch from the center of the applied load). It can be seen from Figure 6.3
that a higher roadbed modulus corresponds to a lower‘deflection at sensor 7.
For test location numbers 12, 15, 17, and 19, the values of the base modulus
is higher than that at location number 3, while they are lower for test location
numbers 24 and 26. In order to probe further into the variation of the base
modulus, the percent differences between the deflections measured at all seven
sensor at test location number 3 and those at locations 15, 17, 19, and 26 are
shown in Figure 6.4. It can be seen that for test location number 17, the
deflections measured by all sensors are appreciably lower than those measured
at other test locations. In particular, the deflections of the middle sensors
(sensors 2 to 5) are much lower, which indicate the presence of a stiffer
(higher modulus) middle layer (in this case, the base layer). Inversely, for test
location number 26, the deflections measured by all middle sensors are

appreciably higher, which indicate softer base layers.

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209
The above observations indicate that the variations in the backcalculated layer
moduli along pavement section "MSUO7F” are very reasonable and consistent with

the variations of the measured pavement deflections and AC thicknesses.

6.4.2 Flexible Pavement Section MSU19F - Uniform Deflections
This pavement section consists of a total of eight test sites divided into two
groups (each consists of four sites) which are separated by a one mile stretch of
pavement. The pavement is in a good condition with no significant distress. The AC
thickness within the section varies from 5.1 to 85-inch. The deflections measured by
all seven sensor locations are shown in Figure 6.5 and the values of the
backcalculated layer moduli are provided in Table 6.7. This pavement section is
representative of those sections whose behavior is more or less uniform along the
length of the pavement.
Examination of the values of the backcalculated layer moduli listed in
Table 6.7 indicates that:
1. The AC modulus varies from a low value of 215,731 psi at test location
number 45 to a high value of 391,656 psi at test location number 10 (a factor
of about 1.82).
2. The base modulus varies from a low value of 56,760 psi at test location
number 45 to a high value of 82,908 psi at test loeation number 17 (a factor of
about 1.46).
3. The roadbed modulus varies from a low value of 40006 psi at test location
number 40 to a high value of 50,857 psi at test location number 15 (a factor of
about 1.27).
4. The maximum values of the root-mean-square of the errors between the seven

calculated and measured deflection values is 3.54%.

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Table 6.7. Backcalculated moduli for pavement section MSU19F .

_ _ _ — A 7 i 7+ ‘— ._ _ ___H_________ _i., . ~~fm_._ __‘

FWD test Test location Backcalculated moduli (psi) RMS Error 1
°°d° N°° AC Base Roadbed (%) ‘

 

 

.______—— _.________ , _ ,__1

? 19113011

2.99

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 346848 71962 50190

' 19118311 8 321499 68224 48739 3.41

' 19121611 10 391656 69329 46408 2.03

[I 19128211 15 271118 77296 50857 3.02

n 19131111 17 257348 82538 50809 1.71 ;
19132312 19 253084 82908 50598 3.39 :
19137411 22 364790 76309 50215 3.19 .
19141811 25 258563 72029 43146 2.57
19148111 31 317965 76003 40839 3.22
19150911 33 263608 74919 41806 3.54
19158411 38 250851 77889 49048 2.45
19161211 40 227458 72986 40006 3.40
19169111 45 215731 56760 41228 3.39 j

212

As for the previous pavement section, the values of the backcalculated layer

moduli provided in Table 6.7, the measured pavement deflections at sensors 1 (the

inner-most sensor) and 7 (the outer-most sensor), and the AC thickness for test

location number 3 were designated as datum values and the percent differences

between the datum values and the corresponding values at other test locations were

calculated and are depicted in Figure 6.6. Examination of the figure indicates that:

l.

The variations in the measured deflections are small and so are the variations
in the values of the backcalculated layer moduli.

For test location number 8, as it is expected, the deflection measured at sensor
1 and the AC layer thickness are higher which lead to a lower AC modulus.
For test location number 10, the deflection measured at sensor 1 is high
because of the AC thickness which is substantially lower than that at location 3
(a difference of about 10 percent). Hence, for this test location high deflection
is caused mainly by a lower AC thickness rather than by a softer AC layer.
An apparent discrepancy exists for test locations 15, 17, and 19. For example,
at test location number 17, the AC thickness is almost the same as that at the
datum (test location number 3) and the difference in the measured deflection at
sensor 1 is moderately low, and yet an appreciable difference in the
backcalculated AC modulus can be noted. This apparent discrepancy led to a
further examination of the measured deflection records. It was noted that the
NDT tests along this pavement section was conducted at noon time on a sunny
summer day. Further, the temperature of the AC surface (which was recorded
during the test) at test location number 17 was ten degrees higher than that
recorded at test location number 3. Hence, the lower AC modulus is mainly
due to the higher temperature of the AC. In order to confirm this, the percent
differences between the deflections measured at all sensor and those measured

at test location number 3 are plotted in Figure 6.7 for test location numbers 8,

213

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10, 17, and 19. It can be seen from the figure that for test location
numbers 8 and 10, the deflections at all seven sensors are higher than
those at test location number 3 which indicate softer materials. For test
location numbers 17 and 19, however the deflection measured at
sensors 1 is higher than that for test location number 3 and the
deflections of all other sensors are lower. This trend is the signature of
higher AC temperatures.
5. For test location number 22, the variation in the AC thickness has the largest

impact on the measured deflection.

Once again, the above observations indicate that the variations in the
backcalculated layer moduli along pavement section ”MSU19F" are very reasonable

and consistent with the variations of the measured pavement deflections and AC

thicknesses.

6.4.3 Flexible Pavement Section MSUIOF - Uniform Deflections

This pavement section has a total of three adjacent sites. Lane shoulder
separation was the only noted distress; otherwise the pavement is in a very good state.
The measured deflections are almost uniform along the length of the pavement section
as shown in Figure 6.8. The typical deflection basin along the section is smooth as
shown in Figure 6.9 and the deflection decreases gradually with increasing lateral
distance.

The values of the backealculated layer moduli are listed in Table 6.8. The
variations in the base and roadbed moduli are consistent with the variations in the
deflections measured along the pavement section. The variations in the AC modulus
for the last three locations is higher than expected despite moderate variation in

deflections. The thickness of the AC layer however, varied between 4.3 to 5.5-inch

216

 

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Table 6.8. Backcalculated moduli for pavement section MSUlOF.
M‘
°°d° __ _ N° __ AC _ Base 4 Roadbed (%) .
r 10131011 2 440713 30169 24368 2.46 1
10131821 3 691145 31533 24070 1.74
10136641 8 630075 28078 23587 1.40
10121711 11 504689 29147 23422 1.72
I 10128121 16 594474 29148 22413 1.17 I
10111711 . 18 3743195 31735 20302 1.51 {
g 10117322 22 4226065 31953 20184 1.56 f
. 10118731 24 4525815 34564 21507 1.36 J

 

 

 

 

 

219
for the first four locations and from 2.3 to 2.4-inch for the last three locations. Given
the almost uniform deflection along the pavement section, the abrupt and substantial
change in the AC layer thickness implies a much stiffer AC as reflected in the

backcalculated AC modulus values.

6.4.4 Flexible Pavement Section MSU13F - Variable Deflections

There are six test sites in this section located in two groups of three sites each
which are approximately 0.4 mile apart. The first three sites have more distress (50 to
100 percent of each site with low to medium severity alligator cracking) than the last
three sites (for which lane-shoulder separation is the only observed distress).
Moderate variations in the measured deflections along the length of the section were
observed and are shown in Figure 6.10.

The values of the backcalculated layer moduli are listed in Table 6.9.
Variations in these values are consistent with those observed in the measured

deflections and AC thickness.

6.4.5 Flexible Pavement Section MSU14F - Variable Deflection

This section consists of six adjacent test sites. The AC layer thickness varies
between 2.4 and 3.1-inch. Hence, the section is placed in the thin pavement category.
Low severity fatigue cracking was observed along almost all test sites. Some high
severity transverse (temperature) cracks were also observed as well as low to medium
severity lane-shoulder separation. In addition, poor drainage conditions were noticed
along the sites.

Figure 6.11 depicts the considerable variation in the deflections measured at all
sensors along the pavement section. This variation can be related in part to the high
severity transverse cracks (except for test location numbers 22 and 26, all other test

locations are in the vicinity of these cracks), and the poor but variable drainage

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Table 6.9. Backcalculated moduli for pavement section MSU13F.

i FWD test Test location Backcalculated moduli (psi) RMS Error 1
N°' AC Base Roadbed (%)

 

 

 

 

 

 

 

 

 

 

 

 

 

code

1 13117121 6 452995 48000 28829 1.34

1 13126311 12 801451 55078 27907 3.03 .

13132911 17 774716 65994 30021 1.33 .
13142311 24 7345505 62207 31031 1.56 f

! 13142922 25 668281 73135 31185 1.48 i

13151511 30 939812 50402 23574 1.09 g

[I 13156621 34 573163 52322 26336 2.31 '

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conditions along the section.

Table 6.10 provides a list of the values of the backcalculated layer moduli. It
should be noted that some existing backcalculation routines (such as MODULUS 4.0)
recommend the use of a fixed AC modulus for thin pavements. In this study, a fixed
AC modulus was not used. All values were backcalculated using the MICHBACK
computer program. Nevertheless, the trends between the values of the backcalculated
layer moduli and the measured pavement deflections and AC thicknesses are

reasonable and consistent.

6.4.6 Flexible Pavement Section MSU29F - Variable Deflections

In this section there are two groups, each group consisting of three test sites.
The groups are separated by a distance of 3.2 miles. Difficulties in the analysis of the
measured deflection basins for this section led to a further investigation of its
conditions. It was noted that at least a portion of the outer pavement lane (the traffic
lane) and the shoulder are located on an old portland cement concrete (PCC)
pavement. The section has 100 percent medium to high severity cracking (mostly a
combination of fatigue and block cracking) which had been sealed. The first three test
sites are in an uphill fill section, whereas the last three sites are in a downgrade. A
wide variation in the drainage conditions along the section was also observed. Some
of the driveways to existing homes along the road were blocking the natural water
drains.

High variations in the deflections measured at all sensors were observed and
are shown in Figure 6.12. The variations follow a specific trend. The deflections
between test location numbers 1 and 28 are comparatively low and are interspread
with approximately equally spaced high blips. The deflections between stations 28 and
40 are however, consistently high for the first few sensors and consistently low for

the last ones. After station number 40, the deflections taper off to lower values. In

224

Table 6.10. Backcalculated moduli for pavement section MSUl4F.

, FWD test Test location Backcalculated moduli (psi) RMS Error 1
°°d° N°‘ AC Base Roadbed (%) +
.__ - _e _ ,, .. _ _ __-- ___-fl- __-- v _
' 1817913 21620 .

14113013

14121713 18887
14137811 31124
14143711 29577
14148213 1976844 29702
14151513 1217635 24865
14155113 38 1568918 23277 20567 1222
14161813 1187707

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addition, the shapes of the measured deflection basins at the various stations are not
consistent as depicted in Figure 6.13.

The values of the backcalculated layer moduli are provided in Table 6.11. It
can be seen that the values are also highly variable and they follow the trends of the
deflections along the road. For example, the values of the layer moduli are
consistently high for all locations where the measured deflections are comparatively
low. Further, the wide variation in the drainage condition has caused compatible
variation in the base and roadbed moduli. Nevertheless, the backcalculated moduli
values should be viewed with caution because of the presence of the PCC slab and the

high distress conditions prevalent in the section.

6.4.7 Flexible Pavement Section MSU35F - Variable Deflections

This test section consists of six almost adjacent sites (the first three sites are
only 0.1 mile away from the last three). The thickness of the AC measured from the
cores varies from 5 to 7.3-inch. A combination of low severity fatigue and block
cracking was observed along the entire test section. One to two high severity
transverse cracks were also noted along each of the test sites.

Figure 6.14 displays the high variations in the deflections measured at all
sensors along the pavement section. Except at a few locations, there is a recurring
pattern of moderate deflection fluctuation which indicates the presence of equally
spaced cracks. However, the shape of individual deflection basins was found to be
consistent when compared to that of section 29F.

The values of the backcalculated layer moduli are listed in Table 6.12. The
values are very much consistent with the variations in the measured deflections and

AC thicknesses.

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Backcalculated modulus for pavement section MSU29F.

 

535056 30363 24682

FWD test Test location Backcalculated moduli (psi) RMS Error é
1 code No. AC Base Roa db ed (%) w
2

   
 

 

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Table 6.12. Backcalculated modulus for pavement section MSU35F.

 

35112211

35114222
35118931
35123311
35128321 862525

 

 

 

 

 

35132611 528756
35136221 718640
35143911 ' 501497
35152311 463521
35159121 365961
35161411 472025
? 35167331 529678

 

 

 

 

 

 

 

 

 

 

 

 

231 p ‘
6.4.8 Flexible Pavement Section MSU43F - Variable Deflections

This test section has a total of three groups, each consists of three test sites.
The groups are separated by distances of 0.3 and 1 mile. The pavement section is
characterized by very high rut depths, especially in the first three sites. Low severity
cracking was also observed along the entire section.

Figure 6.15 depicts the high variations in the measured deflection profiles
along the pavement section. It can be seen that continuously reoccurring blips of high
deflections were measured. The shape of individual deflection basins however, is
mostly smooth and consistent.

The backcalculated layer moduli listed in Table 6.13 have moderate variations
in the base and roadbed moduli and high variation in the AC modulus. These
variations are very much compatible with those of the measured deflections. For
example, the deflections measured at test station number 29 are relatively higher than
those at station 30. Consequently, the values of the backcalculate layer moduli at

station number 29 are lower than those at station number 30.

6.4.9 Composite Pavement Section MSU01C - Variable Deflections

The eight test sites of this section are located in two groups having five and
three sites, and are located 1 mile apart. Beside edge cracking, the main distress
observed along this section is in the form of high severity sealed transverse cracks
(reflective cracking). This section has very heavy truck traffic.

Figure 6.16 depicts the high variations of the measured deflection profile along
the road. The towering blips of high deflections are indicative of the presence of high
severity transverse cracks which are closely spaced in certain locations. The shapes of
the measured deflection basins are not consistent and are not smooth as shown in
Figure 6.17.

The values of the backcalculated layer moduli are listed in Table 6.14. The

232

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Table 6.13. Backcalculated moduli for pavement section MSU43F.

 

 

 

 

 

 

 

 

 

 

 

 

 

FWD Test Test Location Backcalculated Results (psi) RMS Error
C°de N°' AC Base Roadbed V (%)
43111711 2 580509 22886 36221 1.35
43121811 9 873327 13926 46995 2.26
43131911 16 890107 14774 44970 1.65
43141611 23 875335 17540 41522 3.06
43148313 29 597983 19410 42198 1.28
4314831 1 30 422440 24850 38947 1.47
43152311 33 713238 17787 36701 1.10
43161411 39 483639 20058 34977 2.12
43178511 50 589905 19907 39101 1.07
431781 12 51 485790 20296 39462 1.60
43188111 57 531447 21100 40511 1.26
43191411 60 564445 19098 39715 1.64

 

 

 

 

 

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'__._._ _

 

Backcalculated moduli for pavement section MSU01C.

Backcalculated moduli (psi)

 

_M" 1
RMS Error 1

 

 

 

 

 

 

 

 

 

 

g °°d° N°' AC Base Roadbed ‘91)
r1284611 4 337073 5406975 16271 2.28 I
1 01272411 12 319451 2636877 18653 2.36
01261611 17 282635 4694486 23958 1.01
II 01264221 20 195181 1520576 22012 0.92
; 01251611 25 302239 3191544 18924 1.39
1 01240411 31 762348 5040840 18107 0.95
1 01248931 35 1012610 524600 25662 1.12
I 01232611 42 725415 3293690 22761 1.33
3 01221711 47 610169 4900569 35123 1.57
1-01114 55 523795 _ 1‘142 19998 116.

 

 

 

 

237
variations of these values along the pavement section are consistent with those of the
measured deflection profiles. For example, the measured deflections at station location
number 47 are relatively lower than those at station 17. Consequently, the

backcalculated layer moduli are higher at the former station than at the latter one.

6.4.10 Composite Pavement Section MSUOSC - Variable Deflections

There are six test sites inthis section located in two groups of three sites each
which are approximately 1.0 mile apart. Lane-shoulder separation and medium to high
severity transverse cracks (reflective cracking) were observed along the entire section.
The transverse cracks are equally spaced and are occasionally connected by
longitudinal cracks.

Figure 6.18 displays the extremely high variations in the measured deflection
profile along the road. The equally spaced high deflection blips in the figure
correspond to the equally spaced high severity transverse reflective cracking.

Table 6.15 provides a list of the values of the backcalculated layer moduli.
Variations in the moduli values correspond to the variations in the measured
deflection basins. For example, the measured deflections at location number 28 are
much higher than those at locations 8 and 17. Correspondingly, the values of the
backcalculated moduli of the first station are lower than those of the latter two
stations. Further, the MICHBACK computer program did not converge on any set of
moduli values for station number 45. The reason for this is the irregular shape of the
deflection basin. Figure 6.19 displays the deflection basins measured at four location
numbers 45, 46 (located only three feet away from station 45), 43, and 28. It can be
seen that the shape of the deflection basins vary substantially from one station to
another. Such variations in the shape of the deflection basins and in the values of the
Mk deflections are the consequences of the state of distress of the PCC slab.

Therefore, for any distressed pavements, the backcalculated layer moduli (even with

238

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Table 6.15. Backcalculated moduli for pavement section MSUOSC.

1FWD FWDtest Test location Backcalculated moduli (psi) ~__RMS Error 1
1 code N o Roadbed (95 )
h .

 

 

 

 

 

 

 

 

 

1 05218611 1134797 8519459 30247 1.24
; 05229211 17 1292937 7494653 34832 1.11

1 05241411 28 1662644 4757409 33519 2.38 1
1 05258311 43 912615 7436017 20367 2.28
1 05261712 45 No Convergence 1
#012 46 _ 1056789 7104805 19389 _8___ _1

 

 

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small root-mean-square error) must be viewed cautiously.

6.4.11 Composite Pavement Section MSU08C - Variable Deflections
In this section, there are two groups separated by a distance of 2 miles. Each
group consists of three adjacent test sites. There are 5 to 7 transverse (reflective)
cracks in each site. The pavement is constructed on a 4-feet high embankment.
Figure 6.20 depicts the deflection profiles measured along the pavement
section. It can be seen that the profile is characterized by fluctuation caused by the
presence of reflective cracks. These variations in the measured deflections cause the
similar variations in the backcalculated layer moduli provided in Table 6.16.
Figure 6.21 depicts the irregularities of the deflection basins measured at various
stations along the road. As for the previous composite pavement section‘s, these

irregularities raise questions about whether the backcalculated moduli are reasonable.

6.4.12 Composite Pavement Section MSU04C - Variable Deflections

The three adjacent test sites of this section are apparently in good condition
apart from the observed medium severity transverse (reflective) cracks. The section is
located on a 4 to 5-feet high embankment. The thickness of the AC overlay varies
along the pavement from 2.3 to 2.9-inch. During coring, a buried AC pavement was
found underneath what was thought to be the roadbed soil. Because of the limitations
of the MDOT coring equipment, the thicknesses of the various layers of the buried

pavement structure could not be determined beyond the upper 3-inch.

Figure 6.22 shows the unique and moderate variations in the deflection profile
measured along the road. It can be seen that the four lines representing the first four
deflection sensors intersect and criss—cross each other frequently. Further, the
prominent high deflection values in Figure 6.22 correspond to the presence of

transverse cracks.

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Table 6.16. Backcalculated moduli for pavement section MSU08C.

 

I‘"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Test Ilqcziation Backcalculated moduli (psi) RMf%FSrror '

AC hBase Roa__bed __

Faun 1033037 2993202 11126 2.54 fl'
. 03213022 1707413 2639131 20307 1.67
; 03221011 705630 6592433 10362 3.53
i 03231511 15 1516300 2365745 13153 1.86
' 03241011 21 390504 3311759 20363 1.31
03251311 27 437404 4267114 14644 2.03
03260911 33 1350763 2221734 13371 1.31
03261622 34 301636 4523369 22724 2.14

 

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For this section, the MICHBACK computer program did not converge on any
set of layer moduli for any of the test locations. The reason for this is the extremely
irregular shapes of the measured deflection basins. Figure 6.23 depicts the deflection
basins measured at three different locations. Beside the presence of the buried
pavement structure, no other explanation can be offered at this time regarding the

irregularities of the deflection basins.

6.5 BACKCALCULATION OF LAYER MODULI AT DIFFERENT LOAD
LEVELS
During the summer of 1992, the FWD testing was expanded to include
different load levels. All the non-cored pavement sections were tested at the standard
target load of 9000 lbs. At each test location of the cored pavement sections, the NDT

procedure was modified to include seven drops as follows:

1. The first drop 4500 lb (pavement seating).
2. Second drop 4500 lb (the deflection data was used for
backcalculation).

3. Next three drops 9000 lb (the average deflection and the average
load were used for backcalculation)
4. Seventh drop 16000 lb (the deflection data was used for
backcalculation).
To avoid unnecessary repetitions, only the results of backcalculating the layer moduli
for a few typical test locations along two flexible and one composite pavements are
presented and discussed in this section. Table 6.17 provides a list of the types of the
roadbed soils (the information is obtained from the 1970 MDOT Field Manual of Soil

Engineering) encountered in the four pavement sections.

247

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6.5.1 Flexible Pavement Section MSU19F - Variable Load Level
A brief description of this pavement is included in Section 6.4.5. The test

section is located in Otsego County and the roadbed soil is granular in nature. The

backcalculated layer moduli for the three load levels are listed in Table 6.18. The
layer moduli backcalculated at the standard load of 9000 pounds are referred to in the
remaining parts of this discussion as the reference values. The percent differences
between the reference moduli and those calculated at the other two load levels were

‘computed and are listed in Table 6.19.

Examination of the layer moduli calculated at the various load levels and the
percent differences between those calculated at the standard load level and those at the
other two load levels indicates that:

1. Relative to the reference moduli of the AC and base layers, the modulus
values calculated at the low load level are consistently low, whereas those
calculated at the higher load level are consistently high.

2. The variations in the backcalculated roadbed soil moduli are within a tolerable
range.

First, the variations in the AC and base moduli backcalculated at the different
load levels were investigated in relation to the measured deflection basins. Figures
6.24 through 6.27 depict four typical deflection basins measured at three load levels
at test location numbers 19113011, 19118331, 19121611, and 19128221, respectively.
The dotted lines in the figures represent the linearly extrapolated response of the
pavement structure at the low (4648-pounds) and high (16080—pounds) load levels
assuming that the pavement is a linear elastic system. That is, if the deflection basin
measured at the standard target load level of 9000 pounds is used as a reference
basin, and if the pavement response is purely linear with the load, then the measured
basins at the low and high load levels should be exactly the same as those shown by

the dotted lines. Ingreference to Figure 6.24, it can be seen that:

250

   

 

  

 

 

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1. For the lower load level, the measured deflections at the first five sensors are
higher than the linearly extrapolated responses, whereas, the measured
deflections at the outer two sensors are almost the same as those of the linearly
extrapolated responses.
2. For the higher load level, the measured deflections at the first five sensors are
lower than the linear responses, whereas, the measured deflections at the outer

two sensors are almost the same as those of the linearly extrapolated

responses.

The above two observations imply that the increase in the pavement response is not
linearly proportional to the load level. Discussion of this apparent non-linearity in the
pavement response is presented in subsection 6.5.4. In the remaining part of this
section, the trend between the backcalculated layer moduli and the measured
deflection basins at the three load levels is discussed.

Table 6.19 provides a list of the differences between the deflection responses
measured at the three load levels and those calculated by using a linear analysis.
Figure 6.28 and 6.29 show the percent differences between the deflection measured at
sensor locations 1, 2, and 7 due to the low and high load levels, respectively, and the
corresponding linearly extrapolated deflections. Further, the percent differences
between the layer moduli backcalculated at the same load levels and the reference
moduli (obtained from Table 6.19) are also shown in the figures. Examination of the
data listed in Tables 6.18 and 6.19 and shown in Figures 6.28 and 6.29 indicates that
(for ease of discussion, consider test location number 19113011):

1. The measured deflection basins at the 4648 pounds load level are higher than
the corresponding linearly extrapolated responses (Table 6.19). Consequently,
the backcalculated AC and base moduli are lower than the reference values

computed at the 9277 pounds load level (Table 6.18).

 

 

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259

2. The measured deflection basins at the 16080 pounds load level are lower than
the corresponding calculated linear responses (Table 6.19). Consequently, the
backcalculated AC and base moduli are higher than the reference values
computed at the 9277-pounds load level (Table 6.18).

3. For the outer-most sensors, the variations between the measured values and
those calculated by linear extrapolation are insignificant (Table 6.19). Since
the outer sensor measurements strongly influence the backcalculated roadbed
modulus, the values estimated at the various load levels are almost constant
(they vary within a very reasonable range). See Table 6.18.

The three observations indicate that the results produced by the MICHBACK
computer program are compatible with the measured deflection basins. That is, for all
tes¢ location numbers, the values of the layer moduli backcalculated for any load level

are “‘8 her or lower than the reference values if the measured deflection basins are,
“emf-i Vely, shallower or deeper than the linearly extrapolated responses. This tend
to support the contention that the variations in the results obtained by the
MICHBACK computer program are accurate and reflect the variations of the

meaSUI‘ed deflection basins.

5-5'2 Flexime Pavement Sections MSU35F - Variable Load Level

'I‘his test section is located in Cheboygan County and the roadbed soil is
similar to that for section 19F (Table 6.17). The trends of the deflection basins
"‘qu at the three load levels and the corresponding linearly extrapolated basins
for three test locations are shown in Figures 6.30 through 6.32. Table 6.20 provides a
“St of the layer moduli computed at the three load levels and the percent differences
between the reference modulus values (calculated at the standard target load of 9000
pounds) and those determined at the other two load levels. For the three load levels,

T ' . .
able 6.21 provides a list of the differences between the measured deflection basins

260

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265
and those calculated for a linear elastic system. It can be seen that the trends of the
data in the figures and tables are the same as those for pavement section MSU19F

presented in the previous section.

6.5.3 Composite Pavement Section MSU01C - Variable Load Level

This pavement section is located in Lenawee county in the State of Michigan.
The pavement exhibited medium to high severity transverse reflective cracks. The
roadbed soil is cohesive in nature (see Table 6.17).

The percent differences between the layer moduli backcalculated at the three
load levels are listed in Table 6.22. Table 6.23 provides a list of the percent
differences between the measured deflection basins and those computed by assuming a
linear elastic system. Figures 6.33 through 6.35 depict the measured deflection basins
and the linearly extrapolated responses (dotted lines) at the low and high load levels
for test location numbers 01284611, 01272411, and 01261611, respectively.

Besides the difficulties associated with the analysis of a composite pavements
with deteriorated concrete slabs, the trends of the backCalculated results are similar to

those presented above.

6.5.4 Discussion
In this section, the discrepancies between the deflection basins measured at the
three load levels and those calculated by assuming a linear elastic system (i.e, the
apparent non-linearity in the pavement response) is discussed. These discrepancies can
be attributed to several factors including:
1. Poisson’s Ratio - During the analyses of the deflection basins, Poisson’s ratios
of the AC, base and roadbed soil were kept at constant values of 0.35, 0.4,
and 0.45 respectively. Although, these are typical values of Poisson’s ratios,

the actual ones may vary. For example, Baladi ( 1988) stated that Poisson’s

266

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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271
ratio of the AC mix increases with increasing load level. He reported a range
of laboratory measured Poisson’s ratio from 0.1 to 0.45. Likewise, in the
AAMAS study, Vanquintus (1989) reported a range of the Poisson’s ratio of
the AC from negative values to values of over 0.5. Bouldin, et al. (1993)
reported a range of Poisson’s ratio from 0.1 to 7. Therefor, it appears that the
Poisson’s ratio of the AC mix is a function of the magnitude of the applied
load and the stiffness of the AC mix. In order to assess the impacts of
Poisson’s ratio of the AC on the backcalculated layer moduli, two typical
pavement sections (19113011 and 35114222) were analyzed by using Poisson’s
ratios of 0.25 , 0.35, and 0.45 for the target load levels of 4500, 9000, and
16,000 pounds, respectively. Tables 6.24 and 6.25 provide lists of the values
of the layer moduli backcalculated at the three load levels with a constant
Poisson’s ratio of the AC of 0.35 , and the backcalculated values for the other
two Poisson’s ratios. The percent differences between the reference moduli
(calculated at the target load level of 9000 pounds using a Poisson’s ratio of
0.35) and those calculated for the other two load levels are also provided in
the table. In reference to Table 6.24., it can be seen that a significant part of
the apparent non-linearity at the higher load level is eliminated. For example,
The percent difference between the reference modulus of the AC and that at
the higher load level dropped from 9.9 percent to only 3.00 percent. Less
significant improvements were found at the low load levels and in the modulus
of the base layer. Since, the exact values of Poisson’s ratios are not known,
part of the apparent non-linearity in the values of the backcalculated layer
moduli can be attributed to variations in Poisson’s ratios.
Shape Factor - Throughout this study, and because of the configuration of the

steel plate of the FWD, a circular loaded area with uniform contact pressure

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was assumed. In reality, the pressure distribution is a function of the relative
rigidity of the steel plate and the AC layer, the macro-texture of the pavement
surface, the magnitude of the applied load and the interface conditions between
the plate and the pavement surface. According to Saint-Venant’s principle
(Timoshenko and Goodier, 1987) the effect of changes in the pressure
distribution is more significant in the zone near the loaded area while the
response further away is sensitive to the total applied load. This is similar to
the observations of the measured deflections data in which the deviation from
the linear response due to varying load level is more pronounced for the first
few deflection locations than the far ones. Hence, part of the apparent non-
linear behavior may be attributable to the shape of the loaded area and the
pressure distribution.
System Non-Linearity - An earlier study conducted by Nazarian and Chai
(1992) studied the effect of load induced non-linearity. The test results indicate
that the AC modulus increases and the base and roadbed moduli decrease with
increasing load levels. This observation is confirmed by the results presented
earlier. The base modulus was observed to decrease with increasing load
levels, which is opposite to the trends noticed for base material for the
Michigan pavements that were analyzed. But one discrepancy between the
method of data analysis is that for the above quoted study the AC modulus was
fixed at average values after initial backcalculation. In the initial
backcalculation, however, it seems that all the moduli were varied
simultaneously. Backcalculation of the base layer modulus was then performed
at fixed values of the AC modulus. No explanation has been offered for
deviation from the standard procedure of backcalculating all the layer moduli
simultaneously. The same study also concluded that the load induced non-

linearity is more pronounced for KUAB (used by MDOT) than for any other

275
FWD equipment, although, the problem with vibratory devices is certainly
more severe.
Stress Dependency - Boker (1978) conducted study on Michigan cohesionless
soils concluded that the resilient modulus of the soils tested is a function of the
stress level, water content and dry density. In a similar study conducted by
Goitom (1981), the above observation was confirmed for cohesive soils of
Michigan as well. Chatti (1987) found that the resilient modulus of asphalt
paving mixtures increase with an increase in the cyclic load. Tests conducted
by Pronk (1989) with field data using the FWD showed that small changes in
the roadbed modulus due to non-linear behavior can induce greater changes in
the moduli of the other layers. However, he attributed confining pressure or
the dead weight of the pavement as the main contributing factor towards the
non-linear behavior rather than the changes in the applied loads. Hence, the
observed trends can in part be attributed to the non-linearity induced by
loading as well as material behavior. More comprehensive studies are certainly
required to make more forceful claims. 0
Dynamic Behavior - Most existing backcalculation routines, including the
MICHBACK computer program, are based on a linear layered elastic system
subjected to static loading. The FWD delivers dynamic loads to the pavement
structure. Hence, the magnitudes of the measured deflections at the various
sensors are a function of the dynamic (not static) properties of the pavement
. and loading systems. These include, that part of the mass of the pavement
structure affected by the load (higher loads affect a larger mass whose
properties are not constant with depth), the velocities of the compression,
shear, and surface waves, the magnitude of the induced vibration in the system '
(which causes some energy losses), and the damping (viscous properties) of

the various pavement layers. Hence, a part of the apparent non-linearity of the

276
backcalculated layer moduli may also be attributed to the dynamic behavior of

the system.

To this end, one may argue that the above enumerated factors should be
included in any backcalculation routines. Although, from the academic viewpoint, this
is a reasonable argument, in practice, it makes an insignificant impact on the accuracy
of the backcalculated results. To illustrate, consider a pavement structure with AC,
base and subbase thicknesses of 6-inch each, and a roadbed soil thickness of 60-inch
(a total depth to the bedrock or to a stiff layer of 78-inch). These thicknesses are not
accurately known. For example, the true thickness of the AC may vary from 5 to 6-
inch at best. The depth to the stiff layer may vary by several inches or several feet.
For most pavement structures, a variation of the AC thickness of l-incyh from the
mean may cause significant variations in the calculated moduli of the AC, base, and
subbase. These variations, in some cases, are much larger than those due to the
apparent non-linearity of the system. Besides, it is not possible to include all the
factors affecting pavement responses in a backcalculation routine, since the number of
system unknowns cannot exceed the number of deflection sensors (seven in the case
of the MDOT KUAB FWD).

Therefore, it is more reasonable to use a linear elastic layered system whereby
the thicknesses of some pavement layers are treated as unknowns (they possess a
significant impact on the backcalculated results), than to include other factors which
have lesser impact. Nevertheless, it is very important that accurate measurements of
the layer thicknesses must be made before one can achieve accurate backcalculation
results. Systems for making such measurements are currently under development and
the most promising one is a system based on the radar technology.

The results of the analysis of a variety of pavement sections and the associated

discussions presented in this chapter provides enough evidence that the backcalculated

277 ‘
results of the MICHBACK program are consistent with the measured deflections and
thickness variations observed in the field. The difficulty associated with the analysis

of composite pavements has also been highlihgted.

 

 

CHAPTER 7

TEMPERATURE EFFECTS ON THE BACKCALCULATED LAYER MODULI

7.1 GENERAL

In this chapter, the effects of temperature variations on the deflections and
backcalculated layer moduli for Michigan pavements are examined. As stated in
Chapter 6, the pavement sections were tested during various seasons to observe the
seasonal variation effects. Additional tests were designed to monitor the pavement
response to temperature variations and they were performed on three pavement
sections during the summer of 1993. Discussion and analyses of the test results along

with recommendations are presented in this chapter.

7.2 TEMPERATURE EFFECTS

As noted earlier, nondestructive deflection tests (NDTs) are typically
conducted to evaluate the structural capacity and the state of deterioration of the
pavement structure with time. Unfortunately, the measured pavement deflections are
influenced by seasonal variations in moistureand temperature. The moisture variation
influences the stiffness of the base and subbase layers and the roadbed soil.
Temperature variation, on the other hand, affects the stiffness of the AC layer.
Further, any change in the stiffness of any pavement layer causes changes in the
responses of the other layers and of the roadbed soil. This implies that the measured
deflection data are influenced by variations in both the AC temperature and the
moisture level in the other layers and in the roadbed soil. In order to conduct a proper
engineering evaluation of the pavement structure and to assess its rate of deterioration
with time, the deflection data or the backcalculated moduli of the pavement layers

must be corrected to a standard temperature and a standard moisture level.

278

279

Two temperature correction methods can be found: the American Association
of State Highway and Transportation Official (AASHTO) method which calls for the
correction of the measured pavement peak deflection (the deflection under the center
of the load), and the Asphalt Institute (AI) method which corrects the backcalculated
AC modulus to a standard temperature of 77 °F. Existing backcalculation routines,
however, use the temperature correction method. Most routines use the AI
temperature correction equation or some modified form of . the equation. The
AASHTO method is mainly used in the deflection-based design of pavement overlays.

Presently, there is no standard practice regarding seasonal corrections. Some
State Highway Agencies (SHA) have collected seasonal deflection data over several
years. The data were examined and deflection correction factors were deduced. In
some cases the correction factor is constant for all pavements, while in others the
value of the factor is a function of the pavement cross-section and the material
properties. Since the weather elements (freeze-thaw cycles, and amount of rainfall)
are not constant from one year to another, the development of accurate seasonal
correction factors is a long time process that requires deflection data to be collected
on various pavement sections over a long-term period.

In this study, deflection data were collected over a two year period and three
seasons. In addition, during the summer of 1993, NDTs were designed to assess the
impact of the AC surface temperature on its backcalculated modulus values.
Originally, eight pavement sections (6 flexible and 2 composite) were selected for this
part of the study. Unfortunately, because of the weather (the summer was cooler than
normal) and equipment limitation, only three flexible pavement sections were tested.
For each section, the tests were commenced in the morning when the pavement
temperature was around 60 °F, and continued throughout the day at half-hour time
intervals. The tests were conducted at the same location which was previously marked

by the MDOT FWD crew.

280 .

Two of the three pavement sections (MSU13F and MSUl9F) have already
been introduced in Chapter 6. The AC thicknesses for these two pavements are 4.8-
and 6.2-inch, respectively. The third pavement was not included in the study plan but
it was selected because of its near proximity to the MDOT testing facilities. This
pavement has an AC thickness of 4.5-inch. The pavement is in a good condition with
no apparent distresses and it will be referred to as MSU52F.

The test results of pavement section MSU52F are discussed in more detail, it
was tested under better conditions (sunny day with the temperature rising consistently)

and it has the least amount of distress.

7.2.1 Flexible Pavement Section MSUSZF - Temperature Variation
Figure 7.1 depicts the relationship between the measured pavement surface
temperature and the peak pavement deflection (deflection under the center of the
load). The figure indicates that:
l. The peak pavement deflection increases almost linearly with increasing
pavement temperatures. A
2. For a constant temperature, the pavement deflection measured during
the heating cycle is different from that measured during the cooling

cycle.

Therefore, based on the second observation, the FWD test results measured
during the cooling cycle of the pavement are ignored. Table 7.1 provides a list of the
deflections recorded at different sensors and the corresponding pavement
temperatures. The deflections measured at the lowest temperature (78 °F) were taken
as reference values and the percent; variation in the deflections at other temperatures
were calculated and are listed in Table 7.2, and shown in Figure 7.2. Examination of

Figure 7.2 indicates that:

281

 

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10.00
75

Figure 7.1.

l l I I

80 3'5 so 9515015560115150125
Pavement Temperature (F)

Variation of maximum deflection with temperature observed

for pavement section MSU52F.

282

Table7.1. Deflectioneveriationwlthtemperatureforpavementsection MSU52F.

Werner! Measured deflections at dWererrt sensor locations (mils) ‘
. Temp. fl 1 2 3__ 4 5 __6 7
78 10.23 8.11 6.51 4.80 3.62 2.11 1.11
86 10.56 8.24 6.55 4.73 3.53 2.09 1.10
96 1 (1% 8.42 6.53 4.59 3.42 2.04 1 .09
101 1 1 .08 8.27 6.40 4.46 3.29 2.00 1 .08
109 1 1.40 8.32 5.39 4.35 3.22 1 .97 1 .09
1 14 1 1.80 8.43 6.37 4.31 3.19 1 .95 1.08
120 12.23 8.39 6.29 4.25 3.14 1.95 1.10
122 12.23 8.12 6.14 4.15 3.09 1.96 1.08

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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1. The pavement deflections measured at all sensor locations are affected
by the pavement temperature.
2. The deflections of sensor 1 and 2 increase with increasing temperature,
while the deflections for sensor 3, 4, 5, 6, and 7 decrease with

increasing temperatures.

These observations were expected, and are due to the reduction in the ability
of the pavement to spread the applied load radially as the AC layer looses its stiffness
at higher temperatures.

The backcalculated layer moduli are listed in Table 7.3 and shown in Figures
7.3 and 7.4. It can be seen that the AC modulus decreases almost linearly with
increasing temperatures. The rate of change of the AC modulus with temperature is
about 10900 psi per °F. The base modulus also increases with increasing temperatures
as shown in Figure 7.4. The roadbed modulus, on the other hand, is not affected by
the AC temperature. The above observations indicate that the results obtained with the
MICHBACK computer program are consistent and compatible with the measured
deflection basins.

One may argue that the modulus of the base layer (granular material) should
not be affected by the AC temperature. However, there are two factors which may
contribute towards the increase in base modulus:

l. The state of stress in the base layer changes with changes in the AC

modulus and if the base is stress sensitive, then this could cause the

base modulus to change.

2. The Poisson’s ratios of the AC mix (whichwas assumed constant at all
temperatures) increases as the stiffness of the AC decreases. This also

affects the state of stress in the base layer (see Chapter 6).

285

Table 7.3. Backcalculated layer moduli for selected

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

pavement sections.
Pavement Pavement Backcalculated moduli
section temp. (F) (psi)
AC Base Roadbed
56 421429 68053 49339
57 442388 64732 47933
59 430099 64580 47642
MSU19F 80 390032 67622 46814
86 367670 69960 46359
89 339443 70747 47287
97 333389 68595 47038
100 302871 69506 46253
56 878214 54197 30674
57 871973 53457 30654
MSU13F 58 867489 53876 31080
64 857004 53156 30535
75 745520 55459 30882
87 617385 55191 30426
78 1210232 29806 30562
86 1 128475 30243 30834 -
96 1004659 31229 31246
MSU52F 101 916238 32908 31634
109 833275 34108 31653
114 807198 34108 31958
120 751909 35564 31638
122 730563 36920 31881

 

 

 

 

 

 

 

 

 

 

 

 

 

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Therefore an increase in the AC temperature causes a decrease in its modulus and

indirectly causes the base modulus to increase.

7.2.2 Flexible Pavement Section MSU13F - Temperature Variation

The NDTs were conducted on a cloudy day and under a light rainfall. The
pavement deflections measured at different sensor locations are listed in Table 7.4.
Once again the deflections measured at the lowest temperature (57 °F) were taken as
reference values and the percent variation in the deflections at the other temperatures
were calculated and are listed in Table 7.5 and shown in Figure 7.5. Examination of

Figure 7.5 indicates that:

1. Sensor 1 deflection increases consistently with rising temperatures.

2. Sensor 6 consistently registered lower deflections with higher
temperatures.

3. The deflections at all other sensors are erratic and do not display a

consistent change with temperature.

Comparison of the response of the previous pavement (MSU52F) and this
pavement indicates that the way in which the two pavements spread the load is
different and depends on the AC stiffness and on the temperature range. The
thicknesses of the two pavement sections are'almost the same. However, MSU52F
had a higher original stiffness, having been constructed to study the characteristics of
Stone Mastic Asphalt (SMA) mixes. Hence, there is a difference in thebasic AC mix
properties of the two pavements.

The backcalculated layer moduli are presented in Table 7 .3 along with the
results of the other pavement sections and the variation in backcalculated AC modulus
with temperature is shown in Fig 7.6. The rate of change of the AC modulus with

temperature is about 8415 psi per °F. The base modulus increased by a modest

289

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 7.4. Deflection variation with temperature for pavement section
MSU1 3F.
Pavement Deflections at different sensor locations (mils)
temp. (F) 1 2 3 4 5 6 7
56 8.87 6.85 5.53 4.12 3.18 2.09 1.28
57 8.92 6.93 5.58 4.14 3.19 2.09 1.29
58 8.85 6.87 5.49 4.09 3.14 2.06 1.27
64 8.92 6.95 5.54 4.13 3.18 2.08 1.28
75 8.97 6.84 5.41 3.99 3.08 2.04 1 .26
87 9.35 7.07 5.52 3.97 3.08 2.03 1 .29
Table 7.5. Percent variation in deflections from lowest temperature
recorded for pavement section MSU13F.
Pavement Variation at d'rflerent sensor locations (%)
temp. (F) 1 2 3 4 5 6 7
57 0.56 1.12 1.03 0.57 0.31 -0.32 0.52
58 -0.30 0.34 -0.72 -0.65 -1.15 -1.59 -1.30
64 0.49 1.41 0.18 0.32 0.00 -0.64 0.00
75 1.09 -0.19 -2.17 -3.00 ~3.14 2.71 -1.56
87 5.37 3.26 -0.18 -3.56 -3.14 -2.87 0.78

 

 

 

 

 

 

 

 

 

 

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1.83% over the same temperature range. The roadbed modulus, on the other hand is
not affected by the AC temperature. The backcalcualated results seem to be consistent

with the observed deflections.

7 .2.3 Flexible Pavement Section MSU19F - Temperature Variation

This section has a greater AC thickness than the previous two sections and has
a lower distress than MSU13F. The range of temperature during which the FWD tests
were conducted is 56 to 100 °F.

The deflections recorded at different sensor locations and the test temperatures
are listed in Table 7.6. Once more, the deflections measured at the lowest
temperature (56 °F) were taken as reference values and the percent variation in the
deflections measured at other temperatures were calculated and are listed in Table 7.7

and shown in Figure 7.7. It can be seen that:

1. The deflections of sensors 1, 2, 3, 6, and 7 increased with increasing
temperatures.
2. The deflections for sensors 4 and 5 initially increased with increasing

temperatures and then decreased.

The backcalculated moduli are presented in Table 7.3. Variations in the AC
modulus are illustrated in Figure 7.6 along with the results of the other two pavement
sections. The rate of change of the AC modulus with temperature is about 2695 psi
per °F. The base and roadbed moduli remain almost unaffected by the pavement
temperature.

Temperature, deflections, and the backcalculated moduli for the three
pavement sections have a wide variation of trends and ranges. Although the data is
limited, some of the trends observed can be summarized as follows:

1. The effect of the AC temperature on its modulus increases with decreasing AC

Table 7.6. Deflection variation with temperature for pavement section

293

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU19F.

Pavement Deflections at different sensor locations (mils)

temp. (F) 1 2 3 4 5 6 7
56 7.14 5.05 3.85 2.72 2.03 1.28 0.80
57 7.21 5.14 3.99 2.82 2.08 1.32 0.82
59 7.24 5.23 3.98 2.81 2.10 1.31 0.83
80 7.33 5.19 3.95 2.77 2.08 1.31 0.85
86 7.34 5.13 3.89 2.73 2.06 1.30 0.86
89 7.42 5.05 3.82 2.66 2.01 1.28 0.84
97 7.54 5.22 3.88 2.69 2.03 1.30 0.84
100 7.74 5.17 3.89 2.69 2.02 1.31 0.85

Table 7.7. Percent variation in deflections from lowest recorded

temperature for pavement section MSU19F.

Pavement Variation at different sensor locations (946)

Temp. (F) 1 2 3 4 5 6 7
57 1.027 1.7162 3.8126 3.672 2.6314 3.394 1.6606
59 1.4006 3.6303 3.3795 3.0602 3.7826 2.3499 2.9054
80 2.6144 2.7723 2.6862 1.7137 2.4671 2.8715 5.8096
86 2.7545 1.5842 1.1264 0.3672 1.6446 2.0882 7.4689
89 3.9216 0.0659 -0.693 -2.203 -0.823 0.2608 4.1502
97 5.5556 3.3004 0.8665 -1.346 0 1.8274 4.1502
100 8.4034 2.3762 1.213 -1.346 -0.165 2.8715 5.395

 

 

 

 

 

 

 

 

 

 

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thickness, and decreasing pavement distress.
2. For the same AC temperature, the pavement behavior under a cooling cycle is

different than that under a warming cycle.

Unfortunately, the above observations cannot be stated with a good degree of
confidence because of the limited data. Consequently, it is recommended that
additional tests be conducted on various pavement sections. The results of these tests
should enable MDOT to establish temperature and seasonal correction factors.

The applicability of the Asphalt Institute (AI) temperature correction procedure
for the AC modulus and the AASHTO method to impart temperature correction to the

peak deflection (Do) to Michigan pavements are examined in the next subsection.

7.3 THE ASPHALT INSTTTUTE TEMPERATURE CORRECTION
PROCEDURE
Temperature correction to the AC modulus was performed using the AI

Equation introduced in Chapter 2 and repeated here for convenience:

1 1 r,_
logEo=logE+Pm[-(Z); -W] +o.ooooos,/P:[(:,) (0'1

t " r
-.m189fi[%-%1+.9317[i5;-;n1
where l = 0.17033;
n = 0.02774;
E = backcalculated uncorrected modulus;
at, = test and reference temperatures in °F;

fJL = loading and reference frequency in Hz;

 

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The

lem

lam

296
= percentage of asphalt cement in the mix;

= the corrected modulus;

,0 = 1.3 + 0.49825 log (f0):
, = 1.3 + 0.49825 log (t); and
page = the percent aggregate Passing the ”0' 20° Sieve'

For all test sites and measured temperatures, the following data were used in
calculating the AI correction factors:

1. P

at

= 7 percent (the average percent frne content in the AC mixes),
2. f= fo = 25Hz; and
3. to = 77 °F.

The calculated AI temperature correction factors are listed in Table 7.8.

Table 7.8 also provides a list of the backcalculated AC modulus and the ratios
of the backcalculated value at the reference temperature 77°F to that at any other
temperature. Figure 7.8 depicts these calculated ratios and the computed AI correction
factors plotted against the temperature. It can be seen that:

l. The AC mixes encountered in the three pavement sections are less

sensitive to temperature changes than predicted by the AI equation.

2. Thin pavement sections are more sensitive to the AC temperature than thick

sections.

The first observation could be related to the asphalt grades used in Michigan
pavements (softer asphalt grades are typically used in colder regions). The second
observation was expected because the average temperature of a thin pavement is
higher than that for a thick pavement. That is, for a thick pavement section, more

time is required before the temperature at the bottom of the AC starts to increase due

297

Table 7.8. Observed and Asphalt Institute AC modulus temperature

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

correction factor.
Pavement Pavement Backcalculated AC modulus The Al
section temp (F) and ratios correction
Modulus (psi) Ratio factor
56 421425 0.937 0.463
57 442388 0.893 0.503
59 430099 0.918 0.524
MSU19F 77 395000 - 1.000 1.000
80 390032 1.013 1.137
86 367670 1.074 1.443
89 339443 1.164 1.558
97 333389 1.185 2.386
100 302871 1.304 2.586
56 878214 0.816 0.532
57 871973 0.822 0.546
58 867489 0.826 0.562
64 857004 0.836 0.691
MSU13F 75 745520 0.961 0.950
77 716667 1.000 1.000
87 617385 1.161 1.406
77 1313886 1.000 1.000
78 1289605 1.019 1.028
86 1095356 1.200 1.292
96 879087 1.495 1.786
MSU52F 101 759447 1.730 2.070
109 631174 2.082 2.841
114 546395 2.405 3.430
120 443078 2.965 4.228
122 408521 3.216 4.504

 

 

 

 

 

Note: Ratio = Modulus @ measured temp./ Modulus @ 77 F

 

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to increasing surface temperatures.

7.4 THE AASHTO TEMPERATURE CORRECTION PROCEDURE

The 1990 AASHTO Guide for the design of pavement structures introduces the
concept of composite pavement stiffness (Ev) to be determined from NDT data. The
Direct Structural Capacity Method (explained in Appendix L of the guide) requires
the value of E, to be determined along the length of the design project. The guide
further recognizes the fact that the AC stiffness changes significantly with
temperature. Since the peak deflections (D0) are the only information from the NDT
data used to calculate E,, the guide calls for correcting the D, values only. The
reference temperature suggested in the AASHTO method is 68 °F, which is consistent
with the one used in part II of the guide to determine the effective structural number
(SNdf) of the pavement. Further, the AASHTO Guide provides temperature correction
charts. The charts were derived by using the Asphalt Institute equation along with an
elastic layer analysis.

Table 7.9 provides a list of the peak deflection data measured at all 3 sites at
the various test temperatures and Figure 7.9 shows a plot of these. The ratios of the
peak deflection at 68°F (the reference temperature) to that at any other temperatures
are also listed in the table along with the corresponding AASHTO temperature
correction factors. Figure 7.10 shows a comparison of these ratios and the AASHTO
factors. It can be seen that:

1. The trend in the ratios of the measured deflection at the reference temperature
to that at any other temperature is similar for all three pavements.
2. The three pavement sections are less sensitive to temperature variations than

predicted by the AASHTO method.

The above two observations are similar to those presented in the previous

 

11]

 

300

Table 7.9. Observed and AASHTO temperature correction factors for Do.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pavement Pavement Measure deflections and The AASHTO
section temp. (F) ratios correction
Deflections (mils) Ratios factor
56 7.14 1 .020 1 .094
57 7.21 1.010 1.099
59 7.24 1 .006 1 .074
68 7.28 1 .000 1 .000
80 7.33 0.993 0.906
MSU19F 86 7.34 0.992 0.857
89 7.42 0.981 0.846
97 7.54 0.966 0.798
100 7.74 0.941 0.797
56 8.87 1 .008 1 .081
57 8.92 1 .002 1 .078
58 8.85 1 .010 1 .059
MSU13F 64 8.92 1 .002 1 .028
68 8.94 1 .000 1 .000
75 8.97 I 0.997 0.933
87 9.35 0.956 0.962
68 9.82 1 .000 1 .000
78 10.23 0.960 0.860
86 10.56 ' 0.930 0.813
96 10.96 0.896 0.805
MSU52F 101 1 1 .08 0.886 0.784
109 1 1 .4 0.861 0.787
114 11.8 0.832 0.762
120 12.23 0.803 0.541
122 12.23 0.803 0.541

 

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1. I

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303 ,
section. This suggests that the trend of the deflection data with temperature is similar
to that of the backcalculated AC modulus. Hence the accuracy of the backcalculation

is confirmed once again.

7.5 SUMMARY AND RECOMMENDATIONS
The data available to examine the validity of two suggested temperature

correction methods was limited to three pavement sections only. Based on the

analysis, the following conclusions are made:

1. The pavement behavior during the warming cycle is different than that
during the cooling cycle. Hence, different temperature correction
methods should be devised for the two cycles.

2. The three pavement sections included in this temperature correction
study showed less sensitivity to temperature than that predicted by the
AI and the AASHTO methods.

3. It appears that the temperature correction factors should include other
pavement characteristics (such as AC thickness and stiffness, and
asphalt grade) that are not part of the AI and the AASHTO methods.

4. The NDTs should be expanded to include more pavement sites than

those included in this limited study.

 

8.1

mi
thal

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CHAPTER 8

SUMIWARY, ACCOMPLISHNIENTS, CONCLUSIONS
AND RECOMIVIENDATIONS

8.1 SUMMARY
The continuous investment required to design, rebuild, rehabilitate, and

maintain the nation’s transportation infrastructure presents a major and complex task

that challenges the ingenuity of every highway administrator and engineer. The
infrastructure problems cannot be solved by simply studying pavement conditions and
taking corrective actions. Accurate and comprehensive evaluation of the pavement
structural capacity and their rates of deterioration allow the decision makers to direct
the investment where nwded and to properly select and schedule rehabilitation
activities.

The accurate evaluation of the pavement structural capacity requires a
balanced, accurate, robust, comprehensive, and mechanistically-based computer
program for the analysis of the nondestructive deflection test (NDT) data. The
problem associated with such analyses is that existing state-of-the-art cOmputer
programs are often not accurate and, for most programs, the accuracy of their
solutions is dependent on the initial estimates specified by the user. The inaccuracy of
the solution is mainly related to several important problems that affect the analyses of
the NDT data. These problems include:

1. For most pavement structures, the deflection of the roadbed soil due to an
applied load represents the bulk of the measured deflection data. Hence, an
accurate estimate of the roadbed stiffness at the onset of the analysis can
significantly increase the accuracy of the estimates of the stiffnesses of the

other pavement layers.

304

305
The thickness of the roadbed 305 (or the depth to a stiff layer) is typically not
known. Erroneous estimates of this depth causes substantial errors in the
solutions. Thus, an accurate estimate of the stiff layer depth based on the
mechanical behavior of the pavement system should be obtained as a part of
the overall analyses.
The pavement cross-section varies from one point to another. Variations in the
thickness of the asphalt concrete layer causes significant errors in the solution.
Consequently, a mechanistic routine whereby this thickness can be corrected
should be a part of the analyses of the NDT data.

These and other problems were extensively examined during the course of this

study and solutions were obtained and implemented in a computer program named

MICHBACK. The accomplishments of this study are summarized in the next section.

8.2

ACCOMPLISHMENTS

Several major accomplishments have been achieved in this research study and

they are implemented in the MICHBACK computer program. These include:

1.

A new algorithm to accurately predict the roadbed modulus at the onset of the
analysis (after only one call to a mechanistic analysis program) has been
developed, tested, and implemented.

An algorithm using the modified Newton method. to backcalculate layer moduli
and layer thicknesses has been developed, tested, and implemented.

The Newton’s method has been successfully extended to mechanistically
calculate the stiff layer depth from deflection data. Hence, one of the major
shortcomings of existing backcalculation programs has been eliminated.

The sensitivity of the backcalculated layer moduli of flexible pavements to the
user’s initial estimates (seed moduli) has been minimized.

User friendly-features have been developed and implemented in MICHBACK.

8.3

306
These features are designed not only to facilitate the use of the program, but
also to encourage user interaction in the backcalculation process which is felt

to be essential for obtaining meaningful results.

CONCLUSIONS
Based on the analysis of the theoretical and field measured deflection data, on

an exhaustive testing of the MICHBACK program, and on a comprehensive

comparison of the results of MICHBACK with those of other programs, the following

conclusions were drawn:

1.

The new algorithm that has been developed to predict the stiffness of the
roadbed soil at the onset of the analysis by using only one call of the
mechanistic analysis produces very accurate results.

The algorithm using the Newton’s method that has been developed to
mechanistically predict the stiff layer depth is accurate.

The MICHBACK computer program is capable of correcting an erroneous
estimate of any one layer thickness and of accurately estimating the moduli of
the pavement layers.

Poisson’s ratios of the different pavement materials affect the accuracy of the
backcalculated results. Hence, for each material, a range of Poisson’s ratio
must be known and used with caution to achieve good results.

The effect of inaccuracies in the deflections measured by those sensors located
close to the loaded area on the backcalculated results is higher than those
measured by the other sensors.

The original CHEVRON and ELSYM5 computer programs produce deflection
basins that can be significantly different than those produced by the respected
BISAR program (which is considered a very accurate computer program). This

discrepancy increases with an increase in the stiffness of the pavement.

10.

11.

307
Although only limited deflection and temperature data were available in this
study, preliminary results indicate that the Asphalt Institute (AI) and the
AASHTO temperature correction methods have very limited applicability to
the measured deflection basins. Further, results of the limited analysis of the
NDT data obtained from those flexible pavements included in the study
showed that the asphalt concrete layer may be less sensitive to temperature
variations than those advocated by the AI and the AASHTO methods.
The measured deflection basins and the backcalculated results appear to be
affected by the magnitude of the applied load. However, the exact cause of
this effect could not be accurately determined or generalized for all pavement
sections. Possible causes of system nonlinearities could be related to load
magnitude, Poisson’s ratios, and dynamic effects.
For any one pavement section, the variation of the backcalculated results
obtained with MICHBACK from one station to another is compatible with the
variation in the measured deflection basins.
The analysis of composite pavements is a difficult task compounded by the
unknown state of distress of the PCC slabs.
Comparison of the backcalculated results obtained using MICHBACK with
those obtained from other programs indicates:
a) For pavements where a stiff layer is encountered, the
results from MICHBACK are significantly better than
those obtained with the other programs.
b) For flexible pavements with a very deep stiff layer, the results from
MICHBACK are similar to those obtained with the other programs.
The increased accuracy of the results from MICHBACK becomes
noticeable as the number of layers increase.

c), For composite pavements, the results obtained with MICHBACK are

 

 

8.4 I

I
the follc
l.

 

8.4

308
significantly better than those of the other programs.
d) The performance of MICHBACK, measured in terms of the number of
calls made to a mechanistic program, is slightly better than that of the

EVERCALC 3.0 (which is known for rapid convergence).

RECOMMENDATIONS FOR FUTURE RESEARCH

Based on the results, accomplishments, and conclusions of this research study,

the following recommendations are made:

1.

The effect of Poisson’s ratios on the backcalculated results should be examined
in more detail. The feasibility of estimating some of the values of Poisson’s
ratios from the deflection data should be explored.

The effect of the asphalt concrete temperature on its modulus and on the
measured deflection data should be examined in more detail to establish more
dependable temperature correction functions.

The effects of seasonal variations on the backcalculated results and on the
measured deflection basins should be undertaken as a part of a long term
pavement performance (LTPP) study.

The MICHBACK computer program uses a linear elastic multilayer analysis
program (CHEVRONX). The extent and causes of the apparent nonlinearity
observed in the measured deflection data should be further investigated.

The user-friendly features of MICHBACK are similar to those of MICHPAVE
(a linear and nonlinear finite element elastic layer program for the analysis and
design of flexible pavements). The two programs enable the MDOT and other
users to perform forward and backward analyses. However, the MDOT
capability for the design of an overlay is very much limited to experience, a
standard overlay thickness, and existing empirical procedures. It is strongly

recommended mechanistic-based overlay design program be developed as an

309
integral part of MICHBACK. This development will have a major contribution
to the capability of MDOT to perform mechanistic analysis, design, and

evaluation of their pavement structures.

 

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R

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h Cu Cu ‘5

 

 

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