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PILE FOUNDATION DESIGN: IN TERRELATION OF
SAFETY MEASURES FROM DETERMINISTIC
AND RELIABHJTY-BASED METHODS

by

Rosely Bin AbMalik

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

1 992

ABSTRACT

PILE FOUNDATION DESIGN: INTERRELATION OF
SAFETY MEASURES FROM DETERMINISTIC
AND RELIABILITY-BASED METHODS

BY

Rosely Bin AbMalik

An algorithm is developed to interrelate the basic
concepts and procedures commonly used in deterministic design
of axially-loaded piles in cohesionless soil with
reliability—based design methods. The derivation of the
algorithm, uses the commonly‘ accepted "standard" static
formula (Beta-Method) and the in-situ soil exploration data
from Standard Penetration Test (SPT).

For the determination of the allowable capacity (C5) in
the design of a single pile foundation, safety measures are
frequently’ applied tn) the jpredicted capacity HQp). To
determine Q3, this study presents the interrelationship
between the conventional deterministic safety measure (Factor
of Safety, FS) and reliability-based safety measures (Central
Factor of Safety, CFS, Reliability Index, [3, and the
Probability of Failure, Pk) within a systematic and rational
framework. Interrelation equations and design charts are
derived and calibrated from 23 pile loading tests, 11 of
which are on instrumented. piles. Consequently, at the
recommended FS or B, the value of (5 can be determined and
interpreted In! either'rdeterministic cm‘ reliability—based

approaches.

DEDICATION

To ayah, Haji Daud Mamat

(may your soul rest in peace under His mercy)

The constant memory of
your wisdom and vision to
excel (worldly and hereafter)

has helped me accomplish this
study.

To my parents, "... My Lord! Bestow upon them mercy

as they pampered me since childhood."
(Quran: 17,24).

To my dearest wife, N. Hasimah; daughter, Siti

Muhammad Firman; daughter,
Nurrasyila; and the baby to come.

Nurrasyida; son,

who patiently endure
riding the troughs and crests
of the dissertation wave.

May the Almighty make this world

a "greener" place to live in - Amin!

iii

ACKNOWLEDGMENTS

My deep gratitude goes to the chairman of my doctoral
committee, Dr. Thomas F. Wolff, who broadened my avenue to
research in reliability methods. His subtle suggestions,
advice and encouragement were invaluable assets towards the
completion of this research. My appreciation is also extended
to the rest of Im/ conmdttee :members; Dr. Orlando B.
Andersland, Dr. Parviz Soroushian, and Dr. Roy V. Erickson
for their cooperation and support.

It would be impossible to acknowledge all of the people
who have contributed in the ultimate completion of this
dissertation. Nevertheless, I would like to acknowledge the
many individuals and agencies that contributed in various
ways to this study.

The study was made possible by scholarships provided by
the Malaysian Government through Jabatan Perkhidmatan Awam
and the Universiti Sains Malaysia. The cooperation of their
staff if; greatly' appreciated. .Also, 12 would. like to
acknowledge the Department of Civil and Environmental
Engineering’ at time Michigan, State ‘University for the
facilities provided.

Finally, I wish to thank my family members for years of
constant love and support, and for the neglect subjected

during this research.

iv

TABLE OF CONTENTS

CHAPTERS

1 INTRODUCTION

2

ea hsia +4 P’ié

O'NU'irbbJNH

Introduction ...................................... 1
Background ........................................ 2
Objectives ........................................ 5
Scope and Limitation .............................. 7
Definition of Capacity ............................ 8
Organization ...................................... 9

DETERMINISTIC ANALYSIS AND DESIGN

NNNN

\INNmmN

NQWNH

Introduction ...................................... 12
Capacity Prediction ............................... 13
Deterministic Analysis ............................ 21
Standard Method in Sand ........................... 23
.4.1 Shaft Resistance ............................... 26
2.4.1.1 The value of K. ............................ 27
2.4.1.2 The value of 5 ............................. 30
.4.2 Toe Resistance ................................. 32
Design Practice: Limits and Corrections ............. 35
Field Testing ....................................... 40
.6.1 Standard Penetration Test ...................... 41
.6.2 Other Methods .................................. 47
Summary ............................................. 48

INTERPRETATION OF PILE LOADING TEST

3.
3

l
.2

Introduction ...................................... 49

Description of Axial Pile Loading Test ............ 49

V

 

 

3.3 Interpretation of Load Test ....................... 50
3.3.1 2 inch Movement Failure Criterion .............. 54
3.3.2 Davisson's Failure Criteria .................... 54

3.4 Limitations of Davisson's and Chin's Criteria ..... 59

3.5 Separating Shaft and Toe Capacity ................. 62

3.6 Summary ........................................... 65

4 RELIABILITY THEORY IN ENGINEERING

l
.2
4.3
4

4

Uiibibibiblbww

Introduction ...................................... 66
Previous Work ..................................... 67
Structural Reliability Theory ..................... 69
.1. Historical Background .......................... 69
.2 Formats of Reliability Theory .................. 71
3.2.1 Stochastic ................................. 72
.3.2.2 Full Distribution .......................... 72
3.2.3 First Order Second Moment .................. 75
3.2.4 Load and Resistance Factor Design .......... 80

Pile Design: Safety Measures ................... 82

Summary ........................................ 86

5 DEVELOPMENT OF THE ALGORITHM

l
2
5.
5.
5.
3
5.

Introduction ...................................... 87

Data Base ......................................... 89
2.1. Site at Ogeechee River ......................... 89
2.2 Locks and Dam No.4 ............................. 91
2.3 Peck's Collection .............................. 92

The Algorithm ..................................... 93
3.1. Basic Concepts and Assumptions ................. 94
5.3.1.1 Deterministic Formula: QSC & th ............ 94
5.3.1.2 Coefficient of Lateral Earth Pressure: K... 95
5.3.1.3 Soil-Pile Interface Angle: 5 ............... 96
5.3.1.4 Corrected N-Value: N' ...................... 96

vi

6

5.3.1.5 Friction Angle of Soil: ¢ .................. 96
5.3.1.6 Modified Bearing Capacity Factor: N: ....... 97
5.3.1.7 Effective Overburden Earth Pressure: Dev... 97
5.3.1.8 Capacity from Loading Test: Cb, ............. 97
5.3.1.9 Safety Measures: FS & B .................... 98
5.3.2 The Developed Procedure ........................ 101
5.3.2.1 Predicted Capacity: Qp ..................... 101
5.3.2.2 Interrelation of Safety Measures: FS & B... 107
5.3.3 iDetermination of Calibration Parameters ........ 113
5.3.3.1 Equations of Toe Capacity Ratio: Rt ........ 114
5.3.3.2 Shaft and Toe Factors: Pg & Ft .............. 116
5.3.3.3 Bias Factor and Site Variability: Fb & S... 121
5.3.4 Importance of F5 and S .......................... 126
5.3.5 Safety Measures: FS and B ...................... 128
5.4 Summary of The Algorithm .......................... 133
5.4.]. Implied Assumptions ............................ 133
5.4.2 Recommended Calibration ........................ 134
5.4.2.1 Values of Rt, FS & Ft: for Qp ............... 134
5.4.2.2 Values of F1, and S: for Q8 .................. 134
5.4.2.3 Values of FS and B: for Safety Measures.... 135
5.4.2.4 Design Charts .............................. 138
.4.3 Allowable Capacity ............................. 138
5.5 Summary ........................................... 143

TESTING OF THE ALGORITHM

6.1 Introduction ...................................... 145
6.2 Testing of the Algorithm .......................... 145
6.2.1 Typical Example: Pile Test No.26 ............... 148
6.2.1.1 Calculated Capacity: Standard Formula ...... 149
6.2.1.2 Measured Capacity: Loading Test ............ 151
6.2.1.3 Predicted Capacity: The Algorithm .......... 152
6.2.1.4 Design: Deterministic Approach ............. 153
6.2.1.5 Design: Reliability-Based Approach ......... 154

vii

 

 

6.2.1.6 Allowable Capacity: Unknown Loading Test... 155
6.2.1.7 Design: Using The Chart .................... 156
6.2.2 Site at Northwestern University ................ 159
6.2.3 Site at Kansas City ............................ 161
6.2.4 Site at Locks & Dam No.4 ....................... 162
6.2.5 AISI Collection ................................ 163
6.2.6 Site at Locks and Dam No.25 .................... 166
6.3 Discussion of Results ............................. 167
6.3.1. Predicted, Allowable & Measured Capacities ..... 167
6.3.2 Deterministic Vs. Reliability—Based Design ..... 170
6.3.3 'The Algorithm Vs. Previous Studies ............. 177
6.3.3.1 Site at Northwestern University ............ 177
6.3.3.2 Site at Kansas City ........................ 183

6.4 Summary ........................................... 185

7 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

1 Summary ........................................... 186
2 Conclusions ....................................... 188
7.2.1. Predicted Capacity ............................. 189
7.2.2 Safety Measures ................................ 190
7.3 Recommendations ................................... 192
7.3.1. Application of the Algorithm ................... 192
7.3.2 Further Research ............................... 193
APENDICES
It Measured Capacities From Load-Movement Curves ........... 195
I3 A Typical Spreadsheet Calculation, Pipe Pile No.26 ...... 217
C: Determination of Allowable Capacity ..................... 221
I) Measured and Predicted Capacities, Pipe Pile ............ 241
REFERENCES ................................................ 243
viii

———___g

LIST OF FIGURES

FIGURE
1.1 Pile Terms and Definitions. ......................... 11
3.1 Interpretation of Pile Loading Test by

Nine Failure Criteria (After Fellenius, 1980). . 53
3.2 Interpretation of Pile Loading Test,

Davisson's Failure Criteria. ...................... 55
3.3 Interpretation of Pile Loading Test,

Chin's Failure Criteria. ......................... 58
3.4 Distribution of Resistances Along Pile Shaft. ........ 64
4.1 The Model of Performance Function. ................... 78
4.2 Safety Measures - Normally Distributed FOSM

Design. ........................................... 85
5.1 Deterministic and Reliability Models for Safety

Measures. ......................................... 100
5.2 The Schematic of Interrelation Model, Deterministic

and Reliability-Based Approach. .................. 112
5.3 Development of RtFunctions Using 11 Instrumented

Piles. ........................................... 115
5.4 Correction Factors For Shaft and Toe — Pg & Fp ....... 118
5.5 Design Chart - For Constant

Rate of Penetration Test Type (CRP). ............. 140
5.6 Design Chart — For Constant Load Test Type (CL). ..... 141
5.7 Design Chart — For Unknown Loading Test (NLT). ....... 142
6.1 Measured Capacities - Steel Pipe, Pile No.26. ....... 149
6.2 Design By Chart - Davisson's Criteria [D] ............ 158
6.3 Predicted Capacity - The Algorithm Vs.

Measured Capacity. ................................ 176
6.4 Predicted Capacity - The Algorithm Vs.

Other Predictors. ................................. 182
2\ Measured Capacities From Load—Movement Curves ........... 195

ix

 

TABLE

2.

1

LIST OF TABLES

Analytical Equations Used By 24 Predictors

(After Finno et al, 1989c). ....................... 15
Parameters for Analytical Methods Used By 24

Predictors (After Finno et al, 1989c). ............ 17
Typical Coefficient of Lateral Earth Pressure, K”.... 28
Typical Soil Pile Interface Angle, 8. ................ 31

Recommendation of Limiting Shaft and Toe

Resistances by API (1991). ........................ 39
Data Base For The Development of The Algorithm. ...... 93
Equations for R“ I% and FtFactors. .................. 120
The Three Schemes Examined For The Determination

of Calibration Factors — Fb, and S. ................ 122
Bias Factor and Site Variability. .................... 123
The Recommended Functions For Rt, Fs and Ft for Qp. . . .. 136
The Recommended Values of Pb and S for

the Determination of C5. ........................... 136
The Recommended B and F8 for The Deterministic

and Reliability-Based Approaches. ................. 137
Pile Loading Test Data — Illustrative Example. ....... 147
Typical Spreadsheet Calculation, Pile No.26. ......... 151
Typical Output of Allowable Capacity - Pile No.26.... 151

Summary of C5 and Safety Measures From

The Algorithm ..................................... 172
Allowable Capacity - The Algorithm Vs.

Previous Study. ................................... 184
A Typical Spreadsheet Calculation, Pipe Pile No.26... 217
Determination of The Allowable Capacity .............. 221
Measured and Predicted Capacities, Pipe Pile ......... 241

X

CHAPTER 1

INTRODUCTION

1.1 Introduction

.A considerable number of pmobability (n7 reliability
models have been proposed over the years that can be applied
in geotechnical engineering. For example, statistical
approaches have been applied for more than two decades to
model physical characteristics of soils, to recommend number
of soil tests, and t1) quantify characteristics CHE soil,
earthwork, slope stability, settlements and. the Ibearing
capacity of pile foundations (e.g., Zlatarev, 1965; Langejan,
1965; Lumb, 1966; Holtz and Krizek, 1971; Kay, 1976; Kay,
1977; Evangelista et al, 1977; Madhav and Arumugum, 1979;
Biarez and Favre, 1981; Jaeger and Bakht, 1983; Sidi and
Tang, 1987 Rethati, 1988; Alonso and Krizek, 1975; Wolff,
1989; and Wolff and Wang, 1992).

The determination of the allowable capacity for pile
foundations run! be done in! two approaches, namely; the
deterministic (conventional) and reliability-based
(probability) approaches. From a practical standpoint, the
conventional method produces satisfactory designs; and with
few reported failures. Alternatively, design by a
reliability—based approach may provide more information; but

have its own limitations, and the methods are not generally

 

 

understood by designers. Consequently, pile foundations are
not routinely designed by the reliability—based approach. At
present, reliability methods remain largely tin: research
purposes; and today there is 1M) code available tx) guide
design engineers. However, with recent improvement in
reliability theories and with an increase in computational
efficiency, reliability methods continue to gain acceptance
and are expected to be the trend in future.

The algorithm developed in this study could serve as a
bridge Ibetween. these tn“) approaches. It if; a combined
deterministic-reliability approach that is easily used by
design practitioners, while at the same time, is capable of
accommodating the conventional principles.

This study will focus on a practical combined
application of the deterministic and reliability approaches

rather than on the validity of their theories.

1.2 Background

Engineers are faced with the challenge of designing safe
but yet economically feasible structures. For the design of
pile foundations large uncertainties are involved; such as,
soil properties and conditions, applied loads, pile material
properties, methods of construction, and including the choice

of design approaches. In general, the design of pile

foundations should ensure adequate safety measure against
potential failure. The appropriate safety measure depends on
the importance of the structures, possible losses in case of
failure, and the certainty of the information regarding soil
and environmental conditions. The evaluation of safety
measures is more complex in pile foundations as compared to
shallow foundations because of the larger uncertainty in the
soil-pile interaction; and the structure is likely to be more
expensive when piles are used (Bowles, 1988). For pile
foundations, the factor of safety commonly recommended in
practice ranges from 2.0 to 4.0, depending on local practice
and the level of "designers' uncertainties" (e.g., Peck et
a1, 1974; Meyerhof, 1976a; Fuller, 1978; Poulos and Davis,
1980; Poulos, 1981; McClelland and Reifel, 1986; Tomlinson,
1986; Bowles, 1988).

Over the years, many deterministic methods have been
proposed for calculating or estimating the axial capacity of
a single pile foundation. Static formulas were established
using the accepted theory of soil mechanics, often verified
and calibrated with the "true" or “actual" capacity measured
from the full scale loading tests (e.g., Meyerhof, 1951;
Berezantsev, 1961; Vesic, 1963; Nordlund, 1966; Coyle and
Reese, 1966; Housel, 1966; Olson and Flaate 1967;
D'Appolonia, 1968; Meyerhof, 1976a; Coyle and Castello, 1981;
Kulhawy, 1984; Dennis and Olson, 1985; Focht and Kraft, 1986;

McClelland and Reifel, 1986; API, 1991; and Coyle and Ungaro,

1991). Alternatively, the capacity of a pile may also be
estimated from dynamic formulas from the driving data by
using concepts from dynamics. Recently, a more rigorous
method that is becoming more acceptable with improved
computing capabilities is estimating pile capacity using the
one dimensional wave equation (e.g., Smith, 1960; Samson et
al, 1963; Housel, 1966; Lowery et al, 1969; Rausche and
Goble, 1985; Goble and Rausche, 1986; Likins and Rausche,
1988).

Nevertheless, all three approaches described above have
varying success (or limitations) in predicting the capacity
of a pile (e.g., Cheeks, 1978; Lawton et al, 1986). Despite
the many methods and numerous studies on the prediction (or
calculation) of pile capacities, for the most part, there is
still a large scatter between the estimated (analytical)
and the measured capacities from loading tests (e.g., Dennis
and Olson, 1985; Briaud and Tucker, 1988; Finno et al,
1989b). The large scatter might in fact be justification for
the use of a reliability-based method of design; analysis of
a large data set of rtflatively imprecise measurements may
yield more and better information than a few very precise
measurements in a highly variable material such as soil. As
envisioned by Schmertmann (1990), reliability-based methods
might be the trend in the future. However, the statistical
procedures in reliability—based approach demanded an

additional effort over the fundamental design principles of

pile foundation (e.g., Sidi, 1986; Sidi enui Tang, 1987;
Madhav and Arumugam, 1979; Kay, 1976; Kay, 1977). As such,
the design of pile foundation appears "too statistical" for a
practicing geotechnical engineer. Thus, this sfinmhr is an
attempt to interrelate some basic concepts from these two
approaches, within a systematic and rational framework.

In this study, the focus is on developing an algorithm
to interrelate the safety measures from the deterministic and

reliability-based approaches.

1.3 Objectives

The purpose of this study is to quantify the
interrelation of safety measures as defined by the
conventional deterministic and the reliability-based design
approaches for pile foundation design; i.e., the
interrelation of factor of safety (FS) and the reliability
index (B). Consequently, an algorithm is developed using
known design principles from both approaches.

For the development of the algorithm, a unique and
consistent procedure for the determination of the predicted
axial pile capacity (Qp) is needed. This is achieved by
following these specific procedures:

1. A repeatable, well-defined chain of steps is

developed to calculate the axial capacity of a pile

using data from the Standard Penetration Test (SPT)
N-values, derived from a typical "standard"
analytical formula.

2. The calculated. capacity' is calibrated against
"accurate" loading ‘tests tX) predict the axial
capacity; this systematic procedure also greatly
reduces the element of arbitrary judgment with
respect tn) the selection of tine appropriate soil
parameters to be used in the analytical formula.

3. The First Order Second Moment (FOSM) method is
applied from reliability theory for the development
of the algorithm; to interrelate the conventional
factor of safety (FS) with reliability measures,
the central factor of safety (CFS), the reliability
index (BL and the probability of failure (Pfl.

4. The developed algorithm (equations and charts) is

illustrated with typical examples.

Having obtained the predicted capacity ((5). the safety
measure used for the determination of allowable capacity (C5)
in the deterministic approach is the factor of safety (FS),
and the corresponding parameter in reliability—based approach
is the reliability index (B). From the developed algorithm,
the allowable capacity can in: flmnui and interpreted from

either time deterministic (n7 reliability' approaches. The

recommended safety measures (FS and B) in this study are the

ones that can also satisfy the minimum deterministic factor

of safety (i.e., FS=2.00) frequently suggested in practice.

1.4 Scope and Limitation

In this research, the predicted capacity (and
consequently allowable capacity) in cohesionless soil only is
considered. This is done by using data from the Standard
Penetration Test (SPT); and the neasured capacity (C59 .is
determined from the load-movement curves from instrumented
pile loading tests.

The correlation. of SHE? N—values 'with, the internal
friction angle of soil (o), may be considered to provide a
gross approximation an; compared t1) other in—situ soil
exploration methods. Nevertheless, the Standard Penetration
Test is the most commonly used method of in—situ soil
testing, and data are relatively easy to obtain. Since the
algorithni is developed from. the N-values, it is felt
justified to exclude any refinement to the "deterministic"
parameters in the algorithm. Therefore, related issues such
as the effect of residual stresses, sensitivity, degree of
consolidation (normally or overly consolidation state), etc.,
are not explicitly included. Rather, a random variable (Fb) is
introduced to calibrate the predicted capacity. Nevertheless,

the specific parameters obtained from the algorithm could

easily be modified to address those issues by using data from
other more rigorous testing methods and refinements [e.g.,
data from cone penetration test (CPT), or dilatometer test

(DMT) ].

1.5 Definition of Capacity

The terms "ultimate capacity" or "ultimate resistance"
used in many papers can be confusing, sometimes redundant and
useless although they can be understood. In this research,

the specific pile terms as suggested by Fellenius (1990) are

followed.

The terms such as "load capacity,“ “design capacity,"
"carrying capacity," or "failure capacity" are avoided.
"Capacity" (Q) is used as a stand. alone term and as 51

synonym to "ultimate capacity" or "ultimate load“ as found in
most literature; however, "resistance" is sometimes used in
place of the "capacity."

The "measured capacity“ (Qm) is reserved for capacity
evaluated from the results of a static loading test of piles
as defined. by specific criteria (e.g., Davisson's, or
Chin's). “Measured shaft" and "measured toe" capacity is then

represented by Qsm and th. respectively.

“Calculated capacity" (QM is defined as time capacity
calculated. from. static formula. "Calculated shaft" and
"calculated toe" are represented by QSC and Q“; respectively.

"Predicted capacity" (Qp) is the capacity after the
calibration of the "calculated capacity" (Ck) from the static
formula.

The “allowable capacity" (C5) is the value "allowed for
design"; i.e., after the "predicted capacity" «In Inns been

proportioned by the safety measures (FS or B)

Other related pile terms are as shown in Fig. 1.1.

1.6 Organization

Chapter 2 describes current methodology for the
"standard" procedure for the calculation (or estimation) of
axial pile capacity; it provides some background of methods
from deterministic approach. The important considerations and
critical elements for analysis and design of pile foundations
are described.

Chapter 3 describes several methods of interpreting the
measured capacity from full scale pile loading tests for
calibration with the calculated capacity. The presentation of
the methods of interpreting the measured capacity is limited

to the ones that are used in this study.

10

Chapter 4 summarizes historical and theoretical
background of engineering reliability theories that are
applicable for pile design from reliability-based approach.

Chapters 2 and 4 provide the theoretical basis for the
development of the algorithm derived in Chapter 5. Discussion
of the data base, calculation using a spreadsheet program, a
summary (M3 the recommended parameters, design pmocedure,
design charts, and the limitations associated with the
developed algorithm are also included in Chapter 5.

Application of the developed algorithm is illustrated
in Chapter 6, and observations are discussed.

Finally, Chapter 7 provides a summary and the
conclusions of this research. Potential areas of additional

research are also suggested.

 

 

 

 

 

 

Capacity, Q
HEAD
W V
4 i d = diameter of pile
4 P Le = embedment length
i g l
Le :I.‘

1 m P Shaft Capacity, Q.

J’ 4 PTOE

T T T Note :
Since both ends of the pile

could be the "tip". the use
of this term is avoided.

Toe Capacity, Q

 

 

Fig. 1.1: File Terms and Definitions.

 

CHAPTER 2

DETERMINISTIC ANALYSIS AND DESIGN

2.1 Introduction

This chapter presents the basic theory and the general
development CHE static formulas frequently used 1J1 design
practice for the analysis of axial pile capacity. Attention
is focused on the aspects of the theory and limitations that
form a general approach for the development of the algorithm
in Chapter 5.

Estimating accurate and reliable axial pile capacities
has remained a difficult and complex task. Over the years,
there has long been a need for a rational, consistent,
accurate and yet simple method to predict pile capacity. The
term "standard method" referred herein is the commonly
accepted procedure rather than a prescription from any
standard or code. The "standard" formula presented in Section
2.4, will form the general basis for comparison with loading
test (Chapter 3); and the interrelation of safety measures
derived in Chapter 5.

The difficulty in the prediction of axial pile capacity
is well demonstrated by several studies (Section 2.2) which
indicate the scatter of results between designers (and the
theoretical methods used). These studies reflect the state—

of—practice at this time.

12

13

Section 2.6 will briefly describe the principles of in—
situ soil exploration by the Standard Penetration Test (SPT).

From previous studies (Section 2.5.1) and due to other
various difficulties 1J1 predicting axial capacity, in
practice, limits auxa usually' imposed CH1 the calculated

capacity. In some cases, these limits are then used in codes.

2.2 Capacity Prediction

The soil-pile system is highly indeterminate structure,
therefore predicting pile capacity is aa complex task. pm
present, pile capacity is determined by: (i) analytical
formula based on emetics, (ii) numerical models based on
dynamic formulas, cnr wave equation. analysis, and (iii)
measurements and interpretations from loading tests.

It is well recognized that capacities calculated using
static formulas are approximabe. No rational procedure is
available to assist the designer in choosing the various
formulas and types of testing techniques. As such, local
experiences and engineering judgment remain a major component
of the process for determining pile capacity.

.As ea general practice, because ‘various degrees of
uncertainty are involved in both the analytical formulas and
testing techniques, the analytical predictions are
"confirmed" with full scale pile loading tests; especially so

for major projects. However, interpretation of tflue loading

14

test itself involves some degree of uncertainty (see Chapter
3).

A series (ME pile loading' tests ‘were conducted in
conjunction with time 1989 Foundation Engineering Congress
(Finno, 1989d). Information about the soil, foundation and
comparison of the predicted capacity of that study with the
developed algorithm in this research will be presented in
Chapter 6. using the same data, 24 geotechnical engineers
submitted a priori capacity predictions (as plotted in Fig.
6.4 for the pipe and H—pile only). The results of the a
‘priori prediction and loading tests were then compared in
Finno et al (1989c).

As shown in Table 2.1, there was a wide variation of
predicted capacities and methods used, depending on
participant's experience and judgment. In that study,
predictions of axial pile capacities were made with
conventional analytical methods, correlation vdtfii in—situ
test results, load transfer functions and fill one case ea

finite element simulation.

15

Table 2.1: Analytical Equations Used By 24 Predictors

 

 

 

(After Finno et al, 1989c).
PREDICTUR SHAFT ICE REFEREMDES USED
NLABER RESIST-AWE RESISTANCE BY PREDICTORS
(in Sand) (in Clay)
1 F. Ks tan (5)91). As (Ac S. + pee) Poulos 8 Davis, 1980
2 as qc RI/ No ab q. Bustamente et al, 1986
Kulhawy, 1983
3 (K/K.)K.,ran[(5/¢)¢,]e.. N. s. Tomlinson, 1957
KMhawy,1983
4 Km (8) pl. Su Meyerhof, 1956
2 fs q“
5 f-2 Curve Mosher, 1984
6 N / 50 Meyerhof, 1976
K tan (8) p... N. S“ Kulhawy, 1983
CPT Correlations
7 0.5 fs 0 Nottingham, 1975
FHWA 0 Reese & O'Neill, 1988
8 N/SO NC 8.. Meyerhof, 1976
9 K tan (6) 1.3 p'v. NC 8.. (not submitted)
10 CFl‘Correlations C De Beer, 1971/1972
SPT ‘ N. S.
1 1 K tan (8) pt. NC 8“ API, RP2A, 1987
I3 pie or limiting fs c .. Reese & O'Neill, 1988
1 2 limiting fs N. 8.1 Nottingham, 1975
Ktan (8)p'.. N. 3.. Reese & Wright, 1977
13 K (Sin (w + 5)/ Cos (w)) pi. N. s, Nordlund, 1930
14 (W) KaTtan (5M) ¢zpio 0 Poulos & Davis, 1980
0 Stas & Kulhawy, 1983
15 fs with SPT Ne Sn Coyle 8. Castello, 1981
6 pl. N. 8.. Reese & O'Neill, 1988
16 LCPC (qc/Ot)<<11 Azzouz 8 Baligh, 1984
17 Ktan(5) pL. (pipe pile) No S. Coyle & Castello, 1981
fs (PI-Pile) Ne Sn
1 8 K tan (¢i) pm 10 S. NA
1 9 K tan (5) p'... N. 8.. NA
20 SP1“ N/SO Meyerhof, 1976
‘1’ Correlation 0 Poulos & Davis, 1980
CPT fs Nottingham, 1975
21 I3 pl). N: DI. Canadian Fdn Engr Man, 1985
22 CPT fs N. S" Dennis & Olson, 1983
23 K tan (6) p“... N. 8.. NA
24 K tan (6) p'... N. 8. NA

 

 

 

16

As summarized by Finno et al (1989c) who analyzed the
predictions, "standard" analytical methods of celculating
pile capacity were used by 19 out of 24 participants (the
number of individuals making predictions is actually Here
than 24 since "one participant“ in some cases is a group of
more than one individual). These approaches represent typical
practice, and is an indication of the state—of-the-practice.
For the most part, effective stress methods were used to
evaluate shaft resistance in sand and total stress methods
were used to evaluate both shaft and toe resistance in the
clay: The parameters used in! the participants in the
analytical methods are summarized in Table 2.2. From Table
2.2, evidently there is a wide range of interface friction
angles (¢) and lateral stress ratios (K) selected from the
data provided. The variation of K chosen in these studies is
mainly attributable to different judgments regarding effect
of the construction procedures that could cause different
lateral stresses against the pile after installation
(uncertainty regarding the stress state). Also, values of the
lateral earth pressure at rest (K0) supplied in the data
package were based either on Menard Pressuremeter or
Dilatometer results. However, the fact that many participants
used empirical relations to evaluate K0 indicates either lack
of confidence in those results or a lack of experience with

those types of data (Finno et al, 1989c).

17

 

 

Table 2.2: Parameters for Analytical Methods Used By 24
Predictors (After Finno et al, 1989c).
PREDICTOR PlLE SAND CLAY
NUMBER TYPE K 8 Ns 50
(degrees) (b. c. factor) (psi)
1 H-Pile 0.8 30 0.46 900 - 1000
Others 0.4 30 0.23
3 H-Pile K. PMT (2/3) 0 SPT 670
Pipe K. PMT (2/3) 9 SPT
Slurry 0.67 K. PMT (0.8) ¢ SPT
Cased 0.67 K. PMT (2/3) 0 SPT
4 Driven 1.5 - 2.3 40 - 44.5 1.26 - 2.26 800
Drilled 1 40 - 46 0.84 - 1.04
9 H-Pile 0.5 35 0.35 501
Pipe 0.57 0.4
Cased 0.45 0.32
Slurry 0.5 0.35
1 1 H-Pile 0.8 15 - 35 0.21 - 0.56 600
Pipe 0.9 0.24 - 0.63
1 2 Driven 1 24.7 0.46 750
Drilled 1 30 0.58
1 3 H-Pile K. PMT 26 590
Pipe K. PMT 24
Drilled 0.4 37 0.3
1 4 H-Pile K. (0.6) e: 780
Pipe 1.25 K (07) ¢ 0.99 - 1.7
Drilled 0.34
1 7 Pipe 0.7 30.4 - 31.2 0.41 - 0.42 550
18 H-Pile 0.9 28 0.48 0.33 p'...
Pipe K. 28
Drilled K. 40
1 9 All 0.7 47 0.75 740
21 Driven 0.25 above w.t. [0.35]
0.45 above w.t.
23 H-Pile 1.42 - 1.74 27.2 - 30.8 0.73 - 1.04 567
Pipe 2.13 - 2.61 23.8 - 26.9 0.93 - 1.32
Slurry 0.95 - 1.16 30.6 - 34.6 0.56 - 0.8
Cased 1.06 - 1.3 30.6 - 34.6 0.63 - 0.9
24 Driven 1 32 0.62 470 - 620
Drilled l 40 0.84

 

 

 

 

 

18

Approaches to estimate capacity varied from simply using
averages of all types of test results to using normalized
soil properties based on correlation with published data.

Fifteen participants chose to provide an estimate of
capacity for which there would be a 90% probability that the
measured values would exceed the predicted value. Nine
participants used judgment when making their lower bound
predictions by incorporating reduced strength parameters or
lateral stress coefficients, by using different methods for
their estimates, or by reducing their best estimate by an
arbitrary amount. Three participants used a First Order
Second Moment (FOSM) analyses with various normally
distributed random variables. Six participants used
probability approaches to predict lower bound capacities. For
example, Wolff (1989) used the Point Estimate Method (PEM)
and considered shear strength em31a random variable and a.
function of depth. Others used the FOSM method and assumed
other parameters normally distributed. As indicated by Finno
et al (1989c), the fact that only six out of 24 participants
chose a probabilistic approach may indicate the degree, or
lack thereof, to which uncertainties are incorporated into
design of piles for axial load in practice.

In the Northwestern study, measured capacities for the
two driven piles were approximately equal to the most
frequently predicted capacity; however, a relatively large
difference in the predicted capacities for the drilled piers

can be attributed to the effects of installation procedures.

19

In any case, as pointed out by Finno et al (1989c), if one
were to compute capacities of a pile using several different
methods and took an average value of the values to represent
the predicted capacity, the effects of installation
procedures would apparently be masked out. When the measured
capacity and the lower bound predictions made by the same
predictor are compared, it is found that there is an average
reduction of about 25% in the predicted capacities. The range
of reductions of the lower bound predictions for all
participants varies from 10 to 40%.

For the portion of pile in clay, for practical purposes,
the excess pore ‘water pressures were assumed by most
investigators to have been fully dissipated by the end of 52
weeks. Some participants assumed that the 2 week capacity was
the long term capacity.

In sand, the gain in capacity with respect to time is
generally neglected. For toe resistance in the clay, because
of the relatively small contribution to the total capacity,
it was also generally neglected.

However, other aspect (ME human factors might also
influence the outcomes in that study. The participants might
not have devoted enough time with their knowledge realizing
that the prediction symposium is a staged event rather than
an actual professional practice.

Another major study about predicting axial pile capacity
was the one conducted by Briaud et al (1986) and Briaud and

Tucker, (1988) at Texas A & M University. The purpose of that

a.

;

 

20

study was to evaluate 13 specific analytical prediction
methods using 98 tested piles provided by Mississippi Highway
Department. The 13 specific methods as listed by Briaud and
Tucker, (1988) are; (1) Coyle, (2) Briaud-Tucker, (3)
Meyerhof, (4) API Code, (5) Mississippi Highway Department,
(6) Direct Cone Method, (7) deRuiter and Beringen, (8) LPC
Cone, (9) Schmertmann, (10) Tumay and Fakroo, (11) Penpile,
(12) LPC Pressuremeter, and (13) ENR Formula. The outcome
from that study also indicated varied results, especially for
piles driven in mixed soil and with toe in sand, where "no
best results" was found. Some methods seemed to be suitable
onLy for certain soil conditions. For example, for pales
driven in sand, Coyle's method was credited to performed the
"best"; and in clay the Mississippi Method was "the best."
However, Briaud et EH. (1986) concluded tfluu: combining a.
method which works well for piles all in sand with one that
works for piles all in clay does not necessarily produce a
method that works well for piles in layered soil. Among other
findings by Briaud et al (1986) is that, "It was considered
that perhaps an average of several methods would produce
better results than the methods individually."

In short, the studies as briefly presented above reflect
the complexity of pmedicting pile capacity. Inna to large
scatter of various methods used, variation in assumptions and
individual judgment have resulted in.ea range CHE possible

capacities being predicted.

21

Other previous studies related to statistical analysis

and model error will be presented in Section 4.2.

2.3 :Deterministic Analysis

This section presents some background information of
several empirical. methods ‘using' static formulas ‘used. to
calculate capacity of pile foundations. Specific information
about the "standard" Beta (B‘) Method used pmimarily to
calculate pile capacity in sand will be presented in section
2.4.

A number of static, dynamic and wave equation methods
have been proposed over the years for the prediction of axial
capacity' of pile foundations. Sui the effort to better
estimate pile capacity, considerable research is ongoing with
respect to modelling of soil—pile behavior, soil
characterization, reconsolidation and various loading
conditions.

When there is IN) toe bearing layer (e.g., in soft
clay), the toe resistance is almost non—existent and is
assumed to be negligible as compared to the resistance along
the shaft. Therefore, the shaft resistance that (EH1 be
provided by the soil is of primary importance.

Currently, empirical methods are used to estimate shaft
resistance. This is achieved. by means of correlations
established 1J1 similar‘ deposits between values of shaft

resistance backfigured from loading tests and some assumed

 

22

relevant in—situ characteristics of these deposits (Azzouz,
1990). Existing empirical methods for estimating shaft
resistance can be broadly classified into three categories,
namely;

(1) Total Stress Method: This group of methods is
commonly referred to as the Alpha (0) Method; which uses the
total stress approach. This method is pmimarily used for
calculating capacity in clay soil.

(2) Effective Stress Method: Another group of
approach is commonly known as the Beta (Bt) Method. This
method was advocated by Zeevaert in 1959 which uses the
effective stress approach (e.g., D'Appolonia, 1968; Coyle and
Sulaiman, 1970; Meyerhof, 1976a). This method would be
presented in some detail in the next section.

(3) Mixed Method: A quasi—effective stress approach is
also used for the prediction of pile capacity. This third
group is referred to as the Lambda (A) Method. This method
was proposed by Vijayvergia and Focht (1972) based on the
general equation (of LUNA: shaft resistance jpresented. by
D'Appolonia et a1 (1968) and the Rankine equation for passive
pressure. This method has been widely used for computing
axial capacities of pile in offshore structures (Vijayvergia,
1977; Kraft et al, 1981; McClelland and Reifel, 1986; API,
1991). Vijayvergia (1977) used the remolded reconsolidated
shear strength and the Coulomb equation for passive pressure.

In short, estimating the capacity of pile foundation

using static formula may be approached by either Alpha(aJ,

23

Beta (B*), or Lambda (1) Methods. The "standard" Beta (B*)

Method is typically adopted in sand.

2.4 Standard Method in Sand

The "standard" method for calculating pile capacity in

sand is the Beta (5*) Method. In this method, the shaft
resistance is correlated to the initial effective overburden
stress, fin, through the empirical factor B*. The INNS of
effective stress method was advocated by Zeevaert (1959). In
earlier days, this method was used for both sand and clay
(e.g., Burland, 1973). However, present understanding
indicated that application of the Beta (B*) Method is limited
to sand only [e.g., in Finno et al, (1989d). only one out of
24 predictors used this method in the clay layer].

Parry and Swain :hi 1977 extended. Burland's (1973)
concept to include a more realistic assumption for
determining the effective overburden. pressure ukvl at
failure. They assumed that the mw at failure equals to the
initial p...

The unit shaft resistance (9s) from the effective stress

approach may be expressed as;

qs=fs(p},) 2.1

where, f. ie; the unit shaft resistance; and IE is the

effective lateral earth pressure.

 

_.

24

However, an accurate estimate of effective lateral earth
pressure (pg) is not easy. Since p., is relatively easier to
evaluate, for example, Randolph (1983), concentrated on
finding the relationship between Q and inSiCU pev. Equation

2.1 is then modified to include RM as;

q. = fs (ph') 13'.) 2 . 2
Pov
q. = B pay 2 .3

Consequently, the B* coefficient reflects not only the
friction between pile and soil, but also the ratio of
horizontal to vertical stress, K (i.e., Bt=Ktan5). The
values of B. may also 1x2 evaluated by simplified drained
failure criteria (e.g., Burland, 1973).

There is substantial uncertainty associated with qS and
between various versions of the B‘ Method. While there is
still significant scatter between calculated enmi measured
capacities, it does not appear as great as in using a-Method.
Nevertheless, the formulation of B‘ Methods is still based on
several assumptions, e.g., drained [cohesion, c==0; soil pile
interface angle (5) is taken at a reduced angle of internal
friction of soil (0)], and the final coefficient of earth
pressure is assumed to be equal to the initial coefficient
(which is not quite the case after pile installation).

In most cases, existing methods of pile design started

In! estimating' the axial capacity of ea single pile. In

 

25
general, the calculated capacity of a single pile, (2, can be

expressed as (e.g., Winterkorn and Fang, 1975; Meyerhof,
1976a; Fuller, 1978; Coyle and Castello, 1981; Kulhawy, 1984;
Focht enui Kraft, 1986; Tomlinsonq 1986; McClelland and
Reifel, 1986; Olson and Long, 1989; Finno et a1, 1989d; API,

1991):
Q=Qs+Qt‘W 2‘4

where Ckzshaft resistance; thoe resistance; and w=weight of
the pile. The weight of the pile is comparatively small and
is generally neglected in the computation of Q. The shaft and
toe components are further discussed in Sections 2.4.1 and
2.4.2 respectively.

The complete format adopted for the calculation of axial
pile capacity in this study is by combining the shaft and toe

capacity (Eqs. 2.7 and 2.10), i.e.;

Qc='z[(p'ovKtaDSAIAsiiI'I’p'tNaAt 2.5

1=l

where,
on = average effective overburden pressure along

pile segment in soil layer 1

pt = effective overburden pressure at the toe of
the pile
K = coefficient of lateral earth pressure

 

26

5 = interface angle of friction between soil and

pile material

Nd = modified bearing capacity factor
AS = surface area of pile shaft in soil layers i
A, = cross sectional area at the toe of the pile.

The calculated capacity (Ch) is divided by a factor of
safety, F8, to get the allowable capacity (Ch) use for design.
In deterministic analysis, the recommended FS commonly ranges
from 2.0 to 4.0 (Peck et at, 1974; Meyerhof, 1976a; Fuller,
1978; Poulos and Davis, 1980; Tomlinson, 1986; Bowles, 1988),
depending on designer's judgment.

The next two sections briefly discuss factors comprising

the shaft and toe components of Eq. 2.5.

2.4.1 Shaft Resistance

The soil-pile interaction is very complex and poorly
understood. The shaft resistance is commonly estimated based
on the laws of mechanics considering friction between solid
surfaces. The unit shaft resistance (qs) can be represented as
(e.g., Meyerhof, 1976a; Coyle and Castello, 1981; Olson and

Long, 1989; Kulhawy, 1984; Focht and Kraft, 1986; API, 1991);

 

 

 

27
qs=pévKtan5 2.6

therefore the total capacity can be obtained by integrating
over the pile shaft area;

D r

Qs=.2[(p.,KtanSIr(As)1I 2.7

1:

where the parameters are as defined by Eq. 2.5.
Effective overburden pressure is calculated knowing the

location of the ground water table and the unit weight of
sand, 7. To determine qs, factors K and mud need to be

established; these are the most complex terms to evaluate

(e.g., Kulhawy, 1984; Meyerhof, 1976a).

2.4.1.1 The value ofK

The coefficient of lateral earth pressure, K (which is
the ratio of horizontal to vertical effective earth pressure)
is a function of the original in-situ horizontal stresses,
and the stress changes caused in response to pile
installation, loading, and time.

Meyerhof (1959) and Nordlund (1963), e.g., dealt
theoretically with the problem of determining 1( values. In
both studies, it was assumed that the pile displaces the sand
in the horizontal direction, without inducing any vertical

deformation. This displacement compacts the surrounding soil

28

and the compaction is a maximum at the pile-soil interface.
Since the shaft laterally compresses the sand and the
horizontal movement is large (equal to pile radius), it is
theoretically possible that K.could be as high as the passive
earth pressure coefficient(Kp).

Focht and Kraft (1986) took K:0.7 for compressive loads
and K:0.5 for tensile load. Olson and Long (1989) suggested
the value of K=1.0 for displacement piles (i.e., timber,
concrete, closed ended steel pile), and K:O.8 for open ended
pipe piles and H-piles. Other K values suggested by previous
investigators are presented in Table 2.3. In Kulhawy (1984),
the values have been evaluated using an extensive loading
test data from.Stas and Kulhawy in 1984, and the agreement is

said to be good.

Table 2.3: Typical Coefficient of Lateral Earth
Pressure, K .

(a) K Values (After Kezdi, 1975) .

 

 
 
 
  
 
 
   

AUTHOR BASIS OF RELATIONSHIP SOIL TYPE VALUES OF K

 

 

Brinch Hansen theory sand Cosz ¢
Lundgren (1960) pile test sand 0.8
Henry theory sand KP
Ireland (1957) pulling test sand 1.75 to 3.00
Meyerhof (1951) analysis of field data loose sand 0.5

dense sand 1.0
Mansur-Kaufman (1958) analysis of field data silt 0.3 (compression)

0.6 (tension)

Lambs-Whitman (1969) guess 2.0

Kezci (1958) theory granular Kp

 

 

 

 

 

 

29
Table 2.3: Continued.

(b) K Values as Suggested by Kulhawy (1984).

 

FOUNDATION TYPE AND RATIO OF HORIZONTAL SOIL STRESS
METHOD OF INSTALLATION COEFFICIENT TO IN-SITU VALUE ( K/K.)

 

Jetted Pile 1/2 to 2/ 3
Drilled Shaft, Cast-in-place 2/ 3 to 1.0
Driven Pile, Small Displacement 3/4 to 5/4
Driven Pile, Large Displacement 1.0 to 2.0

 

 

 

 

As can be seen of K values reported in the literature
(Table 2.3), the bound approximately ranges from ndnimum
active (Kg) to maximum passive (KP) stress states. Evidently,
it is not an easy task to assign the K value. In
deterministic designs, given the range of possible values of
K and without any other soil data available (say, only the
SPT N-values), then perhaps the appropriate assumption is to
design the pile for a long term capacity. If long term
capacity is considered, the best estimate of K is the
coefficient of lateral earth pressure at rest, K0.
Consequently, for this research K0 is simply adopted (see
also the assumptions in Section 5.3). Kaizumi (1971) and
Kulhawy (1984) pointed out that K may be maximum near the top

and decrease to the minimum near the toe of the pile. By

*
assuming K equal to K0, the "modified B " factor (equal to

30

Ko*mm8) derived in this study could satisfy this
requirement.

Nevertheless, for the development of the algorithm in
this study, the "exact" K.value need not be quantified. From
the method employed to develop the algorithm, the "choice" of
selecting the different K values will show up in the form of
correction and bias factors. However, to calculate pile
capacity for the developement of the algorithm, a consistent
procedure is needed. This is also true for 5 values

presented below.

2.4.1.2 The value of?)

For this research, the interface angle of friction
between soil and pile material (8) is taken as 51 reduced
angle of internal friction of soil (9)- Potyondy (1961) under
the supervision of Meyerhof, determined the coefficient of
friction (or adhesion) between various materials for
cohesionless soils at different densities. The study was made
using direct shear tests in the laboratory. Consequently, it
is possible to develop a relationship between 0 and.tm15, as
shown in Table 2.4.

Vesic (1977) proposed a different approach for the
determination of mnfi. The sand located at the interface

between the soil and the pile is considered to be at a state

of failure for the determination of shaft resistance.

 

 

31

Consequently, 5 is independent of the initial soil density

and pile material. Therefore 5 was considered to be equal to

the residual friction angle (0ND. Ifixflu: and Kraft (1986)
simply adopted 5: (iii-5°); and Kulhawy (1984) recommended
value ranges from 5: (0540 txn 5: (L00), depending on pile
type. The selection within the range for any particular pile
type is typically dependent upon personal judgment.

The 5 values as suggested by Potyondi (1961), Vesic
(1977), Focht and Kraft (1986), and Kulhawy (1984)
suggestions ck) not seem.tx> be significantly (different.
However, a rather rigorous approach as suggested by Potyondy
(1961) is adopted for this study (Chapter 5); as opposed to
merely an intuitive and subjective approach as suggested by
Bowles (1988), Kulhawy (1984), and Focht and Kraft (1986).
References to Potyondy's values were also made in earlier
investigators (e.g., Thurman and D'Appolonia, 1965; Koerner,

1970; Coyle and Tucker, 1989).

Table 2.4: Typical Soil Pile Interface Angle ,5.

(a) 5 Values as Suggested by Kulhawy (1984).

 

 
   

INTERFACE MATERIALS f4, TYPICAL FIELD ANALOGY

 

Sand/ Rough Concrete 1.0 Cast-in-place
Sand/Smooth Concrete 0.8 to 1.0 Precast
Sand/ Rough Steel 0.7 to 0.9 Corrugated
Sand/ Smooth Steel 0.5 to 0.7 Coated

Sand/Timber 0.8 to 0.9 Pressure-treated

 

 

 

Table 2.4: Continued

32

(b) 5 Values as Suggested by Potyondy (1961) .

CONSTRUCTION MATERIAL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SAND COHESIONLESS SILT COHESION

GRANULAR
0.06<D<2.0 0.002<D<0.06 50% Sand+

mm mm 50% Clay

Surface of Construction

Material I.) fo 0); fc
Dry Sat Dry Sat Sat Consistency I

Index
Dense Dense Loose Dense = 1.0 to 0.5 ‘
STEEL SmoothJ Polished 0.54 0.64 0.79 0.40 0.68 0.40 - 9
Rough18usted 0.76 0.80 0.95 0.48 0.75 0.65 0.35
WOOD Parallel to grain 0.76 0.85 0.92 0.55 0.87 0.80 0.02
* At right angLe to grain 0.88 0.89 0.98 0.63 0.95 0.90 0.40
CONCRETE Smooth Made ofiron form 0.76 0.80 0.92 0.50 0.87 0.64 0.42
Grained Made ofwood form 0.88 0.88 0.98 0.62 0.96 0.90 0.58
Rough Made ofadj't ground 0.98 0.90 1.00 0.79 1.00 0.95 0.30

 

 

 

 

 

 

 

 

 

Note: f¢ is the Ratio of Soil-Pile Interface Angle (5) to

Angle of Friction of Soil (0); fq, = (ES/4)); fC

According to Vesic

Toe Resistance

(1968),

(Ca/C)

the theoretical formulation

of the toe resistance was initiated by Caquot and Buisman in

the mid 1930's

(from an extended work on punching failure

done by Prandtl and Reissner approximately 15 years earlier).

33

Among the later contributors were Terzaghi, DeBeer, and Jaky
in the 1940's; Meyerhof, Caquot, and Kerisel in the 1950's.

A somewhat different approach from punching failure was
taken by Skempton, Yassin, and Gibson in the early 1950's
when they dealt with the failure induced by the pile toe as a
special case of the expansion of a cavity inside a solid.
The same concept was used again by Vesic (1977). This time
the approach involves the use of complex soil parameters
(e.g., rigidity index).

In all of the theoretical solutions, the unit toe
resistance, qt, can be represented as (e.g., Coyle and

Castello, 1981);

qt=CN¢sc+yBNys\,+-p',Nqsq 2.8

where Y=effective unit weight of soil at the toe; B=smallest
foundation dimension; mzeffective overburden pressure at the
toe; C=cohesion; sc, 57, sq=shape factors; and NC, N7,
bh=bearing capacity factors (usually dependent upon the soil
friction angle and the assumed pattern cm: mechanian of
failure). This is essentially the formula for the bearing
capacity of shallow foundations, but with modified bearing
capacity factors.

In practice, Eq. 2.8 is usually simplified. Since this
study is for sand, the first term can be eliminated; the
second term is relatively small and this can also be

neglected. Since most piles have circular or square cross

34
sections and the shape factor is the same (Kezdi, 1975;

Vesic, 1967), ii; is reasonable to Luua a modified bearing
capacity factor, N;, that incorporates this constant shape
factor. Therefore, the commonly used form (Coyle and
Sulaiman, 1970) of Eq. 2.8 for unit toe capacity is reduced

to:
q,=p',N:l 2.9

And therefore the total toe resistance is equal to:

Qt:(pIN;)At 2.10

The range of nedified bearing capacity factor (5%)
varies widely among the previous investigators. As presented
by vesic (1963), typical N; values are such.en3 the one
proposed by Vesic, Meyerhof, Hansen, Coquot and Kerisel,
Berezantsev, Terzaghi, Skempton et al, Janbu, and others; and
the "best" 5% Chosen are much depended on local practice or
designer's preference.

In addition to the pile geometry, in most theories the

basic parameters are the effective soil friction angle (0'),
which ii; used to :flhui N9! and the effective confining
pressure. As mentioned by Coyle and Castello (1981), "no
theory" considers the shaft resistance of the soil along the
pile shaft, or a possible interdependence between shaft and
toe resistances. Some of the theories assume soil to be
compressible (Bishop et al, 1948; and Fruco and Associates,

1964) while others (Terzaghi, 1943; Meyerhof, 1951; and

35

Berezantzev et al, 1961) assume soil as a rigid—plastic
system.

Under normal circumstances, there is no clear evidence
that one bearing capacity factor is superior than the other
to provide a more reliable prediction. Therefore in this
study, the Vesic (1963) modified bearing capacity factor
(DGI' is simply chosen (see also Section 5.3). After all,
from the algorithm developed in this study, it is not of
utmost importance which bearing capacity factor is adopted;
the difference would show up in the form of other correction
and bias factors in the developed algorithm as described in
Chapter 5.

In short, the "standard" static formula for the
calculation of axial capacity is presented; and the specific
parameters have been identified. This static formula is the
one most frequently used format by practitioners rather than
a standard. The next section will present the limits imposed
on the calculated capacity of shaft and toe resistances use

by some authorities for the design of pile foundation.

2.5 Design Practice: Limits and Corrections

Studies by Whitaker and Cooke (1966), and Coyle and
Reese (1966) indicated that the slip to develop maximum shaft
resistance is about 5 to 10 mm and is relatively independent
of pile diameter and embedment length, but may depend upon

soil parameters. Mobilization of the ultimate toe resistance

 

 

36

requires a toe displacement about 10 % of its diameter for
driven piles and up to 30 % of the base diameter for bored
piles and caissons.

As pointed out by Coyle and Castello (1981), Kerisel in
1961 observed that different size piles in.tflue same sand
attain a maximum value of unit load resistance (shaft and
toe) which appears to remain constant with increasing
penetration. The depth where the constant value is attained
varies with pile diameter. The larger the pile diameter the
deeper is the required penetration. Vesic (1970) confirmed
Kerisel's finding with field tests; apparent unit resistances
increased with depth to some limiting value. Vesic (1970)
noted, however, that even though the rates (ME increase
sharply decrease at some critical depth, there was an
additional increase with further penetration. This critical
depth was identified as being between 10 pile diameter for
loose sands and 20 diameter for denser sands. In another
study, Hanna and Tan (1973) performed laboratory model test
using relatively long piles and observed that the critical
depth approached 40 pile diameters. Meyerhof and Valsangkar
(1977) obtained additional laboratory evidence of a limiting
value for unit toe resistance. The study also showed that the
critical depth for submerged sands is 1.6 times greater than
that for dry sands. This increased critical depth is probably
caused by buoyancy effects. Coyle and Castello (1981) also
pointed out the study of Biarez and Gresillon in 1972

(France); again limiting values were obtained.

 

 

 

37

For practical purposes, limiting values are placed on
shaft and toe resistances (e.g., API, 1991), in accord with
the above empirical data. The limiting values recommended by
API (1991) are as shown in Table 2.5.

However, as pointed out by McClelland and Reifel (1986)
specifications fur API anus oriented. towards predicting
capacities of large (offshore piles. The upper limits
recommended for shaft and toe resistances are intended to
ensure that capacities of "long" piles (say more than 50 ft.)
are not overpredicted; and this method tends to underpredict
the capacities of "short" piles.

All the above studies (Kerisel, 1961; Vesic, 1970;
Meyerhof and Valsangkar, 1977) indicated some limiting values
for shaft and toe resistances. However, other studies (e.g.,
Kaizumi, 1971; Kulhawy, 1984) argued that shaft and toe
resistances do not reach a limit at a critical depth; they
in fact increase with depth. For the shaft, the rate is a
function of increasing overburden pressure and decreasing K.0
with depth. For the toe, the rate of increase decreases with
depth primarily because of decreasing rigidity with depth.

Therefore from previous studies, evidently the behavior
of soil-pile system Mn: the failure mechanism) ie; not
generally well understood. For the most part, Vesic's (1977)
saying is still a fact in practice at this point in time.
Vesic (1977) said, "...computation of the ultimate load is
quite difficult and a general solution is not yet available

in view of the many uncertainties involved in analysis of

38

pile foundations, it has become customary, and in many cases
mandatory, to perform a certain number of full—scale pile
load tests at the site of more important projects." Loading
tests may provide better estimates of pile capacity compared
to computed values. However, it is also a fact that the
loading tests themselves are subjected to variations (see
Chapter 3).

Dennis and Olson (1983, 1985) recommended empirical
correction factors in lieu of simply placing limits on shaft
and toe capacity. These capacity correction factors are as
represented 13! Eqs. 2.11 auui 2.12 for Shaft and toe

respectively:

F. = 1.0 2.11
0.6 Exp(L'°’6OdI

 

= 1.0
F‘ 0.15 + 0.008 L. 2'12

 

where {fizshaft capacity correction factor; Ifl=toe capacity
correction factor; Lezdistance from ground surface to pile toe
in ft.; d=diameter of pile; (UJd) is dimensionless. These
correction factors are mmltiplied to tflua shaft and toe
components in the static formula (e.g., Eq. 2.5).

In that study, by using the proposed corrections
factors, conformance of calculated to measured capacity is

improved; they may also provide a correction for the fact

39
Table 2.5: Recommendation of Limiting Shaft and Toe
Resistances by API (1991).

 

 

 

 

 

 

 

_
DENSITY SOIL 5 LIMITING SHAFT N; LIMITING UNIT
DESCRIPTION RESISTANCE, TOE BEARING,
kips/sq.ft (kPa) kips/sq.ft (MPa)
1
Very Loose Sand 15 1.0 (47.8) 8 40 (1.9)
Lane Ehmifik
Nbdmn 9R
Loose Sand 20 1.4 (67.0) 12 60 (2.9)
Medum Sand-Silt
Dane 5m
Medum Sand 25 1.7 (81.3) 20 100 (4.8)
Dense Sand-Silt
Dense Sand 30 2.0 (95.7) 40 200 (9.6)
Very Dense Sand-Silt
Dense Gravel 35 2.4 (114.8) 50 250 (12.0)
Very Dense Sand
__ -

 

 

 

 

 

 

 

 

Note: 5 is the Soil-Pile Friction Angle in Degrees; N; is the
Modified Bearing Capacity Factor.

that frictional resistance (consequently 5) decreases as the
stress increases. However, the derived F, is nc3t
dimensionless; which from an analytical standpoint might be

undesirable.

40
For the algorithm developed in this research (Chapter

5), a similar approach for deriving the correction factors
was used. It will be shown that the dimensionless factors (Fs
anuilfl) derived in Chapter 5 are also found to give a good
prediction of capacities as do those factors used by Dennis

and Olson (1985).

2.6 Field Testing

Because of time specific requirements of aa given
structure and the spatial variability of soil properties both
in breadth and depth, there is no single procedure for soil
exploration (Lee et al, 1983). One of the most informative
methods of soil exploration is a trench cut through the soil
deposits, although in loose sands or below the water table
such a method is inapplicable. Trenching is generally cost
effective and appropriate for shallow soil deposits.
Equipment is usually readily available from local sources.
For deep foundations, the most commonly used soil exploration
is perhaps the Standard Penetration Test (SPT).

This section presents a general review of the
principles, application and limitations of time SPT. Other
tests that have the potential to replace the SPT in the
future are only briefly mentioned as they are out of the

scope of this research.

41
2.6.1. Standard Penetration Test

The Standard Penetration Test is one of the earliest,
most economical and. most 'widely used tests for soil
exploration. The test has been "standardized" by ASTM D 1586—
67 (1976); and the basic elements of SPT test can be
summarized as follows;

1. sampling with the standard spoon sampler (1 3/8 in.
inside diameter, 2 :hi. outside diameter, 24 IJL
long).

2. driving the standard spoon sampler with a 140 lbs
hammer; dropped 30 in.

3. driving the spoon 18 in. into the soil, and recording
the number of blows at three 6 in. increments,

4. the N—value is defined as the number of blows to

drive the last 12 in. of the standard spoon sampler.

As stated by Lee at al (1983), the SPT is "good" in
terms of qwualityr and. quantity' (quality' refers to
meaningfulness, i.e., the accuracy and precision with which
the measurements can be made; and quantity refers to whether
a large amount of data can be collected in a reasonably short
time). ‘

The SPT is a crude but useful test because of the
enormous empirical data base obtained over the years. The SPT
may be used in both sand and clay, but the correlation

between N—values and the shear strength of clay is poor

42
(e.g., Schmertmann, 1979; Lee at al, 1983; and Peck et al,

1974). Therefore, it should be treated only as a quantitative
guide. (hi the other hand, a carefully conducted SPT in
cemented sands should give a reliable guide to the in—situ
density and therefore the 0-value.

As reported In! Gibbs and .Holtz (1957), normally
consolidated sands under small overburden pressures tend to
have N—values "too small" for their relative density,
therefore, correction factors were suggested. Other studies
by Bazaraa (1967) and Peck and Bazaraa (1969) also suggested
that the N—values should be corrected for the overburden
pressure. Over time years, there are rmnn/ formulas and
correlation suggested for the correction of the N—values. For
this researoh, a simple format as proposed in! Liao and
Whitman (1986) has been adopted.

The SPT may require careful interpretation in soils
other than sand. In particular, in gravelly sand as large
pieces of gravel or rock may be trapped at the bottom of the
spoon, thus affecting the N—value (Palmer and Stuart, 1957;
Fruco and Associates, 1973). However, for the development of
the algorithm in this research, only SPT data from sandy
sites (and according to the selection criteria as described
in Chapter 5) is considered.

The "standardized" SPT is subject to many sources of
variability; and most of the time in practice, it deviates
from the recommended procedure. This is especially true for

older data sources. For example, Fletcher (1965) discussed

 

 

43
the difficulties associated with the SPT. Earlier effort to

standardize the SPT has resulted in little success (e.g., De
Mello, 1971). Many studies done by Schmertmann (1975) on
various types of penetration tests, for instance, found that
I'reproducing N-values is difficult." There are many factors
attributed to the difficulty in reproducing the N—values,
even in adjacent borings. Kovacs et al (1975) indicated that
using 3 instead of 2 turns of rope around the cathead to
hoist the hammer could increase N—values by as much as 40 %.
Bowles (1988) states that McLean et al in 1975 pointed out
that by using a longer drill rod may increase the N—values by
as much as 14 blows/ft.

The sources of errors (mainly related to poor practice)
and the difficulties associated with the SPT, can be listed
as follows (Bowles, 1988);

1. variations in drop height; most often, this is done
by eye,

2. interference with the free fall of the hammer;
various guides and rope arrangement,

3. use of a drive shoe at the end of the standard spoon
sampler,

4. failure to seat the sampler on undisturbed material;

i.e., on the second 6 inches,

5. failure to maintain sufficient hydrostatic pressure
in the boring; producing a "quick" zone at the
borehole,

6. use of too light or too long a string of drill rods,

44

7. driving gravel ahead of the sampler,
8. use or non usage of liner trap; i.e., a retainer in
the spoon to trap soil samples,

9. human error; careless drill crew.

In spite of the crude nature of the SPT and its high
degree of uncertainties, the test is not easily phased out.
Among the reasons for continued use of the SPT are that it is
economical, cost effective and soil samples can be recovered
for laboratory analysis. It is used routinely as the test is
simple; therefore, enormous experience with the test, and a
huge accumulation of data.

Using the corrected N-values according to Peck et al
(1974), Meyerhof (1976a) presented a "direct" determination

of the bearing capacity from the SPT N—values;

es4N' *A,] (tons) 2.13

 

 

0.4N'L
d

 

where, ET is the average corrected N—values within embedment
length of pile, I...3 (ft.); N is the average corrected N—values
within a distance of three to three quarter pile diameter, d
(ft.) above the pile toe and a distance of one pile diameter
below the pile toe; and AsenmilM are the surface area of the.
shaft and cross sectional area of the toe (sq. ft.),
respectively. The corrected N—values chosen to be used with
Eq. 225K3 is highly subjected, and is Imnfli depended on

designer's interpretation of the "average".

45
Briaud and his group in the early 1980's also directly

correlated the SPT N—values with pile capacity. Using the

uncorrected N—values, the predicted capacity (OP) is

expressed as (Briaud et a1, 1986);

Qp=10.448N_°'29*As I+I39.5 N1 036*A1I (kips) 2.14

where, N is the weighted average of the N—values within
embedment length of pile;this the average N—values at four
pile diameter above and four pile diameter below the toe; and
As and A, are the surface area of the shaft and cross
sectional area of the toe (sq. ft.), respectively.

However, even by using the same data base that was used
to derived the equation (Eq. 2.14), the prediction resulted
in quite a large variation. The standard deviation of the
predicted over measured capacity (Qp/Qm) was found to be
0.364. As reported by Briaud and Tucker (1984), the error was
mainly attributed to two reasons; namely, (i) the error due
to the natural variability of the soil (this is tied to the
fact that the pile loading test and the soil test are not
performed at the same location), (ii) the error in testing of
the soil (this is for example the error on the Nkvalues
associated with time SPT). In another study, EH1 advanced
application of the SPT for the determination of soil
parameters is currently being pursued, by incorporating the
concept of wave equation; e.g., the research led by Goble at

The University of Colorado (personal conversation, 1989).

46

In addition to the difficulties as discussed above,
another issue that contributes to the variability and could
affect the calculation, say pile capacity, is the
interpretation of the N-values; and consequently, its
correlation with the angle of internal friction of soil, 0. A
common practice is to adopt the "average" N-value over the
soil profile. Nevertheless, there are various ways to arrive
at this "average" value. In short, the interpretation of the
N—value remains largely a judgmental procedure.

In this study, the "actual" N-values from the boring
logs are used; and a mdcrocomputer spreadsheet is used to
linearly interpolate and correct the N—values at every foot
of the soil profile. There are many soil parameters that
could approximately be correlated to the N—values; e.g.,
relative density, angle of internal friction, and unit weight
of soil. In this research, the only correlation needed and
used is the correlation with angle of internal friction, 0,
as presented by Peck et al (1974). This relation is adopted
as the friction angle of soil can be obtained as a function
of N-values. A similar procedure has been used earlier by
Wolff (1989); whereby a convenient calculation can be set up
on a computer program. This procedure will also eliminate the
element of arbitrary judgment in choosing the appropriate
value of 0.

The use of N—values, correction and procedure adopted

for this research are further discussed in Chapter 5.

47
2.6.2 Other Methods

To determine the capacity of pile foundations, other
tests are sometimes employed [e.g., the cone penetration test
(CPT), and dilatometers (or pressuremeters)]. The CPT is
popular in Europe and is gaining ground in the United States.
The CPT is equally good in sand and in clay, and provided a
more reliable information as compared to the SPT, e.g., to
quantify shaft resistance or settlement of pile foundation.

The Flat Dilatometer (DMT), e.g., has become one of

geotechnical engineering's more versatile tools (Hryciw,

1990). It has an advantage of being able to measure the
coefficient of lateral earth pressure (K) "directly" on the
site (and consequently the bearing capacity). without any

correlation from an ”inferior" laboratory analysis. Using the
DMT, other information about soil type, density, strength,
compressibility, and the coefficient of consolidation can
also be empirically derived. Analysis of data and current
design recommendations based on DMT test procedure can be
found, e.g., in Marchetti (1980), Baldi et al (1986), and
Schmertmann and Crapps (1988).

It is well recognized that SPT is inferior to the tests
briefly mentioned above. However, in the statistical sense,
the analysis of a large data of relatively imprecise
measurements may yield better information than a far more
precise measurement in a highly variable material such as

soil.

48
2.7 Summary

This chapter has described the "standard,"; i.e., the
most frequently used static formula for calculating (or
estimating) the axial pile capacity of pile foundation. The
important considerations for a typical deterministic design
of pile foundations were described. With the background
information presented, a typical procedure 1x3 estimate
parameter values and design pile foundations from Standard
Penetration Test data is presented. Critical parameters and
the "standard" formula described in this chapter will form

the basis for the development of the algorithm in Chapter 5.

CHAPTER 3

INTERPRETATION OF PILE LOADING TEST

3.1 Introduction

This chapter describes techniques selected to interpret
the measured axial pile capacity (C50 ifixnn a loading test.
The emphasis is limited to the failure criteria that are used
to derive the design charts in Chapter 5; specifically
failure defined by, (i) 22 in. pile head mevement, (ii)

Davisson's criteria, and (iii) Chin's Criteria.

3.2 Description of Axial Pile Loading Test

The most reliable method (as compared to static
formulas, dynamic formulas or the wave equation analysis) to
determine the pile capacity is to perform a loading test. The
test has been standardized as ASTM D 1143—81 (1987). However,
local building codes may stipulate the load increments and
time sequence. The pile can be loaded by using a hydraulic
jack and jacking against reaction piles, or a weighted
platform. Typical load—movement curves from gnlea loading
tests are as found in Appendix A.

Piles in granular soil are often tested 24 to 48 hours

after driving when load test equipment has been made. If the

49

50

loading test is tx3 assess long—term capacity, tflue test is
generally done after transient effects due to installation or
driving have dissipated. In non-cohesive soil, the waiting
period could be, for example, a few days to weeks. For
friction piles in soft to medium clay, a waiting period of
three to six months may be required. For practical purposes,
some contracts may permit loading tests seven days after
driving. As indicated by Leonards and Lovell (1978), Sherman
in 1969 adopted a minimum waiting period of two weeks; and
Roth III 1972 stated that there were ru) additional effects
after five to six weeks.

In any case, "sufficient time" should elapse before
testing to allow partial dissipation of residual compression
stresses in the lower shaft (and toe) from negative shaft
resistance (n1 the upper shaft caused in! shaft expansion
upward as the hammer energy is released. Residual stresses
and/or forces have been observed from previous studies (e.g.,

Hunter and Davisson, 1969; Williams, 1960; Vesic, 1977).

3.3 Interpretation of Load Test

In the 1930's, "failure" load in a pile test was defined
by Terzaghi (1942) as the load that corresponded to movement
of 10% of the pile diameter. Since that time, many
definitions have subsequently been proposed. At present, for

example "failure" can be viewed as a rapid progressive

51

movement at a constant load, or as a load satisfying a
particular criteria, such as a movement of one inch; or twice
the load at which the net movement is 0.25 or 0.50 in; or the
load at which the movement per unit load is 0.01 in/ton, or
when the incremental movement per unit load is 0.03 or 0.05
in/ton; or some similar combination of load and component of
movement (Leonards and Lovell, 1978).

Each criteria has its own practical purpose. Thus, the
interpretation of failure load varies greatly upon local
practice, and local building codes.

It is common in practice that many piles are not tested
to ”failure." Testing may be stopped at say twice the "design
load" according to the quick testing method (Leonards and
Lovell, 1978; Fellenius, 1980). It may also be found that the
pile continues to sustain increasing loads even at relatively
large movements. In non-cohesive soil, this may be attributed
to the continued dilation and/or the crushing of sand
particles beneath the toe of the pile.

Fellenius (1975, 1980) compared nine different failure
criteria using the same load—movement curve to interpret
loading test. The measured capacity ((Ln)'was found to be 181
and 235 tons for the Davisson's and the Chin's criteria
respectively. Comparison of the nine different criteria is as
shown in Fig. 3.1.

All the other seven criteria yield capacity values in
between the Davisson and the Chin values. A similar

indication was obtained from the study of Leonards and Lovell

52

(1978). This gives a notion that the Davisson's criteria is
probably the lower limit and Chin's criteria can probably be
taken an upper limit. The "best" (Ln is still uncertain to
the profession EM: this time. Perhaps the "best single
measured“ capacity lies somewhere in between the Davisson's
and Chin's criteria.

with present knowledge and the complexity of the soil-
pile system, it is difficult to make a rational choice of the
best criteria to use. It is very much dependent on one's
experience. Fellenius (1975, 1978 and 1980) compiled several
methods of interpreting loading tests (i.e., those outlined
by Davisson, Butler and Hoy, De Beer, Fuller and Hoy, Hansen
90%, VanDer Veen, Mazurkiewicz, Hansen 80% eumi Chin). Of
course, for the same loading test data, the interpreted
capacity would not be the same as different methods are used.
Based (n1 those two earlier studies, Fellenius (1980)
preferred using four criteria in INA; practice (namely;
Davisson, Chin, Hansen 80% and Butler and Hoy).

With regards to the loading test program, from the
experience of others (e.g., Fuller, 1978; Bourguard, 1987:
Fellenius, 1980), besides other factors (such as pile depth,
soil type or installation procedures), the leaks in hydraulic
jacks (most commonly used for loading) may also introduce one
of time largest variation lfl obtaining time load—movement

curves. Consequently, the interpreted measured capacity would

be affected.

53

A detailed comparison of the various methods or testing
systems is beyond the scope of this study. However, to
develop the design chart and the calibration of the predicted
capacity in Chapter 5, there is a need to precisely define
and consistently interpret the measured capacity.
Consequently, the 2 in. movement, Davisson's, and Chin's
criteria are considered. The fourth criteria is simply the
average of the measured capacity as found by the Davisson's

and Chin's criteria.

 

 

 

 

 

 

 

 

 

 

 

 

 

250.........i-......
1 Chm-235 \b
1 Brinch Hansen(90%)-205M\azurkitwicz-208
200 1 Fuller& Hey-203 ___.ZO/:>ae~———— g
- /
- Davisson-181 ———1> Brinch Hansen/v .
I I (80%)-211 f
E 150 . / Butler & VanDer yeah-205 / _
t9, : Boy-185 De Beer-186 :
'8 q .
3 100 ......................................................................... _
‘ r
50 d ........................................ f
-/ ,
' I
O f T T f T T T T T I I fl I T T
O (15 1 L5 2

Movement (in.)

Fig. 3.1: Interpretation of Pile Loading Test by Nine Failure
Criteria (After Fellenius, 1980).

54

3 . 3 . 1 . 2 inch Movement Failure Criterion

The 2 inch movement failure criteria is simply defined
as the axial load applied to the pile that causes the head of
the pile to move down 2 in. Coyle and Ungaro (1991) and
Ungaro (1988) indicated that 2 in. movement of the pile head
is needed to mobilize the "maximum" or "limiting" shaft and
toe capacities for H-pile. Consequently, for this research,

the 2 in. movement criteria is arbitrarily considered.

23.3.2 Davisson's Failure Criteria

Davisson developed a method of interpreting pile load
capacity by comparing the results of wave equation analysis
with results of static loading test (Davisson, 1975).
Consequently, the method has an advantage of being compatible
with the wave equation analysis.

From loading test, a load-movement curve can typically
be represented by either curve A, B or C in Fig. 3.2 for
piles that primarily develop their capacity from shaft, shaft
and toe, and toe resistances, respectively.

Davisson (1972, 1975) used an offset criteria similar to
that used for some metals for determining the ultimate
capacity. The criteria has been developed for the toe bearing
pile by considering the deformation required to cause elastic

compression (or quake) of the soil at the toe of the pile.

55

 

Load, Q (tons)

1 .

*4”

 

 

 

 

=_d_ °
are 120 (m)
5Sp or 0.15 (in)

Curve A - Shaft Resistance ,
Curve 8 - Shaft 81 Tee Resistance
Curve C - Toe Resistance

I
--------’--------------
+
L
Ofl

 

5e : elastic compression of the pile

53¢ : elastic compression of soil at the toe

Movement, m (in)

55p : limiting plastic compression of soil at the toe

 

 

 

 

Fig. 3.2: Interpretation of Pile Loading Test, Davisson's

Failure Criteria.

Davisson found that when movement of the toe is 0.15 in.
(limiting plastic compression of the soil at the toe of the
pile) plus quake (0.1 in. for a 12 in. diameter pile - could
directly be measured by mounting a tell-tale device at the
toe of the pile) below the elastic compression line (QUAE),
the ultimate load is presumed to have been reached.
Therefore, from the load-movement plot of the head, the

measured capacity, Qm (or commonly known as "ultimate

56

capacity") is interpreted when the head movement is equal to
5:
a=a.+5..+5,p 3.1
L
5=9__+_d_+015 (in) 3 2
E 120
where,
5e = elastic compression of the pile
5“, =. elastic compression of soil at the toe of the pile
5%) = limiting plastic compression of soil at the toe of
the pile.
23.3.3 Chin's Failure Criteria

From the pioneering work of Kodner in 1963, Chin (1970)
proposed that the load(Q)—movement(m) curve could be

expressed by two main assumptions;

(i) a load vs. movement curve is assumed to follow a

rectangular hyperbola:

Q=———m
Am+c 38
where A and r: are constants, defining the

interaction between the pile and the soil,

57

(ii) on application of load, shaft resistance is
mobilized progressively from.tflu3 ground surface
downwards, and maximum shaft resistance is

achieved before any toe resistance is developed.

Equation 3.3 can be rewritten in the form:

_ 1

A +(c/m) 3.4

which shows that Q approaches (l/A) as m approaches a high
value.

This asymptotic behavior is a fundamental property of a
rectangular hyperbola. Consequently, from the gflxfl: of 0mm»
\n5.1n, measured capacity can be determined, i.e., Chy=lfii . To

determine A, transposing terms in Eq. 3.4, resulted in:

m=Am+c
Q 3.5
Equation 3.5 has the form (y=Ax+c), which is an

equation of a straight line, of slope.A. Thus, Ch,ie; simply
the reciprocal of the slope in the plot of OnKD vs. nL

When the result of a pile loading test is plotted in

this manner (Eq. 3.5), two straight lines ab and bd may be
obtained (Fig. 3.3). To explain this, Chin's second
assumption applies, i.e., maximum shaft resistance is

achieved before toe capacity is developed. The implication of

this assumption is that two separate phases of capacity

58

 

 

 

 

 

 

E
3.,
E“? J
U. I‘___ Qsm Q11 '
:6. |

1‘
>9

a

Movement, m (in)

 

 

 

Fig. 3.3: Interpretation of Pile Loading Test, Chin's Failure

Criteria.

generation governed by two different soil-pile interaction
mechanisms occur; first, the build up of shaft capacity (Chm)
developed only by elastic compression of the pile; second,
the build up to ultimate capacity as toe capacity (Q...) is
developed by penetration of the toe of the pile into the
soil. These two interaction mechanisms possess different A
and c values resulting in two different straight lines on the
plot of OnKD vs. mL This leads to the conclusion that, line

ab represents the build up of shaft capacity, Qsm, with

59

maximum shaft capacity being Qsm=1/Aab and line bd represents
the build up to ultimate capacity, i.e., Qm=l/Abd.

In routine pile loading test, a pile is typically loaded
in) to 1.5 (H? 2.0 times the allowable capacity invariably
reaches a pile head movement in excess of that required to
draw line ab with sufficient additional points to define the
slope of line bd. Therefore, by using Chin's method, an
estimate of Ch,can be made even though the test may not have

been loaded to failure.

3.4 Limitations of Davisson's and Chin's Criteria

With an increased usage of the wave equation method of
analysis, Davisson's method has gained widespread use (since
Davisson's method was developed from the analysis using wave
equation - see also Section 3.3.2). Ist simple application
for static analysis and straight—forward procedure made it
popular and it can be used on routine loading test by
relatively inexperience practitioners. It allows an engineer,
when proof testing a pile for a certain allowable load, to
determine in advance the maximum allowable movement for this
load with consideration of the length and size of the pile.

The Chin's method is founded on an ingenious and
convincing theoretical approach; and it could offer the

advantage of:

60

(i) a possible separation of ultimate capacity into two
components of shaft and toe capacities (However,
from the data considered for this study, as
indicated by the plots in Appendix A, only few
plots are found to have two straight lines).

(ii) estimation of ultimate capacity without loading to
failure.

(iii)identifying pessible structural damaged (Hi the

pile.

From the plot of (m/Q) vs m, a damage pile can be
identified by a non linear plot, and this is generally not
highlighted from the conventional plot of (C) vs In). This
check can be done even when the test is in progress, a sudden
kink or slope changes in the line could prompt the tester of
problems of either the pile or the test instruments used.
Therefore, the presence of damaged in piles or instrumental
errors is consistently revealed by using Chin's method.
However, in using Chin's method, the correct straight line
does not start to materialize until the load has passed the
Davisson's criteria. In many cases, a few points from the
start of the test need to be neglected to avoid getting a
false straight line (see also Appendix A). Another additional
advantage is that the method is less sensitive to
imprecisions of the load and movement values.

The Chin's method is applicable to both quick and slow

tests, provided constant time increments (CRP) euxe used.

61
According to Fellenius (1980), the ASTM "standard" method of

testing is therefore usually not applicable. The number of
points in the standard testing are too few; an interesting
development could well appear between load increment number
7th and 8th and be lost.

As with other methods, the accuracy of Chin's criteria
is also dependent upon the validity of the assumptions made
in formulating the hypothesis. Most piles do exhibit a
hyperbolic (Q \NS m0 plot under loading test, Inn: not all
piles tested actually reach the limiting value. The maximum
mobilization of the shaft capacity before any mobilization of
toe capacity is also questionable. Evidence that toe capacity
develops from the beginning of loading test or that shaft
capacity continues to increase at some additional load can be
found in many of the previous studies and reported tests of
instrumented piles (e.q., Vesic, 1970; Leonards and Lovell,
1978; Fellenius, 1980). These and other limitations indicated
that Chin's hypothesis cannot be completely correct.

Fellenius (1980) indicated a variathi of about 30 %
between the largest (Chin's criteria) and: the lowest
(Davisson's criteria) of interpreting failure load (in Fig.
3.1). From. instrumented. piles studied. earlier. by ‘Vesic
(1970), Leonards and Lovell (1978) pointed out that in some
cases, an additional axial load applied on pile can be
supported solely by shaft resistance without an increase in
toe resistance. Therefore in general, the notion of early

mobilization of shaft resistance or maximum shaft resistance

62

before toe resistance is mobilized could not be true. The
reason as pointed out by Leonards and Lovell (1978) could be
due to a redistribution of effective lateral earth pressure
on the pile shaft. However, there are cases when shaft
resistance is mobilized first, but this cannot be assumed a
priori.

As a rule (Fellenius, 1980), interpretation of measured
capacity using Chin's criteria is about 20 t1) 40% greater
than the measured capacity using Davisson's criteria; when
this is not the case, a closer look at all the test data was

recommended.

3.5 Separating Shaft and Toe Capacity

In the 1950's, it was uncommon to use a tell-tale device
when conducting routine pile loading test. A method of
separating shaft and toe capacity from loading test was
introduced by Van Weele (1957). This required knowledge of
the magnitude and distribution of the unit shaft capacity,
which Van Weele (1957) proposed be obtained by correlation
from Dutch Cone penetration test. Analytically the method by
Van Weele provide a consistent separation of the total
capacity into shaft and toe capacity even though in some
cases showed varying results. However, some investigators
have lately begun to use it (Leonards and Lovell, 1979;

Brierley et al, 1979; and Fellenius, 1980). Nevertheless, in

63

Van Weele's method, the knowledge of toe movement is needed;
consequently this method was not considered in this study
(load—toe movement curves are not available from the data
considered).

However, the separation of shaft and toe capacity can be
estimated according to the interpreted criteria as briefly
described below.

The distribution of axial load in the pile can be
measured if the pile is instrumented with strain gages at a
few locations along the pile (e.g., Williams, 1960; Vesic,
1970; Bustamente, 1982b). With proper calibration, the load
along the pile shaft can be plotted as represented by curve
1km in Fig. 3.4. The load (Q) on the curve amzin Fig. 3.4 is
not typically the measured capacity (Qm) as interpreted by
the chosen criteria. Therefore for this research, the
proportion of the toe capacity, film/Q), is linearly
interpolated according to the interpreted Cb,an3 dictated by
the function of film/Q) for the respective criteria (see also
Step 3 in Section 5.3.2). Consequently, the shaft capacity,
Qsm, is then the difference of the interpreted Qm and On“.
This method provided a consistent method of separating Chm and

(hm from loading test. (see Chapter 5).

64

 

 

Ioacfing Test

interpreted criteria

 

 

 

 

 

 

 

 

illi—

 

 

 

 

 

Distribution of Resistances Along Pile Shaft.

.4:

3

Fig.

65

3.6 Summary

Even though the capacity of pile as determined by
loading test is considered to be the most accurate, the
interpreted measured capacity is highly dependent upon how
the failure criteria is defined. Evidently from previous
studies, the measured capacity could vary ir1tflu3 order of
about 20 to 40 % if different criteria are used.

The four criteria as presented in this Chapter were used
extensively in Chapter 5 to derive the design charts in the

developed algorithm.

CHAPTER 4

RELIABILITY THEORY IN ENGINEERING

4.1 Introduction

In the presence of uncertainties, absolute reliability
is not possible. However, probability theory and reliability-
based design techniques do provide a formal framework for
developing criteria for design. which insure that the
probability of unfavorable performance is acceptably small.

There have been no standards adopted in the US which
synthesize all tflue available informatnmi for purposes of
developing reliability—based criteria for design (Ellingwood,
1980). Prior to inmflementatmmi of Load Resistance Factor
Design (LRFD), the IMHB of statistical methodologies had
stopped at the point where the nominal strength or load was
specified. Additional load and resistance factors, or
allowable stresses, were then selected subjectively to
account for unforeseen ‘unfavorable deviations from the
nominal values. At present however, probability theory and
structural reliability methods make it possible to select
safety factors to be consistent with a desired level of
performance, i.e., acceptably low probability of
unsatisfactory performance.

Some background and findings from previous studies
related tn) the prediction (ME pile capacity have been

presented. in Section. 2.2.2. This section. will present
66

67

previous studies that are related to reliability analysis and
draw from it concepts for the development of the algorithm in

this research.

4.2 iPrevious Work

To estimate pile capacity, it is necessary to assess the
individual pile uncertainties as well as the overall bias and
error associated vntfli design. according to ea specified
recommended procedure. It is only through a complete
uncertainty analysis that the reliability of a pile or pile
system could be estimated. Among previous work in this area
are the studies by Dennis and Olson (1983, 1985), and Olson
(1984). Dennis and Olson developed a computerized data base
of 1004 pile load tests to evaluate the bias and error
associated with specific pile capacity prediction methods.
From that study, it was shown that there is a large scatter
between measured and predicted capacities especially in the
earlier API recommended design practice. Their emphasis have
been on the statistical assessment of the prediction model
error and providing suggestions for improved design
procedures. The correction factors as proposed by Dennis and
Olson (1983, 1985) for the shaft and toe capacities are the
one as presented in Section 2.5.1. However, some other
factors, e.g., loading rate, reconsolidation and nominal

strength were not explicitly accounted for.

68

Bea (1983) identified various factors affecting offshore
pile capacity prediction, and suggested preliminary estimates
of the bias and error associated with each factor. An
extension of the work by Bea (1983) was done by Tang (1989)
and Sidi (1986).

For drilled shafts, in another study by Kulhawy and his
group (Kulhawy, 1984), it was shown that there is a
significant bias anui error between predicted anmi measured
pile capacities.

Kay’ (1976, 1977) jproposed £1 rational. procedure for
consistent design of single pile, correlated from the results
of loading tests. To optimize the testing procedure and to
improve final design of piles, the Bayesian probability
theory was used. In those studies, the First Order Second
Moment (FOSM) method as proposed by Cornell in 1969 was used.
On comparing the results of static pile loading tests on
driven piles and the prediction of pile capacity (using
published data from Whitaker and Cooke in 1966), Kay (1976,
1977) assumed that the capacity values followed a lognormal
distribution. Hewever, it 1mm“: be emphasized that :hi Kay
(1976) the number of the examined piles was only five. The
mean of the ratios of log of measured to predicted pile
capacities ranged from 0.92 txa 1.42 and the standard
deviation of this ratio ranged from 0.14 to 0.35. The
standard deviation of the ratio of the log in those studies
has a large impact on the reliability index, and consequently

the allowable capacity. Also, the measured capacities from

69
the loading tests that were used in that study (also adopted

from reported literature) were not likely interpreted by the
same method.

In short, it can be said that Kay's findings were
derived from a sound theoretical basis, but the accuracy of
the end result is somewhat "of low precision." The research
herein follows Kay's work with regards to the assumption of
scatter of model uncertainty at the site; but the capacities

are determined from a well defined and consistent methods.

4.3 .Structural Reliability Theory

4.3.1 Historical Background

Reliability theory has been used by engineers for some
times in the determination of the reliability of electronic
and mechanical systems in the manufacturing process. For
example, probability methods are commonly used 1J1 circuit
problems or determining the life expectancy of a machine.
Using reliability theory, structures can also be designed to
function for an expected and reasonably predictable time.

Over the lifetime of most structures, they are subjected
to various kinds of loads that are not always constant,
predictable or predetermined. The material used for a support

system, for example is dependent on many uncertainties in the

70

manufacturing' process, material strengths and :modelling
methods.

Until recently, structural design has been primarily a
deterministic procedure using what were perceived the upper
bounds of loads effects and lower bounds of material
strengths. There was an understanding that there existed a
continuum of probable values. As reported by Corotis (1985),
structural reliability research had not gained much attention
for advancement mainly for three reasons, namely; first, the
continuum of probable values could not readily be defined due
to lack of sufficient data bases; second, the mathematical
methods had not yet been developed to define rational safety
margins; and finally, slow change in seructural codes. A.
comprehensive review (Hi early attempts at introducing
reliability methods and practices into structural design can
be found in, e.g., Madsen et al (1986).

It was not until the middle of 1960's that reliability
(1r probability based structural design began tn) gain some
support. Although by this time quite a number of new concepts
had been developed, much of them were in the class of
.academic research rather than being actually used by
practitioners; after all, deterministic design is fairly
straight forward and had served the profession well with very
fewv failures (De Mello, 1971; Corotis, 1985).

.A probability-based structural code based on.ea second

moment approach was proposed by Cornell (1969). His work

gaiuded much attention and attracted others to research on

71

reliability methods because his approaCh had the promising
ability to produce a set of safety factors on loads and
resistances, something that code writing committees
specified. Cornell's work opened the door to the possibility
and acceptance of gnrmebility—based structural standards;
even though problems were encountered in attempting to
implement this approach.

Some examples of usage of system reliability are such as
Frudenthal, (1961, 1966); Kay, (1976, 1977); Ellingwood,
(1978); MadhaV' and .Arumugam, (1979); Ellingwood et .al,
(1980); Grigoriu, (1982/1983); Moses and Rashedi, (1983);
Wolff and Harr, (1987); Sidi and Tang, (1987); and Wolff and

Wang, (1992).

4 . 3 . 2 Formats of Reliability Theory

The general format of reliability theories was

categorized by Corotis (1985) as Stochastic, Full
Distribution, First Order Second Moment (FOSM) , and Load
Resistance Factored Design (LRFD). General definitions of

these formats are briefly presented below.

72
4.3.2.1 Stochastic

A stochastic reliability format can be represented as:

Ps=P[D(s.t)<C(s.t)1 4.1

where, P8 = probability of safe performance; 8 = space
throughout the structure; 1 = time over the economic lifetime
of the structure; D(&0 = various components of loading (or
Demand); C(aO == various components of .resistance' (car
Capacity).

Equation 4.1 indicates that the probability of safe
performance is the probability that each component of [the
load effect vector is less than the corresponding component
of the resistance vector, throughout the space of the
structure and the design life. This approach is simple in
concept but complex and untraceable in application due to the
difficulty‘ of handling' of :multi-dimensional stochastic
variables. Thus, this format remains limited t1) research
status only (but provide an important conceptual

understanding).

4.3.2.2 Full Distribution

This format is a simplified version of the stochastic
format. By assuming that structural resistances do not vary

over time, the time component in Eq. 4.1 is restricted. Then

73

some approximate approaches to load combination theory and
stochastic process are used to replace the time-varying loads
by a few critical load combinations involving ranchnn
variables rather than random process.

A simple and relatively accurate form is such as the one
developed by Turkstra et a1 (1980). It considers N random load
processes through time on a structure. At some point in time
during tine design lifetime (M3 the structure (actually 11
different times in general) each of these processes will
experience its lifetime maximum load, Dm. The assumption is
made such that as each process experiences its maximum, the
other processes assume average (so called arbitrary—point—in-
time) values, Eh. For N different load process, this means
there are N different load combinations to check, each
corresponding to a different process experiencing its maximum.

It has been shown that this method works well (Turkstra
et al, 1980), although there are other load combination
approaches available.

A typical equation for a Full Distribution Format might

take the following form:

i=I,N

Ps=PIm3Xj=1,N[Djm(S)+Z9121(8)]<C(S)I 4.2
I is) I

Equation 4.2 is much simpler than Eq. 4.1 although it
looks complicated since stochastic variables (in time) have
been replaced. by :random. variables. In theory, Eq. 4.2

represents a check for structural performance throughout the

74

structure. In actual practice, however, the vector aspects of
loads (or Demands) and resistances (or Capacity) are
implemented by considering a few key load effects (e.g.,
bending moment and. mid-span shear). Also, the spatial
aspects, 8, are considered by smudying only tflue critical
points in the structure. This reduces the problem to one of
repeated scalar comparisons at single locations. One such

check would take on the following form:

Ps = P ID I CI 4 .3
in which
D = man=1,N (Djm + 2 D18) 4 4
ifI,N '
11‘}

Since both C and D in Eq. 4.3 are random variables, the
evaluation of that probability generally involves a
convolution integral. Two forms of convolution integrals may

be used to evaluate Eq. 4.3. One form is:

co

1),: fD([)[1'FC([)IdI 4.5

This equation represents the probability of safe
performance as the likelihood the load assumes any particular

value RXIImmltiplied by the probability that the resistances

75

exceeds this ‘value [l-Iki[fl, and then this product is
integrated over all possible particular load values. Another

convolution form is:

co

Ps = fc(r) [1:00)] dr 4. 6

This convolution equation can be said to represent the
likelihood that the resistance assumes a particular value fix»
multiplied by the probability that the load is less than the
value [FD(r)], and then this product is integrated over all

possible resistance values.

4 . 3 . 2 . 3 First Order Second Moment

This format was first proposed by Cornell (1969). The
basic premise of this format is that it simplifies the full
distribution format for pmaetical applications. Within ea
deterministic sense, each "variable" assumes a single design
value. Cornell suggested the expression of random variables
using two parameters, rather‘ than. a single value, to
introduce random aspects without causing the problem to
become untraceable. The two quantities are the mean (or the
expected value) and the other is a measure of uncertainty or
variability (commonly accepted is the standard deviation or

variance).

76

This approach (ME using’ the .mean and variance, is
therefore referred to as a first order uncertainty analysis
(Cornell, 1971) or second moment approximation of the Taylor
Series (Harr, 1987).

The real advantage of the FOSM approach is that it
introduces consideration (ME variability vutlmnm: requiring
full distribution analysis. As an example, consider a single
load (or "Demand") effect quantity, D, with mean D and
standard deviation on, and a single corresponding resistance
(or "Capacity," C) with mean C and standard deviation 0C. To
design a structure with a high likelihood of satisfactory
performance, one might pick a design value for the Demand
that is a few standard deviations above its mean and a
resistance (i.e., Capacity) design value 51 few standard
deviations below its mean. The design equation for this
format would then be the design load that does not exceed the

design resistance:

Dd=D+kDoDSCd=C-kcoc 4.7

The reliability implied by Eq. 4.7 depends on RD and kc,
and also on the probability distribution for C and D. Without
knowledge (of time actual. distributions, only’ approximate
probabilities or very wide Chebyshev bounds can.kx2 found.
However, this approach is straight forward, and it does

include direct consideration of variabilities.

77

If both Capacity and Demand are assumed to be
independent and normally distributed, the safety margin, SNL
is also normally distributed.

The reliability is the probability that Shd is positive:

PS=P[SM>0]=I-Fsm(0) 4.8

Since SM is normally distributed, Eq. 4.8 may be
expressed as:

Ps=1-Fu1%i-EI=FUI%ESJI=FU(B) 4'9

where, F000 is the unit, e.g., normal cumulative distribution
function (unit c.d.f). The reliability is uniquely determined
by B, which may be thought of as the number of standard
deviations by which the mean Capacity exceeds the mean
Demand; i.e., the standard deviation of the Sh4.'Fhe quantity
is often referred to as a reliability index, B.

The extension of Eq. 4.9 to multiple loads or resistance
(non-linear functions) causes a problem known as lack of
invariance. To circumvent this, using tflma small variance
approximation, Hasofer and Lind (1974) developed an
approximate procedure by using the concept of performance
function (Ellingwood et al, 1980; Corotis, 1985) as shown in

Fig. 4.1.

78

 

 

 

 

 

 

 

Capacity (C)
1 x,
g?
ihdeSune Ԥ9
(SM>0) v
a
.4»
\4
0.0 Failure State
,9 (SM<0)
45°
‘ ‘ i ) (
. Demand D)
‘ . .
(a) Limit State Space
C!
A
C zfl ; D =JLD
c 0b
Safe State
’8
)>[T
B Failure State

(b) Reduced Limit State Space

 

Fig. 4.1: The Model of Performance Function.

 

79

The general form of performance function, or limit state
equation in terms of Capacity and Demand may be expressed as

(Ellingwood et al, 1980; Ang and Tang, 1984; Harr, 1987);

g = gc (Cu C2 ...) ' go (Du Dz ...) 4.10

The surface in capacity and demand space, i.e., at (g=0)
is termed as the limit state surface. Failure is defined as
any condition when (g<0) or when (g.<gs). By simple
substitution, the limit state surface may 1x2 expressed in
terms of reduced variables (with mean equal to zero and unit
variance as shown in Fig. 4.1(bl). After a transformation to
independent random variables if correlation exists, the limit
state surface is then in terms of so called basic variables
in reduced space.

The shortest distance from the origin to the limit state
surface in this space is defined as the measure of

reliability, i.e., B, which may be approximately expressed

as;

i=5—
01: 4.11

where, g = mean value of g; 0g 2 standard deviation of g.

It is assumed that capacity and demand are random
independent variables, otherwise the shortest distance to the

limit state does not represent the reliability.

80

In terms of SM, Eq. 4.10 can be rewritten as;

81C1DI=SM=0 4.12

Safe state is represented by (SM>0) and failure state by
(SM<0). It can be shown that (e.g., Ellingwood, 1980; Harr,

1987) for normal uncorrelated distributions, the shortest

distance from the origin, thus B value can be expressed as:

13: 65-15
1108 0.3 4.13
where, C: mean value of resistance (or Capacity); and D:

mean value of load (or Demand).
A detailed assessment about the subject can be found in

Ang and Tang (1984), Ditlevsen (1981) and Harr (1987).

4 . 3 . 2 . 4 Load and Resistance Factor Design

A. convenient simplification (M5 the FOSM format is
possible when structural analysis is based on a member
analysis rather than a system analysis. This is the basic
premise of FOSM format. The approximate degrees of safety or
reliability are provided on an element or component basis.
This is accomplished through the use of partial safety

factors applied to nominal values of loads and resistances.

81

Examples of Load Resistance Factor Design (LRFTD can be
found in ACI (1991), or PCA (1989) Code since 1963, AISC
(1980) specification, and Canadian Steel Design (1978); where
the :nominal capacity’ of EH1 element is ImJltiplied. by ea
specific strength reduction factor (value less than 1.0). The
assumed demands (i.e., moments or forces) are multiplied by
specific load factors (values generally more than 1.0). The
nominal values employed are not necessarily the mean values
for strength and are in most cases somewhat conservative. A

typical equation can be expressed as;

er=fDLDL+fLLLL 4.14

where, fl, fin and fii are the factors for resistance, dead load
and live load, respectively.

The left hand side of Eq. 4.14 is referred to as the
required strength based on factored loads, and the right hand
side is the design strength. Although the nominal load
effects and strength as used in ACI (1984) Code are not
necessarily mean values, they are reasonably close
approximations (Ellingwood, 1980).

The LRFD format (e.g., Eq. 4.14) is simple to use and is
not strictly method of reliability analysis. It is simply a
method of safety checking and provides the basis on which
other formats discussed above can be imposed; with various
degrees of pmobabilistic sophistication (Ellingwood, 1978;

MacGregor et al, 1983).

82

As additional data become available, and with an
increases in computer usage and efficiency, the probabilistic
sophistication of design engineers continues to grow, it is
expected that design codes of FOSM or higher formats may
eventually appear. For the next generation of codes, however,
it is clear that LRFD format with factors determined from
probabilistic considerations will In; a compromise that is
acceptable to design engineers, while at the same time
capable to accommodate updated. probability information
(Corotis, 1985). The algorithm developed in this research is

perhaps a step towards this direction.

4.4 Pile Design: Safety' Measures

In the design of pile foundation, one of the major
considerations is to ensure that the load "working" on the
pile (or the allowable capacity) is not to exceed the
"actual" capacity (the pile can sustain) before "failure."
This assurance of safe performance is quantified by the value
of safety measures; which are typically defined in the
proceeding sections.

In deterministic design, the risk of failure is depicted

by the allowable factor of safety, FS. From Harr (1987), ES

can be represented as;

83

FS=§
D 4.15
where, C and D = nominal values of capacity (i.e., pile
resistance) and demand (i.e., allowable load), respectively.

It is also a common practice that the value of resistance is

assigned lower than the mean. This can be expressed as;

C=C-hco. 4.16

Ihi pile design, this generally occurs In! the designer
using some conservatism in assigning the value of resistance.
Likewise, D is assigned higher than the mean. This generally

occurs because the allowable load is generally assigned

higher than actual; and can be expressed as;
6=6+hoon 4.17

Substituting Eqs. 4.16 and 4.17 into 4.15 would give;

C-hcr
FS==-:.———C—L
D+hDoD 4-18

where, C and D are the mean values of Capacity and Demand,
respectively; hcammilm are h sigma units of their respective
functions.

In deterministic design, if the calculated FS is greater
than the specified minimum value (from code) or obtained from
past experience, it is considered satisfactory. In

reliability-based (FOSM) design, C and.I5 can be treated as

84

random variables as they cannot be determined with certainty.
The ratio of the expected values, known as the central factor

of safety, CFS, can be represented as (Harr, 1979; Ellingwood

et al, 1980; and Harr, 1987);

cps = Etc] -

EID] -

EMF“

where, HIS and SIN are the expected values of the Capacity
and Demand, respectively.

As indicated by Fig. 4.2, the probability distributions
of C and D will overlap if the maximum demand, Dmax, exceeds
the minimum capacity, Crnin; and there will be a nonzero
probability of failure.

The probability of failure is the shaded area in Fig.

4.2 (b), i.e., when (SMSO), it can be expressed as;

Pf =1 Fc(x) fD(x)dx

0 4.21

where, Fc = cumulative probability distribution function
(c.d.f) in C and fit: probability density function (p.d.f) for

D. For a normal distribution, e.g., then;

pf=¢[-_£L-_D__
IGc'I'O'D

 

4.22

85

 

 

f (C, D)

 

 

 

£D>
Dmin C0110 Dimx Cmax C, D

(a) Resistance and Load Distribution

f(SND
A 5571
‘— 13051111

"E

    

 

Pf = P [SM<0] P. = P [SM>O]

  

 

 

 

(b) Safety Margin and Reliability Index

 

Fig. 4.2: Safety Measures - Normally Distributed FOSM

Design.

 

86

where, 0[] = standard normal cumulative probability

distribution (c.p.d).
Comparing Eqs. 4.22 and 4.13, the reliability index is

related to the percent point function of the standard normal

distribution according to;

-1
13:911'1’0 4,23
Pr=¢I-I3I 4.24

As a rule of thumb (Harr, 1987), when (1<B<4) the

probability of failure, Pp can be approximated as;

Pr=1*10‘fl 4.25

4.5 Summary

In summary, five safety measures have been defined,
namely; the conventional factor of safety, FS; the central
factor of safety, CFS; the safety margin, 854; the reliability
index, B; and the probability of failure, Pfi. Adaptation of
these safety measures for the development of an algorithm in

this research will be presented in the next chapter.

CHAPTER 5

DEVELOPMENT OF THE ALGORITHM

5.1 Introduction

This chapter presents the derivation and development of
the algorithm to interrelate the safety measures for the
deterministic and reliability—based design approaches.

The uncertainty associated with pertinent variables for
the determination of allowable pile capacity can be
incorporated in a rational design process without requiring a
full and complex probabilistic analysis. The LEM? of only
nominal values of resistances and loads (as in the case of
working stress deterministic designl may ‘work.'well but
provides ‘us IN) information. regarding the (dispersion. of
variables. With the inclusion of probability theory, more
information is incorporated in the analysis.

One scheme to determine the expected values of
resistance and load (or capacity and demand) in the complete
formula (e.g., Taylor series) requires the evaluation of
derivatives. The 'procedure CRHI be simple but often is
cumbersome for complex functions such as shaft resistance;
and certainly is not appealing for use in routine designs. To
circumvent the analytical evaluation of derivatives, a First
Order uncertainty analysis (e.g., Cornell, 1971) can be used.
Some application of these methods can be found in Kay (1976,

1977), Wolff and Barr (1987), Sidi enui Tang (1987), Harr
87

88
(1987), Wolff (1989), Wolff and Wang (1992). For example, Kay

(1976, 1977) used the First Order Second Moment (FOSM) format
as presented by Cornell in 1969. It is assumed that any
uncertainties inherent in either the capacity (i.e.,
resistance) or demand (i.e., load) can be represented by the
expected values (or mean) and the standard deviation of the
pertinent random variables.

This chapter will also present the calibration of the
calculated capacity from static formula for the determination
of the predicted capacity for pile foundations in sand. Data
from in-situ Standard Penetration Test are used. In general,
the assumptions of FOSM method by Kay (1976, 1977), and the
procedure for integration of unit shaft resistance by Wolff
(1987) is adopted.

The derived algorithm will, (i) use the actual Standard
Penetration Test resistance as recorded from the soil boring
logs, and interpolated linearly at small discrete intervals
(herein one foot), (ii) introduce calibration factors into
the "standard" static pile formuLa by using time measured
capacity from time loading' tests, and (iii) interrelate
deterministic safety measure with reliability—based safety
measures.

From the developed algorithm, more consistent designs
are possible. Consequently, engineering judgment is more
explicitly quantified as compared to the present procedures

in conventional design (arbitrary judgment in choosing

89

specific parameters for the standard formula is not

required).

5.2 Data Base

A total of 23 pile tests (Table 5.1) were used for the
calibration of the algorithm. Eleven out of the 23 tests
involved are instrumented piles from Vesic (1970) and Fruco
and Associates (1964). The remaining 12 piles are from Peck

(1961) and were not instrumented. The criteria for choosing

these piles are, (i) SPT N—values were available in the
vicinity of the pile, (ii) piles were predominantly driven
into cohesionless soil, (iii) piles were not enmi bearing

(and/or N-values of more than 100 at the toe, or piles with
hard bearing layer near the toe are excluded).

All of time 23 piles were steel pipe piles. ix brief
summary of pile types, pile testing, pile installation, and

soil profile is presented below.

5 . 2 . 1 Site at Ogeechee River

The first five tested piles (Pile No.1 through No.5)
used in this study are from Test Pile 1 as reported by Vesic
(1970), at the site of Ogeechee River bridge on Interstate
Highway 16; approximately 18 miles west of Savannah, Georgia.

This site is characterized by deep deposits of medium dense

90

to dense well graded sand, typical for this area (ME the
Atlantic Coastal Plain.

Standard penetration records are available from three
adjacent borings; B-1, B—2 and B-69 located at about 17, 15,
and 25 ft. from the test pile respectively. For the developed
algorithm, the N-values are interpolated at every foot of
depth for each boring and the average values from the three
borings are used.

The pile was an instrumented steel pipe of 18 in.
diameter and 1.5 in. wall thickness. The pile consisted of
five sections each 2H) ft. long allowing driving and
successive testing in five stages at depths of approximately
10, 20, 30, 40 and 50 ft. The bottom section was plugged at
the base with a 2 in. thick flat steel plate.

The piles were driven by a McKiernan-Terry diesel hammer
with a ram weighing 2 tons. The tests were loaded by a 500
ton hydraulic jack against. a water filled box girder
supported at its end by reaction piles, after a waiting
period of 12 hours after driving. The loading was done
according to the constant rate of penetration (CRP) method as
described by Whitaker and Cooke (1961).

The interpreted measured capacities, Qm, by the 2 IJL
movement [2"], Davisson's [D], and Chin's [C] criteria are as
presented in Appendix A. For each of these three criteria,

five data points are available from this data set.

91
5.2.2 Locks and Dam No.4

Piles No.6 through No.11 used in this study, are from a
pile testing program reported by Fruco and Associates,
(1964). The test pile program was done the Locks and Dam
No.4, on the lower Arkansas River below Pine Bluffs,
Arkansas. The site is on east bank of the Arkansas River.

From the boring logs reported, three major soil strata
exist; a surface of silt and fine sand (about 13 ft.), a deep
stratum of relatively dense medium to fine sand (about 93
ft.), and a basal stratum of Tertiary clay of unknown
thickness. Dry unit weights ranged from 90 - 109 pcf and did
not show any significant trend with depth.

All the piles were instrumented and driven unplugged and
ranged from 12 — 20 in. diameter. The steel piles were driven
13713 7 ton Vulcan 140C steam hammer. The pile testing was
performed using constant load (CL) increments; it was loaded
by a hydraulic jack reacting against a test frame with
concrete blocks. The loading was done in ten equal
increments, applied and released at a rate of two tons/min.
Each load was maintained for at least one hour, and a new
load was applied after pile movement of 0.01 in./hr. The test

was terminated when the movement was 0.005 in./hr.

92
5.2.3 Peck's Collection

The third set of pile tests (Pile No.12 through No.23)
is from the collection of Peck (1961). Peck compiled pile
tests data from all over the country for the Highway Research
Board. Only the very basic information about pile and pile
testing are available, such as hammer type, pile type,
embedded length, and load—movement curves. No detail of the
soil profile at the various sites is available except for the
location of tested pile and SPT N—values. There is no mention
about water table or any instrumentation. Therefore, it is
assumed that the test sites were free of groundwater and that
the piles were not instrumented and driven unplugged. From
the characteristics of the load—movement curves, apparently
the piles were tested according to the constant load (CL)
procedure.

The locations of the selected piles are from several
different sites an; indicated from Table 5&1” The load-
movement curves for several of these piles had to be
extrapolated to determine the measured capacity using the 2
in. movement criteria [2"]. For the interpretation by the
Davisson's [EH enui Chin Criteria [C], rue extrapolation is

needed.

93

Table 5.1: Data Base For The Development of The Algorithm.

Pile , Length iete Deat ' ’ ' Mercia ” ]
No. Le (it) (1 (in) Tested 1

omxioacnrswro-e

 

Ogeechee.10'
Ogeechee.20'
Ogeechee.30‘
Ogeechee.40'
Ogeechee.50'
L81 D4.TP1

L8 D4.TP2-1
L81 D4.TP2-2
L81 D4.TP3
L81 D4.TP1 0
L8. D4.TP1 6
Peck.15
Peck.22
Peck.51
Peck.55
Peck.206
Peck.208
Peck.272
Peck.274
Peck.3 58
Peck.359
Peck.3 60
Peck.361

 

 

 

‘NA
4NA
4NA
‘NA
4NA
4NA
‘NA
4NA
4NA
“NA
4NA
3.17.54
3.17.54
3.7.53
2.17.53
5.3.56
5.21.56
10.26.56
9.21.56
12.27.55
12.1.55
12.27.55
12.8.55

 

1Ogeechee River
1Ogeechee River
1Ogeechee River
1Ogeechee River
1Ogeechee River

2Locks & Dam No.4
2Locks 81 Dam No.4
2Locks 8 Dam No.4
2Locks 81 Dam No.4
2Locks 8 Dam No.4
2Locks 8. Dam No.4
3New Orleans, Louisiana
3New Orleans, Louisiana
3Jefferson City, Texas
3Brazoria County, Texas
3Richland County, Ohio
3Richland County, Ohio
3Noxon Rapids, Montana
3Noxon Rapids, Montana
3|ndiana

3Indiana

3|ndiana

3lndiana

 

1from Vesic (1970)

2from Fruco 81 Associates (1964)

31mm Peck (1961)

4Exact date of test Not Available from the References
Pile No.11 is jetted

5.3 The Algorithm

The theoretical concepts used as the bases for the

development of the algorithm are described in detail

in

94
Chapters 2 and 4 for the deterministic and the reliability—

based components of the method respectively. Limitations and
difficulties associated with the specific equations and
parameters have also been discussed.

Presented below are the various formulas from both

methods adopted for the derivation of the algorithm.

5.3.]. Basic Concepts and .Assumptions

5 . 3 . 1 . 1 Deterministic Formula: Qsc & th

The analytical formula Um}. 2.5, Section 2.4) for
calculating pile capacity is expressed as the sum of the

calculated shaft and calculated toe capacities, i.e;

Qc=Qsc+th 5.1

From Eqs. 2.7 and 2.10, the calculated shaft and
calculated toe capacities are respectively defined as:

Qsc = : [(Ks pov tan 8)i (As)i] 5 . 2

th = (Pt Na) A1 5 - 3
where other parameters are as previously defined in Section
2.4. For the calculation of the area of the pile at the toe,
A“ it is assumed that the pile is fully plugged (i.e., flu is

the cross sectional area of the pile). For piles driven

95

without a steel cover plate at the toe, this assumes a soil

plug is formed by soil arching.

5.3.1.2 Coefficient of Lateral Earth Pressure: K

The coefficient of lateral earth pressure at the site,
K8, is assumed to be equal to the empirical coefficient of
lateral earth pressure at rest, K0. Assuming that the piles
are designed for long term capacity (and not the capacity
immediately after the pile is driven), then K0 may better
represent the coefficient of lateral earth pressure of the
soil at the site [as opposed to adopting (Kngo), i.e., an
increased Ks immediately after pile driving, or (KS<K0) a
reduction in Ks due to soil sensitivity or a loose soil
condition after driving]. Therefore, as presented by Bowles
(1988), Jaky's empirical correlation in 1948 for K0 is used
for K8 in this study; whereby Kozl-sinq). As mentioned by
Meyerhof (1976a), K0 was also an assumption adopted by
Burland in his previous study.

With the inclusion of calibration factors (i.e., Fs and
Ifl which will be shown in Section 5.4.2), the "calibrated" B*
coefficient ill the standard formula can 1x2 statistically
determined to be at a maximum near the surface of the soil
and decreased to a minimum near the toe of the pile, as

suggested by Kaizumi (1971) and Kulhawy (1984).

96
5.3.1.3 Soil-Pile Interface Angle: 5

The uncertainty associated with the soil—pile interface

angle (5) has been discussed in Section 2.4.1.2. In this

study, 5 is taken as a reduced angle of internal friction of

the soil ((1)); where (8=f¢¢). The reduction factor, f¢, is

adopted from a rigorous study by Potyondi (1961).
Consequently, with the combination of the above assumption

(i.e., KS=K0), therefore (Ks=l-sin8).

5 . 3 . 1 . 4 Corrected N—Value: N
The N-value is corrected for overburden pressure as
proposed by Liao and Whitman (1986), which is represented as:

N'=N i (p; in tsf) 5.4

5.3.1.5 Friction Angle of Soil: 4)

Using a similar method by Wolff (1989), the friction

angle of soil, (1), is correlated from the corrected SPT N-

value, N', using the relationship as presented by Peck et al

(1974), which can be approximated as:

1 1 2
¢ = 26.70 + 0.36 N - 0.0014(N) 5 , 5

97

t

5 . 3 . 1 . 6 Modified Bearing Capacity Factor: Nq

*
The Vesic (1963) modified bearing capacity factor, Na is

adopted; which is equal to:

N3: 63'8¢ta"¢tan2(45+%) 5.6

5 . 3 . 1 . 7 Effective Overburden Earth Pressure: p'ov

Unit weight values for sand are not available for all
the collected data base. The calculated capacity is not
greatly sensitive to the unit weight (about less than one ton
increase for every one pcf increase for 515%) ft length of
pile). Consequently, in all cases the saturated unit weight
of sand,‘fim, and wet unit weights of sand, yum, are assumed
to be 130 pcf and 120 pcf respectively. The surcharge or the
overburden pmessure, pm“ is equal tx) the unit weight
multiplied by the height of the soil, h (i.e.,'nw=%mnh ). For
the soil below water table, the effective overburden

pressure, p5“ is used.

5 . 3 . 1 . 8 Capacity from Loading Test: Qm

In practice, perhaps more than one method is preferable

to interpret the loading tests (i.e., measured capacity, (bd.

The interpreted values should be counter checked by cmher

98

criteria. For this study, therefore the measured capacity

from loading test is interpreted by four criteria:

i. Criteria [2"] - Qm at a settlement of 2 in.

ii. Criteria [D] - Qm determined using Davisson's Method
iii.Criteria [C] - Qm determined using Chin's Method

iv. Criteria [DC] - the average Qm of criteria [D] & [C].

5 . 3 . 1 . 9 Safety Measures: FS & B

From reliability theory as defined by Eq. 4.13, the

reliability index (B) for normally distributed random

variables is;

B=——C'D 5.7
Voé+o§

The deterministic factor of safety (FS) as defined by Eq.
4.15 is;

'11
a:

ll
UZIOI
UT
CD

and the reliability-based central factor of safety (CFS) as

defined by Eq. 4.19 is;

CFS= 5.9

UIIOI

where all the respective parameters are as defined in Chapter 4.

99
In this study, E and 5 are substituted and defined as

the predicted axial pile capacity, Qp, and the allowable
capacity, Cb, respectively as indicated in Fig. 5.1. In slope
stability studies by Wolff (1985) and Wolff and Harr (1987),
a compromised reliability method was used, i.e., the Demand
(D) was assumed as a nominal value (deterministic) instead of
a random variable. In this study, a similar assumption is
adopted, whereby' the .allowable capacity’ is assumed as
deterministic value; as it: is desired tx> define ea single
"comfortable" load be allowed on the pile before "failure."

Therefore, Eq. 5.9 can be represented as:

CFS=%E 5.10

a

Consequently, B can be redefined as:

= 6p ' Qa
00»

B
or* the number‘ of standard. deviations of ‘the 1gredicted
capacity by which the predicted capacity exceeds the
allowable capacity.

If it is desired to express reliability as a probability

of failure (PH. it can be approximated by Eq. 4.25; however,

many agencies and code writers prefer to use only B.

lOO

 

 

 

 

 

Qa Qp

1D

.§ FS-£§
2‘ ' Q.
B

0

d:

(a) Deterministic Model:
Cb mmiCh — Nominal Values.
HQ)

.5

8

5

u.

.‘3‘

2

d

 

 

 

(b) The Assumed Reliability Model:
(%,- Random Variable; Ch - Nominal Value.

 

 

 

Fig. 5.1: Deterministic and Reliability Models for Safety
Measures.

101
5 . 3 . 2 The Developed Procedure

The developed algorithm can be most easily described by
considering the prediction of pile capacity and its
calibration as a sequence of ten steps. Each step is fully
described in the proceeding sections. After the calibration
of the "standard" formula (Eq. 2.5) with the measured
capacity from loading tests (Eq. 5.12), the uncertainty of
the predicted capacity will be lumped in global bias factor

(Fb) to be discussed.

5 . 3 . 2 . 1 Predicted Capacity: Qp

The 'calculated' capacity (Ck) for a given pile in Eq.
2.5 can be corrected to bring it into conformance with the
'measured' capacity (Qm) as defined by one of the four
criteria (see also STEP 1 in the proceeding sections). This
can be done by introducing correction factors for shaft and
toe capacities as developed in Steps 1 tfluxnufli 5 presented

below. Using these factors, a consistent predicted pile

capacityn Cb, can be achieved (STEP 5). Remaining
uncertainties or scatter of C5 about Ch,can.then be expressed
as a ”statistical bias factor" (Pb in STEP 6). The “bias-

corrected“ for the predicted capacity (after STEP 6) will be

used for the determination of the allowable capacity (C5). The

correlation of the safety measures as determined from the

102

deterministic and reliability-based approach are then

developed as in Steps 7 through 10.

STEP 1

W (Qm): The measured capacity (Qm) from
a loading test can be divided into two components of measured
shaft capacity, (km, and measured toe capacity, (hm, using

loading test data from.instrumented piles. Therefore (Ln can

be represented as:

Qm=Qsm+th 5.12

[Note: For the determination of R4 in STEP 2, cnrhy data from.
instrumented piles were used. For the determination of F5, F,
in STEP 4 and Pb in STEP 6, the inclusion of non instrumented

piles are also considered (see STEP 3)].

STEP 2

W (R1): The measured toe capacity

film) can be represented as a portion of the total measured
capacity, Ch“ This portion or percentage typically decreases
as ;pile length increases“ Therefore, tfima percentage of
measured toe capacity (Qun/Qm) for the instrumented and non
instrumented piles, was plotted against the embedded length
of pile, Le, normalized by pile diameter, d (as in Fig. 5.3).
A series of exponential curves fit through these plotted

points allows the development of mathematical expressions to

103

estimate the ratio of measured toe capacity, (th/leth, as a

function of dimensionless Hg/d);

R.=f(%) 5.13

Consequently, the ratio of the measured shaft resistance

“hm/Qh) is simply (l-RQ. And these ratios can be

represented as:

th/Qm=Rt=f(-I-‘d—°) 5-14

Qsm/Qm=1-R,=1-f(—la:) 5.15

Substituting the ratios from Eqs. 5.14 and 5.15 into Eq.

5.12 gives:
Qm=(1'Rt)Qm+(Rt)Qm 5.16
Qm=Qsm+th 5.17
STEP 3
WWW (Qm): By using

the exponential functions of Rt, the measured capacity (Qm)
from instrumented and non-instrumented loading tests can now
be consistently and reasonably allocated into two components,
and interpreted by Eq. 5.17 for the determination of other
factors (i.e., F5, Ft, and Pb in STEP 4 and STEP 6). This
assumes that the division of shaft and toe capacities can be

approximated by the function (Fig. 5.3) rather than the

104

actual individual points from instrumented piles. The
advantage of the interpretation of Q,“ by Eq. 5.17 is that the
proportion of the shaft and toe capacities (Eq. 5.12) need to
be interpolated (linearly) for each. of the respective
criteria considered in Section 5.3.1.8 (and see also Fig.
3.4). If the actual individual points from the loading tests
are used, the interpretation of (1m according to the
respective criteria could not be made. This is true even for
the instrumented piles, but the assumpthmn is especially
important if data from non instrumented piles are to be
included for the determination of FW IR, and Fb (see also the

analysis of the different Cases in Section 5.3.3).

STEP 4
rr ' F (Fs & F0: Ihi practice,
a limiting upper limit on shaft and toe resistances are often
assumed (e.g., as found in methods by API, 1991; Meyerhof,
1976a; and findings by Vesic, 1970). However, others such as
Kaizumi (1971) and Kulhawy (1984) have argued a gradually
decreasing model of unit shaft and toe resistances. In this
study, the depth-decreasing model arises by the introduction
of correction factors as presented below. This portion of
work done for this study is analogous to the previous work by
Dennis and Olson (1983), but the thactor by Dennis and Olson
is not dimensionless (see also Section 2.5).
The measured shaft and toe components obtained from Eq.

5.17 are divided with the respective components from Eqs. 5.2

105
and 5.3 and plotted against the dimensionless (Le/d). Again by

exponential regression (Qsm/Qsc) and (th/th) can be expressed

as functions of (ls/d).

Qsm/Qsc=f(-Ld£) 5.18

th/Q1c=f(l‘C—f—) 5.19

Therefore the correction factors for shaft, F5, and toe,

F“ is the functions in Eq. 5.18 and Eq. 5.19 respectively:

Fad—1:13) 5.20

F,=f(‘:d£) 5.21

The fitted exponential functions for the determination

of Fseuxilfl by Eqs. 5.20 and 5.21 can be found in Fig. 5.4.

STEP 5

2L2Q19L3d_£§p§§iLx.(Cblz The predicted capacity can now
be obtained by modifying the calculated shaft and toe
capacities from Eqs. 5.2 and 5.3 by multiplying them with the
respective Pk, and F“ to bring into conformance with

capacities from the respective loading test, Cb“ resulting;

Qp=Fs Qsc+Ftth 5.22

Qp=i[(Fs p'Ks tan 5% (As)i]+Ft (DLN; At) 5.23

1:1

106

Because of its form as a summation, the calculation of
Qp can be conveniently set up on a spreadsheet program with a
small vertical increment (say, one foot). This procedure is
adopted from Wolff (1989), but extended to include the

correction factors.

STEP 6

Bi F r (Fb): After the calibration of
the calculated capacity by the F5, and Ft functions for the
individual data points (23 data points) in STEP 5, a
statistical evaluation of the match was examined. It was
found that the predicted capacity, Qp, as determined by Eq.
5.23 for the whole 23 data points showed some bias.
Specifically, it tended to "over predict" the capacity as
compared to the respective measured capacity (see Table 5.4).
To further correct this "remaining“ difference or bias, the

"statistical bias factor" (F6). was introduced. It is simply

the mean of the ratio of (Qm/Qp):

Fb=(—_—b—Q:) 5.24

[Note: As Fb is the measured divided by the predicted
quantity, consequently if (Fb>1 . 0) , the pile capacity is
under predicted, and if (Fb<1 . 0) , the pile capacity is

over predicted . ]

107
From the studies of Kay (1976), Kay (1977), Madhav

(1979) and Dennis & Olson (1983), Jaeger and Bakht (1983) the
ratio of measured to predicted (CEMCQ) capacities follow a
lognormal distribution. For design purposes, even though
soil conditions over the site may be defined as "uniform," a
variability in the site capacity will occur. Therefore, the
capacity over a common site is treated as a random variable,
and the assumption of normality for the distribution of log
(Qm/Qp) as used by Kay (1976, 1977) is herein adopted (i.e.,
if a random variable X is lognormally distributed, then the

log of X is normally distributed).

5.3.2.2 Interrelation of Safety Measures: FS & B

STEP 7
BfidJJflLLLiLy__Jfiuhfig (B): Predicted capacity can be

normalized by the measured capacity to remove the influence
of variable geometry. Recalling Eq. 5.11, Qp is taken as a
random variable because it contains inherent uncertainty or
error. Rather than trying to define uncertainty in a specific
pile or specific variables, the reliability index can then be
expressed in terms of the normalized mean of log (Qp/Qm) and
the normalized (Qa/Qm), which is also one of the main
assumptions in Kay (1976, 1977) and adopted in this study.
Therefore, by taking the normal distribution of the logarithm

to the base 10 of the ratios as used by Kay, a simpler

108

reliability index of the lognormal distribution as in Eq.
5.25 can be applied (as opposed to other formats), see also

Table 5.4.

The expected value of the log (Qp/Qm) [herein referred

to as logiQp/th, and the standard deviation of the

distribution of log (Ch/Qm) [herein referred rm) as S] are
measures of the average and scatter associated with the model
uncertainty or bias with the use of the prediction equation
(as found by Eq. 5.23).

Therefore, substituting the respective parameters into
Eq. 5.11, reliability index can be represented as:

B = log (Qp/le - log (0.70...) 5 . 25

S
or

log (Q,/Q,,,)=log (Qp/le- [3 s 5 .26

therefore

(Qa/Qm) = 10 (log (QP/Qm) ' B S) 5 . 27

In the above expressions, S is a measure of uncertainty
within which the predicted and measured capacity can be
matched at a given site. The value of S is expected to be
larger for “non—uniform" sites and smaller for "uniform"
sites. For practical purpose, the "non-uniform" site can be
represented by a larger 8 values, whiCh is reflected by 51

larger variability of the soil properties at the site (e.g.,

109

the site with a combination of sand and clay). Similarly, the
"uniform" site can represent by a tighter S values at the site
(e.g., site that is predominantly in sand). The values of S

for the "non—uniform" and "uniform" site can be quantified

frcmt the statistical "population" HEB data. points) and
"sample" (individual site) considered in this study
respectively.

The mean of the normal distribution associated with the

ratio log, (Qp/Qm), as presented by Kay (1976, 1977) from Ang

and Tang in 1975 is:

 

 

log (Qp/Qm) = log (GP/Qm) - “‘2‘" S2 5 . 28

Therefore tflue estimate CM? normalized capacity, Q,

i.e. , (GP/(2m) , is now

 

(tip/QM = 10 “0g “PM" '"2'° 52’ 5 . 2 9

Substituting Eqs. 5.27 and 5.29 into Eq. 5.10, CFS can

be represented as:

CFS=10<BS+“‘—~.'982) 5.30
or _
Q

Qazfipi 5.31

Alternatively, from Eq. 5.30 reliability index can he

represented as:

 

_ log CFS - W s2
S

5.32

l3

110
From Eq. 5.32, for any quantity of S values, the

reliability index, B, can be directly related to CPS.

STEP 8

Allflflflhl§__flflnd£ill (Q9: After' the correction for

statistical bias factor, Fb from Eq. 5.24, euui using Cb as

found by Eq. 5.23, the final allowable axial pile capacity,

Ch. can be expressed as;

10(BS+J%980

 

Qp 5.33

.8

The denominator of the first term cflflflq. 5.33 is the

CFS; and knowing the quantity of S, therefore at any quantity

of B values, a "unit allowable capacity," qa, can kxa found;

114.

whereby (qa=CFS

STEP 9

Design_§hartz Consequently, the relationship between Ga
and the safety measures (FS, B, CPS and PH can.be represented
graphically (as shown in Fig. 5.5). Thus, Eq. 5.33 could be

presented in graphical format which might be used as a quick
design chart. The allowable pile capacity, C5, at 51 desired
safety' measure can 1x3 determined. by ImJltiplying (h as

determined from Fig. 5.5 (or using Eq. 5.33), and Qp as

determined from the spreadsheet program (i.e., Eq. 5.23).

lll
STEP 10

WW (FS. CFS & P1): The conventional

factor of safety (FS) can be back—calculated by substituting
Qp as determined by Eq. 5.23 and Q2, as determined by Eq. 5.33
as the nominal resistance and load respectively into Eq. 5.8,

consequently;

=1:pr

=CFS 5.34
Q.

FS

Therefore, given tflua axial predicted capacity and
applying the recommended factor of safety frequently used in
practice, the allowable pile capacities determined from SPT
N-values can be found. From the derivation above, not only
the FS is available (as in typical deterministic design
procedures), but that FS can also be interrelated to CFS, B,
and approximately related to PL

In this study, from the analysis of some "minimum
required" FS (see Table 5.7, Section 5.3.4.3), values of FS
and B are recommended for design purposes. The schematic
representation of interrelation model developed in this study
between the deterministic and reliability-based design

approach is as shown in Fig. 5.2.

In general, if one can predict the axial pile capacity
(as in Eq. 5.23), apply the recommended safety measure (e.g.,

F8 from codes) and have a reasonable estimate of the site S

112

 

 

Deterministic
Approach

‘_ » Reliability-Based
1 Approach

 

 

 

 

Interrelation to
Reliability-Based

 

 

 

Predicted
Capacnty (Qp)
III-IIIIIIIIIII~ r-—
I I
I I
I l
I 1
Central Factor of

Safety (CFS)

44‘

 

 

 

 

 

 

I 1
I 1
I l
I l
Allowable '
1—9 Capacity (Qa) I I I I I J :
I
I I
I I
'_ _____________ l
<. _ I § Interrelation to

Deterministic

      
 

Reliability
Index (B)

 

 

 

Fig.

5.2: The Schematic of Interrelation Model,

and Reliability—Based Approach.

Deterministic

113

values, a similar design chart (as in Fig. 5.5) as developed
in this study, can easily be constructed. Such design chart
can be considered as a "direct interrelation" of the safety
measures as determined from the deterministic and
reliability—based approach of design (see also Design Using

The Chart, Section 6.2.1.7).

5 . 3 . 3 Determination of Calibration Parameters

All the factors subsequently derived (i.e., Fs and IR,
and consequently Pb, and S) relate back to the accuracy of the
equation of R4 (see STEP 2 and STEP 3). However, a rigorous
parametric analysis was not considered in this study for
determination of these factors. Instead, simple curve fitting
using a computer program was employed. They are found to best
fit exponential functions in all cases (other simple curve
fitting capabilities in the program are such as linear,
polynomial, logarithmic and jpower with the options of
smoothing, weighted, cubic spline and interpolation).

The proceeding sub-sections will present the
determination. and analysis of In, FM Ifl, Pb, and S.
Ultimately, the recommended values for the determination of
the allowable capacity (Qa) using the algorithm will be

summarized in Section 5.4.2.

114
5.3.3.1 Equations of Toe Capacity Ratio: R,

The measured capacity (C50 for the 11 instrumented piles
according to the three criteria ([2"], [D] and [C])

respective criteria are presented in Appendix A. For the

determination of R, in STEP 2, the curves of (Qm/Qm) vs (Le/d)
are plotted as shown in Fig. 5.3for the respective criteria
(i.e., [2"], [D], [C], and [DC]). The curves in Fig. 5.3 use
data from the 11 instrumented piles only.

In Fig. 5.3, for each criteria it seemed that two curves
cflfIh could be plotted independently for the five piles from
the Ogeechee site and six piles from Locks and Dam No.4 site.
However, assuming that the represented population is many
more pile tests, this tendency would be "masked out" as more
points are added and scattered around the curves. Therefore,
"an average of the two sites" is considered and only one
curve of Rtisspdotted for each criteria. What is important in
Fig. 5.3 is the general trend and the coefficients of the
functions.

The form of the exponential functions in Fig. 5.3 is:
R,=a*Exp(-b*Le/d)
where a and b are constant coefficients.
As indicated in Fig. 5.3, the coefficients a for all of

these equations are found to be very close to unity, and it

seemed appropriate to adjust the coefficient a to unity.

115

 

   
 
     

 

 

 

1 17f I Y ‘T n J1 I I I I I Y r f 11 1 T r I I 1 r t
- [2,] —o— y - 1.1776 ' e"(-0.031425x) Ra 0.90456 [2"]]
_ [DC] —o— y . 1.0749 ' e"(-0.030272x) R: 0.86877 [D] ,
O
0-3 ‘7 o + y . 1.072 ' eA(-0.028621x) Rs 0.91495 [C] “t
)- X 4
t o 2 —x— y - 1.1042 ' sly-002942510 R- 0.90408 [DC],
0 9
- “ [c1 - l
a: 0.6 —- o 3 __
" ’ [D] x
a
O .
\ 1.. 4
E
O 0.4 -"- —h—
r. -l
0.2 "l’ -(-—
l: l
L.
O 1 L l 1 % 4L 1 1 L I J 1 1 J % 1 1 1 1 % 1 l I 1 J 4 # L A
0 10 20 30 4O 50 60

I./d

Fig. 5.3: Development of RtFunctions Using 11 Instrumented

Piles.

Another practical reason for this adjustment is that, at the
surface of the soil, the shaft capacity is zero, and capacity
is only attributed to the toe. The toe capacity [consequently
the ratio (th/lel is a maximum for a pile placed at the soil
surface and this ratio decreases with depth. Conversely, the
shaft capacity increases gradually from zero an: the soil
surface. However, when a is adjusted to unity, in all cases
the predicted shaft capacity tended.tx> be "over estimated"

quite substantially, especially for piles of more than 50 ft.

116
of embedded length. Consequently, the equations of Rt used in

subsequent steps are unadjusted, but interpreted by equations
as found in Fig. 5.3 (see STEP 2 and STEP 3). Nevertheless,
in practice, this is generally not a concern as piles of
[(Le/d)<10] are seldom used.

The ratio of the toe capacity, th, to the total measured
capacity, Qm, does not show a significant variation across

the four criteria.

5.3.3.2 Shaft and Toe Factors: F5 & F,

The interpreted measured shaft capacity is simply the
difference between the total measured capacity, Qm, and the
interpreted measured toe capacity, On“.

For the determination of correction factors in STEP 4, the
calculated shaft capacities, Qsc, and the calculated toe
capacities, Q10, are obtained from Eqs. 5.2 and 5.3
respectively. Following STEP 4, the ratios of estimated
measured to calculated shaft and toe capacities (Qsm/Qsc) and
(th/th), (or F5 and Ft) were respectively plotted against
(Le/d) as shown in Fig. 5.4. All points show a substantial
scatter within each of the methods. However, a trend is
clearly observed for all the curves, i.e., they decrease with
an increase in depth. All curves are found to best fit to

exponential functions as shown in Fig. 5.4.

117
A similar study by Dennis and Olson (1983) for the

determination of Fsamuilfl in a similar manner but by plotting

(Qsc/Qsm) vs. (Le/d) and (QC/QM) vs. (Le) respectively. That

study was done on a large collection of tested piles (over

1004), but only 21 data points from instrumented piles were
use for the determination of Fs and F, (i.e., piles with
similar consistency in terms of properties, types, etc.). In

their study, substantial scatter was also observed. From the
points plotted in that study, the general trend (an increase
in their case) of Ig and F, is not clearly seen” Zni their
study, even though the F; was found to be dimensionless, the
F, obtained yum; not dimensionless. From an analytical
standpoint, dimensionless factors seem preferable (and was
used herein).

Table 5.2 presents the equations for RU.I% and.Ffl factors
as found from Figs. 5.3 and 5.4. The recommended equation for

the determination of Qp by Eq. 5.23 (STEP 5) will be

presented Table 5.5.

Qsm / QSC = F5

=F

cam/0..

Fig.

118

 

 

 

 

 

 

    

 

 

 

..;...:fi..;...+...
‘ —o— y - 5.1644 ' e"(-0.025202x) R= 0.57172 [2"]
—o— y . 5.5853 ' e"(—0.030873x) R- 0.67105 [Di 1
__ o o + y - 6.7277 ' e"(~0.033297x) 6: 0.86036 [Cl :—
[C] +— y .. 6.54 ' e"(-0.030612x) as 0.75111 [DC] ‘
0 100
(a) F5 — 23 Data Points
l l l l
T ' l ' ' ' l ' ' *‘r I f Y
o + y = 7.4704 ' e"(-0.044729x) R= 0.67664 [2]
_ 3 —o- y . 4.9679 - e"(-0.041895x) R: 0.63642 [D]
——0— y . 6.1619 ' e"(-0.043376x) R: 0.94562 [Cl 1
X
—x— y . 6.6921 - e"(<0.043045x) 9. 0.92706 [DC] -
. X a
l' O
' 0
—1l— .—
I: o _‘_
. [DC] -
. a o 8 .
Q
l l l I
0 20 40 60 80 100
L /d
c
(b) F, - 23 Data Points
5.4: Correction Factors For Shaft and Toe — FS & F,.

10

Qsm / QSC = F

12

10

Q.../Q..=F.

Fig.

119

 

  

 

 

 

 

 

 

 

 

 

l l l l _l
I I 1 I I I I I I I I I I I f I I I I I I I I T I I I
- —o— y - 3.5251 ' e"(-0.0016832x) Ra 0.24357 [2"] *
. —o— y - 4.1626 ' e"(—0.00952x) R= 0.44426 [D]
‘5 o 0 —0— y . 9.657 ' e"(-0.026425x) R. 0.89671 [C] i—
’ C
- l ] —::— y .. 5.8616 ' e"(-0.016217x) R- 0.66614 [DCl‘
,
,
-1- ~1-
_ I
1 1 l 1 1 1 1 l 1 .1. L 1 1 .l 1 1 l 1 J 1 1 J. 1 1 k 1
I I I T T
O 10 20 30 40 50 60
L /d
C
(c) FS - 11 Data Points
1 l 1
fi I I I I I I I I I I I I I I T I I I I I T I I fir I I I
' . —o—— y - 11.596 ' e"(-0.049267x) Ra 0.83822 [2"]]
_'_ 3 —o— y - 6.4652 ‘ e"(-0.03929x) n... 0.76736 [D] i
r + y .- 15.824 ' e"(-0.055396x) R- 0.96934 [C] J
[ x [C] , ‘
, + y .. 11.525 e"(-0.049707x) a. 0.92591 [DCl~
P X «
o .
1 , .
q— o —n—
. [DC] . .
: [2"] x 1
>- O O '4
l. ..
i- [D] o a
C 8 8 "IS\\‘ 8 :
'- L i 4 l 1 1 l L l A l J; J A d
I I I I I
0 10 20 30 40 50 60
L /d
c
(d) F, — 11 Data Points
5.4: Continued.

120

Table 5.2: Equations for R,, FS and F, Factors.

FACTOR CRITERIA EQUATION CORRELATION
COEFFICIENT

Exp(-0.03l4*Le/d)
Exp(-0.0327*Le/d)
Exp(-0.0288*[e/d)
Exp(-0.0294*Le/d)

 

.00168*Le/d)
.00952*Le/d)
.02643*Le/d)
.01622*1¢/d)

.04927*L¢/d)
.03929*Le/d)
.0554o*L¢/d)
.04971*Le/d)

 

.02520*Le/d)
.03087*1¢/d)
.03330*L¢/d)
.0306l*[e/d)

.04473*Le/d)
.04190*Le/d)
.04338*LQ/d)
.04305*Le/d)

 

 

 

 

121
5.3.3.3 Bias Factor and Site Variability: Fb & S

For the determination of Fb and S, three different cases
were examined as listed in Table 5.3. The "best" parameters
are compared and recommended in Section 5.4.2.2.

Case (i) represents the viewpoint that a greater number
of points with less precision will provide the most well-
found information; Case (ii) represents precision j£;:more
important tflun1 quantity; enui Case (iii) represents the
viewpoint that precision should be examined for FsemuiIfl, but
quantity is important for the determination of Pb and S.

To quantify the "best“ values of Fb and S, within the
three cases, the values from 23 data points could be taken as
the "population" representing the "non-uniform" site.
Similarly, the values from the individual sites could be
taken as the "sample" representing the "uniform" site (see
also the assumptions in STEP 7).

In Table 5.3, 11 data points are from instrumented piles
and 12 are from non instrumented piles. Table 5.4 are the
results of Fb and S for the three cases examined.

Recalling STEP 6, Fb is the statistical bias factor

associated vfijfll the predicted capacity, Ck, an; determined

from Eq. 5.23. As shown in Table 5.4, the bias factor is

simply the mean of (Qm/Qp). Consequently, if (Fb<1.0) the

capacity is over predicted, and if (Fb>1.0) the pile capacity

is under“ predicted. If tflua predicted capacityn Cb, as

determined from Eq. 5.23 is "perfect," than Fb should he

122

unity. However, it was found in this study is that most
calculated Fb factors are less than 1.0 (Table 5.4). This
indicates that the derived prediction equation will somewhat
"over predict" pile capacities with respect to the ”true"
measured capacities. An exception is the criteria [2"] from
Case (ii) which showed under prediction. Another exception is
the Ogeechee site when considered on its own, for all Cases
(i), (ii) and (iii). With known quantities of Pb factors, the
allowable capacity, C5, can easily kxa determined from Thy
5.33.

Comparing among the cases, the "best" Fb to be suggested
appears to be from Case (ii), at Fb equals to 1.136, 0.977,
0.863, and 0.952 for criteria [2"], [D], [C], and [DC]
respectively. This is also true for S which ranges from 0.10
to 0.12. For Cases (i) and (iii), the S values are at about
0.27; which matches well with the implied larger uncertainty

of S of the "population."

Table 5.3: The Three Schemes Examined For The Determination

of Calibration Factors - Fb, and S.

ACTOR 1 NO. OF 0AA POINTS 1 1
USED FOR CALIBRATION
1 1

Case (i) Case (ii) Case (iii)

 

 

23 11 11
23 11 11
23 11 23
23 11 23

 

 

 

 

123

 

 

 

 

 

 

 

 

 

Table 5.4: Bias Factor and Site Variability.
(a) F} & S: Case (i).

FILE [2"] [D] [0] [DC] [2"] [0] [0] [00}

Log Log Log L08

Qm/QE Qm/QB Qm/QE Qm/QB Qm/QE Qm/QE Qm/QE Qm/QE

1 Ogeechee.10' 1.024 0.844 1.672 1.325 0.01 -0.07 0.22 0.12
2 09960119620 2.113 1.943 1.810 1.869 0.32 0.29 0.26 0.27
3 Ogeechee.30' 1.692 1.381 1.461 1.446 0.23 0.14 0.16 0.16
4 Ogeechee.40' 1.425 1.398 1.186 1.288 0.15 0.15 0.07 0.11
5 Ogeechee.50' 1.157 1.150 1.078 1.117 0.06 0.06 0.03 0.05
6 L&D4.TP1 1.392 1.443 1.116 1.283 0.14 0.16 0.05 0.11
7 L804.TP2-1 1.180 1.135 0.985 1.072 0.07 0.06 -0.01 0.03
8 L804.TP2-2 1.157 1.161 0.968 1.072 0.06 0.06 -0.01 0.03
9 L804.TP3 0.776 0.792 0.626 0.709 -0.11 -0.10 -0.20 -0.15
10 L804.TP10 1.127 1.075 0.896 0.993 0.05 0.03 -0.05 0.00
11 L804.TP16 0.883 0.821 0.685 0.759 -0.05 -0.09 -0.16 -0.12
12 Peck.15 0.266 0.260 0.230 0.249 -0.58 -0.59 -0.64 -0.60
13 Peck.22 0.346 0.321 0.303 0.319 -0.46 -0.49 -0.52 -0.50
14 Peck.51 0.342 0.354 0.285 0.322 -0.47 -0.45 -0.55 -0.49
15 Peck.55 0.497 0.546 0.368 0.454 -0.30 -0.26 -0.43 -0.34
16 Peck.206 0.464 0.420 0.361 0.398 -0.33 -0.38 -0.44 -0.40
17 Peck.208 0.744 0.551 0.840 0.740 -0.13 -0.26 -0.08 -O.13
18 Peck.272 0.558 0.621 0.464 0.522 -0.25 -0.21 -0.33 -0.28
19 Peck.274 0.967 1.115 0.982 1.058 -0.01 0.05 -0.01 0.02
20 Peck.358 0.485 0.365 0.414 0.405 -0.31 -0.44 -0.38 -0.39
21 Peck.359 0.232 0.177 0.157 0.230 -0.63 -0.75 -0.80 -0.64
22 Peck.360 0.806 0.552 0.771 0.702 -0.09 -0.26 -0.11 -0.15
23 Peck.361 0.623 0.326 0.576 0.486 -0.21 -0.49 -0.24 -0.31

Mean (Fb) Standard Deviation (S)

23 Data pts 0.881 0.815 0.793 0.818 0.26 0.28 0.29 0.26
Ogeechee Site 1.482 1.343 1.441 1.409 0.13 0.13 0.10 0.08
L&D4 Site 1.066 1.071 0.660 0.981 0.09 0.10 0.10 0.10
Peck's Data 0.527 0.467 0.479 0.490 0.19 0.21 0.24 0.20
[2"] [D] [C] [DC]
Pb (23 pts) 0.881 0.815 0.793 0.818

S (23 pts) 0.26 0.28 0.29 0.26

S (Ogeechee Site) 0.13 0.13 0.10 0.08

S (L&D4 Site) 0.09 0.10 0.10 0.10

S (Peck's col'n) 0.19 0.21 0.24 0.20

 

124
Table 5.4: Continued

(b) Fb & S : Case (ii).

 

PM? [2"] [D] [C] [00} [2"] [D] [0] [00}

Log Log Log Log
Qm/QJ, Qm/Qp Qm/QE Qm/Qp Qm/Qp Qm/QE Qm/QE Qm/QE

 

AOQGNGUIAWN-‘i

dd

 

 

 

Ogeechee.10' 0.733 0.689 1.004 0.896 -0.14 -0.16 0.00 -0.05
09990119920 1.715 1.678 1.244 1.425 0.23 0.22 0.09 0.15
09996119930I 1.450 1.175 1.067 1.150 0.16 0.07 0.03 0.06
09999119940 1.256 1.148 0.901 1.042 0.10 0.06 -0.05 0.02
09996h99.50' 1.012 0.893 0.838 0.898 0.01 ~0.05 -0.08 -0.05
L804.TP1 1.264 0.997 0.856 0.990 0.10 0.00 -0.07 0.00
L804.TP2-1 1.093 0.862 0.771 0.868 0.04 -0.06 -0.11 -0.06
L804.TP2-2 1.072 0.881 0.758 0.868 0.03 -0.05 -0.12 -0.06
L804.TP3 0.717 0.641 0.487 0.584 -0.14 -0.19 -0.31 -0.23
L804.TP10 1.046 0.811 0.701 0.803 0.02 -0.09 -0.15 -0.10
L804.TP16 0.697 0.621 0.536 0.591 -0.16 -0.21 -0.27 -0.23
Mean (Fb) Standard Deviation (S)

11 Data p18 1.136 0.977 0.863 0.952 0.12 0.12 0.11 0.10

099331998119 1.233 1.117 1.011 1.082 0.14 0.14 0.07 0.08

 

 

 

L&D4 Site 0.982 0.802 0.685 0.784 0.11 0.08 0.10 0.10
[2"] [D] [C] [DC]
Pb (11 pts) 1.136 0.977 0.863 0.952
s (11 pts) 0.12 0.12 0.11 0.10
S (Ogeechee Site) 0.14 0.14 0.07 0.08

S (L&D4 Site) 0.11 0.08 0.10 0.10

 

125

 

 

 

 

 

 

 

 

Table 5.4: Continued
(c) Fb & S Case (iii).
FILE [2"] [D] [0] [DC] [2"] [D] [C] [00}
Log Log Log Log
Qm/QE Qm/QE Qm/QB Qm/QB Qm/QE Qm/QB Qm/QE Qm/QE
1 Ogeechee.10' 0.733 0.689 1.004 0.896 -0.14 -0.16 0.00 -0.05
2 Ogeechee.20' 1.715 1.678 1.244 1.425 0.23 0.22 0.09 0.15
3 Ogeechee.30' 1.450 1.175 1.067 1.150 0.16 0.07 0.03 0.06
4 Ogeechee.40' 1.256 1.148 0.901 1.042 0.10 0.06 -0.05 0.02
5 Ogeechee.50' 1.012 0.893 0.838 0.898 0.01 -0.05 -0.08 -0.05
6 L804.TP1 1.264 0.997 0.856 0.990 0.10 0.00 -0.07 0.00
7 L&D4.TP2-1 1.093 0.862 0.771 0.868 0.04 -0.06 -0.11 -0.06
8 L804.TP2-2 1.072 0.881 0.758 0.868 0.03 -0.05 -0.12 -0.06
9 L&D4.TP3 0.717 0.641 0.487 0.584 -0.14 -0.19 -0.31 -0.23
10 L&D4.TP10 1.046 0.811 0.701 0.803 0.02 -0.09 -0.15 -0.10
11 L804.TP16 0.697 0.621 0.536 0.591 -0.16 -0.21 -0.27 -0.23
12 Peck.15 0.223 0.155 0.166 0.173 -0.65 -0.81 -0.78 -0.76
13 Peck.22 0.312 0.218 0.231 0.243 -0.51 -0.66 -0.64 -0.61
14 Peck.51 0.306 0.234 0.214 0.241 -0.51 -0.63 -0.67 -0.62
15 Peck.55 0.485 0.462 0.287 0.386 -0.31 -0.34 -0.54 -0.41
16 Peck.206 0.437 0.306 0.276 0.315 -0.36 ~0.51 -0.56 -0.50
17 Peck.208 0.621 0.326 0.606 0.514 -0.21 -0.49 -0.22 -0.29
18 Peck.272 0.463 0.449 0.374 0.413 -0.33 —0.35 -0.43 -0.38
19 Peck.274 0.727 0.569 0.675 0.665 -0.14 -0.25 -0.17 -0.18
20 Peck.358 0.445 0.256 0.318 0.316 -0.35 -0.59 -0.50 -0.50
21 Peck.359 0.220 0.165 0.155 0.171 -0.66 -0.78 -0.81 -0.77
22 Peck.360 0.733 0.381 0.589 0.540 -0.14 -0.42 -0.23 -0.27
23 Peck.361 0.562 0.225 0.447 0.378 -0.25 -0.65 -0.35 -0.42
Mean (Fb) Standard Deviation (S)
23 Data p18 0.765 0.615 0.587 0.629 0.25 0.30 0.27 0.27
OgeecheeSite 1.233 1.117 1.011 1.082 0.14 0.14 0.07 0.08
L804 8119 0.982 0.802 0.685 0.784 0.11 0.08 0.10 0.10
Peck's Data 0.461 0.312 0.361 0.363 0.18 0.18 0.22 0.19
[2"] [D] [C] [DC]
Pb (23 pts) 0.765 0.615 0.587 0.629
S (23 pts) 0.25 0.30 0.27 0.27
S (Ogeechee Site) 0.14 0.14 0.07 0.08
S (L&D4 Site) 0.11 0.08 0.10 0.10
S (Peck's col'n) 0.18 0.18 0.22 0.19

 

126
5.3.4 Importance ofI$ and S

The values of Pb and S are important, especially the S
values as a small change in S could affect Q,, by a
substantially amount. Similarly, the safety measures are also
sensitive to the S values (see Design Charts in Figs. 5.5, 5.6
and 5.7).

Nevertheless, low S values were Observed for each site,
i.e., when they are considered for individual sites only (for
all the Cases). For Case (i), S ranges from 0.09 to 0.10 and
0.13 tn) 0.08 for Locks and Dam No.4 and Cgeechee sites
respectively (Peck's collection cannot be considered as a
"site" since the piles were collected from several locations
as shown in Table 5.1. For Case (ii), S ranges from 0.11 to
0.10 and 0.14 to 0.08 for Locks and Dam No.4 and Ogeechee
sites respectively. Overall, the site S values are remarkably
low at about 0.08 to 0.14. These values coincide very well
with site S values of 0.12 as previously proposed by Kay
(1976) , who used published values of Qm, and Qp as determined
from dynamic formula. In a similar study by Kay (1977) in
clay, a site S value of 0.08 was used. In another study
(Bourquard, 1987), the proposed value Of site S was 0.09. In
Bourquard (1987) study, however the methods of determining
Qm, and Qp were not mentioned.

Therefore, the S values Obtained from this study compare
vary well with values found in previous studies (Kay, 1976;

Kay, 1977; anui Bourquard, 1987). However, tine algorithm

127

developed in this study has the advantage of being consistent
and with repeatable calculation; consequently, no "arbitrary"
judgment is required in choosing the specific parameters in
the standard static equation is required. What is required is
only the SPT N-values from the boring log.

Another trend that is observed from the values of
(ChMCb) in Table 5.4 is that the derived algorithm tends to
I'over estimate" the predicted capacity, especially for Locks
and Dam No.4 and Peck's collections) and the algorithm tends
to "under estimate" the predicted capacities from the
Ogeechee site. This gives a notion that at least two set of Pb
should be suggested according to loading test procedure,
i.e., Constant Rate Of Penetration (CRP) or Constant Load, CL
(recall from the data base in Section 5.2: Ogeechee site is
CRP type of loading test, and Locks and Dam No.4 and Peck's
collections are CL type of loading test). Consequently, three
values of Pb are recommended in Table 5.6. The "unknown
loading test" condition is where the determination of
measured capacity from loading test to be run has run:.been
decided with respect to type; or the condition where no
loading test is anticipated (NLT) at the site. (Note: the
loading test of piles could be run according to CRP, CL, or
some other types of loading schemes).

The I% factors and S values suggested in Table 5.6 are
from the results of Ogeechee site for CRP type of loading
test [i.e., values from Case (ii)] and values from Peck's

collection for CL type of loading test [i.e., values from

128

Case (iii)]. In cases of predicting pile capacity where type
of loading tests is unknown (NLT), only relying on the
available SPT N—values, the Fb factor from the average of
Ogeechee and Locks and Dam 4 from Case (ii) is recommended.
For the purpose of determining the allowable capacity,
tine "uniform" site may now be quantified from the tighter S
values from each Of the individual sites where uniform soil
properties at the site is expected. Another words, it can be
said that the site is predominantly in sand with no clay. The
recommended S values for the "uniform" site are recommended
from the average Of Ogeechee and Locks & Dam No.4 sites from
Case (ii). Likewise, the "non-uniform" site may now be
quantified from the larger S values of the "population", where
non-uniform site pmoperties are stipulated. “flue site of
predominantly in sand with some clay. The S values for the
"non—uniform" site in Table 5.6 are recommended from the

"population"S values from Case (iii).

5.3.5 Safety Measures:F6 and B

For design purposes, the determination of the "best"
safety measures recommended in Table 5.7, tflua following
examination was made.

The bias factors, Fb recommended for the design charts,

are from the 11 instrumented piles from Case (iii), therefore

129

for the determination of the recommended safety measures, Qh
from Case (iii) of the "population" were examined.
The "minimum required" FS is defined as time average

value of FS when the predicted capacity is divided by the

measured capacity [FS=(Qp/Qm)] for the 23 data points,
instead of the normal definition of FS=(Qp/Qa) . This is the
condition when the load allowed on the pile (C5) "is not
greater than" the measured capacity from loading test (C50;
i.e., the condition of safe state at the lower bound. The
minimum required FS typically ranges from 1.79 to 2.25; and
the values are the same for the "uniform" site and "non-
uniform" site. This indicates that if the design is done
according to the deterministic approach, the FS applied could
be the same for the "uniform" and "non—uniform" sites, and it
is not possible to quantify the uncertainty at the unknown
site. What is commonly done in practice is that, knowing that
the site has a "non—uniform" soil properties, a higher FS
value is typically "assigned."

Similarly as in the case of deterministic FS, a "minimum
required“ B is determined by using the relation as given by
Eqs. 5.32 and 5.33, and by assuming that (FS=CFS). Typical
values for the "minimum required" B ranges from 1.43 to 2.93
and 0.46 to 0.88 for the "uniform" and "non—uniform" site
respectively. The lower B values for time "unknown site"
indicate that the reliability is reduced at the "non—uniform"
site due to inherent "uncertainties of the non—uniform site."

This is perhaps one of the main advantage of reliability

130

method as compared to deterministic approach, whereby the
"non—uniform" or the variability at a particular site can
rationally be quantified.

In practice for deterministic designs, a minimum FS of
2.0 is frequently provided (e.g., Fuller, 1978).
Consequently, in this study FS=2.0 or greater than the
"minimum required" (and rounded to one decimal place) are
recommended in Table 5.7 for the "uniform" sites. For a "non-
uniform" site the FS is recommended at 3.0, at which the

equivalent B is not less than 1.0.

For a "non—uniform" site where S is relatively larger
than the "uniform" site, the equivalent B at the "minimum
required" FS is found to be 0.46, 0.88, 0.75, and 0.79 for
criteria [2"], [D], [C], and [DC] respectively. In other
words, to provide FS at the "minimum required," the "minimum
required" B could be very low. From deterministic
perspective, considering that time "non—uniform" is; more
uncertain, intuitively it should be given a higher FS, say
twice the:FS value at the "uniform" site, i.e., ES=4.0).

When (FS=4.0) is assigned to the "non—uniform" site, the

respective B was found to be 1.86, 1.59, 1.56, and 1.71 for

criteria [2"], [D], [C], and [DC] respectively; which is

substantially higher than the "minimum required" B. This

higher value is about the same value as proposed by Meyerhof

(1970), i.e., at B=1.7. Therefore, the FS=4.0 seems to be an

appropriate value for the "non—uniform" site if the design is

done from deterministic approach.

131

If a design is done from reliability-based approach, the

recommended B are 2.00, 3.00, 2.50, and 3.00 for criteria

[2"], [D], [C], and [DC] respectively for the "uniform" site

(values larger than "minimum required" B, not less than an

equivalent FS=2.0 and rounded to one decimal place) . At the

recommended B values, the equivalent values of F8 are 2.10,
2.51, 2.43, and 2.33 for the respective criteria. Therefore,
these B values are recommended in Table 5.7. For the "non-
uniform" site, all criteria at B=1.00 are found to be
adequate (against the "minimum required" B), which is also
equivalent to F8 of 2.10, 2.67, 2.82, and 2.57 for criteria
[2"], [D], [C], and [DC] respectively. At these FS, [3 is
higher than the "ndnimum required" and also adequate to
satisfy the minimum (FS=2.0). In other words, for the "non-
uniform" site, a B of only 1.00 could have been recommended,
at which the equivalent FS value of at least 2.00 could be
met.

Nevertheless, the B values for the "non—uniform" site
recommended in Table 5.7 for the reliability—based approach
are the ones that could also satisfy deterministic FS of at
least 3.0, considering arguments below.

For tine FS of the "non-uniform" site, comparing the
higher FS of the first assumed at FS=4.00 from the
deterministic approach, this is perhaps on the conservative
side. Comparing the equivalent F8 from reliability approach,

which could in fact be smaller than 4.00, the FS is revised

to 3.00. At FS=3.0, the equivalent B are found to be 1.36,

132
1.17, 1.10, auxi 1.25 criteria [2"], ND], [C], enui [DC]

respectively. As these values are also higher than the
"minimum required" these values are finally recommended in
Table 5.7 for deterministic approach.

Therefore from this analysis, it can be said that the
same FS could result in a different B (and consequently the
probability of failure), and that the deterministic FS alone
is insufficient to assure acceptable reliability (thus, also
an economic design) at the applied factor safety. The design
by deterministic approach could also be overly conservative.
It is clear that the reliability approadh does tell more
about the uncertainty (which can also be quantified) as
compared to the deterministic approach. In general, from the
analysis done using the reliability approach in this study,
the recommended deterministic FS higher than 3.0 frequently
applied in practice for pile design should be examined
closely as it could be on the high side.

Table 5.7 presents the recommended safety measures for
design purposes either from deterministic or reliability—
based approaches; and their respective equivalence is
presented in italics. When these recommended values are used
to check the 11 instrumented piles, in all cases, it was

found that «ZKCEJ7 which is necessary for safe design.

133
5.4 Summary of The Algorithm

From the developed algorithm in this study, the
determination of the allowable pile capacity from the SPT N—
values is summarized in four steps as presented in Section
5.4.3. Section 5.4.1 will present the assumptions adopted;
and section 5.4.2 will present the recommended calibration

parameter to be used with the "standard" static pile formula.

5.4.1 Implied Assumptions

For the determination of predicted capacity, C5, the

following assumptions are implied:

(i) the correlation of N—values and ¢ is adopted from

Peck's approximation; i.e., Eq. 5.5,

(ii) the soil-pile interface angle, 5, is a reduced ¢
using factors adopted from Potyondy (1961); i.e.,
0.76 and 0.80 for above and below water table
respectively (Table 2.4),

(iii)the SPT N—values are corrected for overburden
pressure using correlation from Liao and Whitman

(1986): i.e., Eq. 5.4,

(iv) the wet unit weights (Ywet) and saturated unit

weights (753!) are assumed to be 120 and 130 pcf

respectively,

134

(v) the coefficient of lateral earth pressure at the
site, K5, is taken as equal to the coefficient of

lateral earth pressure at rest Ko [i.e.,

KS=KO =(1-sin5)] .

5.4.2 Recommended Calibration

From the previous sections, this section summarizes the
recommended calibration parameters to "modify" the standard

static formula.

5.4.2.1 Values of Rt, FS and Ft: for Qp

Table 5.5 presents the recommended equation of the
percentage of the toe over the total capacity (R), the
reduction factors for shaft (F5) and toe (Ft) for the
determination of predicted capacity (Qp) by Eq. 5.23. The
factors are the values as derived from the 11 instrumented

piles from Case (ii).

5.4.2.2 Values of Fb and S: for Q3

Table 5.6 presents the bias factor and the standard

deviation of the predicted capacity for the "uniform" and

135

"non—uniform" sites to be used for determination of allowable

capacity; C5, by Eq. 5.33.

5.4.2.3 Values of FS and B: for Safety Measures

Table 5.7 presents the recommended safety measures. The
allowable capacity can be determined either from
deterministic or reliability—based approaches. Their
respective equivalent is presented in italics. The lower
reliability index (B) of about 1.25 to 1.50 recommended for
the "non—uniform" site are tine ones implied in pmactice,
which is equivalent to deterministic factor of safety (FS) of
about 3.00 to 3.50. Although these Bvalues appear low
compared to other application, e.g., in structural

engineering, tflunr are practical values 1J1 this study.

Recommending higher B values for the "non-uniform" site is
impractical, i.e., if B values are recommended equal values
for the "uniform" and "non—uniform" site, than the equivalent
(or at the respective) F8 values for the "non—uniform" site

would be substantially higher than the maximum FS usually

applied in practice (which is about 4.00 to 5.00).

136
Table 5.5: The Recommended Functions For Rt, FS and Ft for Q).

 

FACTOR CRITERIA

  

 

  

 

 

  

 

    
 

 

 

EQUATION

R4 (11 pts) [2“] 1.1775 Exp(-0.03l4*Le/d)
[D] 1.0748 EXp(-0.0327*Le/d)

[C] 1.0720 Exp(-0.0288*Le/d)

[DC] 1.1042 EXp(-0.0294*Le/d)

Fs (11 pts) [2"] 3.5251 EXp(-0.0017*Lc/d)
[D] 4.1626 Exp(-0.009S*Le/d)

[C] 9.6570 Exp(-0.0264*le/d)

[DC] 5.8616 Exp(-0.0162*Le/d)

Ft (11 pts) [2'] 11.596 Exp(-0.0493*1e/d)
[D] 6.4852 EXp(-0.0393*Le/d)

[C] 15.824 EXp(-0.0554*Lc/d)

[DC] 11.525 Exp(-0.O497*Lc/d)

 

The Recommended Values of
Determination of Q3.

Table 5.6: Fb and S for the

CRITERIA

 

FACTOR

[D] [C]

 

~Fb (CRP Test)

Fb (CL Test)

‘Fb (Unknown Load Test)

S ('Uniform“ Site)

S ("Non—uniform“ Site)

 

 

 

 

 

137

Table 5.7: The Recommended B and F8 for The Deterministic
and Reliability—Based Approaches.

 

 

 

 

 

 

 

 

 

 

 

 

 

1
average of (Qm /Qp) from Case (iii); to ensure Qa would not be more than Qm

from Eq. 5.32; and CFS is from Eq. 5.34

Recommended F8 from Deterministic Approach; its Equivalent B is shown in italics

Recommended [5 from Reliability-Based Approach; its Equivalent

F8 is shown in italics

CRITERIA
[2"] I [D] L [C] | [DC] 1,
Unif. Non-Unif. Unif. Non-Unif. Unif. Non-Unif. Unif. Non-Unif.
Site , e ,, , Site M Site ,, Siet ,, Ste ywSite . ”i te ,
1Minimum Required
FS 1.79 1.79 [2.46 2.46 [2.42 2.42 I 2.25 2.25
l
2
‘ Minimum Required
[3 1.43 0.46 2.93 0.88 2.48 0.75 2.85 0.79 ‘
l
3Deterministic Approach
(Recommended)
FS 2.00 3.00 2.50 3.00 2.50 3.00 2.00 3.00
([3) (1.82) (1.36) (2.99) (1.17) (2.61) (1.10) (2.34) (1.25)
~———~-- -— l
4Reliability-Based Approach
(Recommended)
B 2.00 1.50 3.00 1.25 2.50 1.25 3.00 1.25
(FS) (2.10) (3.25) (2.51) (3.17) (2.43) (3.30) (2.33) (3.00)

 

138
5.4.2.4 Design Charts

Figures 5.5, 5.6, and 5.7 presents plots of the related
safety measures that could be easily used for rapid design
checks. These figures use the F5 factors for constant rate of

penetration test (CRP), the constant load type of loading

test (CL), and the case for "unknown loading test" (NLT)
respectively.
5.4.3 Allowable Capacity

The determination of Ck (and consequently the allowable
capacity, C5) is computed tyrea depth integration process
preferably set up on a spreadsheet for calculations for every

foot of the embedded length of pile. The recommended

procedures for the determination of C5 are as presented in the

following four steps:

STEP 1

Select the recommended factor (n3 safety, FS, or
reliability index, B, from Table 5.7 for [fine respective
method of determination (i.e., criteria [2"], [D], [C], and

[DC]).

FS/1.23

   

139

 

 

 

 

 

 

FS/1.12

 

   
   
  

 

 

 

 

 

 

 

 

  
  

 

 

 

    

 

 

 

 

 

   
  
  

 

 

 

 

 

5.00 2.50 1.67 1.25 1.00 0.83 5.00 2.00 1.25 1.00 0.83
51 = 53= . f
_ [2']- CREE: 1.23 . [Dl- CRPzFb=1.12_f_
4- +S=0.12 1110‘ 4‘:- +s=0.12 é-1/104
--+-s=0.15 _E_ we s=0.15 i
‘ Wts=0.20 g M"- s=0.20 3
3.] +S=O.25 1,103 35:]- —°—s=o-30 €F1/103
P 1% _ P
f B E Qa-qa* Qpi f2
2+ 1/102 2': -.~1/10
_ l,
1~,— mo 1 E 31 1°
I L ;_
OJ ' o- m. -e u
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0-0 0-2 0'4 0-6 0-3 ‘-° 1-2
qa=1.23/CFS qa=1.12/CFS
(a) 2" Movement (b) Davisson's
FS/1.01 FS/l.08
5.00 2.00 1.25 1.00 5.00 2.00 1.25 1.00 0.83
5 A difi§IT-#IY I%VIIU%Y YT%VT 1%IVII%UIIY:UIVI‘ 5'> . ‘ 4'
.; [C]-CRP:FD=1.01§_ '1 [DC]-CRP:FD=1.08.3_
I j ; 1.. j
4‘2" +s=0.11 ‘3‘“104 411 ' +s=0.10 3-1/10‘
_=. ...... s=0.15 g- .1 Mos=0.15 3-
E """ °'" s=0.20 3 3 : ----- °-"s=0.20 3 3
3-2- —o—s=0_27 €~1l10 3f -°-s=0.27 43-1/10
;. _ 1 er P 1 _ =1: 1- P
: 0,41, Q9: 1 B i (1413 Q9: r
2+;- 54/102 2+ .11/10’
14% é-i/io 1E 1.1/1o
1
o ’1111%L1LL%1111%11H£1111%1111%1111%1111lv.3}? “" 0": 5.. ' .'_ ‘-
00 02 04 06 03 10 00 02 04 06 08 10 12
qa:],0]/CFS qa=1.08/CFS
(c) Chin's (d) Ave Davisson's & Chin's

Fig. 5.5: Design Chart - For Constant Rate of Penetration
Test Type (CRP).

‘Ai

10.00

I-

140

FS /0.46

5.00 3.00 2.50 2.00
i i i l l i

 

 

I Y'Uq'l
' 0

E C

0.1

(a)

- Qa=q,*Q-;~P.

l
IVIIYUU

,....,....,.......,..."an":

[21- 01:11: 0.465
+s=o.12 5-1/10‘
«+- s=0.15
"...... 5:020 '5’
+5=0-25 ~f-1/1o3

 

[AA

 

 

 

 

o ‘n {l-
'-. ‘u. {-1110
I. 4
o 0. {~-
1
b

0.2 0.3 0.4

qa=0.46/CFS

2" Movement

FS / 0.36
4.00

2.50

 

L
'V'rVTYr'VYT'TVVY

 

0—

... . __ * -: f
"-. u a a {61/102

..,....,....,....,....,....+
[Cl- CLzFb=0.36 j

 

+s=o.11 11,104
m... s=0.15 _:
, s=0.20 3
'0. -°- s=0.27 41/103

 

 

 

 

. h ‘0-
\‘ :
\ I

v n 1"1/10

o. 'D. il-
..... . 1
.. ,
1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Fig.

5.6:

q =0.36/CFS
a

(c) Chin's

Design Chart - For Constant Load Test Type

 

FS / 0.31

10.00 5.00

[01- 01:11: 0.31

 

-°- s=0.12
.1..- s=0.15
-------° s=0.20
+ s=0.30

Qa=q,*Qp

 

 

 

q =0.31/CFS
a

(b) Davisson's

FS / 0.36
4.00

3.00

 

0.00 0.05 0.10 0.15 0.20 0.25 0.30

2.50

 

    

V'II‘I'VT—rTITI'UIUUTf

 

 

 

 

 

L [DC]- CLzFb= 0.363t
4-3 + .10 +100“
1"”: .15 5-
E ’ 20 3
3‘1” —<>— .27 +1110"
L I
B :L 3’ P1
2.; {—11102
14; 5L1/1o
0 P111111111%n 11 I I Yiné‘il'l 1‘

 

 

 

 

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

(d)

qa=0.36/CFS

Ave Davisson's & Chin

' S

(CL).

141

FS / 1.14 FS /0.98
5.00 2.00 1.25 1.00 0.83 5.00 2.00 1.25 1.00

[2'] . NLT:Fb=1.14

+ s=0.12 4
m0"FQU
“‘"'"° s=0.20
"fi-Fflfi 3

[01- NLT : 1=b = 0.98.5-

 

 

   
 

_.. s=0.12 Eel/10‘
......, s=0.15 EL
960.20 3
—+-F0wgqnd

 

 

 

 

 

 

  

B qu *Qpi" Pi
a a 1 2

2 rum
1 fiHO

 

 

 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0
qa=l'14/CFS qa=0.98/CFS

(a) 2" Movement (b) Davisson's

FS / 0.86 FS /0.95

5.00 2.00 1.25 1.00 5.00 2.00 1.25 1.00
4-1 1 l 1 l 1 J_ 5 . .

 
   
   

 

: . WW... ‘
1 ‘1, [01- NLTzFb=0.86.f_ [001- NLTzFb=0.95.f.
+ s=0-10 é-i/i 0‘
-----o s=0.15 3

.... .Q. .. 8:0.” '3"

. a. ..... .... 8:020 : .1
31:- . "q. '0. —°—s=0.27 5-1/103 3 +s=0'27 t-1/1o

B _; . ‘2.“ ‘b\“ Qa : qa * Qp-i- Pf B . 3 ‘ “‘- Qa : qa * Qpé- Pf

 

 

4f 1. "0 +541,“ 5-1/10‘ 4
- ' m-o s=0.15 g

3

 

 

 

 

 

 

1
2 -- . 0“ 44/102 2 411102
-t D .11“ air— -1.
1 E s. “6‘ 1-1/10 1%1/10
‘. 1 1
1* : ""1 L‘n.‘ it 1

 

 

 

OD 02 0! QG‘ZOB H) 00 02 04 06 03 f L0

(c) Chin's (d) Ave Davisson's & Chin's

Fig. 5.7: Design Chart — For Unknown Loading Test (NLT).

142
STEP 2

Determine the perimeter surface area of pile shaft, A“
and the toe bearing area, A“ from pile properties. Following
parameters are needed;

a. outside diameter,d

b. length of pile embedment,[c.

STEP 3

Determine(},from Eq. 5.23, i.e.;

Qp= i [ (Fsp' Kstanfi ), (As); ] + i:t (plN; At)

The following parameters are needed;

a. use correction factors F; and PR for shaft and toe
respectively from the recommended equations in
Table 5.5.

b. SPT N—values, interpolate at every foot of soil

profile by the spreadsheet.
STEP 4
DeternujmaCh from Eq. 5.33, i. e:

= Fb *
10(1318 + "'—,'—‘l 82)

 

Qa

Qp

143

The recommended bias factor (Fb) and the variability of
the predicted capacity of a particular site (8) can be found
in Table 5.6. Alternatively, the charts in Figs. 5.5 through

5.7 can be used for the determination oflQh

5.5 Summary

This chapter has presented the development of an
algorithm and calibration of the static pile formula for the
determination of predicted axial pile capacity associated
with four different interpretations of loading test. The
algorithm uses SPT N—values from boring logs, and the N-
values at every foot of the soil profile are interpolated.
The predicted shaft and toe capacity are determined by
adjusting the "modified" standard formula to bring them into
conformance with the measured capacity from loading tests.
The total capacity is again corrected by using a random
variable bias factor reflecting the variability of the ratio
of the measured. to jpredicted capacity at the site.
Consequently, with the knowledge of the type of loading test,
the allowable capacity associated with the recommended safety
measures (FS or B) can be determined. The algorithm in this
study interrelates safety measures from.tju3 conventional
deterministic design and reliability-based approach; thus at

the recommended safety measures interpretation and design

144

from either deterministic or reliability—based approaches is
possible.

In short, with the combination of the concepts from
first order uncertainty analysis and the deterministic
approaches, the algorithm, permits; (1) a systematic
determination of the predicted and allowable pile capacity
from SPT N-values, with much of the need for arbitrary
personal judgment eliminated, and (2) a rational evaluation

of factor of safety (FS) and reliability index (B) that could

be used in design.

CHAPTER 6

TESTING OF THE ALGORITHM

6.1 Introduction

This chapter presents some illustrative examples as to
how the developed algorithm can be used to predict axial pile
capacity. Consequently, at the recommended safety measures,
the allowable capacity can be determined. Data from 20 pile
loading tests are used; 8 loading tests are available from 7
pipe piles, 9 loading tests are available from 8 H-piles, and
3 loading tests are from 3 concrete piles. These data have
not been used to develop the appropriate parameters as
described in Chapter 5. However, the criteria for choosing
these piles are the same as the criteria used for the
development of tine algorithm 1J1 Chapter 5, in e, (i)
availability of the SPT N-values at the vicinity of the pile,
(ii) piles are predominantly driven into cohesionless soil,
(iii) piles are not end bearing (N-values of more than 100 at
the toe, or piles with hard bearing layer near the toe are

excluded).

6.2 Testing of the Algorithm

By using only 23 pile loading tests to calibrate the

standard formula in Chapter 5, and with the limitations of
145

146

data quality (e.g., unknown water table in Peck's collection
which is used to derived the algorithm) and the methods of
collection [recreation of the points for the load-movement
curves from the selected references], it is perhaps
inconclusive to claim that the method developed in this study
is superior to other methods (e.g., Dennis and Olson, 1985;
Coyle and Ungaro, 1991; Coyle and Ungaro, 1991; Ungaro, 1988
API, 1991). However, the predicted capacities determined from
the algorithm are better than the unadjusted values from the
"standard formula" as will be demonstrated in the subsequent
sections. Twenty pile loading tests are felt enough to
demonstrate the primary purpose of this study, which is to
directly interrelate the safety measures from the
deterministic and reliability design approaches in a
consistent manner.

The algorithm is also extended for the determination of
the allowable capacity for time H-piles. The equivalent
circular pile diameter for all the H—pile is computed from
the cross sectional area of the H—pile assuming the flanges
are fully plugged. The equivalent pile diameter, dc, is

therefore:
:=2‘/EEE
dc u

where; w = the width of the flange; and h 2 height of the web
as given by the Tables of properties of steel sections. A
similar computation was used for the square concrete piles;

whereby “(and h are the length of the sides.

147
The pile loading test data which are used to verify the

developed algorithm are as presented in Table 6.1. The load-
movement curves and the output from the algorithm for these
20 loading tests are presented in Appendix A and Appendix C
respectively, except for Pile No.26 which is also presented
in the next section as a typical example of the output. Other
detail about Pile No.26 with regard to the site, the soil

profile and the loading tests is presented in Section 6.2.3.

Table 6.1: Pile Loading Test Data — Illustrative Example.

 

 

 

PILE PILE Embedded Length Diameter Source
M3 Le(fl) d(h)

PmeFme
24 Northwestern (AT) 50 18.00 Finno (1989a)
25 Northwestern (SH) 50 18.00 Finno (1989a)
26 No.3, Kansas City 55 12.75 Williams (1960)
27 No.3A, Kansas City 55 14.00 Williams (1960)
28 No.7, Kansas City 55 14.00 Williams (1960)
29 No.7A, Kansas City 55 16.00 Williams (1960)
30 No.8, Aliquippa 88 12.75 AISI (1985)
31 No.28, Hamilton 95 12.75 AISI (1985)

li-Hb
32 Northwestern (AT) 50 H14x73 Finno (19898)
33 Northwestern (SH) 50 H14x73 Finno (1989a)
34 No.7, Locks&Dam4 52 H14x73 Fruco 8 Associates (1964)
35 No.9, Locks&Dam4 54 H14x73 Fruco & Associates (1964)
36 No.4, Kansas City 55 1ZBP53 Williams (1960)
37 No.8, Kansas City 55 14BP73 Williams (1960)
38 No.2, Weirton 75 W14x102 AISI (1985)
39 No.17, S Lake City 59 H14x73 A181 (1985)
40 No.21, E. Chicago 102 H14x73 AISI (1985)

Concrete Pile

41 No.4, Locks&Dam4 40 16" Square Fruco & Associates (1964)
42 No.5, Locks&Dam4 51 16" Square Fruco 8 Associates (1964)
43 Locks&Dam25* 13 16" Octagonal Conroy (1992)

 

 

 

 

148
6.2.1 Typical Example: Pile Test No.26

Pile No.26 is selected as a typical example of use of
the developed algorithm. The determination of tflue measured
capacities, C5“ from the loading test as interpreted by the
three test interpretation criteria (i.e., [2"], [D], and [C])
is as indicated in Fig. 6.1. A sample calculation of shaft
and toe capacities as calculated from the "standard“ formula,
the calibrated shaft and toe capacities (for criteria [D]
only) determined from the algorithm is as shown in Table 6.2.
The detailed calculation (long output) for this pile can be
found in Appendix C. The predicted capacities that are used
for the determination of the allowable capacity in the design
process are summarized in Table 6.3.

In. Table 6.3, adj. calculations are set in) on. a
spreadsheet program. The Table is the actual output from the
spreadsheet. Since the focus is on the design and determining
the allowable capacity, C5, the arrangement of numbers is not
in a specific order.

The embedment length, Le, of Pile No.26 is 55 ft. with an
outside diameter (OD) of 12.75 in. The SPT N-values is
available at several locations down the soil profile (bold
print in column {2}, Table 6.2). Values are interpolated at
every foot. Examples of other calculations are as listed in
Table 6.2, and discussed below are the capacities in the

design process as presented in Table 6.3.

149
6.2.1.1 Calculated. Capacity: Standard. Formula

In Table 6.3, for comparison with other capacities, the
calculated shaft capacity, Q“, and calculated toe capacity,
lQm, using Eqs. 5.2 and 5.3 are found to be 77 and 24 tons
respectively. The sum of these two capacities is the total
calculated capacity from the standard formula, Ck, which is

equal to 101 tons.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pile No. 26 (No.3, Williams, 1960). Pile No. 26 (No.3, Williams, 1960).
QC . H .n .H .n .n he (HH6 rrrrr he ................
: j - m I o - 0.0024245 + 0.0084354 (m) 1
‘f\ \ 1 ~ 1 F1 - 0.99651 ) 1
05 _ .
1:“ 1.0 ’ V: ....... i O
'5 [ [Dl] : Q m = 80 ton!) \ t 1 \ 0-008—
E 1.5 * ; 4.. E ’
: . 1 0.004 '
2.0 ......... - .= . .- .
f [2"] 1 Qm== 11.1 tons; N 3 »
2.5‘... “.1” 1... 0.0001 ...-..- ......-..i.--m--..
0 20 40 6O 80 100 120 140 0.00 0.- 0 1.00 150
Q (tons) m (in)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. 6.1: Measured Capacities — Steel Pipe, Pile No.26.

. .

150

 

 

 

8.8 o ..m 8.. 8 88 8.8 88. 88 88 88 88 8.8 88. .8 88 8 .V 8.8 8 . 8 r 8
8.8 .88 8.. 8 88 8.8 88 88 88 88 88 88 88. .N 88 8 .. 88 8. o .9 2
8.8 88 8.. 8 8 .N N... .m 88 o ..m 88 88 88 88 88. 8 88 8 m 88 .N 8 . 8 m 2
8.8 8.8 ...... 8 8.8 8.8 8.... 8.8 88 88 88 88 88. 8 88 8 m 82 8. o m 8.
8.8 88 8.8 8 82 8.8 .88 8.8 88 88 88 88 88. 8 88 8 8 82 8. o 8 8.
8.8 88 88 8 882 m ..8 8.8 88 88 88 88 88 88. 8 88 8 8 88. 8. o 8 2
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8.8 .8... 8.8 m 82 8.8. 2.... 88 .88 .88 8.8 88 88. 8 88 8 8 882 8. o 8 2
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8... 8... 88.8 2 88 88 88 88 m .8 88.. 88 mo... 88. 8 88 8 2 88 8. o 8 m
8.». No.8 88 8 88 :8 8 .8 88 888 8.. 88 mo... 8 8. 8 88 8 8 8. 8. o m N
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.26.. .85 .86... 88. .86». .5: .88..
.8. .8. .8 8. .8. .8 .8. .8 .8. .8 .8. .88. .8... ..8. 8 oz ......
so ... .8 .2 ... ...o 98 ...... ...... .. .. .0. a. 8 .. .. .2 ...... .. a. z .8686
.878.” ..8. 8888.13 L278.” .2. 282.88.88.48 8.8». 8. .... 8 v.
m... 8.8.. ..N. 88.1.... 4.2.4.8.. .2. 82.88.8888 .8. 9.8. 88 SJ.
888.... L252.” .8. 2......” .2. .8288 83.6.23“ .8. 8. 8. .58. N: .88...
8828838882 .2. 3:48.. .2. .258. .m. ....8. 88 .13
3...... .2. 88 8.8.. .... 86. 85.82.8282 8.8.8 c. ..68. .88. .... 28 .
.226 .52 .... .28-.. .2. 88.2-2 8.8.2.8....” .N. .63» 8.. .5. 8.2 oo
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.mm.oz mafia .COHumasono Doonmpmonam H808Q>B .m.m canoe

 

Table 6.3: Typical Output of Allowable Capacity — Pile No.26.

151

 

Calculated (Formula)

 

 

 

 

 

 

 

 

 

Qsc th Qc th/ Qc RELIABILITY APPROACH Deterministic
77 24 101 0.24 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
Qsp Qtp Qp S B Qa CPS FS
256 22 277 [2"] 0.12 2.00 71 1.81 1.81
231 20 251 [D] 0.12 3.00 33 2.38 2.38
311 22 333 [C] 0.11 2.50 62 1.95 1.95
261 21 282 [DC] 0.10 3.00 5 0 2.05 2.05
Non-Uniform
Measured (Loading Test) CL Site Provide Equiv.
Qsm th (Qt/ Q) Fb S B Qa CFS FS
88 27 0.23 0.461 0.25 1.50 46 2.80 2.80
62 18 0.22 0.312 0.30 1.25 26 3.01 3.01
90 29 0.24 0.361 0.27 1.25 46 2.64 2.64
76 24 0.24 0.363 0.27 1.25 39 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp' Fb/ Qm Provide Site
Qm Qp' Fb PS Qa S CPS B
[2"] 1.11 115 128 2.00 64 0.12 2.00 2.37
[D] 0.98 80 78 2.50 31 0.12 2.50 3.18
[C] 1.01 119 120 2.50 48 0.11 2.50 3.49
[DC] 1.03 100 102 2.00 51 0.10 2.00 2.90
Non-Uniform
STEEL PIPE PILE Site Non-Uniform
CD 12. 75 (in) Provide Site Equiv.
t 0.19 (in) F8 Qa s CFS B
[Asli 3.34 (sq.ft) [2"] 3.00 43 0.25 3.00 1 .62
A steel 7.42 (sq in) [D] 3.00 2 6 0.30 3.00 1. 25
A toe 0.89 (sq.ft) [C] 3.00 40 0.27 3.00 1.46
Le 55 (It) [DC] 3.00 34 0.27 3.00 1.46
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Uniform Equivalent
Output Bold NLT Site Provide Equiv.
Fb S B Qa CFS F5
[2"] 1.136 0.12 2.00 174 1.81 1.81
[D] 0.978 0.12 3.00 1 03 2.38 2.38
[C] 0.863 0.11 2.50 148 1.95 1.95
[DC] 0.952 0.10 3.00 131 2.05 2.05

 

 

 

 

152
6 . 2 . 1 . 2 Measured Capacity: Loading Test

The measured pile capacities according to the [2"], [D],
and [C] criteria are obtained from Fig. 6.1, which are equal
to 115, 80, and 119 tons, respectively. The [DC] criterion is
the average of the [D] and the [C] criteria, which is equal
to 100 tons.

The proportion of the measured toe capacity; (hm, follows
the equation of the toe capacity ratio, R4, as found in Table
5.5. For example, for the [2"] criteria, Rp=Hl/CD=O.23, which
resulted in the measured toe (le) and the measured shaft
capacities (Qsm) of 27 and 88 tons respectively. A similar
calculation procedure is done for the [D], [C] and [DC]
criteria.

The Qsm and th values are not used in the subsequent
calculations (was used in Chapter 5 for the derivation of Fs
and Ft). Therefore, Qsm and th in Table 6.3 serve only as
comparison with the respective values as determined from the

standard formula and the algorithm.

6 . 2 . 1 . 3 Predicted Capacity: The Algorithm

The predicted capacity for the shaft (Qsp) and toe (Qtp)
are determined from Eq. 5.23; and the total predicted
capacity from the algorithm is found to be 277, 251, 333 and

282 for the [2"], [D], [C] and [DC] criteria respectively.

153
The factors for shaft 0%) and toe (F0 that are used with Eq.

5.23 are as found in Table 5.5.

Since the loading test for Pile No.26 is the constant
load (CL) type, the capacities are corrected according to the
recommended bias factor (Fb) of 0.461, 0.312, 0.361 and 0.363
for the [2"], [D], [C] and [DC] criteria respectively (see
Table 5.6). Therefore, the corrected predicted capacities
(i.e., Qp*Fb) are equal to 128, 78, 120 and 102 for the [2"],
NH, US] and [DC] criteria respectively. These corrected
predicted capacities are the ones used for the subsequent

calculations for design (or the allowable capacity).

6.2.1.4 Design: Deterministic Approach

The capacity that is used for design is the allowable
capacity, Q3. For design according to the deterministic
approach, the recommended factor of safety, FS, is taken from
Table 5.7; which is equal to 2.00, 2.50, 2.50 and 2.00 for
the [2"], [D], [C] and [DC] criteria respectively. By
dividing the (Cb*Fb) with FS (or Eq. 5.23), C5 is found to be
64, 31, 48 aux} 51 tons for the [2"], [EH, NH and [DC]
criteria respectively.

To determine the equivalent reliability index, fl, the
values of s from Table 5.6 are used. The recommended value of
s for the "uniform" site is equal to 0.12, 0.12, 0.11 and 0.10

for the [2"], [D], [C] and [DC] criteria respectively. The

154

respective central factor of safety (CFS) is determined by
assuming that it is equal to the deterministic factor of
safety (FS, see Eq. 5.32). Thus, the equivalent B is
determined from Eq. 5.32; and is found to be 2.37, 3.18. 3.49
and 2.90 for the [2"], [D], [C] and [DC] criteria

respectively.

Similarly, the procedure is repeated for the "non—

uniform" site, but with a higher recommended FS.

6.2.1.5 Design: Reliability—Based Approach

The design from the reliability—based approach starts by
selecting the recommended 8 values from Table 5.7; which are
equal to 0.12, 0.12, 0.11 and 0.10 for the [2"], [D], [C] and
[DC] criteria respectively. The provided reliability index
(B) is taken from the recommended values as found in Table
5.7; which is equal to 2.00, 3.00, 2.50 and 3.00 for the
[2"], [D], [C] and [DC] criteria respectively. The allowable
capacity (C5) is than calculated from Eq. 5.33; which is equal
tn) 71, 33, 62 and 50 tons for the [2"], [D], [C] and [DC]
criteria respectively. Knowing the Q3, the CFS and the
equivalent FS is determined from Eq. 5.34; which is equal to
1.81, 2.38, 1.95 and 2.05 for the [2"], [D], [C] and [DC]

criteria respectively.

155

Similarly, the procedure is repeated for the "non-
uniform" site, but with a different set of s values (see also

Table 5.6).

6 . 2 . 1 . 6 Allowable Capacity: Unknown Loading Test

Table 6.3 also presents the allowable capacity from the
reliability-based approach by assuming that unknown type of
loading test (NLT) will be done. That is, the allowable
capacity is determined only from the SPT N—values, and no
comparison with loading test would be made (see also Section
5.3).

The procedure to determine the allowable capacity for
the NLT case is the same as in Section 6.2.1.5, except that
the respective recommended Fb factors are used (see Table
5.6). At the recommended Fb (for NLT), for the "uniform” site,
and at the recommended 3, the allowable capacity is found to
be 174, 103, 148 enui 131 for the [2"], UN, H3] and [DC]
criteria respectively.

Since the interpreted measured capacity from the loading
txast is itself dependent upon the type of loading test (i.e.,
CL or CRP type), the bias factor for the NLT condition should
be used if no comparison is to be made with any loading test.
If the loading test would be carried on the pile, the

:respective F5 should be used.

156
6.2.1.7 Design: Using The Chart

The allowable capacity as presented in Table 6.3 can be
determined by using the Design Charts as presented in Section
5.3.4.4. Determination of the allowable capacity ((5) 1A; as
illustrated in Fig. 6.2 (for Pile No.26). The pile was tested
according to the Constant Load (CL) type; and the curve in
Fig. 6.2 is the Davisson's [D] criteria.

The predicted capacity (Qp) as determined from the
algorithm using the N—values on a spreadsheet program is
found to 1x3 251 tons (Table 6.3). The allowable capacity
determined from tflue deterministic and :reliability—based

approaches are as described below.

(a) Reliability-Based Approach: Ekm‘ the [D]

criteria, the recommended [3 from Table 5.7 is 3.00. At

B=3.00, entering Fig. 6.2 from the scale on.tflua left hand

side, and deflecting downwards at 820.12 (for the "uniform"
site), the "unit allowable capacity" (Qa) is found to be equal
to 0.13. The allowable capacity, (Qa=Qa*Qp), is then
(O.13*251)=32.6 tons. Deflecting upwards from the 8 curve, or
by taking the reciprocal of the QF0.13 (which is 7.69), the
(PS/0.31) is equal to 7.69. Therefore, the equivalent FS is
than equal to (7.69*O.3l)=2.38. The approximate probability
of failure (Pk) can be found on the scale on the right hand

side of Fig. 6.2 (or simply LHOfi).

157

(b) Deterministic Approach: Similar values as obtain
from above can be obtained if the design is to be done from
the deterministic approach. For the deterministic approach,
the recommended F8 in Table 5.6 is 2.50. Entering the scale
at the top side of Fig. 6.2, i.e., at (2.50/O.31)=8.06 (or by
taking the &064, and enter the chart from the bottom scale).
the qa is found to be 0.124. The allowable capacity (C5) is
then (O.124*251)=31.1 tons. Deflecting tx> the left an: the
"uniform" site HM: $20.12), the equivalent B=3.18. And
deflecting to the right from the 3 curve, the Pf is found to

be at about 2H03; or simply lflflfi.

158

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

FS / 0.31
8.06
7.69 5.00 3.00
5 T I I L l
: 4X Constant Load (CL)
: ~§ Davisson's Criteria [D]
I E
_ 2 ...
~ o F]; ‘ 4
4 l- 2 qt: l/lO
_:_ ...................... a ............ Qa = qa ... Qp :_
3 . _ % 1/103
: Rehab My 5 . Sand _
t .‘ \\ (Uniform Soil) —-O—a~ s=0.12
B b - a 3 I l P
: . \ mun s=0.15j f
g ..... 0-.. = 1
2 _ \ ...... 5 0.201 1/102
i _ —o—— s=o.3o:
_ ‘e t}
K ‘ \‘ -(
1 _; fl 29‘ .......:.b ....... -< l 10
_ g // \\\ .x. .‘ ] /
: SandeLClay ‘~ 1
~ (Non-Uniform Soil) ‘ .‘ X a
......................... bumh‘ .................. .—4)—
c ° . 3
L l l l l I l l l l 1 1W L l L i l l l l l l ‘1“; ‘1 d
O I l ”I v U
0124
0.13

0.00 0.05 0.10 0.15 0.20 0.25 0.30
qa=031/CFS

Fig. 6.2: Design By Chart - Davisson's Criteria [D]; Constant
Load Test Type (CL).

159
6 . 2 . 2 Site at Northwestern University

Several axial loading tests were made in conjunction
with tine Foundation Engineering Congress an: Northwestern
University, Chicago, in June 1989 (Finno et al, 1989b). The
purpose of that exercise was to evaluate the state of the
profession's ability to pmedict pile response under axial
load. Extensive laboratory and in-situ tests were made
available to the 24 participants prior to the loading tests.
The comparison of the predicted capacity as determined from
the developed algorithm and the 24 participants will be
presented in Section 6.3.

The stratigraphy at the test location is rather unusual;
i.e., strong sand overlaying weak soft clay layer. The soil
profile consists of 23 ft. of fine grained sand, then 45 ft.
of soft to medium clay, then 12 ft of stiff clay and finally
10 11;. of hard silt. Beneath the silt, Niagaran dolomite
bedrock is encountered. The water table is at about 15 ft.
below the ground surface.

Four types of pile were tested (one HP14x73, one 18 in.
diameter pipe pile, and two drilled piers); and each of the
piles was tested three times at 2, 5, enui 43 weeks after
installation. Only data from the pipe pile and the H—pile are
considered.

The pipe pile is 18 in outside diameter with the wall
thickness of 0.375 in. The embedment length was 50 ft. The

end of the pile was closed with a 19 in. outside diameter,

160
3/4 in thickness boot plate. The H—pile was also embedded at

50 ft.

All the piles were driven by Vulcan 06 hammer. To assist
the driving, a 12 in. diameter hole was preaugered to a
depth of 23 ft. at the location of the pipe pile (Finno et
al, 1989a). The loading tests were performed in general
conformance with ASTM standard D—1143-81. "Failure" (i.e.,
end to testing) was noted when the load could not be held
constant (thus CL type of loading test) unless the hydraulic
jack was continuously pumped.

For the Standard Penetration Test (SPT), there are two
sets of N-values available. One set was obtained using an
automatic trip hammer and the other set was obtained using
the safety hammer. Therefore, two independent predictions of
the capacities can be made for a single pile (listed in
Table 6.1 as Pile No.24 and No.25 for the pipe pile, and Pile
No.32 and No.33 for the H-pile).

The load-movement curve for the interpretation of
ultimate capacities according to criteria [2"], [D], and [C]
is presented in figures in Appendix A. The summary of
capacities from the prediction and other related parameters
are presented in Appendix C. The results will further be

discussed in Section 6.3.

161
6 . 2 . 3 Site at Kansas City

Six piles were considered from Williams (1960), i.e.,
Pile No.26, No.27, No.28 and No.29 for pipe piles and Pile
No.32 and No.33 for H—pile.

This project was a joint effort by the Kansas and
Missouri Highway Departments for the bridge connecting Kansas
City, Kansas and Kansas City, Missouri. The central portion
of the intercity viaduct is located in the flood valleys of
the Kansas River and the Missouri River not far from the
junction of these two rivers.

Bedrock was approximately 85 to 65 ft. below ground
level. Soil bmrings were made according tx> the proposed
method for penetration tests and split spoon sampling of
soils, ASTM Committee D—18 of 1958. The borings showed that
the soil classification was fairly uniform for tflua entire
structure. Fine sand is at the top 10 or 15 ft, the next 25
ft. consists of silty sand and sandy silt, and the balance
consists of fine to coarse sand and gravel. The bedrock was
shale and limestone. The ground water table was indicated at
about 28 to 30 ft. below the ground surface. However, the
distance of SPT borings and the actual locations of the
respective piles were not available from Williams (1960).

The diameters of the pipe piles were 12, 14, 14, and 16
in. for Pile No.26, No.27, No.28 and No.29 respectively. The
pipe thickness was 3/16 in; and were closed at the toe with

flat metal plates. The H—pile, Pile No.32 and No.33 were of

 

162
type 12BP53 and 14BP73 respectively. The embedment length of

all of the piles was 55 ft. The piles were all driven with a
modified Vulcan No. 1 Steam Hammer.

The loading tests were carried out not earlier than 48
hours after the driving of the piles. The load was maintained
at all times during the test by a constant attention to load
gage :readings enmi jacking' application (thus (H; type of
loading test). The first application of load was
approximately 50 tons for Pile No.26, No.27, and 65 tons for
File No.28 and No.29. The load increment after the first
application ii; 25 tons per increment, applied IKM: earlier
than 1 lunnr after all measurable movement (M3 the initial
loading had ceased. The least movement considered measurable
was 0.012 in. Failure (or termination of loading test) was
defined when the rate of gross movement exceeded 0.03 in/ton
for the last movement of load applied.

The respective measured capacities as well as the output
from time spreadsheet according to interpretation criteria
used in this study can be found in Appendix A and C. The

:results will further be discussed in Section 6.3.

6.2.4 Site at Looks & Dam No.4

Six pipe piles at the site of Locks and Dam No.4 (Fruco

amid Associates, 1964) have been used earlier in Chapter 5 to

(derive the appropriate factors in Section 5.3.2. The soil

163

IDIOfile and the related pile testing procedures can be found
in Section 5.2.2.

There are two H—piles and two concrete piles that
<:onform to the selection criteria (Section 6.2). The two H—
Ipiles are of type 14BP73 which is represented by Pile No.34
and No.35. The two square 16 in. concrete piles is as
represented by Pile No.41 and No.42.

The respective measured capacities as well as the output
from the smmeadsheet according to interpretation criteria
used in this study can be found in Appendrx A and C. The

results will further be discussed in Section 6.3.

6.2.5 AISI Collection

Two steel pipe piles (Pile No.30 and No.31) that satisfy
the selection criteria as presented in Section 6.2 are
considered from the collection of AISI (1985). The H—piles
are as represented by Pile No.38, No.39, and No.40.

Only the basic information about the piles and pile
driving data were available; such as location, date of test,
hammer type, pile type, embeddment length, and tin; load-
movement curves. Pk) detailed. informatitnl about the soil
profile: is available; except for SPT iN-values and the
location of the water table.

Pile No.30 is from the site in Aliquippa, Pensylvania.

The pile was a 12.75 in. outside diameter with 3/8 in. wall

 

164
thickness; the toe closed with a 1—1/4 in. flat boot plate.

The embedment length of the pile is 88 ft; and filled with
5,000 psi concrete. With increasing depth from the ground
surface, the soil consists of 40 ft. of fill slag and
alluvium, 10 ft. of soft organic silt, 40 ft. of dense gravel
and beneath this the medium hard sandstone. The water table
was about 45 ft. below the ground surface. The N—values are
available to about 40 ft. below the ground surface. The
loading test was performed in accordance to ASTM D1143-61T.
The load was supplied using a hydraulic jack against a load
platform, and Raymond hammer. Termination (ME each loading
occurred when the settlement was approximately 0.001 in/hr.
Pile No.31 is from the site in Hamilton, Ontario. The
pile was a 12.75 in. outside diameter with 3/8 in. wall
thickness; toe closed with concrete core. The embedment
length of the pile is 95 ft. With increasing depth from the
ground surface, the soil consists of 30 ft. of fill sand and
gravel, 30 ft. of fine to medium loose sand, 15 ft. of very
stiff clayey silt, 25 ft. of very dense fine to medium gravel
and beneath this is the weathered queenstone shale. There is
no indication of water table. The loading test was performed
in accordance to ASTM D1143—81. The load was supplied from
two 400 ton hydraulic jacks against a dead load, and Demag
D30—23 hammer. There is no indication of the type of loading

test performed.

165

From the characteristics of the load—movement curve, it
aappears that both pipe piles were tested according to CRP
‘type of loading test.

H—pile No.38, No.39, and No.40 did not quite satisfy the
selection criteria (the N>va1ues and tflma soil profile as
Inentioned in Section 6.2). Nevertheless, they were tried upon
to observe any dispersion of the predicted capacity. From the
characteristics of the load—movement curve as presented by
AISI (1988), it appears that the loading test for these piles
is of CL type.

Pile No. 38 is from the site in Weirton, West Virginia.
The pile type is W14 X 102, A36 steel, with an embedment
length of 75 ft. With increasing depth from the ground
surface, the soil consists of about 40 fig tof medium dense
fine sand with some silt, the next 40 fix. is medium dense
fine sand with some gravel. At depth of 80 ft. and below, the
bearing layer consists of hard silting shale and very hard
sandy siltstone. The water table is about 40 ft. below the
ground surface. The loading test was in accordance to ASTM
D1143—61T. The loading is done by hydraulic jacking against
load frame anchored to nearby reaction piles. The hammer type
is Vulcan 80C weighing 8000 lbs. The test was terminated at
450 tons because of oil leakage from the hydraulic jack.

Pile No. 39 is the H-pile of type HP14 X 73, A36 steel
driven at Salt Lake City, Utah. The toe of the pile is at 78
ft., but the head of the pile is embedment 19 ft. below the

ground surface, resulting in the embedment length of the pile

 

166

of 59 ft. The soil consists of silt and clay with traces of
sand up to the depth of about 50 ft. below the ground
surface; 30 ft. below that is sandy gravel with N-values of
more than 100. Therefore, the pile is predominantly embedded
irz clay which also function as EH1 end bearing"pile. The
loading device is similar to Data No.15, but the pile is
driven by Delmag D—22 hammer.

Data No.17 is the H—pile of type H12x53, A36 steel. The
embedment length of the pile is 102 ft. 1km) 50 ft. of the
soil profile is fill slag, and the next 50 ft. is silty clay
with sand (thus, predominantly in clay). The pile is driven
with a Vulcan 140C hammer.

The respective measured capacities as well as the output
from the smmeadsheet according to interpretation criteria
used in this study can be found in Appendix A and C. The

results will further be discussed in Section 6.3.

6.2.6 Site at Locks and Dam No.25

One 16 in. octagonal concrete pile is used to test the
algorithm (Conroy, 1992). The pile is supporting a kmidge
structure. The toe of the pile was embedded to a depth of 54
ft. Due to erosion and scouring of the soil at the site, the
present ground level is at an elevation of 41 ft., leaving an
embedment length of only 13 ft. No load test was done, but

the SPT N>values is available from the nearby boring. The

167

prediction of capacities from the algorithm using only the N-
values can be found in Appendix C. The analysis of the

capacities is presented in Section 6.3

6.3 Discussion of Results

Comparison (Hi the measured capacities (C50 and the
predicted capacities (Cb*Fb) is shown 1J1 Appendix [L It is
found that for all criteria there is no significant different

between Qm and Qp*Fb. However, the student t-test was

conducted for pipe pile only.

6.3.1 Predicted, Allowable & Measured Capacities

A summary of the outputs from the algorithm is presented
1J1 Tables 6.4 fin: the respective interpretation criteria
respectively (Note: from Section 5.3.1, the [DC] criterion is
not the average of the [D] and [C] outputs, but rather the
parameters, i.e., Rh 1%, and.FR are derived from the average
of measured capacities (Qm) as determined from the
Davisson's and Chin's criteria). The predicted capacities
H%#f$) as found in Table 6.4 are plotted against the measured
capacities (C50 as shown in Fig. 6.3.

The mean an of the predicted capacity from the

algorithm divided by the measured capacity (Qp*Fb/Qm), is

168
found to be 1.33, 0.98, 1.04 and 1.03 for the [2"], [D], [C]

and [DC] criteria. respectively for time pipe pile. The

standard deviation (6) is 0.21, 0.08, 0.21 and 0.13 for the

[2"], [[H, [C] and. HXH criteria respectively. Ehxxn Table
6.4, the interpretation criteria of [2"] tends to
overestimate the pile quite substantially (about 33%). This

is probably due to an overestimate of the shaft capacity
(especially for longer piles), since the factor F5 is run:
decreasing at an increasing depth but rather flat (see Fig.
5.4(c)). For the other criteria, the predicted capacities are
found to be good, i.e., (Qp*Fb/Qm) of about 1.00.

Overall, the [D] criteria showed the best prediction of
capacities when compared to measured capacities, H== 0.98 and
(S: 0.08; followed by [DC], [C] and [2"]. A larger bias (0)
and a larger scatter (0') is obtained when all the 20 data
points representing pipe pile, H—pile and concrete piles are

used (see Table 6.4).

From the determined (Cb*Fb), the allowable capacity (Cb)
can be determined by using Eqs. 5.3.3 and 5.3.4 for the B and
FS respectively.

Table 6.4 also presents the C5 assuming that the type of
loading test is unknown (NLT). These Qa (and other Q. as
determined from the algorithm) are the long term capacities
(see assumptions in Section 5.3.1). The B and s for the
"uniform" site are recommended if the pile is predominantly

in sand (say, more than 50 % of embedded length), or else the

169

parameters from the "non—uniform“ site are recommended (see
also the recommended values in Section 5.3.4).

The C5 for the unknown loading test (NLT) condition is
found to be at higher values since the Fb for the NLT
condition is recommended higher (uncertainty whether the
loading test would be done according to the CL or CRP type).
The justification for higher recommended Fb factors has been
discussed in Section 5.3.3 and 5.3.4. If however, the C5 is to
be compared with "future loading test," the Fb from the
anticipated testing methods should be used (see also Fb
factors for CL and CRP in Table 5.6).

The choice of Fb, loading test methods (CL or CRP) and
the interpretation criteria ([2"], [D], [C], or [DC]) for the
determination of (Qp*Fb) and Qm can be illustrated by
examining Pile No.43 in Table C43 in Appendix C.

Table B20 presents the output from the spreadsheet
program. Say for example the comparison of allowable capacity
is tun be made for CL type of loading test, and Ch.tx3 be
interpreted by the criteria [D], then (C5*Fb)=66 tons. If the
deterministic approach is used (at FS=2.50) the allowable
capacity (Qa) is 26 tons. Similarly, if the reliability
approach is used (B=3.00 and $20.12) the allowable capacity
(C5) is 28 tons. From the analysis done by Conroy (1992) for
this pile, the equivalent (Qp*Fb)=47 tons, with a large
standard deviation of 24 tons. This indicates that the

Exossible range of (C5*Fb) from Conroy's analysis could be in

the wide range of (-25 to 119 tons) from negative 3 and

170

positive 23 standard deviations from time expected value.
Similarly, the equivalent C5 is 111 tons unth.ea standard
deviation of 4.9 tons, which indicates that (5 from Conroy's
analysis could lie in between 16 to 46 tons. Therefore, the
values from the algorithm from [D] criteria "are within"
Conroy's values.

Looking at this data from the other perspective, it may
suggest that the "real probable" Cb could in fact be higher.
Considering that the Davisson's interpretation of the loading
test (Qm) could be the lower limit and the Chin's
interpretation could possibly be the upper limit, perhaps the
values from the [DC] criteria should be used. At the
recommended safety measures for the [DC] criteria, the C5 is
found to be 61 and 59 tons from the deterministic and
reliability—based design approaches respectively (which is

also within the Conroy's range).

6.3.2 Deterministic Vs. Reliability-Based Design

Using the recommended safety measures (FS or B, in Table

5.7) the allowable capacity as determined by the reliability-
based approach could.kx3 slightly lower tflmui the allowable

capacity from the deterministic approach. This is because at

the recommended FS, "the equivalent" B values are not

recommended. The equivalent B values at the corresponding FS

values are rounded up to one decimal place for convenience.

171

I’or example, at the recommended FS of 2.00, the “equivalent"
c>r the B value that corresponds to FS=2.0 is actually 1.83
(the [2"] criteria for the "uniform" site in Table 5.7), but

for convenience if time design is fitml the reliability

approach "the recommended B" value is rounded up to 2.00. The
reverse is true when the recommended B is actually lower than
"the equivalent" FS, e.g., criteria [C] fin: the "unknown"
site; whereby the recommended B is 2.50 instead of
recommending "the equivalent" value of 2.61 at the respective
recommended {*3 of 2.50. The small difference can be

considered insignificant considering that both approaches are

independent of each other.

172

Table 6.4: Summary of C5 and Safety Measures From The
Algorithm.

(a)

Criteria [2"].

 

 

 

 

 

 

 

 

 

 

PILE PILE TYPE [2"] CRITERIA ALLOWABLE NLT4 NLT4
NO. CAPACITY3 Uniform Non-Unit.
Site Site
Pipe Pile Le Qm Qp' Fb Qp' Fb 1Q8, 2Q8 Qa Qa
(it) (tons) (tons) /Qm (tons) (tons) (tons) (tons)
24 Northwestern (AT) 50 100 122 1.22 61 68 - 108
25 Northwestern (SH) 50 100 124 1.24 62 69 - 109
26 No.3, Kansas City 55 115 127 1.11 64 71 174 -
27 No.3A, Kansas City 55 112 144 1.29 72 80 197 -
28 No.7, Kansas City 55 130 148 1.14 74 82 203 -
29 No.7A, Kansas City 55 140 181 1.29 91 100 247 -
30 No.8, Aliquippa 88 480 760 1.58 380 421 388 -
31 No.28, Hamilton 95 580 923 1.59 461 511 471 -
H - Pile
32 Northwestern (AT) 50 103 102 0.99 51 56 - 90
33 Northwestern (SH) 50 103 104 1.01 52 57 - 91
34 No.7, Locks&Dam4 52 250 117 0.47 58 65 - 103
35 No.9, Locks&Dam4 54 260 128 0.49 64 71 - 113
36 No.4, Kansas City 55 124 136 1.10 68 75 - 120
37 No.8, Kansas City 55 122 179 1.47 90 99 - 158
38 No.2, Weirton 75 550 317 0.58 159 176 - 208
39 No.17, S Lake City 59 375 791 2.11 396 438 - 697
40 No.21, E. Chicago 102 280 421 1.50 211 233 - 371
Concrete Pile
41 No.4, Locks&Dam4 40 225 110 0.49 55 61 - 96
42 No.5. Locks&Dam4 51 295 148 0.50 74 82 - 131
43 Locks&Dam25 1 3 NA 153 NA 77 85 - 1 35
Pipe H-Pile All
Pile5 Only6 Data
(Qp’ Fb/ Qm) p 1.33 0.92 1.19
o 0.21 0.38 0.45

 

1Qa from DETERMINISTIC approach for the "Uniform" Site at FS=2.00; equivalent B=2.37
2Q,. from RELIABILITY-BASED approach for the "Uniform" Site at (3:200; equivalent FS=1.81
3Al|owable capacity (Qa) as compared to Measured Capacity (Qm)
4Allowable Capacity from SPT only (unknown loading test, NLT)

5Excluding Pile No.24 8 No.25 - hole preaugered before pile is driven

6Excluding Pile No.38, No. 39, and No.40 (Pile No.38 & Pile No.39 - Toe bearing;
Pile No.39 & Pile No.40 - pile is predominantly embedded in clay)

 

 

 

173

Table 6.4: Continued

(b) Criteria [D].

 

 

 

 

 

 

 

 

 

 

PILE PILE TYPE [D] CRITERIA ALLOWABLE NLT4 NLT4
IND. CAPACITY3 Uniform Non-Unit.
Site Site
Pipe Pile L.e Q"n Qp‘ Pb Qp' Fb 1Qa 2Qa Qa Qa
(ft) (tons) (tons) IQm (tons) (tons) (tons) (tons)
24 Northwestern (AT) 50 60 79 1.32 32 33 - 83
25 Northwestern (SH) 50 60 81 1.35 32 34 - 84
26 No.3, Kansas City 55 80 78 0.98 31 33 103 -
27 No.3A, Kansas City 55 95 90 0.95 36 38 119 -
28 No.7, Kansas City 55 110 93 0.85 37 39 122 -
29 No.7A, Kansas City 55 115 115 1.00 46 48 151 -
30 No.8, Aliquippa 88 500 551 1.10 221 232 203 —
31 No.28, Hamilton 95 640 638 1.00 255 268 235 -
H - Pile
32 Northwestern (AT) 50 90 66 0.73 26 28 - 69
33 Northwestern (SH) 50 90 67 0.74 27 28 - 70
34 No.7, Locks&Dam4 52 220 73 0.33 29 31 - 76
35 No.9, Locks&Dam4 54 240 80 0.33 32 34 - 83
36 No.4, Kansas City 55 90 85 0.94 34 35 - 80
37 No.8, Kansas City 55 102 113 1.11 45 48 - 118
38 No.2, Weirton 75 440 194 0.44 78 82 - 203
39 No.17, S Lake City 59 340 510 1.50 204 214 - 531
40 No.21, E. Chicago 102 260 217 0.83 87 91 - 226
Concrete Pile
41 No.4, Locks&Dam4 40 190 66 0.35 26 27 - 68
42 No.5, Locks&Dam4 51 245 91 0.37 37 38 - 95
4 3 Locks&Dam25 1 3 NA 6 6 NA 2 6 2 8 - 6 9
Pipe H-Pile All
Pile5 Onlye Data
(Qp* Fb/ Qm) )1 0.98 0.70 0.91
o 0.08 0.32 0.31

 

 

1Qa from DETERMINISTIC approach for the "Uniform" Site at FS=2.50; equivalent B=3.18
2Qa from RELIABILITY-BASED approach for the "Uniform" Site at 8:300; equivalent FS=2.38
3Allowable capacity (Qa) as compared to Measured Capacity (Qm)

4Allowable Capacity from SPT only (unknown loading test, NLT)

5Excluding Pile No.24 & No.25 - hole preaugered before pile is driven

6Excluding Pile No.38, No. 39, and No.40 (Pile No.38 & Pile No.39 - Toe bearing;
Pile No.39 & Pile No.40 - pile is predominantly embedded in clay)

 

 

174

Table 6.4: Continued

(c) Criteria [C].

 

 

 

 

 

 

 

 

 

 

PILE PILE TYPE [C] CRITERIA ALLOWABLE NLT4 NLT4
NO. CAPACITY3 Uniform Non-Unif.
Site Site
Pipe Pile Le Qm Qp' Fb Qp" Fb 1Qa 2Q, Q. Qa
(ft) (tons) (tons) IQm (tons) (tons) (tons) (tons)
24 Northwestern (AT) 50 119 149 1.25 60 76 - 135
25 Northwestern (SH) 50 119 152 1.28 61 78 - 138
26 No.3, Kansas City 55 119 120 1.01 48 62 148 -
27 No.3A, Kansas City 55 121 144 1.19 58 74 177 -
28 No.7, Kansas City 55 137 148 1.08 59 76 182 -
29 No.7A, Kansas City 55 150 193 1.29 77 99 238 -
30 No.8, Aliquippa 88 495 508 1.03 203 261 223 -
31 No.28, Hamilton 95 827 550 0.67 220 283 241 -
H - Pile
32 Northwestern (AT) 50 108 119 1.10 47 61 - 109
33 Northwestern (SH) 50 108 121 1.12 49 62 - 110
34 No_7’ Locks&Dam4 52 297 124 0.42 49 64 - 112
35 No.9, Locks&Dam4 54 316 133 0.42 53 68 - 120
36 No.4, Kansas City 55 143 133 0.93 53 68 - 120
37 No.8, Kansas City 55 132 191 1.45 76 98 - 173
38 No.2, Weirton 75 986 285 0.29 114 147 - 258
39 No.17, S Lake City 59 482 623 1.29 249 320 - 564
40 No.21, E. Chicago 102 339 243 0.72 97 125 - 220
Concrete Pile
41 No.4, Locks&Dam4 40 228 127 0.56 51 65 - 115
42 No_5, Locks&Dam4 51 321 163 0.51 65 84 - 148
43 Locks&Dam25 1 3 NA 159 NA 64 82 - 1 44
Pipe H-Pile All
Piles Only6 Data
(Qp* Fb/ Qm) )1 1.04 0.91 0.97
o 0.21 0.41 0.35

 

 

1Qa from DETERMINISTIC approach for the "Uniform" Site at FS=2.50; equivalent [5:349
20,, from RELIABILITY-BASED approach for the "Uniform" Site at (3:250; equivalent FS=1.95
3Allowable capacity (Q3) as compared to Measured Capacity (Qm)

4Allowable Capacity from SPT only (unknown loading test, NLT)

5Excluding Pile No.24 & No.25 - hole preaugered before pile is driven

6Excluding Pile No.38, No. 39, and No.40 (Pile No.38 & Pile No.39 - Toe bearing;
Pile No.39 & Pile No.40 - pile is predominantly embedded in clay)

 

 

175

Table 6.4: Continued

(d) Criteria [DC].

 

 

 

 

 

 

PILE PILE TYPE [DC] CRITERIA ALLOWABLE NLT4 NLT4
NO. CAPACITY3 Uniform Non-Unit.
Site Site
Pipe Pile Le Qm Qp' Fb Qp' Fb 1Q,l 2Qa Q. Qa
(ft) (tons) (tons) lQm (tons) (tons) (tons) (tons)
24 Northwestern (AT) 50 90 114 1.27 57 56 - 113
25 Northwestern (SH) 50 90 116 1.29 58 57 - 115
26 No.3, Kansas City 55 100 102 1.02 51 50 131 -

27 No.3A, Kansas City 55 108 120 1.11 60 58 153 -
28 No.7, Kansas City 55 124 123 0.99 62 60 158 -
29 No.7A, Kansas City 55 133 157 1.18 78 76 201 -

 

 

 

 

30 No.8, Aliquippa 88 498 531 1.07 266 259 228 -
31 No.28, Hamilton 95 734 598 0.81 299 292 257 -
H - Pile
32 Northwestern (AT) 50 99 93 0.94 46 45 - 92
33 Northwestern (SH) 50 99 95 0.96 47 46 - 94
35 No.9, Locks&Dam4 54 278 109 0.39 55 53 - 109
36 No.4, Kansas City 55 117 112 0.96 56 54 - 111
37 No.8, Kansas City 55 117 155 1.32 77 76 - 154
38 No.2, Weirton 75 713 249 0.35 124 121 - 247
39 No.17, S Lake City 59 411 599 1.46 300 292 - 595
40 No.21, E. Chicgago 102 300 246 0.82 123 120 - 244
Concrete Pile
41 No.4, Locks&Dam4 40 209 98 0.47 49 48 - 98
42 No.5, Locks&Dam4 51 283 130 0.46 65 64 - 130
43 Locks&Dam25 1 3 NA 122 NA 61 59 - 1 21
Pipe H-Pile All
Piles Only6 Data
(Qp' Fb/ Qm) l1 1.03 0.83 0.96
o 0.13 0.37 0.33

 

 

1Qa from DETERMINISTIC approach for the "Uniform" Site at FS=2.00; equivalent [3:290
2Qa from RELIABILITY-BASED approach for the "Uniform" Site at 8:300; equivalent FS:2.05
3Allowable capacity (0,.) as compared to Measured Capacity (Qm)

4Al|owable Capacity from SPT only (unknown loading test, NLT)

5Excluding Pile No.24 6 No.25 - hole preaugered before pile is driven

6Excluding Pile No.38, No. 39, and No.40 (Pile No.38 8 Pile No.39 - Toe bearing;
Pile No.39 8 Pile No.40 - pile is predominantly embedded in clay)

 

 

176

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Predicted Capacity - The Algorithm Vs.

I‘m A A I A A A J A l l A
A .4 >
g «numb: ° ‘
c 800 '
LL19 -: + o .
«n . .
500. _
>2 * - ’
... i m clay
.8 4 \
a 400: * toe bearing -
a . g' .
U . t -
g 200; ‘0 (QP * Ft) 3 [2"] _
u-t ‘ D P. Pi] .
E ‘ 0’ o agile c
‘ oncretePrle
o -. ,. .r. .....LTTW.
0 200 400 6m 8m 1000
Qm (MS)
(a) 2" Movement
I“ A A A l A A A l l A l A A
A
g 3 (Q, * F.) : [C] ;
c l o ' .Pile >
mfg”: 3 Eggmnk f
a: . .
of“; . L
5‘ toe bearing 0 b
.g )-
D. 400 - L
a It F
U 1 .
o-
3 . , ’4 .
.2 200‘ *0 a toe bearing "
B < 0 ++ 1n clay )
cl: « .
o . ,. ., . .,. ,. .
0 200 400 600 800 1000
Qm 00m»
(c) Chin's
Fig. 6.3:

 

 

 

 

 

 

 

 

 

7m A 1 All Ali LLJ A A1 A4 A l 1 1 L l L A 1

A 4 F
g . (Qp *F): [D] .
an: L
c: . g -“k .
u“ o ConcrctcPilc ° :
OF : toe bearing I
.. 400~ -
.3: l l
8 300.1 L
5' ] toe bearing I
§ 2"? \ f :—
§ 100: in clay l

o .--.-..,...,...,...T--.,--.
0 100 200 300 400 500 600 700

Qm(ton8)
(b) Davisson's

800 1A1 1 A A l A l A
g .«5; *i=)2[DC1 ;
c 7001 Pi Pu: locum 8 7
.9 .4 + H- 1C / :
L1. 600— :: Compile + o ,_
* .
. o :
03500: _.
.2? 4003 "-
é : :
d g + '
g 2001 . I L
8 1 .0 1“ clay toe bearing ’
ope d D _
'o lm—r n 0‘ i—
a 1 ’

0 ‘ U U‘ T V I I V I V V I If? V I I U I I TTTr
0 100 200 300 400 500 Gm 700 8G)

Qm (mm)
(d) Ave Davisson's & Chin's

Capacity.

Measured

177
6 . 3 . 3 The Algorithm Vs . Previous Studies

6 . 3 . 3 . 1 Site at Northwestern University

One specific comparison of the predicted capacity from
the developed algorithm and previous studies can be made by
examining the pipe and H—pile tested for the pile capacity
prediction event at NOrthwestern University (Finno et al,
1989b). Since there are two sets of SPT N—values available,
the pipe pile in that particular study is represented by File
No.24 and No.25 for Automatic Trip (AT) Hammer and Safety
Hammer (SH) respectively. Similarly, the H-pile is
represented by Pile No.32 and No.33 for the AT and SH
respectively.

As indicated by the tables of output in Appendix C, the
[predicted capacities (Cb*Fb) do not vary much between the two
types of SPT hammers (only in the order of 2 to 3 tons).

From the load-movement curves (Fig. A24), the
interpreted measured capacity, Qm, according to [2"], [EH,
[C], and [DC] criteria are found to be 100, 60, 119, and 90
tons respectively for the pipe pile. Similarly for the H-pile
(Fig. A32), Ch.is interpreted at 103, 90, 108 & 99 tons using
criteria [2“], [D], [C], and [DC] respectively.

Comparing the Qm with the predicted capacities from the
algorithm, say Pile No.24, the predicted capacities from the
algorithm somewhat "overpredicts" the capacity. This is

indicated by the ratio of (Qp*Fb/Qm) from the algorithm (Table

178
C24) which are found to be 1.22, 1.32, 1.25, & 1.27 for [2"],

[D], [C], and [DC] criteria respectively. For the H—pile, the
ratio of (Qp*Fb/Qm) is found to be at 0.99, 0.73, 1.10, & 0.94
for the [2"], [D], [C], and [DC] criteria respectively;
indicating no trend of "overprediction."

The “overprediction” of the pipe pile No.24 could be due
to preaugered hole of 12 in. diameter for the 18 in. pipe
pile prior to installation (see Section 6.2.1). The other
reason is that because the developed algorithm was designed
to determined the long term capacity (see Section 5.3.1).
From the load—movement curve (in Appendix A), clearly if the
measured capacity is determined from the loading test at 43
weeks, the algorithm would not "overpredict" the capacity
(i.e., using data points at 43 weeks instead of data points
at 2 weeks to determine the measured capacities). However,
the data points of the loading test at 43 weeks were not
considered in this example since for all the other piles, the
loading tests were done at relatively shorter time, data
points at 2 weeks were considered in this case to maintain
the consistency of interpreting Qm at "shortly" after pile is
driven. Thus, for this particular pile, it is not entirely
true to say that the algorithm "overpredict" the capacity,
but rather the Qm might be "underestimated. "

Therefore, for this particular site, it is not quite
valid to compare the (Qp*Fb) from the algorithm with the Qm
from the loading test. The predicted capacities from the

algorithm can however be fairly compared to the other 24

179

participants who had made prediction at the foundation
congress. The "long term" (after one year) capacity as
reported by Finno et al (1989b) by the 24 participants for
the pipe pile ranges from 63 tons (about 125 kips) to 185
tons (370 kips) with the mean of 108 tons (215 kips). For the
pipe pile as indicated in Fig. 6.4(a), the predicted
capacities from the algorithm in general were found to be in
agreement with the range of predicted capacities submitted by
other participant (Predictor No.25 is the result from the
developed algorithm). The predicted capacities from the
algorithm were found to be 122, 79, 144, and 114 tons using
criteria [2"], UN, [C], and UXH respectively. Tflme [DC]
criterion (at 114 tons) gives the best result and matches
well with the mean of the 24 predictors (i.e., at 108 tons).
The [DC] criteria would be the choice if a single value is to
be chosen for actual design ([D] is the lower limit and [C]
is the upper limit, see also the assumptions in Section
5.3.1).

As indicated in Fig. 6.4(a), the predicted capacity from
the [D] criterion lies within the lower range, together with
cather predictors. Conversely, the predicted capacity from [C]
criterion lies within the upper range. In fact, this is the
(general trend for the developed algorithm.

For the H—pile in Fig. 6.4(b), the algorithm somewhat
Igredicted lower capacities as compared to the mean of the 24

gxredictors for criteria [D] and [DC]. In fact, this general

tzrend is also shown by the mean, u, for the H—piles in Table

180

6.4; which is less than unity. However, good agreement is
obtained for the interpretation by criteria [2"] and [C].
This gives the notion that for H-pile, "maximum mobilization"
of the shaft resistance may have occurred (which is one of
the main assumptions of these 2 criteria, see also Sections
3.3.1 and 3.3.3), thus resulting in a better prediction (as
compared to [D] and [DC] criteria). Nevertheless (for H-Pile,
No.32), good. agreement it; obtained VHHNI the predicted
capacity from the algorithm is compared to the measured
capacity as indicated by the ratios of the predicted to the
measured capacities of 0.99, 0.73, 1.10 and 0.94 by using
criteria [2"], [EH, U3] and [DC] respectively ixl'Table B9
(Appendix B).

In Fig. 6.4, predictors No.3 and No. 17 represent the
capacities as predicted by Wolff (1989) and Coyle and Tucker
(1989) respectively.

For the pipe pile in Fig. 6.4(a), both predictors
predicted somewhat lower values [at 75 tons (150 kips) and 67
tons (134 kips) by Wolff and Coyle and Tucker respectively],
as compared to the mean of the 24 predictors (at 108 tons).
However, like many other predictors, the predicted capacity
of 75 tons by Wolff is among "the comfortable" single value
for design since it is within the "lower limit" of criteria
[D] and "upper limit" of criteria [C].

For the H—pile, both. Wolff and Coyle and Tucker
jpredicted the closest value as compared to the mean of the 22

gxredictors (at 112 tons). Wolff and Coyle and Tucker

181
predicted the capacity at 105 tons (210 kips) and 119 tons

(238 kips) respectively; which is also 7 tons below and above
the mean of the 22 predictors respectively. However, for
practical purpose in actual design, and following the general
recommendation in this study (i.e., interpret loading test
from the average of criteria [D] and [C]), then among the 22
predictors, Wolff's prediction of 105 tons is found to be the
nearest to [DC] criteria (at 99 tons).

Using the developed algorithm in this study, the
predicted capacity of the H-pile as interpreted by [2"]
criterion (at 102 tons) is the closest to the measured [DC]
criteria (99 tons); and the predicted capacity using the [C]
criterion (at 119 tons) is the closest to the mean of the 22
liredictors an: 112 tons). This gives ea notion that the
algorithm should be limited to predict capacity only by
criteria [2"] or [C] for H—pile to obtain “good results."

The algorithm developed in this study is tin: the most
part an improvement of the method by Wolff (1989), i.e., the
characterization of tflua relevant parameters 1J1 the static
exyiation by integrating the shaft resistance over the
corresponding' surface area (M3 the pile. However, the
algorithm uses a.sfindlar static equatbmi as presented by
(Coyle and Castello (1981) for the shaft resistance (see also
'Tabde 5.2); and modified by the inclusion of various factors

eas presented in Chapter 5.

182

Pipe Pile No.24 (Finno et at, 1989c)
mm 11 11 11.1 11 11 11 11 11 11 11 11,11 1
. Qm , 24Predictors I 185

_ [2"] = 100 tons 13:13038 I .23: (Qp*Fb)

 

 

T I T 1

 

 

 

 

 

 

 

 

 

  

A l [D] = 60 =1};
5 15° . [C] = 119 ,._ :1.)— lg.-
v . 1DC1= 90 1:5: {31 ii? 51::
d" : .. :21 a};
23 l 21': “E? 32-122. j 114
'6 ‘ " 1'5" 5." ": ‘
8 0 :2. .... . r3... .....1 (...? .
.0 ... ............. .2 .1 f2... ...-"1 :41 n
E -:-..I .2: 2.. 1::- -:-; :2-:-.l:

.' ...: p’ .0 :0... ...0.1 E:- .

f- i-Z- [2: :.-'..11-._-.: f'.

0 . ._- . .3 511,.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'I'TII ‘ I‘I‘ ‘ '
7171318310241122 21916209 8 21235 611514124 25252525
Predictor'sNo.

(a) 18" Pipe Pile, No.24.

H-Pile No.32 (Finno et al, 19890)
llllllllllllllllllllllllll
200 . Q,11 , 22 Predictors I 190
- [2"] :103 tons “113132 I
'11)] =90 “-
‘50‘101 =108
=99

 

 

 

T T T T

 

   
 

 

 

 

119 {-1}: .3}:

 

 

Predicted Capacity. Qp (tons)

0 0 0 '0 0 0 '0 0
v. '. V. V. V. V. V. T. '-
‘0 .0 .0 '0 '0 '0 '0 '0 '0
0 0 0 0 0 0 0 0 0
. C . . O . ‘ .

      

 

 

 

 

 

 

 

 

 

0 0
‘ 0 ' 0 ° 0 ° 0 ’ 0 ' 0 ' 0 ' 0 ‘ 0 ' 0 ' 0 ' 0 0
- . . . U . . . . . C ' . . . . C . . . ' . C . ' . C . C
0 0 0 0 0 0 0 0 0 0 0 0 0
‘- ‘_ L_ L— L A- L‘ A— . A- L k
i O C .7 I C i O C I O . ‘ I
0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 0

 

 

 

 

 

 

 

 

'0.'0.'0.'0_'0.'0.'0.'0‘ I. l-
0 0 0 0 0 0 0 0
.0 .0 .0 .0 .0 .0 '0 .0 .0 .0
A 4‘ _‘ .A J ‘ .A

 

 

 

 

 

 

1 1 ' ' '1 1 ' I 1
1322112418231410 916192021317 2 6115124 3 7 5 25252525
Predictor'sNo.

(b) H14x73 Pile, No.32.

Fig. 6.4: Predicted Capacity - The Algorithm Vs. Other
Predictors.

183
6 . 3 . 3 . 2 Site at Kansas City

The other set of data that could be compared to the
previous study is the data taken from the site in Kansas City
(Williams, 1960). Columns [3} and {4} in Table 6.5 are the
measured and allowable capacities respectively as reported by
Fuller (1960). Columns {5} through [8} aura the allowable
capacities from the algorithm as calculated from the
deterministic approach at the recommended factor of safety
(see also the Recommended F8 in Section 5.3.4). In columns
{5} through {9}, the equivalent reliability index is also
presented.

At the recommended FS, the general trend as before for
the allowable capacities is also observed (i.e., [2"] give
the highest Cb, followed by [C], and [D] give the lowest). The
allowable capacity for the [DC] criterion is somewhat higher
than both the [D] and the [C] criteria mainly because the FS
is recommended at 2.00. If the FS=2.50 and criteria [DC] is
used (column {9}). the allowable capacities are found to be
very close to the values as reported by Fuller, especially
for the pipe piles. For the [DC] criteria, using the FS=2.5
i£5 perhaps (H1 the conservative side since time equivalent
reliability index is 3.86 (high). Therefore, for the [DC]
criteria, the recommended FS=2.00 (at EH1 equivalent 3:2.90)
is felt reasonable. Since the allowable capacities determined
by the algorithm is very close to Fuller's values (at

FS=2.5), lower safety measures (i.e., minimum of FS=2.00

184

widely used in practice) can in fact be considered with

confidence.

Table 6.5: Allowable Capacity - The Algorithm Vs. Previous

 

Study.
PILE PILE TYPE AS REPORTED BY OUTPUT FROM THE ALGORITHM
NO. FULLER (1960)

 

At the Rec‘md FS (Table 5.7)

 

[2"] [D] [0] [DC] [DC]

FS=2.0 FS=2.0 FS=2.5 FS=2.5 FS=2.0 FS=2.5

B B 13 B B
2.37 3.18 3.49 2.90 3.86

Qm Qa Qa Qa Qa Qa Qa

(tons) (tons) (tons) (tons) (tons) (tons)

{1} {2} {3) {4} {5} {6} {7} {8} {9}

 

 

Pipe Pile
26 No.3, Kansas City 85 42.5 64 31 48 51 41
27 No.3A, Kansas City 105 52 .5 72 36 58 60 4 8
28 No.7, Kansas City 110 5 5 74 37 59 62 4 9
29 No.7A, Kansas City 123 61.5 91 46 77 78 6 3
H - Pile
3 6 No.4, Kansas City 110 5 5 68 68 53 56 4 5

 

 

 

 

 

3 7 No.8, Kansas City 116 5 8 90 90 76 77 6 2

 

185

6.4 Summary

This chapter has illustrated how the developed algorithm
could be used to determine the allowable capacity either from
deterministic or reliability—based approaches. Using the
recommended safety measures, the appropriate allowable
capacity can be found from the predicted capacity. The
predicted capacity as determined from the algorithm compares
very well with other studies. In design process, the charts
can be used for rapid determination of allowable capacities.

The predicted capacities (i.e., Qp*Fb) for pipe piles
compare very well with the measured capacity from loading
test values; the (Qp*Fb) normalized by Qm is found to be very
close to unity for all the criteria, except the [2"] criteria
which is slightly overestimated.

For the H—piles, the predicted capacity (i.e., (5*Fb) is
slightly underestimated, but the [2"] and [C] criteria can be
used.

The developed algorithm perhaps works best fin: pipe
piles. This could be due to the parameters in the algorithm,

'which was derived using only data from pipe piles.

CHAPTER '7

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

7.1 Summary

The purpose of this research was to develop a direct
relation of safety measures as determined from the
conventional deterministic approach and the reliability—based
approach. It was felt that a direct interrelation between the
two approaches could help the interpretation of safety
measures (factor of safety, FS, and reliability index, B),
and the design process itself (i.e., the determination of the
allowable capacity for pile foundation).

At present, the determination of the allowable capacity
from Standard Penetration Test N—values is pmimarily done
either kn; deterministic or reliability-based approach. In
current design methods, the safety measures as found by the
two approaches, in general, have not been correlated; i.e.,
no direct interrelation between the deterministic (FS) and
reliability index (8).

In the deterministic design process, the procedure with
respect to assigning the factor of safety is a "straight
forward" procedure from static formula, thus routinely used
by practitioners. On the other hand, design of pile
foundatitni by reliability' methods, besides the need to

"select" the critical parameter values in the static formula

186

187

(as in the case of deterministic approach), demands an
additional statistical procedure. Therefore, sometimes design
by reliability approach gives an impression that the process
is aa "statistical procedure" rather than a: "geotechnical
problem". Due to the unfamiliar theories and an added effort
(to geotechnical engineers), the reliability-based methods
have lagged behind in application and have not been applied
on routine basis. Nevertheless, with recent improvement in
reliability theories, and with added improvement in computing
capabilities, reliability methods could be the trend of the
future. For example, tedious calculations once not possible
to do manually are now possible on micro computers.

Thus, this sflnuhr was concentrated CH1 developing au1
interrelation algorithm of safety measures which are
applicable by both design approaches; in the form of
equations and design charts. The developed charts could
possibly help designers in understanding the safety measures
involved; and serve as a transition tool towards reliability—
based design of the future.

Due to the complexity of problems associated with pile
foundations, one major issue was immediately encountered when
emu attempt was made to develop the interrelation, i.e, the
determination of the predicted capacity, Ck. Therefore, the
secondary work in this research was to define a consistent
and systematic procedure to determine Qb. This was achieved
byu (i) identifying a specific analytical formula to

calculate Qp, and (ii) calibrating the calculated Qp with the

188
measured capacity (Qm) from the loading test. In the

Calibration process of the predicted capacity (Qp) with the
"true" measured capacity (Qm), the ratio of (Qp/Qm) was taken
as a random variable and defined as the bias factor (Fb).

To interrelate the deterministic factor of safety (FS)
and the equivalent safety measure from the reliability—based
([3) , first—order uncertainty analysis was then applied. The
usage of the developed model was then illustrated by

examples.

7 . 2 Conclusions

The algorithm developed in this research is not intended
to replace proven and well established methods for the
determination of allowable capacity of a pile foundation.
Nevertheless, it is felt that the recommended equations,
de'Sign charts and the recommended safety measures could be a
Valuable tool in the design process of a pile foundation. The
direct interrelation of FS and B could be an alternative
method of understanding the reliability of pile foundation
design. Thus, the algorithm developed in this research could

be a supplementary tool for designers, and specification and

Code writers .

The major conclusions which resulted from this study can

be Stated as follows.

'7 .2.1

189
Predicted Capacity

With respect to the predicted capacity (C%), following

C3c>nclusions can be made:

1.

In using data from Standard Penetration Test (SPT),
the "high degree of engineering judgement” required
to select a realistic N-value for design in routine
design practice is virtually' eliminated in the
developed algorithm. This is also true about the
complex issue related to the "selection" of the
site lateral earth pressure (Ks) and other
parameters used (see implied assumptions in Section
5.4).

The ratio of the toe capacity to the total capacity
Uh), the shaft correction factor (F3), and the toe
correction factor (Fa can be expressed as functions
of the embedment length of the pile (Le) and pile

diameter (d). The inclusion of correction factors

(Fsand F0 is in essence what is better called as

fi
the "modified B-Method" .

Different bias factors (Fb) should be used for the

determination of predicted capacity ((5), depending

on what loading test criteria the comparison is to

be made (i.e., according to the 2" Movement [2"],
Davisson's [D], Chins' [C] or the average of
Davissons' and Chins' [DC]). Also, the bias factor

chosen is dependent upon the type of loading test

- 2

190

(i.e., Constant Rate of Penetration, CRP, or
Constant Load, CL). If the type of loading test is
unknown, the Fb as recommended for NLT should be
used.

The predicted capacity is sensitive to the
underlying variability at the site, i.e., the
standard deviation of the distribution of measured
capacity over predicted capacity (8 values); small
changes in 8 could affect the value of allowable
capacity, (5, quite measurably. Therefore, it is
appropriate that the (1, determined for "non-
uniform" site soil pmoperties (i.e., sites with
sand enui clay) based (M) a :relatively larger 8
values is conservative. For "uniform" site soil
properties (i.e., site which is predominantly in
sand) lower 8 values should be applied.

As indicated by the value of it (i.e., Qp*Fb/Qm).
the predicted capacity for the pipe piles are found
to have shown better results as compared to the H-

piles or the concrete piles.

Safety Measures

With. respect to (fine safety' measures (deterministic

factor of safety, FS, or reliability index, B), the following

(:Cnlclusions can be made:

191

For the determination of allowable capacity, the
factor of safety (FS) as used for design in
deterministic approach can be interrelated to
the reliability index (B).as found in reliability-
based approach.

The recommended safety measures are dependent upon
the value of the statistical bias factor of the
prediction U%) and the variability of the
predicted capacity at the site (S).

The reliability-based approach provides more
information about scatter and dispersion associated
with uncertainties of soil properties at the site.
For example, if designing by the deterministic
approach and without any knowledge about the value
of s (which was actually derived from the
reliability approach), the same value of FS might
be» assigned. for £1 "uniformfl and "non-uniform"
sites. However, if designing In! the reliability
approach, this study indicated that different value
of safety measure should be used (i.e, at the
respective value of 8). And rational selection of

safety measures can be made.

192
'7 .3 Recommendations

The algorithm was developed from past experience of
Several previous studies with proven acceptable results. The
recommended parameters (Rt, FS, Ft, Pb and s) are derived in a
systematic and rational manner. A similar procedure can be
followed for the derivation of new sets of parameters (i.e.,
Rt! FS, F‘, F1, and s) for other set of situation (e.g. other
in—situ soil tests and/or for cohesive soils).

Following are recommendations with respect to the

application of the developed algorithm and further research.

7 . 3 - 1 Application of the Algorithm

This study was limited to using soil exploration data
from the Standard Penetration Test (SPT), and the loading
test: data was limited to certain selection criteria as
described in Section 5.2. With respect to application of the
algorithm, the following suggestions and limitations should

be realized:

1. Application of the developed algorithm is intended
and most appropriately used only for cohesionless
soil.

2. In the derivation of the recommended parameters

(i.e., Rt, FS, Ft, Fb and S);

193

(i) certain important issues related. to jpile
foundations which may directly affect the predicted
capacity' are run: specifically' addressed (e.g.,
residual stresses imi piles after driving, and
stress history of soil),

(ii) the parameters are derived from limited SPT
data base and limited load—movement selection (see

Section 5.2).

7 . 3 . 2 Further Research

Potential refinement to the recommended parameters, and

<:orisseequently the algorithm, may be explored by;

1. Use more data and better "data quality" for the
derivation.
2. Employ more rigorous curve fitting procedures (such

as step-wise regression analysis for better curve
fitting and determine which pile or soil parameter
affect the desired factors the most).

3. In this study, the determination. of the bias

factor, Fb, was lumped together for the shaft and

toe to determine the predicted capacity; Cb.
Perhaps better prediction of (5 could be achieved
if separate bias factors were found for the shaft

and toe.

194

Perhaps tine most important consideration for time
overall prediction of pile capacity is to obtain an
entirely new set of Rh I1, F“ F% and s. This can
be done by using data from other rigorous and more
versatile soil exploration methods (such an; Cone
Penetration Test or Dilatometer test) or
correlation from laboratory analysis. IX similar
derivation as used in this research can be
employed, which in addition could also include the

above three recommendations.

APPENDICES

APPENDIX A

Fig. A: Measured Capacities From Load—Movement Curves

 

0'0 vvvv vvvv VYV Yva vvvv
> 1
h \\ 44 4
(H- )—- 01—— ---4 -§\o-—00-4L-000--0-0 Hy—o : v---
0.5 ’ x
C \\ I
L 4
A”) > i ...... T
E I 1
1.5 ......
’ i
: ' : d
. E : 7‘2 4
20’ Mi ...... " I.
I a 1
r \ 4
2.5 bl A LLIL AlJli 114111 A 111 l l LLJL Alll<
0 20 40 60 80 100

0.00

0.50

m (in)

200’

2.50

 

10', Ogeechee

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Criteria

(a)

[2"]

&

[D]

195

rn/Q

 

    

 

10', Ogeechee

  

 

 

Fig. Al Measured Capacities - Pipe Pile No.1.

20', Ogeechee

 

 

 

 

 

 

 

 

 

V V V V V YT ‘— T—V V Y Y V V V
’ \o\ ‘
h 4
.C___ r\e\ 1m .
*
p w h ‘
. l——
: l \
i D ‘
E
. I
" 5 i :
> s 2
~ = . s
» 2
p 3
» i
P 1
d
4
. B0 «
- i
P
. i
J ‘_L L A LA 1 A l A A A I I A A l I A L 1 l

 

 

 

 

 

 

l 50 200

Q (tons)

0 50 100

Criteria

(a)

[2"]

 

250

&

 

[D]

 

 

 

 

0m . .i. ,. ,.n., hi.
i .

i i

0.04 “P2 ~1—
0.03 4 :_
i o I

0.02 J _‘_
MO 2

0m.’ ;
- y = 0.0034946 4 0.0l26l2x 11— 0.99904 -

" y I 0.0I37Sl +0.007I453x Rs 0.99829
0' .11....1....1....1ii.iiiri.
o 1 2 3 4 5 6
“160)
(b) Criteria [C]
20', 09 echee
0025 .1....;....:....:.. .ii.--
.
0020<~ 1—
0015-— i.
0.010-- i
, M9 :
0.005-’— L-
’ i
—E— y - 000063865 + 0.0040249)! R0 0.99995 j
0moieuin-4eu-pxuiu:¢-u-
0 1 2 3 4 5 6
m (In)

(b) Criteria [C]

Fig. A2 Measured Capacities — Pipe Pile No.2.

 

30',Ogeechee
0m ..nn.n..n.nn.n.. .
. “N
0.50 1 “Hit-
L
i
ALDO . \
E 1.50 ‘
I
2.00
- ms
250 b1111 1111 1111 1111 1111 111 1111 1111
0 50100150 200 250 300 350 400
Q(t0ns)
(a) Criteria [2"] & [D]
40', Ogeechee
0.00 ... . ..-. -...
0.50 \KN
,KLM). ;:
€1.50 '
um'
: 3501
2.50 ' .... ...i .... 1... .... ...
0 mm mm mm «m
Q(t0ns)
(a) Criteria [2"] & [D]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

196

 

 

 

 

30', Ogeechee
0.018 i-..;....;...fil.-..:.”.....-
1
0.013”- “1"
P -1
1. 4
O _
\0.009-~ ..
E 1-
» 328 :
0.004-1- -_
ro '
-; y = 0.00034145+0.00305351 R: 0.99958 '
0.000 1LL1 1111%1111j14441#1111:1111
O 1 2 3 4 5 6
m (In)
(b) Criteria [C]

Fig. A3 Measured Capacities — Pipe Pile No.3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    
 

40', Ogeechee

 

 

 

0.005 _:_
0’ :
\ 0.004 .3.—

E 0.003 ~3-
377 1
0.002 0:.

. 0 0 :
0001.} €_

—0:1.-. 910994.795: masks: 9199297.:

7 i I I —r
0 05 1 L5 2 25 3
m (in)
(b) Criteria [C]

Fig. A4 Measured Capacities - Pipe Pile No.4.

197

50', Ogeechee 50', Ogeechee

 

 

0000 If T 1' f V V V V V 00006 j—V Vi #j Vj—r‘l—V Vfi1 VfT‘V’ I ' V V V

L . . L
‘t\::\\ 3 0.005 f
t \Q§ 342 I ;
1 . 0.004 4

A 1.00 ’ Y‘ ‘ ’

1 \ 0.003 -

1111—1L

0.50

 

IV]

I

 

 

lLLLJl

[IVY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5150’ E : .
; 1 0.002-; 1 . :
a ; ,mo: t m7 i
"00 _ . 0.001-} 1
. . I :— y = 0.000617 + 000205421 R: 0.9995
2.50 .... .1411.... .... 1L. 0 .1..1....i....i....1..1.
O 100 200 300 400 500 0 0.5 1 1.5 2 2.5
Q (tons) m (in)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A5 Measured Capacities — Pipe Pile No.5.
TP1, Locks & Dam No.4 TP1, Locks & Dam No.4
000 .. . .. . .. .. .. .. 0108 _4.e+...:.i.+-..i-9.i...:.ss‘
F \*N \ I 0007‘}
050 '-i\ \ f
1. N \ x 3 163 ] 0.006 :- :
r ‘ 1- .
1.00 ' = l ‘ 0.00549 5
A : y. 1
.S I = 2 CV : i
E . 4 \ 0.(X)4 "L’ 1
~ « E c :
150 T .......................... 4 0.003 1:” J
; . 1 : I85 :
. g . 0002-}
2.00 __ .................... .. t
. ‘ ”Bi . 0m1§
C ‘ —:— y - 000056971 4 0005397111 R. 099986
2.50 1 1T 1 1 1 1 1 1 1 1 1 A_ 1 0 p1 14 1 1 1 I LgLI 1 LLI 1 1 1 1 1 § 1 1 1
0 .0 id) mo 2m 0 02 04 06 08 1 12

Q (ton) m (in)

(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A6 Measured Capacities - Pipe Pile No.6.

 

0.00

TP2-1. Locks & Dam No.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

198

TP2-1. Locks & Dam No.4

 

0.008 _

 

 

 

Fig. A7 Measured Capacities — Pipe Pile No.7.

 

 

 

 

 

 

 

 

 

 

 

 

‘;\+\ \ 1
0.50 \> \_ .
1 x 1 .
Z 7N) {220
A 1.00 1 1
.s . \ .
v 4
0i
E 1.50 i *
C i
I 5 2601
2.00 _ g
i : :
L 5 E \ 1
2.50 p1111*1111 1111lr1111 1L14% L11
0 -0 100 150 200 250 300
Q (1011)
(a) Criteria [2"] & [D]
TP2-2. Locks & Dam No.4
0.00 ..-. -.-. .fi. “1....
O 50 [\TL \ih \ i
C \ ..., .
i \* N. 325. 1
1.00 a» ----------- . N?
A _ : .
C 1. .
C i- 1
E 1.50 ........................ i
5 255 1
2,00 in - ......... -..
z
2.50 11+ 11. .. .i.. 1%. ..i'enii
0 50 100 150 200 250 300

(a)

Criteria [2"] &

[D]

 

I l I l .1
- i
> -1
0.007 :— €-
0.006 «E— ~5—
0.005 4; 3-
O :
\ 0.004 {1- ‘P
0.003 4— ~-
: 285
0.002 {— ~—
0.001—L, _-
b y - 000082954 + 0.003515X R- 0.99976
0 i i i i
0 0.4 0.8 1.2 1.6 2
"1011)
(b) Criteria [C]

 

TP2-2. Locks & Dam No.4

  
  
    

 

 

Fig. A8 Measured Capacities — Pipe Pile No.8.

 

0.008_. .,...,..-, fl ‘
0.007—E- 1"
0.006—{- 5-
t :
0.005 -} -j~
C7 : :
\ 0.0044} —}
E : :
0.003 -j— {—
: 280 :
0.002-E -j~
0.001~ {L
—E— y 0 000077767 9 0.0035678! R0 0.99852 :1
O ’- 1 1 1 g 1 1 1 % 1 1 1 % 1 1 1 % 1_1 1 .4
0 0.4 0.8 , 1.2 1.6 2
m (m)
(b) Criteria [C]

199

 

 

TP3, Locks & Dam No.4 TP3, Locks & Dam No.4

 

 

 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

0.00 . e. 0.006 .. ,....1....1....i....1
. 1 I 1
b -( 0 q
5 x \\ 1 0.005-; 3..
0.50 \ \1 - «
. \ 4 : 2
“x, ‘ 1 .
1 00 _ \. \ 3 0.004 A: T
A , 1' iv 4
r 1 1 O' t :
é : 245 \ j \ 0.003 4; 1—
E 1.50 l E i 3
I , 1 0.002 4,» .1
, 0 Z 4 I 293 :
~-0 275 . 0.001 -' {-
_ i —E— y . 000063303 + 0003413331 R- 0.99965 ‘
2.50 1 1 1 1 1 L11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1% 1 1 1 l # 1 1 ‘lfil 1 l 1 L117 1 1 1 1 ¥ 1 1 1 1
0 50 100 150 200 250 300 0 0.25 0.5 075 1 1.25 1.5
Q (ton) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A9 Measured Capacities — Pipe Pile No.9.
TP10. Locks & Dam No.4 TP10. Locks & Dam No.4
0.00 WWW“ .-.-i... -... 0.006 ”.1“..L...:...1...lr...:..T
1- E ‘ : I
\+ \.\1 I 1
\1 \ 0.005 -- --
0.50 _"' """""""" {UNUQL \ ~ —11— 1: 1
1 ‘Pix ' : 1
+ x], 210 ~ 0004 -_ .1-
1. 1 . -1
A100 . ‘ O’ : :
é : \\ j \0003 4} {—
51.50 ’ ‘ E E 1
’ : 0.0021— {—
250 2 ~ 261 3
2'00 “E """"" . 0.001 — g-
C I —:- y . 000078995 4 0003831311 R- 0.99974
2'50 111 1 1 1 1 1 1 1 1 14 1 1 LL 1 1 1 1 O 1 1 1 l 1 1 1 § 1 1 1 1 1 1 § 1 1 1 I 1 1 1 % 1 1 1

 

 

 

 

 

 

 

 

 

 

 

‘ 1
0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Q(ton) “1011)

(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A10 Measured Capacities — Pipe Pile No.10.

200

TP16, Locks & Dam No.4 TP16, Locks & Dam No.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 .1... 1. .99. 0.006 _ , , . . . , . . .Afif.
5“ x \ 4 0.005-” -_
0w "‘\1 ,\ j
: N .\ 160 : 3
: .+ 1 0.004” 1L
Egla)[ j C7 3
v . q \ 0.0031 1..
5150' 1 E E j
: 1 0.0021 1*
am)“ ‘
" 195 I : 0.001-1 .21..
: j —E— y .- 000085378 + 0005023911 R- 099786 E
2.50 1 1 14 1 1 1 1 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 % 1 1 1 jl 1 1 J % L 1 1 1r 1 1
0 50 100 150 200 250 300 0 0.2 0.4 . 0.6 0.8 1
Q (ton) mom
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. All Measured Capacities — Pipe Pile No.11.
No.15, Peck No.15, Peck
000 . T1. . . .99 ... (Hus ,..1..j;.,.:.-.;...4-..:.._
p 4 . .
‘*--1 « 0014—; :_
050’ h“‘\\\m\. , ‘ E 3
: 7O 1 0.012-“:- #:1-
1.00 ’ ‘ 00101: 1*
A 1- 4 O : 2
{5, " j \ 0.008 “: 1—
E 1.50 1 4 E 0006']? . O _}_
L 1 : 89 1
: : o.o04T __
200 u : :
3 0.0029} .j-
: j -_— y . 0.0012802 + 0.011238): R- 0.9796 3
2.50 1 11 1 11 1 1 1 1 1 1 1 1 1 1 1 1 0000 111:111l111%111%1111r111}111
0 20 40 60 80 100 120 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Q (MS) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A12 Measured Capacities - Pipe Pile No.12.

201

No.22, Peck No.22, Peck

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0m>r ..1...;... 0mm_f..4.. ,.H.,....Lq..
0.50 ’ N 1 0.005-,- :-
: N ' I j
: : 0.004“:- . ‘3-
.00 . 1
31 - 1 0’ : :
V I j \ 0.003-1f j”
E1.50' ‘ E : :
1 0.002-; .2-
: I _ n3 ‘
2.00 L 1
1 100 k : 0.001-u.- .11.
I i —5— y . 0.0016059 + 0.0088628): n. 0.99293 3
2.50 1 1 L 1 1 1 1 1 1 1 1 1 1 1 1 14 1 0 1 1 1 1+14 1 1 % 1 1 1 1 § 1 1 1 1 'LL 1 1 1
0 20 40 60 80 100 120 0 0.1 0.2 0.3 0.4 0.5
Q (tons) m (in)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A13 Measured Capacities — Pipe Pile No.13.
No.51, Peck No.51, Peck
(Hm47q_4 9.9. ......-r.: 0mm 4”,:wfi9111Hn:nn:nfl4nn
. r 1
‘t\.‘ 1 ..
0.50 ’ NN‘ ‘ 0003 ' d
b 1 , .1... ....
97Y\‘\\~ : . .
1.00 ‘ ' 1
E; . . C7 . .
L, I l \ 0.002.- ..
E150 ‘ E : . j
1 3 » m2
: . 0.001-- 0 -1
szl ....... 1
95 j _ <
I I —=— y .. 000060851 + 000979991 11. 0.99527 1
250 1111 111. 1111 111 1111 1111 0.000 11.1:1111%....111..:11.1:111.:....:.114
0 25 50 75 100 125 150 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A14 Measured Capacities - Pipe Pile No.14.

No.55, Peck

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

202

No.55, Peck

 

 

 

 

 

 

 

 

(100 .. . .- . .. ... ... ... (1004 . . . . § . . . . , . . . . 1 ... ...
01 \
. N11... .
0050 v D 4
' 105 (1003-- fi_
100 ’ t t
’s‘ t 0 * ‘
L! L \ 0.002 —]— ..
E 1.50 ‘ E i
_ x . ° m7
C (1001.1 j-
200 ”6 . .
r
t i —L' y 1 000025242 1 0.0093631x R- 0.99782 1
2.50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 4 1 1 1 % 1 1 1 1 P 1 1 1 % 1 1 1 1
0 20 40 60 80 100 120 140 160 0 0.1 0.2 0.3 0.4
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A15 Measured Capacities — Pipe Pile No.15.
No.206, Peck No.206, Peck
0'00 v v Y v v v v v v 0.015 v r % v v : v r # I v # fi—r
[Ex _ 53 : '
050’ ' ‘ . .
- < 00”-- 1
100’ > .
g; . . C7 . .
v _ : \ 0.007 —11— ‘1-
5150' * E - ,
~ « 67 ‘
I 65 i (1004-- __
200 . .
1 i : _ .
: j — y . 0.0014015 + 0.01503x R- 0.99928 1
250 .._. £444 - 11,. 0000 . . g . 1,: - +7; 4. . g - .
0 20 40 60 80 100 0 0.15 0.3 . 0.45 0.6 0.75
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A16 Measured Capacities — Pipe Pile No.16.

203

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No.208, Peck No.208, Peck
0m) ..-. ....2 .... ....‘ 00H . ..(..-:...§...f..-j
4 I .
0y)%\\\“::é&$1 ‘ _ 4
’ 1 0.008 df -*-
: 100 VP 1 ‘
,2100. 4 o F j
'v , j \ 0.005 ~~ ~~
E 1 : 1 E 1 1
150’ \ ‘ . u9 *
. « » J
I 1 0.003 -_ 1-
200 ”5 , ,
: j ——- y 1 00031335 1 0.0045667): R- 0.99465 1
2.50 1 . 1 1 1 1 1 1 1 1 1 1 1 111 0.000 1 1 1 1 1 1 1 = 1 14 1 1 1_1 : 1 1 .
0 50 100 150 200 0 0.4 0.8 . 1.2 1.6 2
Q (mm) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A17 Measured Capacities - Pipe Pile No.17.
No.272, Peck No.272, Peck
0.00-4mm '1. .11.:1... 0.002 YT..§.-.r#vrvv#vvvv%r..v4rvwry
1 g 4 1 1
‘ 5 < 1 1
%‘**< 0 n2 1 I 1
0.50 \ 0.002 -_ 1-
E ] E :
A 1.00 _ ‘ 0000]“? j.
.s . \ . \ . .
v . . E 1 4
E 1.50 0001.”. L.
1 r ,
I \ 1 C n7 1
1 125 1 v- <
2.00 .1 0.000 ._ __
1 4 )- 4
L 4 b. <
* j —:— y .. 000031597 + 0.0078651): 52- 0.99041 1
2.50 .... 11.. .11. 0.000 W%%.%%. ”#111.
0 50 100 150 200 250 0 0.05 0.1 0.1.5 0.2 0.25 0.3
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A18 Measured Capacities — Pipe Pile No.18.

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No.274, Peck
0.00-4 . . . . . , . v
a I
0.50; ‘
,Joo’
s ’ :
E 1.50 ' J
2m3’ ‘
: “Cl 1
250’ 11, 1.11 11. 1111‘
0 50 10) no mm
Q(t0nS)
(a) Criteria [2"] & [D]
Fig. A19 Measured
No.358, Peck
0M) .1. ... .-.]... .
{imp . E
050’ ke~fi
1 so .
t \K :
,KLMJ: .......... {_
.5 . \
v i-
5150’ .
2.00 ’
E 90
250'1 1 111111 1 1 111
0 20 40 60 80 100 120
Q(t0ns)
(a) Criteria [2"] & [D]

204

 

 

  

 

 

No.274, Peck
0m: #4 .§ [.11]
. O
0010. ._
0008~ -_
C7
~\0mm- __
E :
0mm: 1
0002. ;_
y - 0.0011279 + 0.006205): R. 0.99384 2
0.000 T 1 1 1 i 1 1 1 1r 1 1 1 : 1 1 1 1 1 1
0 04 08 12 L6 2
m (m)
(b) Criteria [C]

Capacities — Pipe Pile No.19.

No.358, Peck

 

 

 

 

0.012_-..4,..-,...,
0.0101; .1-
’ 1
> ‘1
0008-; ' L-
o t .

\0.006.L -..
E I I
0004.; j-
J
i la) .
0002.; :_

t— y - 0.0022137 + 0.010046)! Ru 0.9968

0.000 1 1 1 i 1 1 1 § 1 1 1 1 1 1 IL 1 1 1
0 02 04 .05 08 1

m (m)
(b) Criteria [C]

Fig. A20 Measured Capacities - Pipe Pile No.20.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

205

 

 

 

 

 

 

 

 

 

No.359, Peck No.359, Peck
0M) ... ... ... ... 0m2 .n.:n..L..41.fi;.n.ln u
‘E'\-< 38 1 I 1
0.50 [ ‘ 0010‘? T
F )- .
; 0008-1 £—
1.00 : 2
E ; O . .
V E \ 0.006-:- 1*-
E1.50 E ; 3
; 1 0.004-t)- _1...
L * , .1
L 45 1 48 "
100 L i """ 1 0002-- 31
t : -:— y - 0.0018822 + 0.020887)! R- 0.99905
2‘50 1 1 111 11 1 (1000 11:11.1111411111i1111:1111
0 20 40 60 80 100 0 0.1 0.2 0.3 0.4 0.5 0.6
Q (tons) m (in)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A21 Measured Capacities - Pipe Pile No.21.
No.360, Peck No.360, Peck
0.00 v. ...' w—vvv 1’vK 0.005 vvrv§uvfirvvv§fivvf111v
r : I
N 1 .
0.50 1 ........... 0.004 .1 __
t 85 I E .
\ 4 L :
A 1.00-4.. .................. . .1 o 0.003___ . . q[_
6 b E\ : \ 1 O :
E 1.50—(1- ............. _: E 0002‘:- :0-
\\ . H4 1
2.00-“. ......................................... 0.001 1; 1
. M0 * 1
: -:— y . 00024074 + 0.0057608): R. 0.9855 j
250 L 1 1 l 1 1 1 1 1 1 1 1 O 1 1 1 : 1 1 1 1 % 1 1 1 1 : 1 1 1 1 § 1 L1 1
0 50 100 150 200 0 0.1 0.2 0.3 0.4 0.5
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A22 Measured Capacities - Pipe Pile No.22.

206

No.361, Peck No.361, Peck

 

 

 

00m V T T T V V V 1i V V V V V I Y V V 0.0] l V V V # V V V ' V V V l V V V #
4 b
0.50 “a

 

 

» \ 1 0.008 -L

Aloo’ \ ' '

 

 

I l A L J L L L A i I l A
1

 

 

 

 

 

 

 

 

 

 

 

 

 

. p ‘ CV _
é : \ : \ 01005-0- '-
E ' \ ‘ E -'
1.50 . ........... .1; 1 ”3
I 0.0031- F
aw) .
1 1m _ _ ‘
: .— y . 0.0044016 o 0.0089879): R. 0.99797 1
250 1111 1111 1111 1111 111 1111 0.000 #11iui1111n1iig1
0 25 50 75 100 125 150 0 0.2 0.4 0.6 0.8 1
Q (tons) m (m)

(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A23 Measured Capacities - Pipe Pile No.23.

m (in)

m (in)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0

0.5

1.0

-s
U!

3.0

3.5

207

Pipe Pile, Northwestern Univ.

1 tips

 

0 50 100 ' 150 200 250
Q (laps)
(a) Criteria [2"] & [D]

Pipe Pile, Northwestern Univ.

 

      

 

 

 

0M4 1 1 1 1 l I-”
0.012-- J-
00104: i-
i I
o 0.008 1- L-
\ I 1
E 0.006 1; j-
I 238 kips I
00041; (1 19 tons) _1_
00021; :L
— y .- 0.00085282 + 0.0042051): R- 0.99781 :
0'000 A A A A # A A A A :1 A A A :7 l A A A # A A A 1% A A A A % A A A A
0 05 1 15 2 25 3 15
m (In)
(b) Criteria [C]

Fig. A24 Measured Capacities - Pipe Pile No.24.

Pipe Pile, Northwestern Univ.

1 :kips

 

50 100 . 150 200 250
Q (RIPS)
(a) Criteria [2"] & [D]

0.014
0.012
0.010

o 0.008

E 0.006
0.004
0.002

0.000

  
  
   

Pipe Pile, Northwestern Univ.

  

 

238 kips
(1 19 tons)

 

#JIAAALLAAIAAA

 

y - 000085282 4» 0.0042051):

  

0 0.5 1 1.5 .2 2.5 3 3.5
m(1n)
(b) Criteria [C]

Fig. A25 Measured Capacities - Pipe Pile No.25.

208

Pile No. 3, Kansas City. Pile No. 3, Kansas City.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00 . . -f.. .H 00w ......... , ......... , .........
1' I P
T‘\~ h\\\\\ . .
05 ~
1 “:k 1 0m2-
: : f
1 0 80 tons v0 < _
E ' 1 C7 *
v ; 4 \ 0.008 -1 .
E * E
1'5 1 i r 119tons
p 4 1
: 1 0.004 -_
20 , . '
E ”5'?“ \. : —:—- y - 00024245 1 0.008435“ R- 0.99651
2.5 111 111 114 111l11l1110.000 111111111 i 111111111 114 11111111
0 20 40 60 80 100 120 I40 0 0.5 .
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A26 Measured Capacities - Pipe Pile, No.26.
Pile No. 3A, Kansas City Pile No.3A, Kansas City
0.0 .. “a”... 0.020 ...;.-.:.fi:...;...
’ 1 4
05' s ‘ 0M6“ a
1 ‘N 1
95 N . 1
,~.10 0012__ 1
.E C’ r i
v \ l J
E 1 5 ..... E 0.0081; .3
: : g j ' lZl tons
20 ' . i mm4¢
1 H2\ « 1
C 3 ._ y . 0.0016145 + 0.0082535x a. 0.9998
25 111111 111111 O-OOOW}1‘§{*L‘
o 20 40 6O 80 100 120 140 0 0.4 0.8 1.2 1.6
Q (tons) m (in)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A27 Measured Capacities - Pipe Pile, No.27.

 

Pile No. 7, Kansas City

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00 .. ~\;.l ..-. ...
1i\ \ 1
0.5 ' \ \\ ‘
’ 10? i
A1.0 +
a \ 1
515 l i
\ ‘
20' ‘
’ 13“:
r 1
25 111 111 111 111 111 111 1
0 20 4o 60 80 100 12m 140
Q (mm)

(a) Criteria [2"] & [D]

Pile No. 7A, Kansas City

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00 .;;; .fl - .-
(K, \\ ‘
0.5 P \ \\ \
b \
' 115 \o i
,\L0 , 1
515 '
20' ‘
: 140
2.5.1. 111 11 111
0 20 40 60 80 100 120 1410 160
Q (tons)
(a) Criteria [2"] & [D]

209

Pile No. 7, Kansas City

 

 

 

 

0.010 --.,...,..f,...:...:...
, -(
l
0.008-4: L-
0mm1- i.
0.004-: i-
L 137 tons ‘
0002-- -+
-L-- y 1. 0.0016082 1 0.007289): a. 0.99854 ‘
0.m A 1% A 14%4 A J_% A A A : A A A : l A A
0 0.2 0.4 0.6 0.8 1 1.2
m (in)

Fig. A28 Measured Capacities - Pipe Pile,

(b) Criteria [C]

No.28.

Pile No. 7A, Kansas City

 

 

 

 

0.014b11fi...,...,..1,...
r

0012-: -1
01010-1; -)-
0008.: ;_
figomm11 J-
: 150tons 1
0004-1 1.
0.002—L .‘L
-I— y - 0.0013831 + 0.0088477): a. 0.99916 2

0'1100011#1111111111L1:%1
0 0.4 0.8 _ 1.2 1.6 2

HIGH)
(b) Criteria [C]

Fig. A29 Measured Capacities — Pipe Pile, No.29.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

210

 

 

 

 

 

 

 

 

 

No.8, Aliquippa No.8, Aliquippa
00,.. ..n. 1“ H...Hu 0mw* 11n1L.¢1fl4.H:H.L11
0.5 ' \ ‘ : :
I \ 1 0.0025 -;- :-
l.0 \\ \ : 1
I 0.0020-L J»
: m0 cy * ‘
kg 2.0 : \ E 0.00151;— 12
E : \\ ~ :
2.5 ’ Z 1
: V 500 0001011 1-
3'0 \ \ I 495 tons ‘
5 (100051; 1-
15, 1 1
: 3 —1—- y - 000026319 + 0002019811 R- 0.99979 1
4.0 - 1 A AALJ 141 1 11 1 1 1111 11114 0.0000 F1 1 1 % 1 1 1%1 1 1%1 1 1%1 1 1IA1 #1 A1 11‘
um xm M» «n am an 0 02 04 06 00 1 12 L4
Q (tons) m (m)
Criteria [2"] & [D] (b) Criteria [C]
Fig. A30 Measured Capacities - Pipe Pile, No.30.
No.28, Hamilton No.28, Hamilton
01) ...... .... .... .... -.. .... J (10045 . .. .1 .. .. 1. .. .. .. .. 1.1.. .
*\ N ‘ F ‘
~ ‘\\\\\\ “~ 1 (10034—— ~-
4 > 1
1 5m l
,120 \\\ C7 1 :
:Ei _ K\\\ \ ; ~1.0002211 ..
E 10‘ K ‘ E ° .
\ * 827 tons ‘
' 640 (10011 ’ <
4.0 > \\ ' 1' T
—:——y 1. 0.0010385 + 0.0012099)! R- 0.99827 ‘
5.0 111 1111 1111 1111 1111 1111 1 11 1111 0.0000 1.11%1111%1141%1111:11L1
up am mm «m am am Km &m 0 05 1 15 2 25
Q (tons) m (m)

Criteria [2"] & [D]

Fig. A31 Measured Capacities — Pipe Pile,

(b) Criteria [C]

No.31.

 

211

 

     
   

H-Pile, Northwestern Univ. H-Pile, Northwestern Univ.
00 0m4_-H.:H..L..4..n§.n.+h..
2 1 u ’

P5 > 4
0.5 0.012-1:- j-
0.010-L J-

1.0 : j
E O 0.008-— _‘_
'\-/ 1.5 \ : I
E £50mx-L :-
: 215tons 3
2.0 kips 0.004 4 (108 tons) ;_
03tons I i
2-5 0.002-- Jr
_’ y .. 000044002 1 0004050411 R- 0.99862 1

 

 

 
    
 

3.0

  

 

 

200 O 0.5 1 1.5 2 2.5 3

so 1 1
Q (kips) m (in)

(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A32 Measured Capacities - H-Pile, No.32.

 

     
   

 

 

 
 

 

 

H-Pile, Northwestern Univ. H-Pile, Northwestern Univ.
00 0m4_- : g . L..-L..¢. H‘
2 . J
1 laps .
05 00121. 1
0010_- i
1.0 2
7:? o 0.008 -- _‘
'C‘z 1.5 \ I 1
E Eiomm-1 J
I 215tons j
2'0 0.004 +; (108 ‘0“5) _
i I
2-5 0.002-“- J
-—' y - 000044002 1 0004050411 R.- 000002 I
3.0 0.000
50 1 . 1 0 0.5 1 1.5 2 2.5 3
Q (RIPS) m (in)

(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A33 Measured Capacities - H—Pile, No.33.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

212

 

    
  
 

 

 

 

 

 

 

 

No.7, Locks & Dam No.4 No.7, Locks & Darn No.4
00 H........fl ... H.. 0mm_.. r1...,. ..1-.. 1...“
r r ‘
1’ ooo7ii :—
05 5\‘\‘_ k\\\“\ t i
. WKN \ 3 0006+ €-
1 no < : :
1 0 - L.\“‘ 1 (1005-3 :_
A ‘ , 1 O I I
'3 E j E 00041;. f
E 1-5 _ 4 0.0031: -—
' 1 I 297 tons
. 3 0.0021: _-
20 :
: 250 : 0.001 «E- ""
: : _H y . 0.0011382 + 0.0033704x R- 0.99934
25 1L11 1111 1111 L111 1111 1111 0‘000'111:111IL111%111#114‘
o 50 100 150 200 250 300 0 0.4 0.8 1.2 1.6 2:
Q (mm) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A34 Measured Capacities - H Pile, No.34.
No.9, Locks & Dam No.4 No.9, LOCKS & Darn No.4
00 ..n n...n.... ”...“. 0mm ......... 1 ......... 1 .........
> 4 P 01
V “\x l : 3
o_ 5 \x‘ \ 3 0.0051- :-
: \ 1 0.004-7 :-
,\L0 .
S r 240 O ;
'v t \ 0.0031- 0 --
E15 ' E :
I 1 0002-; _-
’ L
2.0 . 260 :.1 3161003 -
)- 1 0100‘ 4’- —11—
1 1 o 1
: j -_— y - 0.001051 + 0003167131: R- 0.99548 ‘
25 1111 1111 1111 1111 1111 1111 1111 0000 111111111 # 111111111 % 111111111
o 50 100 150 200 250 300 350 0.0 0.5 1.0 1.5
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A35 Measured Capacities — H Pile,

No.35.

 

213

No.4, Kansas City

 

No.4, Kansas City

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q (mm)

(a) Criteria [2"] & [D]

n1fin)

(b) Criteria [C]

Fig. A37 Measured Capacities - H Pile, No.37.

00 n. ... . ...H 0.()16_.1.1 .1..-1... ""1
* \ : P A
{E'\ ' ‘
* 0.0 4“ _
05 ’ ~““‘~\'\ ‘ 1 : i
)- ’ ‘ , 4
: 90 \ 1 01012-4,— :11—
Lo’ ‘ i 1
A . . 0.010" --
OS 1 g ' .1
" < E 1
E I s ' ‘ 01m8-U- .41-
. \ 1 z 143 tons
: 124 1 0.0061- :-
2.0 : j
’ : 0.004 ~41— -u-
~ ; —h—y-0w&“5+QM“UMFhQ”“8 4
2.5 .L-LL JLA 141 111 141 11 111 0.w2 p411%+1 11L1 1 1 i 1 L1%1 1 1‘
0 20 40 60 80 100 120 MO 160 0 0.4 0.8 1.2 1.6 2
Q (mm) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A36 Measured Capacities - H Pile, No.36.
No.8, Kansas City No.8, Kansas City
00_“ .......n “.....n‘ 0m4_...11...1.-.1. ..1...‘
J ‘\\ j : :
0.5 ,, xx. 102 ‘ 0.012-["- 1%
I 0.0101”. :-
g”) , 00008-: :-
.\1/ b \ : 1
81.5 E 0006+ €~
F 0 : 132 tons :
)- 01m4-‘F -0—
1 122 r 1
2.0 ; 3
: : 0.002-P 11
. i . y . 00010005 1 0.0075931: 11. 0.9900 2
2.5 '41. 111 1.. 111 11111 1.. 1.. 0.000 141:1..T1.111111:1.
0 20 40 60 80 100 120 1410 160 0 0.4 0.8 1.2 1.6 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

214

 

 

 

 

 

 

 

 

 

No.2, Weirton No.2, Weirton
00* A H..... n.. .- omno¥ .1 -1H.:n.,.n,..4.‘
L \\ : .1
1
- 00025-; :.
05 \~ . .
. '\ I 1
; \\ 00020-; 1.
"Lo \%\1 4w C? E 3
é : K \ 0.00151; -‘~
5 1.5 ’ E I 986 tons I
I \ : 00010:. J.
: .fim E 3
2'0 . . 0.0005; .2.
L 4 ’ ‘
* : —L——y . 00015040 + 000101451: R- 097029 3
2.5 P. 1 .111 .111 11 . .1 1 0.0000 . .111111L11.L111111111‘
0 100 200 300 400 500 600 0 o. 2 0. 4 0.6 0.8 1 1. 2 1.4
Q (tons) m (m)
(a) Criteria [2“] & [D] (b) Criteria [C]
Fig. A38 Measured Capacities - H Pile, No.38.
No.17, Salt Lake City N047. Salt Lake City
00 .. "..."...u H..." .. 0mm b....+j...: 1... : ‘
. ~2~ I .1
‘Kxe 0mM1L :.
0.5 L \\ E 3
1- \\\ 0.005-4E- J)—
10: “‘ E 1
g ' . 340 O 0.004-.- 1*
‘\./ : \ : 3
E 1.5 i ‘Y ‘ E 0.003-:- ‘ _:_
. J : :
. i 0.002—‘— 482 tons :1
.- : . .1
20 .
: 375 0.0011} -_
1 -':-— y - 0.001026 1» 0.0020767)! R- 0.99261
2.5111... 1... ..1........1. 0.000*11..:...1111..111.111..1
0 50 100 150 200 250 300 3:30 400 0.0 0.5 1.0 1.5 2.0 2.5
Q (tons) m (in)
(a) Criteria [2"] & [D] (b) Criteria [C]

Fig. A39 Measured Capacities — H Pile, No.39.

 

No.21 , East Chicago

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

215

No.21, East Chicago

 

 

 

 

 

 

 

 

0.0 . - 0.008_.-.1,....1.-..,.1..T...n
' \ 3 0.007—:— 3—
0.5 T\ \ ‘ E 5
: \\ \1 I 0.006-{- ~3~
L 4
> \ \ 0.005-; 1-
’5? 1'0 ‘1‘ 1 O’ E 3
'1, ; A 260i \ 0.004 .1 -1
51.5 ' t“ E 0003f. ;
E \ j ' ; 339 tons 1r
1 I 0.002.; -1
2.0 E
; 23° : 0.001 1:1 ~-
: g : -:— y - 0.0011835 + 0002948111 R- 0.99927
2.5 A A A A A A A A A A A LA 1 g A A A A A 1 1 0.000 . A A A J 1 LL A L L4 A j A : A A A A % A I A 1
0 50 100 150 200 250 300 0.0 0.5 1.0 1.5 2.0 2.5
Q (tons) m (m)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A40 Measured Capacities - H Pile, No.40.
No.4, Locks & Dam No.4 No.4, Locks & Dam No.4
0.0 . .11- .1. 0.0040 _....:....;....:....:....:....,”4.1.1
“\0-1 .00- «L 1.
1 H > ‘1]
0.5 M : 1
: 190 3 00030-3 1:-
A 1.0 K 4 0.0025-12— u;-
ii 5 1 \ 0.0020-E- ~31
E 5 1 E :
"5 1 4 0.00151;— .3-
t * E 228 tons I
: ‘ 0.0010-1 . _1
2.0 Eco
; 22 ] 0.00051: -~
1 —E—- y - 0.0004168 + 0004395611 R. 0.99955
2.5 h .1 .111 1111 111. .... 11.. 0.0000 *1111111111111111111111.111.111.1111111.‘
o 50 100 150 200 250 300 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Q (tons) m (in)
(a) Criteria [2"] & [D] (b) Criteria [C]
Fig. A41 Measured Capacities - Concrete Pile, No.41.

 

No.5, Locks & Dam No.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0 .A ..-1. .
I *‘H I
‘H‘im 4
0.5 ’ "*
’ 1
A1.0
.S : I
v ’ .
E 1.5 ’
2.0 ‘ i
I i
2.5 All] All] 1111 1111 ILAI 1‘11 AAA:
0 50 100 150 200 250 300 350

 

Q (tons)

(a) Criteria [2"] & [D]

216

m/Q

No.5, Locks & Dam No.4

 

0.005
0.004 1’
0.003 J

0.002 1’

321 tons

0.001 1;

 

 

 

q
0000 AAAAAAAAA llAAAAlAAAl 11111 AAAJ

(b) Criteria [C]

Fig. A42 Measured Capacities - Concrete Pile, No.42.

 

1.5

 

APPENDIX B

Table B: A Typical Spreadsheet Calculation, Pipe Pile No.26

Table Bl:

DepflnSPT DJ ‘yw

(ft.) No 26
0
1 O
2 3
3 7
4 10
5 11
6 11
7 12
8 12
9 10
10 8
11 8
12 7
13 7
14 6
15 6
16 6
17 5
18 5
19 4
20 4
21 4
22 5
23 5
24 6
25 6
26 6
27 5
28 5
29 4
30 4
31 6
32 8
33 10
34 12
35 14
36 16
37 18
38 20
39 22
40 24
41 22
42 19
43 17
44 14
45 12
46 12
47 11
48 11
49 10
50 10
S1 10
52 9
S3 9
54 8
55 8

0.00
0. 00
0.00
0.00
0.00
0. 00
0.00

0. 00
0.00
0. 00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0. 00
0.00
0.00
0.00
0. 00
0.00
0.00
0.00
0.00
0.00
0. 00
0. 00
0.00
0. 00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

Spreadsheet Calculation,

'7

120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00
120.00

[povli N.

(W0

60
180
300
420
540
660
780
900
1020
1140
1260
1380
1500
1620
1740
1860
1980
2100
2220
2340
2460
2580
2700
2820
2940
3060
3180
3300
3420
3540
3660
3780
3900
4020
4140
4260
4380
4500
4620
4740
4860
4980
5100
5220
5340
5460
5580
5700
5820
5940
6060
6180
6300
6420
6540

d—A—l—l—i—d—d-‘d
Abmmmmmmwwwwdmhm‘iwmdocofimbww-bammmb-hAbbmmmmwmm

217

0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76

Pipe Pile No.26

Ks

.654
.617
.586
.572
.573
.579
.579
.583
.597
.610
.612
.619
.620
.626
.626
.627
.632
.633
.637
.638
.638
.635
.635
.632
.632
.633
.637
.637
.640
.641
.635
.629
.623
.618
.613
.608
.603
.599
.594
.590
.596
.604
.609
.617
.622
.623
.626
.626
.628
.629
.629
.632
.632
.634
.635

R

[2"]

3.52
3.51
3.51
3.50
3.50
3.49
3.49
3.48
3.48
3.47
3.46
3.46
3.45
3.45
3.44
3.44
3.43
3.43
3.42
3.42
3.41
3.40
3.40
3.39
3.39
3.38
3.38
3.37
3.37
3.36
3.36
3.35
3.35
3.34
3.33
3.33
3.32
3.32
3.31
3.31
3.30
3.30
3.29
3.29
3.28
3.28
3.27
3.27
3.26
3.26
3.25
3.25
3.24
3.24
3.23

R

[D]

4.13
4.09
4.05
4.02
3.98
3.94
3.91

3.87
3.84
3.81

3.77
3.74
3.70
3.67
3.64
3.61

3.57
3.54
3.51

3.48
3.45
3.42
3.39
3.36
3.33
3.30
3.27
3.24
3.21

3.18
3.15
3.12
3.10
3.07
3.04
3.01

2.99
2.96
2.93
2.91

2.88
2.86
2.83
2.81

2.78
2.76
2.73
2.71

2.68
2.66
2.64
2.61

2.59
2.57
2.54

R

[C]

9.42
9.19
8.96
8.74
8.53
8.32
8.11

7.91

7.72
7.53
7.35
7.17
6.99
6.82
6.65
6.49
6.33
6.17
6.02
5.87
5.73
5.59
5.45
5.32
5.19
5.06
4.93
4.81

4.69
4.58
4.47
4.36
4.25
4.15
4.04
3.94
3.85
3.75
3.66
3.57
3.48
3.40
3.31

3.23
3.15
3.08
3.00
2.93
2.85
2.78
2.72
2.65
2.58
2.52
2.46

E

[DC]

5.77
5.69
5.60
5.51
5.43
5.35
5.27
5.19
5.11
5.03
4.96
4.88
4.81
4.73
4.66
4.59
4.52
4.45
4.39
4.32
4.25
4.19
4.13
4.06
4.00
3.94
3.88
3.82
3.77
3.71
3.65
3.60
3.54
3.49
3.44
3.38
3.33
3.28
3.23
3.18
3.14
3.09
3.04
2.99
2.95
2.90
2.86
2.82
2.77
2.73
2.69
2.65
2.61
2.57
2.53

cm

0.24
0.26
0.27
0.27
0.27
0.27
0.27
0.27
0.26
0.26
0.26
0.26
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.26
0.26
0.26
0.26
0.26
0.26
0.27
0.26
0.26
0.26
0.26
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25

Table Bl:
t t
B B

[2"] [D]

0.85 1.00
0.90 1.05
0.93 1.08
0.95 1.09
0.95 1.08
0.94 1.06
0.94 1.05
0.93 1.04
0.91 1.01
0.90 0.98
0.89 0.97
0.88 0.95
0.88 0.94
0.87 0.93
0.87 0.92
0.87 0.91
0.86 0.89
0.86 0.89
0.85 0.87
0.85 0.86
0.84 0.85
0.85 0.85
0.85 0.84
0.85 0.84
0.85 0.83
0.85 0.82
0.84 0.81
0.84 0.80
0.83 0.79
0.83 0.78
0.84 0.79
0.84 0.79
0.85 0.79
0.85 0.78
0.86 0.78
0.86 0.78
0.87 0.78
0.87 0.78
0.87 0.77
0.88 0.77
0.87 0.76
0.86 0.74
0.85 0.73
0.84 0.72
0.83 0.71
0.83 0.70
0.83 0.69
0.82 0.68
0.82 0.67
0.82 0.67
0.82 0.66
0.81 0.65
0.81 0.65
0.81 0.64

0.80

0.63

[Q51]

cal
(Tons)

0.02
0.08
0.13
0.19
0.24
0.30
0.35
0.40
0.45
0.49
0.54
0.59
0.64
0.68
0.73
0.78
0.83
0.88
0.92
0.97
1.02
1.07
1.12
1.18
1.23
1.28
1.32
1.37
1.41
1.46
1.52
1.59
1.65
1.71
1.78
1.84
1.91
1.97
2.03
2.10
2.14
2.17
2.20
2.23
2.26
2.31
2.35
2.40
2.44
2.49
2.54
2.58
2.63
2.67

Continued.
0 t
B B
[C] [DC]
2.27 1.39
2.35 1.45
2.39 1.49
2.37 1.49
2.31 1.47
2.23 1.44
2.18 1.42
2.12 1.39
2.03 1.34
1.95 1.30
1.89 1.28
1.83 1.25
1.78 1.22
1.72 1.20
1.68 1.18
1.63 1.16
1.58 1.13
1.54 1.11
1.49 1.09
1.46 1.07
1.42 1.05
1.39 1.04
1.36 1.03
1.33 1.02
1.30 1.00
1.26 0.98
1.23 0.96
1.19 0.95
1.16 0.93
1.13 0.91
1.11 0.91
1.10 0.90
1.08 0.90
1.06 0.89
1.04 0.88
1.02 0.88
1.00 0.87
0.98 0.86
0.97 0.85
0.95 0.84
0.92 0.83
0.89 0.80
0.86 0.79
0.83 0.77
0.80 0.75
0.78 0.74
0.76 0.72
0.74 0.71
0.72 0.70
0.70 0.69
0.68 0.68
0.66 0.66
0.65 0.65
0.63 0.64
0.61 0.63

2.72

[(1511
[2"]

0.09
0.27
0.47
0.67
0.85
1.03
1.22
1.40
1.55
1.71
1.88
2.03
2.20
2.35
2.52
2.69
2.84
3.00
3.14
3.31
3.47
3.65
3.81
4.00
4.16
4.32
4.45
4.61
4.74
4.90
5.11
5.31
5.52
5.73
5.93
6.13
6.34
6.54
6.74
6.94
7.06
7.14
7.25
7.33
7.43
7.58
7.70
7.85
7.97
8.12
8.26
8.38
8.53
8.64
8.79

218

[QSli
[D]

0.10
0.31
0.54
0.76
0.97
1.17
1.37
1.56
1.72
1.87
2.04
2.20
2.36
2.51
2.67
2.82
2.95
3.10
3.23
3.37
3.51
3.67
3.80
3.95
4.08
4.21
4.31
4.43
4.52
4.64
4.80
4.96
5.11
5.26
5.41
5.55
5.70
5.83
5.97
6.10
6.16
6.19
6.23
6.25
6.29
6.37
6.43
6.50
6.56
6.63
6.70
6.74
6.81
6.85
6.92

[Qsli
[C]

0.23
0.71
1.20
1.66
2.08
2.46
2.84
3.18
3.45
3.70
3.98
4.21
4.46
4.66
4.87
5.07
5.23
5.40
5.53
5.68
5.83
5.99
6.1 1
6.26
6.36
6.45
6.50
6.58
6.61
6.68
6.80
6.91
7.01
7.11
7.19
7.27
7.33
7.39
7.45
7.49
7.44
7.36
7.30
7.20
7.13
7.1 1
7.06
7.03
6.97
6.94
6.90
6.84
6.80
6.73
6.69

[(151]
[DC]

0.14
0.44
0.75
1.05
1.32
1.58
1.84
2.08
2.29
2.47
2.68
2.87
3.07
3.23
3.42
3.59
3.74
3.90
4.03
4.18
4.33
4.49
4.63
4.78
4.91
5.03
5.12
5.23
5.30
5.41
5.56
5.70
5.84
5.98
6.1 1
6.23
6.35
6.47
6.57
6.68
6.70
6.69
6.70
6.67
6.67
6.71
6.73
6.77
6.78
6.81
6.84
6.84
6.87
6.86
6.89

cal
(Tons)

0.02
0.10
0.23
0.42
0.67
0.96
1.31
1.72
2.16
2.65
3.20
3.78
4.42
5.10
5.84
6.62
7.45
8.32
9.24
10.21
11.23
12.30
13.42
14.60
15.82
17.10
18.42
19.78
21.19
22.65
24.17
25.76
27.41
29.12
30.90
32.74
34.65
36.62
38.65
40.75
42.89
45.05
47.26
49.48
51.75
54.06
56.41
58.81
61.26
63.75
66.29
68.87
71.50
74.17
76.89

Qsp
[2"]

0.09
0.36
0.82
1.49
2.34
3.37
4.59
5.99
7.55
9.25
11.13
13.16
15.36
17.72
20.24
22.93
25.76
28.76
31.91
35.21
38.68
42.33
46.15
50.14
54.30
58.61
63.06
67.67
72.42
77.32
82.42
87.74
93.26
98.98
104.92
111.05
117.39
123.92
130.67
137.61
144.66
151.81
159.06
166.38
173.81
181.39
189.08
196.93
204.90
213.02
221.28
229.66
238.19
246.83
255.62

Qsp
[D]

0.10
0.41
0.95
1.72
2.69
3.85
5.22
6.78
8.50
10.37
12.41
14.61
16.97
19.48
22.15
24.97
27.92
31.02
34.25
37.62
41.12
44.79
48.59
52.54
56.62
60.83
65.14
69.57
74.09
78.73
83.52
88.48
93.59
98.85
104.26
109.81
115.51
121.34
127.31
133.42
139.57
145.76
152.00
158.25
164.54
170.92
177.34
183.85
190.40
197.03
203.73
210.47
217.29
224.14
231.05

 

311.45

Table Bl:
Qsp Qsp
[C] [DC]
0.23 0.14
0.93 0.58
2.13 1.32
3.79 2.37
5.87 3.69
8.33 5.28

11.17 7.12
14.35 9.20
17.80 11.49
21.50 13.96
25.48 16.65
29.70 19.52
34.15 22.58
38.81 25.82
43.68 29.23
48.75 32.82
53.98 36.56
59.39 40.46
64.92 44.49
70.60 48.67
76.43 53.00
82.42 57.49
88.54 62.12
94.79 66.90
101.16 71.81
107.61 76.84
114.11 81.96
120.69 87.18
127.31 92.49
133.98 97.89
140.78 103.45
147.69 109.16
154.70 115.00
161.81 120.98
169.00 127.09
176.27 133.32
183.60 139.67
190.99 146.14
198.44 152.71
205.93 159.39
213.37 166.09
220.73 172.78
228.03 179.47
235.23 186.15
242.37 192.82
249.48 199.53
256.54 206.26
263.57 213.03
270.54 219.81
277.48 226.62
284.39 233.46
291.23 240.30
298.03 247.17
304.76 254.03

260.92

Continued.

pt
toe

(psf)

120
240
360
480
600
720
840
960
1080
1200
1320
1440
1560
1680
1800
1920
2040
2160
2280
2400
2520
2640
2760
2880
3000
3120
3240
3360
3480
3600
3720
3840
3960
4080
4200
4320
4440
4560
4680
4800
4920
5040
5160
5280
5400
5520
5640
5760
5880
6000
6120
6240
6360
6480
6600

N9

dd d—I-I—J—I—I—l-O—I
(3(349co<n<x<»-u~q~q~4aaaaa>a>a>~1\4x1a>a1a>a1a>u>u>c,o.d.».b‘b‘fl‘fi‘n1o<n

11

10

oocooooooooooooooococom

QIC

cal

(Tons)

657
L03
215
337
456
463
345
392
371
354
397
610
652
664
205
246
256
296
605
644
683
655
695
1020
1150
1L50
1L53
1L92
1L94
1253
1349
1421
1602
17A0
1686
2640
2202
2373
2353
2243
2645
2488
2406
2271
2202
2243
2230
2271
2258
2299
2340
2326
2367
2353
2393

Ft
[2"]

1L0?

1057

1609
663
620
678
638
600
264
729
696
665
635
606
528
552
527
303
480
459
438
418
359
381
364
347
352
357
302
289
275
263
251
240
229
218
209
L99
L90
L81
L73
L65
L58
151
154
L37
L31
L25
L20
154
L09
L04
699
055
051

219

F1
[D]

625
602
380
359
339
559
301
482
465
4A8
452
456
401
386
322
359
356
353
321
350
258
257
227
257
257
258
259
250
222
254
206
159
151
154
128
121
155
159
153
158
1A2
157
152
127
123
158
154
150
L06
L02
058
055
051
058
055

F1
[C]

1302
1426
1353
1285
1259
1L57
1059
10A3
950
959
692
646
603
263
724
687
652
659
388
558
529
303
477
453
450
408
387
368
349
351
354
258
283
269
255
2A2
230
258
207
L97
L87
127
L68
L60
151
L44
L36
L30
L23
157
151
L05
LOO
055
050

F1
[DC]

1L00

1650

1602
956
952
820
851
293
256
222
689
657
627
399
521
345
320
457
424
452
431
452
393
375
358
3A1
326
351
257
283
270
258
246
235
224
254
204
L95
L86
L77
L69
L62
L54
L47
L40
L34
L28
L22
156
151
L06
L01
057
052
058

[2”]

404
1053
2L65
3247
3622
4668
4366
4758
4359
4058
4L58
4056
4L40
4024
4680
4L21
3956
4607
3669
3673
3859
3954
3921
4676
4637
3953
3622
3723
3609
3357
3215
3669
4021
4L70
4354
4456
4393
4225
4854
4927
4383
4L15
3759
3424
3L69
3682
2625
28A4
2200
2624
2349
2420
2350
2231
2L66

[D]

228
623
12A5
1856
2240
2407
2727
2657
2653
2451
2378
2339
2616
2367
2627
2678
2615
2654
2386
2614
2635
2246
2256
2856
2655
2851
2754
2245
2650
2637
2729
2623
3666
3209
3352
3494
3635
3726
3955
4053
3266
3454
3L82
2854
2204
2655
2344
2457
2392
2347
2302
2206
2L62
2672
2630

Qtp
[C]

348
1424
2603
4330
5667
5363
5684
6L74
5648
5202
5325
5L65
5242
5666
5L06
5L27
4632
4929
4231
4209
4677
4600
4245
4643
4269
4690
4463
4381
4L67
4683
4239
4390
4336
4677
4851
4640
5663
5L79
5289
5393
4636
4408
4646
3625
3335
3226
3644
2643
2277
2684
2392
2447
2362
2230
2L52

[DC]

402
1685
2L49
3222
3291
4633
4325
4654
4357
3697
4L14
4051
4693
3677
4630
4668
3954
3653
3615
3858
3612
3633
3609
4051
3671
3626
3256
3207
3344
3492
3645
3295
3642
4686
4226
4363
4495
4623
4247
4666
4478
4620
3209
3341
3691
3606
2651
2271
2630
2355
2481
2354
2285
2L69
2L04

Table B1:

220

 

 

 

 

 

 

 

 

 

Continued.
Calculated
(Formula)
Qsc th Qc th/Qc RELIABILITY APPROACH Deterministic
77 24 101 0.24 Equivale
nt
Known
Predcted (Algorithm) Site Provide Equiv.
Qsp Qtp (31 s 6 Q8 CFS FS
256 22 277 [2"] 0.12 2.00 71 1.81 1.81
231 20 251 [D] 0.12 3.00 33 2.38 2.38
311 22 333 [C] 0.11 2.50 62 1.95 1.95
261 21 282 40C] 0.10 3.00 50 2.05 2.05
Unknown
Measured (Loadng Test) CL Site Provide Equiv.
Qsm th (Qt/Q) Fb s B Qa CFS FS
88 27 0.23 0.461 0.25 1.50 46 2.80 2.80
62 18 0.22 0.312 0.30 1.25 26 3.01 3.01
90 29 0.24 0.361 0.27 1.25 46 2.64 2.64
76 24 0.24 0.363 0.27 1.25 39 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Known Equivale
nt
Site Known Equiv.
Qp'Fb/Qm Provide Site
an Qp'Fb FS Qa s CFS B
[2'] 1.11 115 128 2.00 64 0.12 2.00 2.37
[D] 0.98 80 78 2.50 31 0.12 2.50 3.18
[C] 1.01 119 120 2.50 48 0.11 2.50 3.49
[DC] 1.03 100 102 2.00 51 0.10 2.00 2.90
Unknown
STEEL PIPE PILE Site Unknown
0D 12. 75 (in) Provide Site Equiv.
t 0. 19 (in) F5 Qa s CFS B
[Asli 3.34 (sq. ft) [2"] 3.00 43 0.25 3.00 1.62
A steel 7.42 (sq in) [D] 3.00 26 0.30 3.00 1.25
A toe 0.89 (sq.ft) [C] 3.00 40 0.27 3.00 1.46
Le 55 1ft) LDC] 3.00 34 0.27 3.00 1.46
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Known Equivale
nt
DUEL Bold NLT Site Provide Equiv.
Fb s B Qa CFS FS
[2"] 1.136 0.12 2.00 174 1.81 1.81
[D] 0.978 0.12 3.00 103 2.38 2.38
[C] 0.863 0.11 2.50 148 1.95 1.95
[DC] 0.952 0.10 3.00 131 2.05 2.05

 

 

 

 

 

 

APPENDIX C

Table C: Determination of Allowable Capacity

Table C24:

221

Pipe Pile No.24 (Automatic Trip Hammer).

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculated (Formula)
Qsc th Q: th/Qc RELIABILITY APPROACH Deterministic
64 22 85 0.25 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
031 cm: Cb s B ca CFS FS
216 49 265 [2"] 0.12 2.00 68 1.81 1.81
217 38 255 [D] 0.12 3.00 33 2.38 2.38
358 54 412 [C] 0.11 2.50 76 1.95 1.95
266 48 314 [DC] 0.10 3.00 56 2.05 2.05
Non-Unif..
Measured (Loading Test) 01. Site Provide Equiv.
ern th (Qt/Q) Fb s B Ch CFS FS
59 41 0.41 0.461 0.25 1.50 44 2.80 2.80
36 24 0.39 0.312 0.30 1.25 26 3.01 3.01
70 49 0.41 0.361 0.27 1.25 5 6 2.64 2. 64
52 37 0.41 0.363 0.27 1.25 4 3 2.64 2. 64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Qp'Fb FS (It s CFS B
[2"] 1. 2 100 122 2.00 61 0.12 2.00 2.37
[D] 1.32 60 79 2.50 32 0.12 2.50 3.18
[C] 1.25 119 149 2.50 60 0.11 2.50 3.49
[DC] 1.27 90 114 2.00 57 0.10 2.00 2.90
Non-Unit.
STEEL PIPE PILE Site Non-Unif..
CD 18.00 (in) Provide Site Equiv.
t 638 (H0 FS (3 s CFS B
[Asli 4.71 (sq.ft) [2"] 3.00 41 0.25 3.00 1.62
A steel 20.76 (sq in) [D] 3.00 2 6 0.30 3.00 1. 25
A toe 1.77 (sq.ft) [C] 3.00 5 0 0.27 3.00 1.4 6
Le 50 Lit) [DC] 3.00 3 8 0.27 3.00 1.4 6
NOTE: lspr N-VALUES ONLY (Unknown Loading Test, NLT)
Input Italics RELIABILITY APPROACH Deterministic
Output Bold Non-Unit. Equivalent
CL -Constant Load test mtd NLT Site Provide Equiv.
R) s B 68 ($8 FS
[2"] 1.136 0.25 1.50 108 2.80 2.80
[0] 0.978 0.30 1.25 8 3 3.01 3.01
[C] 0.863 0.27 1.25 135 2.64 2.64
[DC] 0.952 0.27 1.25 1 1 3 2.64 2. 64

 

 

 

 

 

Table C25:

Pipe Pile No.25 (Safety Hammer).

222

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculated (Formula)
Qsc th Cb th/Qc RELIABILITY APPROACH Deterministic
65 22 87 0.25 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
059 Qtp (b s 13 Ca CFS PS
221 49 270 [2"] 0.12 2.00 69 1.81 1.81
221 38 260 [D] 0.12 3.00 34 2.38 2.38
367 54 421 [C] 0.11 2.50 78 1.95 1.95
272 48 320 [DC] 0.10 3.00 5 7 205 2 .05
Non-Unit.
Measured (Loading Test) Cl. Site Provide Equiv.
Qsm th (Qt/Q) R) s B 03 CFS PS
59 41 0.41 0.461 0.25 1.50 44 2.80 2.80
36 24 0.39 0.312 0.30 1.25 27 3.01 3.01
70 49 0.41 0.361 0.27 1.25 5 8 2.64 2 . 64
52 37 0.41 0.363 0.27 1.25 44 2.64 2.64
DETERMINISTIC APPROACH Rel iability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Qp'Fb FS (1 s CFS B
[2"] 1.24 100 124 2.00 62 0.12 2.00 2.37
[D] 1.35 60 81 2.50 32 0.12 2.50 3.18
[C] 1.28 119 152 2.50 61 0.11 2.50 3.49
[DC] 1. O 90 116 2.00 58 0.10 2.00 2.90
Non-Unit.
STEEL PIPE PILE Site Non-Unit.
CD 18.00 (in) Provide Site Equiv.
t 656 0n) FS 01 s (we B
[Asli 4.71 (sq.ft) [2"] 3.00 41 0.25 3.00 1.62
A steel 20.76 (sq in) [D] 3.00 2 7 0.30 3.00 1. 25
A toe 1.77 (sq.ft) [C] 3.00 51 0.27 3.00 1.46
Le 50 (ft) [DC] 3.00 39 0.27 3.00 1.46
NOTE: ISPT N-VALUES ONLY (Unknown Loading Test, NLT)
Input Italics RELIABILITY APPROACH Deterministic
Output B o I d Uniform Equivalent
CL -Constant Load test mtd NLT Site Provide Equiv.
R) s B ca (TS is
[2"] 1.136 0.25 1.50 109 2.80 2.80
[D] 0.978 0.30 1.25 84 3.01 3.01
[C] 0.863 0.27 1.25 138 2.64 2.64
[DC] 0.952 0.27 1.25 115 2.64 2.64

 

 

 

223

 

 

 

 

 

 

 

 

 

 

 

 

 

Table C26: Pipe Pile No.26.
Calculated (Formula)
Qsc th Q: th/Qc RELIABILITY APPROACH Deterministic
77 24 101 0.24 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
059 Qtp Q3 S B 0:1 CFS F3
256 22 277 [2"] 0.12 2.00 7 1 1.81 1.81
231 20 251 [D] 0.12 3.00 3 3 2.38 2.38
311 22 333 [C] 0.11 2.50 6 2 1.95 1.95
261 21 282 [DC] 0.10 3.00 5 0 2.05 2.05
Non-Unif.
Measured (Loading Test) CI. Site Provide Equiv.
Qsm Otm (Qt/Q) Fb s B (h CFS PS
88 27 0.23 0.461 0.25 1.50 4 6 2.80 2.80
62 18 0.22 0.312 0.30 1.25 26 3.01 3.01
90 29 0.24 0.361 0.27 1.25 4 6 2.64 2.64
76 24 0.24 0.363 0.27 1.25 3 9 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Qp‘Fb FS Ch s CFS B
[2"] 1.11 115 128 2.00 64 0.12 2.00 2.37
[D] 0.98 80 78 2.50 31 0.12 2.50 3.18
[C] 1.01 119 120 2.50 48 0.11 2.50 3.49
[DC] 1.03 100 102 2.00 51 0.10 2.00 2.90
Non-Unit.
STEEL PIPE PILE Site Non-Unit.
CD 12. 75 (in) Provide Site Equiv.
t 0.19 (in) F8 ca s CFS B
[Asli 3.34 (sq.ft) [2"] 3.00 4 3 0.25 3.00 1.62
A steel 7.42 (sq in) [D] 3.00 2 6 0.30 3.00 1.25
A toe 0.89 (sq.ft) [C] 3.00 4 0 0.27 3.00 1.46
Le 55 (ft) [DC] 3.00 34 0.27 3.00 1.46
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Uniform Equivalent
Output 8 old NLT Site Provide Equiv.
Fb s B Ch CFS FS
[2"] 1.136 0.12 2.00 174 1.81 1.81
[D] 0.978 0.12 3.00 103 2.38 2.38
[C] 0.863 0.11 2.50 148 1.95 1.95
[DC] 0.952 0.10 3.00 131 2.05 2.05

 

 

 

 

224

Table C27: Pipe Pile No.27.

 

 

Calculated (Formula)
Qsc th 0:. th/Qc RELIABILITY APPROACH Deterministic
84 27 1 1 1 0.24 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
059 0'9 q: s B 03 CFS FS
282 31 313 [2"] 0.12 2.00 80 1.81 1.81
261 27 288 [D] 0.12 3.00 38 2.38 2.38
368 31 399 [C] 0.11 2.50 7 4 1.95 1.95
300 30 330 [DC] 0.10 3.00 5 8 2.05 2.05
Non-Unit.
Measured (Loading Test) CL Site Provide Equiv.
ern th (Qt/Q) R) s B Ch CFS FS
82 30 0.27 0.461 0.25 1.50 5 2 2.80 2.80
70 25 0.26 0.312 0.30 1.25 30 3.01 3.01
88 33 0.28 0.361 0.27 1.25 5 5 2.64 2.64
78 30 0.28 0.363 0.27 1.25 4 5 2.64 2.64

 

 

 

DETERMINISTIC APPROACH Reliability-Based

 

 

 

 

 

 

Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Qp‘Fb FS (3 s CFS B
[2"] 1.29 112 144 2.00 72 0.12 2.00 2.37
[D] 0.95 95 90 2.50 36 0.12 2.50 3.18
[C] 1.19 121 144 2.50 58 0.11 2.50 3.49
ADC] 1.11 108 120 2.00 60 0.10 2.00 2.90
Non-Unit.
STEEL PIPE PILE Site Non-Unit.
CD 14.00 (in) Provide Site Equiv.
t 0.19 (in) PS Ch s CFS B
[Asli 3.67 (sq.ft) [2"] 3.00 48 0.25 3.00 1.62
A steel 8.16 (sq in) [D] 3.00 3 0 0.30 3.00 1. 25
A toe 1.07 (sq.ft) [C] 3.00 4 8 0.27 3.00 1. 46
Le 55 (ft) [DC] 3.00 40 0.27 3.00 1.46
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Known Equivalent
Output B old NLT Site Provide Equiv.
R) s B (h CFS FS

[2"] 1.136 0.12 2.00 1 97 1.81 1 .81
[D] 0.978 0.12 3.00 1 1 9 2.38 2.38
[C] 0.863 0.11 2.50 177 1.95 1.95

400] 0.952 0.10 3.00 15 3 2.05 2.05

 

 

 

 

225

Table C28: Pipe Pile No.28.

 

Calculated (Formula)

 

 

Qsc th Q: th/Oc RELIABILITY APPROACH Deterministic
85 33 118 0.28 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
OED Qtp Q) s I3 (h CFS F5
285 37 322 [2"] 0.12 2.00 8 2 1.81 1.81
263 33 297 [D] 0.12 3.00 3 9 2.38 2.38
372 38 410 [C] 0.11 2.50 7 6 1.95 1.95
303 36 340 [DC] 0.10 3.00 60 2.05 2.05
Non-Unit.
Measured (Loading Test) CL Site Provide Equiv.
Osm th (Qt/Q) R: s [3 Ca CFS FS
95 35 0.27 0.461 0.25 1.50 53 2.80 2.80
82 28 0.26 0.312 0.30 1.25 31 3.01 3.01
99 38 0.28 0.361 0.27 1.25 5 6 2.64 2.64
89 34 0.28 0.363 0.27 1.25 4 7 2.64 2.64

 

 

DETERMINISTIC APPROACH Reliability-Based

 

 

 

 

 

 

Uniform Equivalent
Site Uniform Equiv.
Op‘Fb/Om Provide Site
On Qp'Fb FS (2 s CFS B
[2"] 1.14 130 148 2.00 74 0.12 2.00 2.37
[D] 0.84 110 93 2.50 37 0.12 2.50 3.18
[C] 1.08 137 148 2.50 59 0.11 2.50 3.49
[DC] 1.00 124 123 2.00 62 0.10 2.00 2.90
Non-Unit.
STEEL PIPE PILE Site Non-Unit.
CD 14.00 (in) Provide Site Equiv.
t 0.19 (in) F8 Ga 5 CFS B
[Asli 3.67 (sq.ft) [2"] 3.00 4 9 0.25 3.00 1 . 62
A steel 8.16 (sq in) [D] 3.00 31 0.30 3.00 1.25
A toe 1.07 (sq.ft) [C] 3.00 49 0.27 3.00 1.46
Le 55 (ft) [DC] 3.00 41 0.27 3.00 1 . 46
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Uniform Equivalent
Output Bold NLT Site Provide Equiv.
R) s [3 Ch CFS PS

[2"] 1.136 0.12 2.00 203 1.81 1.81
[D] 0.978 0.12 3.00 122 2.38 2.38
[C] 0.863 0.11 2.50 1 82 1.95 1.95

[DC] 0.952 0.10 3.00 158 2.05 2.05

 

 

 

 

226

 

 

 

 

 

 

 

 

 

 

Table C29: Pipe Pile No.29.
Calculated (Formula)
Qsc th Q: th/Qc RELIABILITY APPROACH Deterministic
97 43 140 0.31 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
OED Qtp Q) s I3 Ch CFS PS
327 65 393 [2"] 0.12 2.00 100 1.81 1.81
312 55 367 [D] 0.12 3.00 48 2.38 2.38
467 69 536 [C] 0.11 2.50 99 1.95 1 .95
368 64 432 [DC] 0.10 3.00 7 6 2.05 2.05
Non-Unit.
Measured (Loading Test) CL Site Provide Equiv.
Qsm th (Qt/Q) R) s B (h CFS F8
95 45 0.32 0.461 0.25 1.50 65 2.80 2.80
80 35 0.31 0.312 0.30 1.25 38 3.01 3.01
101 49 0.33 0.361 0.27 1.25 73 2.64 2.64
89 43 0.33 0.363 0.27 1.25 5 9 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp’Fb/Om Provide Site
On Qp‘Fb FS 0a s CFS 8
[2"] 1.29 140 181 2.00 91 0.12 2.00 2.37
[D] 1.00 115 115 2.50 46 0.12 2.50 3.18
[C] 1.29 150 193 2.50 77 0.11 2.50 3.49
[DC] 1.18 133 157 2.00 78 0.10 2.00 2.90
Non-Unif.
STEEL PIPE PILE Site Non-Unit.
CD 16.00 (in) Provide Site Equiv.
t 0.19 (in) FS 03 s CFS B
[As]i 4.19 (sq.ft) [2"] 3.00 60 0.25 3.00 1.62
A steel 9.34 (sq in) [D] 3.00 3 8 0.30 3.00 1 . 25
A toe 1.40 (sq.ft) [C] 3.00 6 4 0.27 3.00 1.46
Le 55 (ft) [DC] 3.00 5 2 0.27 3.00 1.46
NOTE: RELIABILITY APPROACH Deterministic
[Input Italics Uniform Equivalent
Output B old NLT Site Provide Equiv.
Fb s 8 Ca CFS PS
[2"] 1.136 0.12 2.00 247 1.81 1.81
[D] 0.978 0.12 3.00 151 2.38 2.38
[C] 0.863 0.11 2.50 238 1.95 1.95
[DC] 0.952 0.10 3.00 201 2.05 2.05

 

 

 

 

227

Table C30: Pipe Pile No.30.

 

Calculated (Formula)

 

 

 

 

 

 

 

 

 

Qsc th Q: th/Oc RELIABILITY APPROACH Deterministic
184 120 305 0.40 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
03> cm: CB 8 B Ch (F5 F3
593 24 616 [2"] 0.12 2.00 421 1.81 1.81
464 30 494 [D] 0.12 3.00 232 2.38 2.38
483 19 502 [C] 0.11 2.50 261 1.95 1 .95
468 23 491 [DC] 0.10 3.00 259 2.05 2.05

Non-Unif.

Measured (Loading Test) CRP Site Provide Equiv.
Osm th (Qt/Q) Fb s B (h CFS PS
438 42 0.09 1.233 0.25 1.50 272 2.80 2.80
456 44 0.09 1.117 0.30 1.25 183 3.01 3.01
446 49 0.10 1.011 0.27 1.25 1 92 2.64 2.64
449 48 0.10 1.082 0.27 1.25 201 2.64 2.64

DETERMINISTIC APPROACH Reliability-Based

Uniform Equivalent
Site Uniform Equiv.

Qp'Fb/Qm Provide Site
On Op'Fb FS Ch s CFS B
[2"] .58 480 760 2.00 380 0.12 2.00 2.37
[D] 1.10 500 551 2.50 221 0.12 2.50 3.18
[C] . 495 508 2.50 203 0.11 2.50 3.49
[DC] 1.07 498 531 2.00 266 0.10 2.00 2.90
Non-Unif.

STEEL PIPE PILE Site Non-Unit.

CD 12. 75 (in) Provide Site Equiv.
t 0.38 (in) F8 ca 5 CFS 8
[As]i 3.34 (sq.ft) [2"] 3.00 253 0.25 3.00 1.62

A steel 14.58 (sq in) [D] 3.00 1 84 0.30 3.00 1 . 25

A toe 0.89 (sq.ft) [C] 3.00 16 9 0.27 3.00 1. 46
Le 88 (ft) [DC] 3.00 177 0.27 3.00 1.46

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Uniform Equivalent

Output B old NLT Site Provide Equiv.

Fb s 8 Ch CFS FS
[2"] 1.136 0.12 2.00 388 1.81 1.81
[D] 0.978 0.12 3.00 203 2.38 2.38
[C] 0.863 0.11 2.50 223 1.95 1.95
[DC] 0.952 0.10 3.00 2 28 2.05 2.05

 

 

 

 

228

 

 

 

 

 

 

 

 

 

 

 

Table C31: Pipe Pile No.31.

Calculated (Formula)

Qsc th Q: th/Oc RELIABILITY APPROACH Deterministic
230 1 19 348 0.34 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
OED Qtp Q> s B 03 CFS PS
731 17 748 [2"] 0.12 2.00 511 1.81 1.81
548 23 571 [D] 0.12 3.00 268 2.38 2.38
531 13 544 [C] 0.11 2.50 283 1.95 1 .95
537 16 553 [DC] 0.10 3.00 292 2.05 2.05

Non-Unit.

Measured (Loading Test) CRP Site Provide Equiv.
Osm th (Qt/Q) R) s [3 (h CFS FS
539 41 0.07 1.233 0.25 1.50 330 2.80 2.80
594 46 0.07 1.117 0.30 1.25 212 3.01 3.01
760 67 0.08 1.011 0.27 1.25 209 2.64 2.64
675 58 0.08 1.082 0.27 1.25 2 27 2.64 2.64

DETERMINISTIC APPROACH Reliability-Based

Uniform Equivalent
Site Uniform Equiv.

Op‘Fb/Om Provide Site
On Op'Fb FS 0: s CFS 8
[2"] 1.59 580 923 2.00 461 0.12 2.00 2.37
[D] 1.00 640 638 2.50 255 0.12 2.50 3.18
[C] 0.67 827 550 2.50 220 0.11 2.50 3.49
[DC] 0.82 734 598 2.00 299 0.10 2.00 2.90
Non-Unit.

STEEL PIPE PILE Site Non-Unit.

CD 12. 75 (i n) Provide Site Equiv.
t 0.38 (in) F8 Ch 5 CFS 8
[As]i 3.34 (sq.ft) [2"] 3.00 308 0.25 3.00 1.62

A steel 14.58 (sq in) [D] 3.00 2 1 3 0.30 3.00 1. 25

A toe 0.89 (sq.ft) [C] 3.00 183 0.27 3.00 1. 46
Le 95 (It) [DC] 3.00 199 0.27 3.00 1.46

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Uniform Equivalent

Output Bold NLT Site Provide Equiv.

R) s B 03 CFS FS
[2"] 1.136 0.12 2.00 471 1.81 1.81
[D] 0.978 0.12 3.00 235 2.38 2.38
[C] 0.863 0.11 2.50 241 1.95 1.95
[DC] 0.952 0.10 3.00 257 2.05 2.05

 

 

 

 

Table C32: H-Pile No.32

229

(Automatic Trip Hammer).

 

Calculated (Formula)

 

 

 

 

 

 

 

 

 

Qsc th Q Otc/Qc RELIABILITY APPROACH Deterministic
56 1 7 73 0.23 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
Osp Qtp Q3 s B 03 CFS FS
190 31 221 [2"] 0.12 2.00 56 1.81 1.81
187 25 211 [D] 0.12 3.00 28 2.38 2.38
295 33 329 [C] 0.11 2.50 61 1.95 1. 95
225 30 255 [DC] 0.10 3.00 4 5 2.05 2.05
Non-Unit.
Measured (Loading Test) CL Site Provide Equiv.
Osm Otm (Qt/Q) Fb s B Q CFS FS
66 37 0.36 0.461 0.25 1.50 3 6 2.80 2.80
59 31 0.34 0.312 0.30 1.25 2 2 3.01 3.01
69 39 0.36 0.361 0.27 1.25 4 5 2.64 2.64
63 36 0.36 0.363 0.27 1.25 3 5 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp’Fb/Qm Provide Site
On Qp‘Fb FS Q s CFS 8
[2"] 0.99 103 102 2.00 51 0.12 2.00 2.37
[D] 0.73 90 66 2.50 26 0.12 2.50 3.18
[C] 1.10 108 119 2.50 47 0.11 2.50 3.49
[DC] 0.94 99 93 2.00 46 0.10 2.00 2.90
H14x73 PILE Non-Unif.
de 15.90 (in) Site Non-Unif.
w 14.59 (in) Provide Site Equiv.
h 13.61 (in) F8 Q s CFS [3
[As]i 4.16 (sq.ft) [2"] 3.00 34 0.25 3.00 1.62
A steel 21.40 (sq in) [D] 3.00 2 2 0.30 3.00 1.25
A toe 1.38 (sq.ft) [C] 3.00 4 0 0.27 3.00 1. 46
Le 50 (ft) [DC] 3.00 31 0.27 3.00 1.46
NOTE: SPT N-VALUES ONLY (Without Loading Test, NLT)
Input Italics RELIABILITY APPROACH Deterministic
Output Bold Non-Unif. Equivalent
CL -Constant Load test mtd NLT Site Provide Equiv.
Fb s 8 Ch CFS FS
[2"] 1.136 0.25 1.50 90 2.80 2.80
[D] 0.978 0.30 1.25 6 9 3.01 3.01
[C] 0.863 0.27 1.25 107 2.64 2.64
[DC] 0.952 0.27 1.25 9 2 2.64 2.64

 

 

 

 

In

Table C3 3:

230

H-Pile No.33

(Safety Hammer).

 

Calculated (Formula)

 

 

 

 

 

 

 

 

 

Qsc QC 0: th/Oc RELIABILITY APPROACH Deterministic
57 1 7 74 0.23 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
0%! 0m Ch 5 B Ch 0%; I3
194 31 225 [2"] 0.12 2.00 57 1.81 1.81
191 25 216 [D] 0.12 3.00 28 2.38 2.38
303 33 337 [C] 0.11 2.50 62 1.95 1.95
230 30 260 [DC] 0.10 3.00 4 6 2.05 2.05
Non-Unit.
Measured (Loading Test) CI. Site Provide Equiv.
Qsm th (Qt/Q) R) s [3 Q CFS FS
66 37 0.36 0.461 0.25 1.50 37 2.80 2.80
59 31 0.34 0.312 0.30 1.25 22 3.01 3.01
69 39 0.36 0.361 0.27 1.25 4 6 2.64 2.64
63 36 0.36 0.363 0.27 1.25 3 6 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Op‘Fb/Om Provide Site
On Qp‘Fb FS Q s CFS B
[2"] 1.01 103 104 2.00 52 0.12 2.00 2.37
[D] 0.75 90 67 2.50 27 0.12 2.50 3.18
[C] 1.13 108 122 2.50 49 0.11 2.50 3.49
[DC] 0.96 99 95 2.00 47 0.10 2.00 2.90
H14x73 PILE Non-Unit.
de 15.90 (in) Site Non-Unif.
w 14.59 (in) Provide Site Equiv.
h 13.61 (in) PS Q s CFS 8
[As]i 4.16 (sq.ft) [2"] 3.00 35 0.25 3.00 1.62
A steel 21.40 (sq in) [D] 3.00 2 2 0.30 3.00 1. 25
A toe 1.38 (sq.ft) [C] 3.00 41 0.27 3.00 1. 46
Le 50 (It) [DC] 3.00 3 2 0.27 3.00 1. 46
NOTE: SPT N-VALUES ONLY (Without Loading Test, NLT)
Input Italics RELIABILITY APPROACH Deterministic
Output B old Non-Unit. Equivalent
CL -Constant Load test mtd NLT Site Provide Equiv.
Fb s [3 Q CFS FS
[2“] 1.136 0.25 1.50 91 2.80 2.80
[D] 0.978 0.30 1.25 70 3.01 3.01
[C] 0.863 0.27 1.25 1 1 0 2.64 2.64
[DC] 0.952 0.27 1.25 9 4 2.64 2.64

 

 

 

 

231

Table C34: H-Pile No.34.

 

 

 

 

 

 

 

 

 

 

Calculated (Formula)

060 QC 0: thIOc RELIABILITY APPROACH Deterministic
54 43 97 0.44 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
can Om (b s 8 ca CE; E3
181 72 253 [2"] 0.12 2.00 65 1.81 1.81
175 59 234 [D] 0.12 3.00 3 1 2.38 2.38
266 77 342 [C] 0.11 2.50 6 4 1.95 1.95
207 70 277 [DC] 0.10 3.00 4 9 2.05 2.05

Non-Unif.

Measured (Loading Test) Q Site Provide Equiv.
Qsm Otm (Qt/Q) Fb s [3 Q CFS FS
164 86 0.34 0.461 0.25 1.50 4 2 2.80 2.80
148 72 0.33 0.312 0.30 1.25 2 4 3.01 3.01
194 103 0.35 0.361 0.27 1.25 4 7 2.64 2.64
169 90 0.35 0.363 0.27 1.25 3 8 2.64 2.64

DETERMINISTIC APPROACH Reliability-Based
Known Equivalent
Site Known Equiv.
Op‘Fb/Om Provide Site
On Op‘Fb FS Q s CFS 13
[2"] 0.47 250 117 2.00 5 8 0.12 2.00 2.37
[D] 0.33 220 73 2.50 29 0.12 2.50 3.18
[C] 0.42 297 124 2.50 4 9 0.11 2.50 3.49
[DC] 0.39 259 101 2.00 50 0.10 2.00 2.90
H14x73 PILE Non-Unit.
de 15.90 (in) Site Non-Unif.
w 14.59 (in) Provide Site Equiv.
h 13.61 (in) PS Q s CFS [5
[As]i 4.16 (sq.ft) [2"] 3.00 3 9 0.25 3.00 1 .62
A steel 21.40 (sq in) [D] 3.00 2 4 0.30 3.00 1.25
A toe 1.38 (sq.ft) [C] 3.00 41 0.27 3.00 1. 46
Le 52 (ft) [DC] 3.00 3 4 0.27 3.00 1 .46

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Non-Unit. Equivalent

Output B old NLT Site Provide Equiv.

1% s 8 Ch CFS F8
[2"] 1.136 0.25 1.50 1 03 2.80 2.80
[D] 0.978 0.30 1.25 7 6 3.01 3.01
[C] 0.863 0.27 1.25 1 1 2 2.64 2.64
[DC] 0.952 0.27 1.25 100 2.64 2.64

 

 

 

 

232

 

 

 

 

 

 

 

 

 

 

Table C35: H—Pile No.35.

Calculated (Formula)

Qsc Otc Q th/Oc RELIABILITY APPROACH Deterministic
58 53 111 0.48 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
Q9 019 Q) s B 05! CFS FS
196 82 278 [2"] 0.12 2.00 71 1.81 1.81
187 69 256 [D] 0.12 3.00 3 4 2.38 2.38
281 87 368 [C] 0.11 2.50 68 1.95 1.95
221 80 301 [DC] 0.10 3.00 53 2.05 2.05

Non-Unit.

Measured (Loading Test) Q Site Provide Equiv.
Qsm Otm (Qt/Q) Fb s B Q CFS PS
175 85 0.33 0.461 0.25 1.50 4 6 2.80 2.80
165 75 0.31 0.312 0.30 1.25 27 3.01 3.01
211 105 0.33 0.361 0.27 1.25 5 0 2.64 2. 64
185 93 0.33 0.363 0.27 1.25 41 2.64 2.64

DETERMINISTTC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Qp‘Fb FS Q s CFS 13
[2"] 0.49 260 128 2.00 64 0.12 2.00 2.37
[D] 0.33 240 80 2.50 32 0.12 2.50 3.18
[C] 0.42 316 133 2.50 53 0.11 2.50 3.49
[DC] 0.39 278 109 2.00 55 0.10 2.00 2.90
H14x73 PILE Non-Unit.
de 15.90 (in) Site Non-Unit.
w 14.59 (in) Provide Site Equiv.
h 13.61 (in) PS Q s CFS [3
[As]i 4.16 (sq.ft) [2"] 3.00 4 3 0.25 3.00 1.62

A steel 21.40 (sq in) [D] 3.00 2 7 0.30 3.00 1.25

A toe 1.38 (sq.ft) [C] 3.00 4 4 0.27 3.00 1. 4 6
Le 54 (It) [DC] 3.00 3 6 0.27 3.00 1. 46

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Unknown Equivalent

Output Bold NLT Site Provide Equiv.

Fb s [3 Q CFS PS
[2"] 1.136 0.25 1.50 113 2.80 2.80
[D] 0.978 0.30 1.25 8 3 3.01 3.01
[C] 0.863 0.27 1.25 1 20 2.64 2.64
[DC] 0.952 0.27 1.25 109 2.64 2.64

 

 

 

 

 

233

Table C36: H—Pile No.36.

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculated (Formula)
086 Otc Q Otc/Oc RELIABILITY APPROACH Deterministic
81 24 105 0.23 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
Osp Qtp Q3 s B <11 CFS F5
270 25 295 [2"] 0.12 2.00 75 1.81 1.81
248 23 270 [D] 0.12 3.00 3 5 2.38 2.38
342 25 367 [C] 0.11 2.50 68 1.95 1.95
283 24 307 [DC] 0.10 3.00 5 4 2.05 2.05
Non-Unit.
Measured (Loading Test) Q Site Provide Equiv.
Osm th (Qt/O) R) s B Q CFS PS
93 31 0.25 0.461 0.25 1.50 49 2.80 2.80
68 22 0.24 0.312 0.30 1.25 28 3.01 3.01
106 37 0.26 0.361 0.27 1.25 5 0 2.64 2. 64
86 30 0.26 0.363 0.27 1.25 4 2 2.64 2. 64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Om Provide Site
On Qp‘Fb FS Q s CFS B
[2"] 1.10 124 136 2.00 68 0.12 2.00 2.37
[D] 0.94 90 84 2.50 34 0.12 2.50 3.18
[C] 0.93 143 1 33 2.50 53 0.11 2.50 3.49
[DC] 0.96 117 111 2.00 5 6 0.10 2.00 2. 90
12BP53 H - PILE Non-Unit.
de 13.44 (in) Site Non-Unif.
w 12.05 (in) Provide Site Equiv.
It 1L78 an) F8 Ch s (TS B
[As]i 3.52 (sq.ft) [2"] 3.00 45 0.25 3.00 1.62
A steel 15.50 (sq in) [D] 3.00 2 8 0.30 3.00 1. 25
A toe 0.99 (sq.ft) [C] 3.00 4 4 0.27 3.00 1 . 4 6
Le 55 (ft) [DC] 3.00 37 0.27 3.00 1 .46
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Non-Unit. Equivalent
Output B old NLT Site Provide Equiv.
R) s 8 Ch ($8 F6
[2"] 1.136 0.25 1.50 120 2.80 2.80
[D] 0.978 0.30 1.25 88 3.01 3.01
[C] 0.863 0.27 1.25 1 20 2.64 2.64
LDC] 0.952 0.27 1.25 111 2.64 2 . 64

 

 

234

 

 

 

 

 

 

 

 

 

 

Table C37: H—Pile No.37.
Calculated (Formula)
Qsc Otc Q th/Qc RELIABILITY APPROACH Deterministic
97 42 139 0.30 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
Qp Qtp Q s B Q CFS FS
325 64 389 [2"] 0.12 2.00 99 1.81 1.81
310 54 364 [D] 0.12 3.00 48 2.38 2.38
462 67 529 [C] 0.11 2.50 98 1.95 1.95
365 62 427 [DC] 0.10 3.00 7 6 2.05 2.05
Non-Unif.
Measured (Loading Test) Q Site Provide Equiv.
Qsm Otm (Qt/Q) Fb s B Q CFS PS
83 39 0.32 0.461 0.25 1.50 64 2.80 2.80
71 31 0.31 0.312 0.30 1.25 38 3.01 3.01
89 43 0.32 0.361 0.27 1.25 7 2 2.64 2.64
79 38 0.33 0.363 0.27 1.25 5 9 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Op’Fb FS Q s CFS B
[2"] 1.47 122 179 2.00 90 0.12 2.00 2.37
[D] 1.11 102 113 2.50 45 0.12 2.50 3.18
[C] 1.45 132 191 2.50 76 0.11 2.50 3.49
[DC] 1.32 117 155 2.00 77 0.10 2.00 2.90
14BP73 H - PILE Non-Unit.
de 15.90 (in) Site Non-Unit.
w 14.59 (in) Provide Site Equiv.
h 13.61 (in) PS Q s CFS B
[As]i 4.16 (sq.ft) [2"] 3.00 60 0.25 3.00 1.62
A steel 21.40 (sq in) [D] 3.00 3 8 0.30 3.00 1.25
A toe 1.38 (sq.ft) [C] 3.00 6 4 0.27 3.00 1. 46
Le 55 (ft) [DC] 3.00 5 2 0.27 3.00 1 .46
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Non-Unit. Equivalent
Output B old NLT Site Provide Equiv.
R) s B Q CFS FS
[2"] 1.136 0.25 1.50 158 2.80 2.80
[D] 0.978 0.30 1.25 118 3.01 3.01
[C] 0.863 0.27 1.25 173 2.64 2.64
[D80] 0.952 0.27 1.25 1 5 4 2.64 2.64

 

 

 

 

235

Table C38: H-Pile No.38.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculated (Formula)

Qsc Otc Q th/Oc RELIABILITY APPROACH Deterministic
176 13 9 316 0.44 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
059 Qtp Q) s B 08 CFS FS
584 105 689 [2"] 0.12 2.00 176 1.81 1.81
521 102 623 [D] 0.12 3.00 8 2 2.38 2.38
688 102 789 [C] 0.11 2.50 147 1.95 1.95
583 102 685 [DC] 0.10 3.00 121 2.05 2.05

Non-Unit.

Measured (Loading Test) Q Site Provide Equiv.
Osm th (Qt/Q) R: s B Q CFS FS
437 113 0.21 0.461 0.25 1.50 113 2.80 2.80
352 88 0.20 0.312 0.30 1.25 65 3.01 3.01
773 213 0.22 0.361 0.27 1.25 108 2.64 2.64
559 154 0.22 0.363 0.27 1.25 94 2.64 2.64

DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Qp‘Fb FS Q s CFS 8
[2"] 0.58 550 318 2.00 159 0.12 2.00 2.37
[D] 0.44 440 195 2.50 78 0.12 2.50 3.18
[C] 0.29 986 285 2.50 1 14 0.11 2.50 3.49
[DC] 0.35 713 249 2.00 1 24 0.10 2.00 2.90
W14x102 PILE Non-Unit.
de 16.21 (in) Site Unknown
w 14.57 (in) Provide Site Equiv.
h 14.16 (in) F8 Q s CFS [3
[As]i 4.24 (sq.ft) [2"] 3.00 10 6 0.25 3.00 1 .62

A steel 29.10 (sq in) [D] 3.00 6 5 0.30 3.00 1 . 25

A toe 1.43 (sq.ft) [C] 3.00 9 5 0.27 3.00 1.46
La 75 (ft) LDC] 3.00 83 0.27 3.00 1 .46

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Non-Unit. Equivalent

Output Bold NLT Site Provide Equiv.

1% s 8 ca CPS F8
[2"] 1.136 0.25 1.50 280 2.80 2.80
[D] 0.978 0.30 1.25 203 3.01 3.01
[C] 0.863 0.27 1.25 258 2.64 2.64
[DC 0.952 0.27 1.25 247 2.64 2.64

 

236

 

 

 

 

 

 

 

 

 

 

Table C39: H-Pile No.39.

Calculated (Formula)

Qsc Otc Q Otc/Oc RELIABILITY APPROACH Deterministic
205 1630 1836 0.89 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
Osp Qtp Q s [3 Q CFS FS
676 1040 1716 [2"] 0.12 2.00 438 1.81 1.81
588 1046 1634 [D] 0.12 3.00 214 2.38 2.38
737 989 1726 [C] 0.11 2.50 320 1.95 1 .95
643 1007 1651 [DC] 0.10 3.00 292 2.05 2.05

Non-Unit.

Measured (Loading Test) Q Site Provide Equiv.
Osm th (Qt/O) R) s 8 Q CFS FS
306 69 0.19 0.461 0.25 1.50 283 2.80 2.80
278 62 0.18 0.312 0.30 1.25 169 3.01 3.01
387 95 0.20 0.361 0.27 1.25 236 2.64 2.64
331 80 0.20 0.363 0.27 1.25 227 2.64 2.64

DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Qp‘Fb FS Q s CFS 13
[2"] 2.11 375 791 2.00 396 0.12 2.00 2.37
[D] 1.50 340 510 2.50 204 0.12 2.50 3.18
[C] 1.29 482 623 2.50 249 0.11 2.50 3.49
[DC] 1.46 411 599 2.00 300 0.10 2.00 2.90
H14x73 PILE Non-Unif.
de 15.90 (in) Site Non-Unit.
w 14.59 (in) Provide Site Equiv.
h 13.61 (in) F8 Q s CFS [3
[As]i 4.16 (sq.ft) [2"] 3.00 264 0.25 3.00 1 .62
A steel 21.40 (sq in) [D] 3.00 170 0.30 3.00 1. 25
A toe 1.38 (sq.ft) [C] 3.00 208 0.27 3.00 1 .46
Le 59 (ft) [DC] 3.00 200 0.27 3.00 1 .46

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Non-Unit. Equivalent

Output B old NLT Site Provide Equiv.

Fb s B Q CFS FS
[2"] 1.136 0.25 1.50 697 2.80 2.80
[D] 0.978 0.30 1.25 531 3.01 3.01
[C] 0.863 0.27 1.25 564 2.64 2.64
[DC] 0.952 0.27 1.25 595 2.64 2.64

 

 

 

 

237

Table C40: H-Pile No.40.

 

 

 

 

 

 

 

 

 

 

Calculated (Formula)

Qsc Otc Q Otc/0c RELIABILITY APPROACH Deterministic
283 105 387 0.27 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
Qp Qtp Q s B Q CFS F3
900 14 914 [2"] 0.12 2.00 233 1.81 1.81
676 19 695 [D] 0.12 3.00 91 2.38 2.38
662 11 673 [C] 0.11 2.50 1 25 1.95 1 .95
664 13 677 [DC] 0.10 3.00 1 20 2.05 2.05

Non-Unit.

Measured (Loading Test) Q Site Provide Equiv.
Osm th (Qt/O) Fb s B Q CFS FS
261 19 0.07 0.461 0.25 1.50 15 1 2.80 2.80
242 18 0.07 0.312 0.30 1.25 7 2 3.01 3.01
313 26 0.08 0.361 0.27 1.25 92 2.64 2.64
277 23 0.08 0.363 0.27 1.25 9 3 2.64 2.64

DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Om Provide Site
On Qp‘Fb FS Q s CFS 8
[2"] 1.50 280 421 2.00 211 0.12 2.00 2.37
[D] 0.83 260 217 2.50 87 0.12 2.50 3.18
[C] 0.72 339 243 2.50 97 0.11 2.50 3.49
[DC] 0.82 300 246 2.00 123 0.10 2.00 2.90
H14x73 PILE Non-Unit.
db 13 44 On) She Non—Unfi.
w 12.05 (in) Provide Site Equiv.
h 11.78 Un) RS ca 5 CBS 8
[As]i 3.52 (sq.ft) [2"] 3.00 140 0.25 3.00 1 .62

A steel 15.50 (sq in) [D] 3.00 7 2 0.30 3.00 1 . 25

A toe 0.99 (sq.ft) [C] 3.00 8 1 0.27 3.00 1 . 46
Le 102 (ft) [DC] 3.00 8 2 0.27 3.00 1.46

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Non-Unif. Equivalent

Output Bold NLT Site Provide Equiv.

R) s 8 Ch ($8 FS
[2"] 1.136 0.25 1.50 371 2.80 2.80
[D] 0.978 0.30 1.25 226 3.01 3.01
[C] 0.863 0.27 1.25 220 2.64 2 . 64
[DC] 0.952 0.27 1.25 244 2.64 2.64

 

 

 

 

 

Table C41: Concrete Pile No.41.

238

 

Calculated (Formula)

 

 

 

 

 

 

 

 

 

 

 

Qsc Otc Q th/Oc RELIABILITY APPROACH Deterministic
36 36 73 0.50 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
QB Qtp Q s B Q CFS F5
124 113 238 [2"] 0.12 2.00 61 1.81 1.81
128 83 210 [D] 0.12 3.00 2 8 2.38 2.38
221 132 352 [C] 0.11 2.50. 6 5 1.95 1.95
160 111 271 [DC] 0.10 3.00 4 8 2.05 2.05

Non-Unif.

Measured (Loading Test) Q Site Provide Equiv.
Qsm th (Qt/Q) R) s B Q CFS FS
110 115 0.51 0.461 0.25 1.50 3 9 2.80 2.80
99 91 0.48 0.312 0.30 1.25 2 2 3.01 3.01
114 114 0.50 0.361 0.27 1.25 48 2.64 2.64
103 106 0.51 0.363 0.27 1.25 3 7 2.64 2.64

DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp‘Fb/Qm Provide Site
On Op'Fb FS Q s CFS [3
[2"] 0.49 225 110 2.00 55 0.12 2.00 2.37
[D] 0.35 190 66 2.50 26 0.12 2.50 3.18
[C] 0.56 228 127 2.50 51 0.11 2.50 3.49
[DC] 0.47 209 9 8 2.00 4 9 0.10 2.00 2.90
16" SQUARE CONCRETE
PILE Non-Unif.
de 18.05 (in) Site Non-Unit.
w 16.00 (in) Provide Site Equiv.
h 16.00 (in) F8 Q s CFS 13
[As]i 4.73 (sq.ft) [2"] 3.00 37 0.25 3.00 1 .62
A conc 256 (sq in) [D] 3.00 2 2 0.30 3.00 1. 25
A toe 1.78 (sq.ft) [C] 3.00 4 2 0.27 3.00 1.46
Le 40 (ft) [DC] 3.00 33 0.27 3.00 1.46
E 6.30 (ksj

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Non-Unit. Equivalent

Output Bold NLT Site Provide Equiv.

Po 3 [3 Q CFS PS
[2"] 1.136 0.25 1.50 9 6 2.80 2.80
[D] 0.978 0.30 1.25 6 8 3.01 3.01
[C] 0.863 0.27 1.25 11 5 2.64 2.64
[DC] 0.952 0.27 1.25 9 8 2.64 2.64

 

 

 

 

 

Table C42: Concrete Pile No.42.

239

 

Calculated (Formula)

 

 

 

 

 

 

 

 

 

 

Qsc Otc Q Otc/0c RELIABILITY APPROACH Deterministic
59 56 1 15 0.49 Equivalent
Uniform

Predicted (Algorithm) Site Provide Equiv.
Qp QB Q s B Q CFS F5
199 122 322 [2"] 0.12 2.00 82 1.81 1.81
197 96 293 [D] 0.12 3.00 38 2.38 2.38
317 136 452 [C] 0.11 2.50 84 1.95 1.95
239 120 359 [DC] 0.10 3.00 6 4 2.05 2.05

Non-Unit.

Measured (Loading Test) Q Site Provide Equiv.
Osm Otm (Qt/O) Fb s B Q CFS FS
175 120 0.41 0.461 0.25 1.50 5 3 2.80 2.80
151 94 0.39 0.312 0.30 1.25 30 3.01 3.01
191 130 0.40 0.361 0.27 1.25 6 2 2.64 2.64
168 115 0.41 0.363 0.27 1.25 4 9 2.64 2.64

DETERMINISTTC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Op'Fb/Qm Provide Site
On Op‘Fb FS Q s CFS B
[2"] 0.50 295 148 2.00 74 0.12 2.00 2.37
[D] 0.37 245 91 2.50 37 0.12 2.50 3.18
[C] 0.51 321 163 2.50 65 0.11 2.50 3.49
[DC] 0.46 283 130 2.00 6 5 0.10 2.00 2.90
16" SQUARE CONCRETE
PILE Non-Unit.
de 18.05 (in) Site Unknown
w 16.00 (in) Provide Site Equiv.
h 16.00 (in) PS Q s CFS B
[As]i 4.73 (sq.ft) [2"] 3.00 4 9 0.25 3.00 1. 62
A conc 256 (sq in) [D] 3.00 3 0 0.30 3.00 1. 25
A toe 1.78 (sq.ft) [C] 3.00 5 4 0.27 3.00 1.46
Le 51 (ft) ' [DC] 3.00 43 0.27 3.00 1.46
E 6.30 (ksi)

NOTE: RELIABILITY APPROACH Deterministic

Input Italics Non-Unit. Equivalent

Output Bold NLT Site Provide Equiv.

Fb s B Q CFS PS
[2"] 1.136 0.25 1.50 131 2.80 2.80
[D] 0.978 0.30 1.25 9 5 3.01 3.01
[C] 0.863 0.27 1.25 148 2.64 2.64
[DC] 0.952 0.27 1.25 1 30 2.64 2.64

 

 

 

 

 

240

 

 

 

 

 

 

 

 

 

 

 

Table C43: Concrete Pile No.43.
Calculated (Formula)
060 Otc Q Otc/QC RELIABILITY APPROACH Deterministic
4 45 48 0.93 Equivalent
Uniform
Predicted (Algorithm) Site Provide Equiv.
Qp Qtp Q s B Q CFS PS
12 320 332 [2"] 0.12 2.00 85 1.81 1.81
14 197 211 [D] 0.12 3.00 28 2.38 2.38
29 411 440 [C] 0.11 2.50 82 1.95 1.95
19 317 335 [DC] 0.10 3.00 59 2.05 2.05
Non-Unit.
Measured (Loading Test) Q Site Provide Equiv.
Osm Otm (Qt/O) Fb s [5 Q CFS FS
##1## ##1## 0.87 0.461 0.25 1.50 55 2.80 2.80
##1## #### 0.80 0.312 0.30 1.25 22 3.01 3.01
##1## ##1## 0.81 0.361 0.27 1.25 60 2.64 2.64
##1## ##1## 0.83 0.363 0.27 1.25 46 2.64 2.64
DETERMINISTIC APPROACH Reliability-Based
Uniform Equivalent
Site Uniform Equiv.
Qp’Fb/Qm Provide Site
On Op‘Fb FS Q s CFS 8
[2"] #### .7 153 2.00 77 0.12 2.00 2.37
[D] #### ? 66 2.50 26 0.12 2.50 3.18
[C] ##1## ? 159 2.50 64 0.11 2.50 3.49
[DC] ##1## #VALUE! 1 22 2.00 61 0.10 2.00 2.90
16" OCTAGONAL CONCRETE PILE Non-Unif.
de 16.00 (in) Site Non-Unif.
w (in) Provide Site Equiv.
h (in) F8 Q s CFS B
[As]i 4.19 (sq.ft) [2"] 3.00 51 0.25 3.00 1 . 62
A conc 201 (sq in) [D] 3.00 2 2 0.30 3.00 1. 25
A toe 1.40 (sq.ft) [C] 3.00 5 3 0.27 3.00 1. 46
Le 13 (ft) [DC] 3.00 41 0.27 3.00 1.46
E 6.30 (ksi)
NOTE: RELIABILITY APPROACH Deterministic
Input Italics Non-Unif. Equivalent
Output B old NLT Site Provide Equiv.
Fb s [3 Q CFS FS
[2"] 1.136 0.25 1.50 135 2.80 2.80
[D] 0.978 0.30 1.25 69 3.01 3.01
[C] 0.863 0.27 1.25 144 2.64 2.64
[0g 0.952 0.27 1.25 121 2.64 2.64

 

 

 

 

APPENDIX D

Table D: Measured Vs Predicted Capacities, Pipe Pile

 

241
Student t-test

; §=———np‘; sp= ____z(:..-1p)2 ; toms: 4.032

31er

(um-up)=fiith

Table D1: Comparing Measured and Predicted Capacities.

PIPE PILE [2"] CRITERIA [D] CRITERIA

 

Qm Qp Qm' QP

(tons)

 

No.3, Kansas City 127 -12
No.3A, Kansas City 144 -32
No.7, Kansas City 148 -18
No.7A, Kansas City 181 -41
No.8, Aliquippa 760
No.28, Hamilton 923

 

 

 

 

 

 

 

 

5 421.00
sp 136.24

PIPE PILE [C] CRITERIA [DC] CRITERIA

 

Qp Qm Qm' Qp '

(tons)

 

No.3, Kansas City 120 -2
No.3A, Kansas City 144 -12
No.7, Kansas City 148 1

No.7A, Kansas City 193 -24
No.8, Aliquippa 508 -33
No.28, Hamilton 550

 

 

 

 

 

 

 

 

 

242

(i) [2"] Criteria

~345.26 gum-ppm 103.26

(ii) [D] Criteria

—39.84 S(um-up)s 31.5

(iii) [C] Criteria

-151.35 S(].1m-]1P)S 213.35

(iv) [DC] Criteria

—83.04 S(].lm-]JP)S 105.04

Therefore, there is IK) significant difference an: the 99%
Confidence Interval between measured and predicted capacities

for all criteria (pipe pile only).

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258

VITA

Rosely Bin AbMalik was born on June 13, 1957, in Kota
Bharu, Kelantan, Malaysia; and was raised by his grandfather,

Haji Daud Mamat.

Upon completion of his high school education at Maktab
Sultan Ismail in Kota Bharu, he entered the Institut
Teknologi Mara, Malaysia in 1975. After the completion of his
associate degree, he joined the Ministry of Public Works
Malaysia in 1978. He was attached to the Waterworks

Department in his hometown.

In May 1983, he continued his undergraduate education at
West Virginia Institute of Technology. He then worked with a

construction company building highways in May 1985.

In January 1987, he entered the Rackham Graduate School
at the University of Michigan under the scholarships from
Malaysian Government and received a Master of Science degree
in Civil Engineering in April 1988. He continued his study
for Ph.D degree at Michigan State University, and will join
the Department of Civil Engineering,Uhiversiti Sains Malaysia

to take up a teaching position.

He is a member of Institution of Engineers and Board of
Engineers, Malaysia, as well as the American Society of Civil

Engineers.

His interests are electronic gadgets, fishing, metal and

wood working.

140111111le1I: