Modelling Pile Capacity and Load-Settlement Behaviour of

Faculty of Engineering and Computing

Department of Civil Engineering

Modelling Pile Capacity and Load-Settlement Behaviour of Piles Embedded in Sand & Mixed Soils Using Artificial Intelligence

Iyad Salim Jabor Alkroosh

This thesis is presented for the Degree of Doctor of Philosophy

of Curtin University

May 2011

ii

DECLARATION This thesis contains no material which has been accepted for the award of any other degree or diploma in any university. To the best of my knowledge and belief this thesis contains no material previously published by any other person except where the acknowledgement has been made. The following publications have been resulted from the work carried out for this degree. Refereed journal papers

1. Alkroosh, I., and H. Nikraz. 2011a. Correlation of pile axial capacity and CPT data using gene expression programming. Geotechnical and Geological Journal. (Accepted, DOI: 10:1007/s10706-011-9413-1).

2. Alkroosh, I., and H. Nikraz. 2011b. Predicting axial capacity of driven piles

in cohesive soils using intelligent computing. Engineering Applications of Artificial Intelligence. (Accepted, DOI: 10.1016/j.engappai.2011.08.009).

3. Alkroosh, I., and H. Nikraz. 2011c. Simulating pile load-settlement behaviour

from CPT data using intelligent computing. Central European Journal of Engineering. 1(3), 295-305.

Refereed conference papers

1. Alkroosh, I., M. Shahin, and H. Nikraz. 2008. Modelling axial capacity of bored piles using genetic programming technique. In Proceedings of GEO-CHIANGMIA Conference. Thailand.

2. Alkroosh, I., M. Shahin, and H. Nikraz. 2009. Genetic programming for

predicting axial capacity of driven piles. In Proceedings of the 1st International Symposium on Computational Geomechanics. Cote d’Azur, France.

3. Alkroosh, I., M. Shahin, and H. Nikraz. 2010a. Modeling load-settlement

curves of behaviour of bored piles using artificial neural networks. In Proceedings of the XIVth Danube European Conference on Geotechnical Engineering. Bratislava, Slovakia.

4. Alkroosh, I., M. Shahin, and H. Nikraz. 2010b. Prediction load-settlement

relationship of driven piles in sand and mixed soils using artificial neural networks. In Proceedings of the Twin International Conference on Geotechnical and Geo-Environmental Engineering. Seoul, S. Korea.

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5. Alkroosh, I., and H. Nikraz. 2011. Modeling load-settlement behaviour of driven piles in cohesive soils using artificial neural networks. In Proceedings of the 14th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering. Hong Kong.

Signed ………………………………… Date ………………………………….

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Abstract This thesis presents the development of numerical models which are intended to be

used to predict the bearing capacity and the load-settlement behaviour of pile

foundations embedded in sand and mixed soils. Two artificial intelligence techniques,

the gene expression programming (GEP) and the artificial neural networks (ANNs),

are used to develop the models. The GEP is a developed version of genetic

programming (GP). Initially, the GEP is utilized to model the bearing capacity of the

bored piles, concrete driven piles and steel driven piles. The use of the GEP is

extended to model the load-settlement behaviour of the piles but achieved limited

success. Alternatively, the ANNs have been employed to model the load-settlement

behaviour of the piles.

The GEP and the ANNs are numerical modelling techniques that depend on input data

to determine the structure of the model and its unknown parameters. The GEP tries to

mimic the natural evolution of organisms and the ANNs tries to imitate the functions

of human brain and nerve system. The two techniques have been applied in the field

of geotechnical engineering and found successful in solving many problems.

The data used for developing the GEP and ANN models are collected from the

literature and comprise a total of 50 bored pile load tests and 58 driven pile load tests

(28 concrete pile load tests and 30 steel pile load tests) as well as CPT data. The bored

piles have different sizes and round shapes, with diameters ranging from 320 to 1800

mm and lengths from 6 to 27 m. The driven piles also have different sizes and shapes

(i.e. circular, square and hexagonal), with diameters ranging from 250 to 660 mm and

lengths from 8 to 36 m. All the information of case records in the data source is

reviewed to ensure the reliability of used data.

The variables that are believed to have significant effect on the bearing capacity of

pile foundations are considered. They include pile diameter, embedded length,

weighted average cone point resistance within tip influence zone and weighted

average cone point resistance and weighted average sleeve friction along shaft.

v

The sleeve friction values are not available in the bored piles data, so the weighted

average sleeve friction along shaft is excluded from bored piles models. The models

output is the pile capacity (interpreted failure load).

Additional input variables are included for modelling the load-settlement behaviour of

piles. They include settlement, settlement increment and current state of load-

settlement. The output is the next state of load-settlement.

The data are randomly divided into two statistically consistent sets, training set for

model calibration and an independent validation set for model performance

verification.

The predictive ability of the developed GEP model is examined via comparing the

performance of the model in training and validation sets. Two performance measures

are used: the mean and the coefficient of correlation. The performance of the model

was also verified through conducting sensitivity analysis which aimed to determine

the response of the model to the variations in the values of each input variables

providing the other input variables are constant. The accuracy of the GEP model was

evaluated further by comparing its performance with number of currently adopted

traditional CPT-based methods. For this purpose, several ranking criteria are used and

whichever method scores best is given rank 1. The GEP models, for bored and driven

piles, have shown good performance in training and validation sets with high

coefficient of correlation between measured and predicted values and low mean

values. The results of sensitivity analysis have revealed an incremental relationship

between each of the input variables and the output, pile capacity. This agrees with

what is available in the geotechnical knowledge and experimental data. The results of

comparison with CPT-based methods have shown that the GEP models perform well.

The GEP technique is also utilized to simulate the load-settlement behaviour of the

piles. Several attempts have been carried out using different input settings. The results

of the favoured attempt have shown that the GEP have achieved limited success in

predicting the load-settlement behaviour of the piles. Alternatively, the ANN is

considered and the sequential neural network is used for modelling the load-settlement

behaviour of the piles.

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This type of network can account for the load-settlement interdependency and has the

option to feedback internally the predicted output of the current state of load-

settlement to be used as input for the next state of load-settlement.

Three ANN models are developed: a model for bored piles and two models for driven

piles (a model for steel and a model for concrete piles). The predictive ability of the

models is verified by comparing their predictions in training and validation sets with

experimental data. Statistical measures including the coefficient of correlation and the

mean are used to assess the performance of the ANN models in training and validation

sets. The results have revealed that the predicted load-settlement curves by ANN

models are in agreement with experimental data for both of training and validation

sets. The results also indicate that the ANN models have achieved high coefficient of

correlation and low mean values. This indicates that the ANN models can predict the

load-settlement of the piles accurately.

To examine the performance of the developed ANN models further, the prediction of

the models in the validation set are compared with number of load-transfer methods.

The comparison is carried out first visually by comparing the load-settlement curve

obtained by the ANN models and the load transfer methods with experimental curves.

Secondly, is numerically by calculating the coefficient of correlation and the mean

absolute percentage error between the experimental data and the compared methods

for each case record. The visual comparison has shown that the ANN models are in

better agreement with the experimental data than the load transfer methods. The

numerical comparison also has shown that the ANN models scored the highest

coefficient of correlation and lowest mean absolute percentage error for all compared

case records.

The developed ANN models are coded into a simple and easily executable computer

program.

The output of this study is very useful for designers and also for researchers who wish

to apply this methodology on other problems in Geotechnical Engineering. Moreover,

the result of this study can be considered applicable worldwide because its input data

is collected from different regions.

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ACKNOLEDGEMENT I thank God for giving me the guidance, strength, support, patience, determination, and endurance to complete this work. I wish greatly to thank Professor Hamid Nikraze, the Head of Civil Engineering Department, Curtin University of Technology, Perth, Western Australia, for his valuable technical advice, assistance and encouragement during this course. Indeed, Professor Nikraz is great in motivating and creating optimism and confidence in students. I wish also to thank Dr. Mohamed Shahin, the Senior Lecturer at the Department of Civil Engineering, Curtin University, for his technical advice and contribution in the papers that have been obtained from this study. I thank Dr. Shahin again for his valuable views and comments on research methodology and results. I extend my thanks to Dr. Ian Misich, the Co-supervisor and Professor David Scott, the Chair of the Research Committee for being members of the research team. I would like to gratefully acknowledge the financial supported provided in a form of Australian Postgraduate Award (APA) and Curtin Research Scholarship (CRS). My great thanks are to my wife for her support and encouragement. Thanks to all of my research fellows, particularly AliReza, who provided me with very useful comments and opinions.

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TABLE OF CONTENTS

Contents Page Declaration……………………………………………………………………… ii

Abstract…………………………………………………………………………. iv

Acknowledgement……………………………………………………………… vii

Table of Contents……………………………………………………………….. viii

List of Figures…………………………………………………………………... xi

List of Tables…………………………………………………………………… xv

List of Notations………………………………………………………………... xvi

1.0 INTRODUCTION ………………………………………………………... 1

1.1 Background……………………………………………………………… 1

1.2 Research Significance…………………………………………………… 4

1.3 Research objectives……………………………………………………… 4

1.4 Outline of Thesis………………………………………………………… 5

2.0 ARTIFICIAL INTELLIGENCE TECHNIQUES………………………… 7

2.1 Introduction ……………………………………………………………... 7

2.2 Genetics and Evolutionary Algorithms …………………………………. 8

2.2.1 Definition and Brief History ………………………………………... 8

2.2.2 Biological Genetics …………………………………………………. 12

2.2.3 Gene Expression Programming Structure & Operation ……………. 13

2.3 Artificial Neural Networks ……………………………………………... 19

2.3.1 Definition and Brief History………………………………………… 19

2.3.2 Natural Neural Networks …………………………………………… 21

2.3.3 Artificial Neural Networks Structure & Operation…………………. 22

2.4 Modelling With Artificial Intelligence (GEP & ANNs) ………………... 27

2.4.1 Input Selection ……………………………………………………… 28

2.4.2 Data Division ……………………………………………………….. 30

2.4.3 Data Pre-processing ………………………………………………… 33

2.4.4 Choosing of Model Parameters ……………………………………... 33

2.4.5 Learning …………………………………………………………….. 42

2.4.6 Model Performance Measurements ………………………………... 46

2.5 Shortcomings of Artificial Intelligence Algorithms ……………………. 46

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3.0 PILE FOUNDATIONS: CLASSIFICATION, BEARING CAPACITY &

LOAD- SETTLEMENT BEHAVIOUR …………………………………...

48

3.1 Introduction ………………………………………………………………. 48

3.2 Classification of Pile Foundations ………………………………………. 49

3.2.1 Non-Displacement Piles ……………………………………………… 50

3.2.2 Displacement Piles …………………………………………………… 51

3.3 Design of Pile Foundations ………………………………………………. 51

3.3.1 Pile Capacity From Static Methods …………………………………... 52

3.3.2 Pile Capacity From Pile Load-Test …………………………………... 56

3.3.3 Pile Capacity From Dynamic Methods ………………………………. 57

3.3.4 Pile Capacity From In-Situ Tests …………………………………….. 59

3.4 Settlement Prediction …………………………………………………….. 74

3.4.1 Load Transfer Approach ……………………………………………... 75

4.0 DEVELOPMENT OF GEP MODEL ……………………………………… 87

4.1 Introduction ………………………………………………………………. 87

4.2 Data Collection …………………………………………………………… 87

4.2.1 Description of Piles …………………………………………………... 87

4.2.2 Source of Data ………………………………………………………... 88

4.2.3 Pile Load Tests ……………………………………………………….. 88

4.2.4 CPT Results …………………………………………………………... 88

4.2.5 Soil Profile …………………………………………………………… 95

4.3 Selection of Input Variables ……………………………………………… 95

4.3.1 The Primary Factors …………………………………………………. 96

4.3.2 The Secondary Factors ………………………………………………. 103

4.4 Data Division …………………………………………………………….. 103

4.5 Determination of Setting Parameters & GEP Model Selection ………….. 107

4.5.1 Determination of Optimum Values of Setting Parameters …………... 107

4.5.2 Selection of GEP Model ……………………………………………… 111

4.5.3 Optimization and Simplification of GEP Model ……………………... 112

4.6 Model Formulation ……………………………………………………….. 113

4.7 Model Validation ………………………………………………………… 115

4.7.1 Evaluating the Model Performance in Training & Validation Sets ….. 115

4.7.2 Conducting Sensitivity Analysis …………………………………….. 116

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4.7.3 Comparing GEP Model With Number of CPT-Based Methods ……... 121

5.0 SIMULATION OF LOAD-SETTLEMENT BEHAVIOUR ………………. 128

5.1 Introduction ………………………………………………………………. 128

5.2 Simulation of Load-Settlement Behaviour Using GEP ………………….. 128

5.2.1 Including Additional Input Variables ………………………………… 128

5.2.2 Modelling Approach …………………………………………………. 128

5.2.3 Results ………………………………………………………………... 131

5.3 Simulation of Load-Settlement Behaviour Using ANNs ………………… 133

5.3.1 Modelling Approach …………………………………………………. 133

5.3.2 Input Setting ………………………………………………………….. 134

5.3.3 Data Pre-Processing ………………………………………………….. 135

5.3.4 Network Geometry and Model Parameters ………………………….. 136

5.3.5 Results and Model Validation ……………………………………….. 139

5.3.6 Output Computer Program …………………………………………… 168

6.0 CONCLUSIONS AND RECOMMENDATIONS ………………………… 170

6.1 Conclusions ………………………………………………………………. 170

6.2 Recommendations ………………………………………………………... 172

7.0 REFRECENCES …………………………………………………………… 173

Appendix A ……………………………………………………………………… 191

Appendix B ……………………………………………………………………… 244

Appendix C ……………………………………………………………………… 274

Appendix D ……………………………………………………………………… 306

Appendix E ………………………………………………………………………. 309

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LIST OF FIGURES Figure No. Title Page Figure 2.1 The common structure of problem solving strategy by

evolutionary algorithms 9

Figure 2.2 Base pairing in the double stranded DNA (Source: Ferreira

2002)

12

Figure 2.3 A chromosome composed of two genes 14

Figure 2.4 The translation of the chromosome in Figure 1 into sub-expression trees

15

Figure 2.5 Roulette wheel selection 16

Figure 2.6 One point mutation 17

Figure 2.7 One point recombination 18

Figure 2.8 Flow chart of gene expression algorithms 19 Figure 2.9 The biological neuron (Source: Lee 1991) 21

Figure 2.10 Information into and out of the artificial neuron 23

Figure 2.11 Common nonlinear activation functions 24

Figure 2.12 Three layers feed forward neural network 25

Figure 2.13 Two layer feedback neural network 26

Figure 2.14 Genetic operators and their power (Source: Ferreira 2002) 36

Figure 2.15 Neuron j in a hidden layer 44

Figure 3.1 Pile categories based on load transfer 50

Figure 3.2 Several functions of q

N vs φ have been proposed (Source:

Coduto 1994)

53

Figure 3.3 Soil undrained strength and α (Source: Tomlinson 1971; API 1984)

54

Figure 3.4 Discrete elements of the pile soil system (Source: Smith 1960) 58

Figure 3.5 Begemann cone pentrometer (Source: Sanglerat 1972) 60

Figure 3.6 Electrical friction cone pentrometer (Source: DeRuiter 1971) 61

Figure 3.7 Assumed failure patterns under pile foundations (Source: Visc, 1976)

64

Figure 3.8 Dutch method for calculating end bearing from CPT (Source: Schmertmann 1978)

65

Figure 3.9 LCPC method to calculate equivalent cone resistance at pile tip (Source: Bustamante and Gianeselli 1982)

67

Figure 3.10 Idealized model used in load-transfer analyses (Source: Pando 2003)

76

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Figure 3.11 Assumed pile load-settlement behaviour (Source: Verburgge

1981)

78

Figure 3.12 Pile division to n elements 78

Figure 3.13 Stresses acting on element i as a result of pile loading 80

Figure 3.14 Simplified method of calculating elastic shortening (Source: Fleming 1992)

83

Figure 4.1 Comparison of averaging methods for cone point resistance within tip influence zone

100

Figure 4.2 Summary sheet for steel driven pile case record 15

101

Figure 4.3 Summary sheet for steel driven pile case record 1 102

Figure 4.4 Summary sheet for the bored pile case record 45

102

Figure 4.5 Effect of number of chromosomes on the performance of the GEP model

108

Figure 4.6 Effect of gene’s head size on the performance of the GEP model 109

Figure 4.7 Effect of number of genes per chromosome on the performance of the GEP model

109

Figure 4.8 Effect of mutation rate on the performance of the GEP model 110

Figure 4.9 Effect of the gene recombination rate on the performance of the GEP model

110

Figure 4.10 Expression tree (ET) of the GEP model formulation for bored piles

112

Figure 4.11 Expression tree (ET) of the GEP model formulation for driven concrete piles

113

Figure 4.12 Expression tree (ET) of the GEP model formulation for driven steel piles

114

Figure 4.13 Performance of the GEP models in the training and validation sets: (a) bored piles; (b1) driven concrete piles; (b2) driven steel piles

117

Figure 4.14 Sensitivity analyses to test the robustness of the GEP bored piles model

119

Figure 4.15 Sensitivity analyses to test the robustness of the GEP driven piles models

120

Figure 4.16 Performance comparison of GEP bored piles model and CPT based methods

122

Figure 4.17 Performance comparison of GEP concrete driven piles model and CPT based methods

123

Figure 4.18 Performance comparison of GEP steel driven piles model and CPT based methods

124

Figure 5.1 Performance of the GEP model applied on Case 42. (a) in validation set; and (b) after formulation

131

Figure 5.2 Schematic representation of the structure of ANN model for bored piles

134

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Figure 5.3 Influence of number of hidden nodes on ANN model performance in validation set. MSE: mean squared error

137

Figure 5.4 Influence of learning rate on ANN model performance in validation set. MSE: mean squared error

138

Figure 5.5 Influence of momentum term on ANN model performance in validation set. MSE: mean squared error

139

Figure 5.6 Simulation results in training set of the developed ANN model for bored piles

140

Figure 5.7 Simulation results in training set of the developed ANN model for bored piles.

141


142


143


144


145


146

Figure 5.13 Simulation results in testing set of the developed ANN model for bored piles

147

Figure 5.14 Simulation results in validation set of the developed ANN model for bored piles

148

Figure 5.15 Simulation results in training set of the developed ANN model for driven concrete piles

149


150


151


152

Figure 5.19 Simulation results in validation set of the developed ANN model for driven concrete piles

153

Figure 5.20 Simulation results in training set of the developed ANN model for driven steel piles

154


155


156


157


158

Figure 5.25 Simulation results in validation set of the developed ANN model for driven steel piles

159

Figure 5.26 Comparison performance of ANN bored piles model and load-transfer methods

163

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Figure 5.27 Comparison performance of ANN bored piles model and load-transfer methods

164

Figure 5.28 Comparison performance of ANN driven concrete piles model and load-transfer methods

165

Figure 5.29 Comparison performance of ANN driven steel piles model and load-transfer methods

166

Figure 5.30 The flowchart of the ANN models computer program 169

xv

LIST OF TABLES Table No. Title Page Table 3.1 Values of adhesion factor for piles driven into stiff to very

stiff cohesive soils for design (after Tomlinson 1971) 55

Table 3.2 Ranges of β coefficient (after Fellenius 1995) 56 Table 3.3 w values for use in Equation 3.8 (after DeRuiter and

Beringen 1979) 66

Table 3.4 Empirical coefficients for LCPC method (after Bustamante & Gianeselli 1982)

68

Table 3.5 Shaft correlation coefficient Cs (after Eslami 1996) 73 Table 3.6 The recommended values for constructing the t-z curve for

axially loaded single pile (after API 1993). 85

Table 3.7 The recommended values for constructing the q-z curve for axially loaded single pile (after API 1993).

85

Table 4.1 Summary of data used for developing GEP model for bored piles

89-91

Table 4.2 Summary of the data used for developing the GEP model for driven concrete piles

91-92

Table 4.3 Summary of the data used for developing the GEP model for driven steel piles

93-94

Table 4.4 GEP models input and output statistics 104-105 Table 4.5 t-and F-tests to examine the statistical consistency of the

training and testing data sets of the GEP model input and output variables

106

Table 4.6 Optimum GEP models parameters 111 Table 4.7 Performance of the GEP models in the training and

validation sets 115

Table 4.8 Performance of the GEP models versus available CPT-based methods

122-123

Table 5.1 Sample of data input setting used to develop the GEP model 129-130 Table 5.2 Results of GEP model predictions for case 42 in validation

set and after formulation 132

Table 5.3 A sample of data input setting used to develop the ANN models

134-135

Table 5.4

Performance of the ANN models in the training and validation sets

160

Table 5.5 Performance of the ANN models versus the load-transfer methods

167

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NOTATIONS A Pile cross sectional area A Average cone point resistance within tip influence zone a, b, c, d, e, f, g, h Compound parameters Ab Area of shaft base ANN Artificial Neural Network B Shaft coefficient BEM Boundary Element Method C Cohesion C Dimensionless coefficient c0, c1, c2 Constants Co. Concrete piles CPT Cone Penetration Test Cs Shaft correlation coefficient Ct Tip correlation coefficient D Pile diameter d1, d2, d3, d4 Symbolic representation of input variables of GEP program dk Targeted output DNA Deoxyribonucleic acid Dr Relative density E Global error function E Pile elastic modulus EB Deformation secant modulus E0 Soil modulus under the tip Ec Young modulus for pile under compression Ei Soil modulus around element i Ei Mean squared error of an individual program i Ep Pile material modulus ETs Expression trees FEM Finite element method f(.) Activation function f(zt) Function of summed input fs Side friction

sf Average sleeve friction along shaft fx(x), fy(y) Probability density functions fx,y(x,y) Joint probability density function G Shear modulus of soil GA Genetic algorithms Gb Deformation secant modulus for soil at 25% of ultimate stress GEP Gene expression programming GP Genetic programming H Head size Hi Height of element i IS Insertion sequence J Damping constant j Neuron symbol K Dimensionless coefficient, coefficient of lateral earth pressure Kc End bearing coefficient

xvii

KE Effective column length of shaft transferring friction, divided by Lf

K0 Coefficient of earth pressure Ks Friction coefficient Ks Horizontal stress coefficient L Embedded length L0 Friction free zone Lf Friction load transfer length MAPE Mean absolute percentage error MI Mutual information Ms Flexibility factor N Number of layers N Arty N Number of observations N Number of values Nc Capacity factor

γN Capacity factor Nk Cone factor Nq Capacity factor OCR Over consolidation ratio P Applied load P Cumulative probability P50 50% cumulative probability Pi Currant state load Pi+1 Next state load

Pij Value retained the individual program i for fitness case j out of n fitness cases

Pm Measured load Ppr Predicted load PR Penetration ratio Ps Applied load to pile carried by friction Pt Load applied at pile tip Q Mobilized end bearing capacity Q Total applied load qc Measured cone tip resistance qc (mechanical) Readings of tip resistance of mechanical cone

qc(electric) Suggested electrical cone tip resistance reading corresponding the mechanical cone readings

qc(tip) Averages of cone point resistance over tip influence zone qc1, qc2 Averages of cone point resistance qc1, qc2, qcn Measured cone tip resistance qc-arth Arithmetic average of cone tip resistance values qc-eq Equivalent average cone resistance qc-geo Geometric average of cone tip resistance values qc-wetd Weighted average of cone tip resistance values qe Effective cone resistance qEg Geometric cone tip resistance over tip influence zone Qm Measured pile capacity Qp Total end bearing capacity Qp Predicted pile capacity

xviii

qt Total measured cone resistance Qu Ultimate pile capacity

tipcq − Average cone tip resistance within tip influence zone

shaftcq − Average cone tip resistance along shaft R Instantaneous soil resistance R Point coefficient R Coefficient of correlation R1, R2, R3 Ranking criteria rc Pile radius RI Ranking index RIS Root insertion sequence RNA Ribonucleic acid rm Radius at which shear stress becomes negligible Rs Static soil resistance Rs Total shaft resistance Rs Applied load to pile carried by friction Rs Ultimate shaft friction rs (max) Maximum unit shaft resistance rs, rsi Unit shaft resistance Rsu Ultimate shaft friction r t Unit end bearing Rt Total tip resistance Rt Load applied at pie base S Weighted sum SA Surface area SD Standard deviation St. Steel piles Su Undrained shear strength Su (shaft) Undrained shear resistance T Chromosome tail size, Mobilized soil pile adhesion tmax Total shear resistance (API method) Tj Target value of fitness case j u2 Pore water pressure V Instantaneous velocity VE Variation element w Weight vector

1−iw Vertical displacement at the lower face of element i

jiw′ New weight after adjustment wji Value of weight between node j and node i before adjustment

0w Tip settlement X Value of variable x0, x1, xn Input nodes xj Input from node j xmax Maximum value of variable xmin Minimum value of variable xn Scaled value of variable yk Predicted output Z Local pile deflection

xix

zt Summed input φ Internal friction angle

E∆ Total elastic shortening ∆εi Settlement increment Α Adhesion factor β Skin friction factor, shaft coefficient ∆ Settlement ∆1, ∆2, ∆3 Components of elastic shortening of pile ∆B Settlement of pile tip under applied load ∆l Length of segment between two consecutive qc values ∆s Settlement of pile shaft under applied load ∆T Total settlement of rigid pile under applied load P ∆wkj weighted increment from nod j to nod k εi Measured settlement over pile diameter η learning rate λ shape coefficient µ Mean µln Logarithmic mean ξ = ln(rm/rc) SD Standard deviation σ0 Stress at soil pile tip interface σi Normal stress at the top of element i σi-1 Normal stress at the bottom of element i σln Logarithmic standard deviation

σvo Effective earth pressure on the shaft, total stress at shaft base, total Stress at mid-depth of soil layer

σ Effective vertical stress at the soil layer of interest

0vσ Effective earth pressure on pile shaft Φ Activation function δ Soil shaft friction angle τ Damping constant

iτ Mobilised shaft friction

kδ Global error Φ′ Derivative of the activation function γ Soil unit weight α Adhesion factor

1

CHPTER ONE

INTRODUCTION

1.1 BACKGROUND

Bearing capacity and settlement are considered to be the principal factors that govern

the design of pile foundations. Therefore, they have been the subject of interest for

many researchers throughout the history of the geotechnical engineering profession.

As a result, numerous theoretical and empirical methods have been proposed to

determine the bearing capacity and settlement of pile foundations.

The most reliable method for determining the pile capacity and load-settlement

behaviour is from results of in-situ pile load tests, however, such tests are expensive,

time consuming and require the availability of skilled personnel to conduct them

(Coduto 1994). Therefore, pile capacity and load-settlement behaviour are very often

predicted and used for design.

In general, pile capacity is predicted based on static analyses using soil properties or

in-situ tests and dynamic analysis based on pile-driving dynamics, while settlement is

estimated based on load-transfer, theory of elasticity or numerical analysis (Poulos

and Davis 1980).

The complexity of pile behaviour under axial loads and the lack of a certain

interpretation of pile soil interaction, however, have created shortcomings in the

prediction methods and limited their success in achieving accurate estimate of pile

capacity and settlement.

The static methods, that employ the theory of bearing capacity to calculate the pile

shaft and tip resistance, involve shortcomings resulting from considerable uncertainty

over the factors that influence the bearing capacity. For example, the ratio of

horizontal to vertical effective stresses, Ks, is constantly changing throughout the

period of installation and therefore several choices for Ks given in the texts have been

2

suggested by different authors. Although Ks values tend to provide reasonable

answers for some designers, they have the habit of giving unpredictable results for

others (Bowles 1988).

The dynamic methods which are applied to driven piles suffer from several setbacks.

First of all, the dynamic analysis involves great uncertainties because of inaccurate

estimates of energy losses (Coduto 1994). Furthermore, the methods tend to equate

the load bearing capacity with driving resistance which of course, is hardly logical

and can be misleading (Young 1981). They also depend on input assumptions which

can considerably bias the results (Eslami 1996); the parameters, such as the efficiency

of energy transfer and the pile/soil quake, are assumed, and therefore may not reflect

the high variability of the field conditions. Moreover, the theoretical analysis of the

“rational” pile formula relates the energy transfer mechanism to the Newtonian

analysis of ram pile impact. This formulation is theoretically invalid for representing

the elastic wave propagation mechanism which actually takes place (Ng, Simons, and

Menzies 2004).

Recently, the CPT-based methods, in particular, those that employ direct correlation

of CPT data with pile capacity have become favourable and widely used. This is

because the CPT can be conducted in soils, e.g. cohesionless soil, from which

undisturbed samples are very difficult to obtain. Moreover, the CPT data can be

correlated with soil properties or directly factored and used to predict pile bearing

capacity without the need to furnish intermediate parameters such as horizontal stress

coefficient, Ks, and bearing capacity factor, Nq, (Eslami 1996). However,

comparative studies of the available CPT based methods carried out by a number of

researchers (e.g. Briaud 1988; Roberston et al. 1988; Abu-Farsakh and Titi 2004; Cai

et al. 2009) have shown that the capacity predictions can be very different for the

same case depending on the method employed. It is also found that these methods can

not provide consistent and accurate prediction of pile capacity.

The methods that have been proposed to predict the load-settlement behaviour involve

a number of limitations. The load-transfer methods pay no attention to the continuity

of the soil mass as a result they are not suitable for analysing load settlement

characteristics of pile groups.

3

They also tend to extrapolate test data from one site to another which is not always

entirely successful (Poulos and Davis 1980). The methods that apply the theory of

elasticity provide approximate solutions to the settlement of piles installed in

nonhomogeneous soils and may include great amount of error if sudden large

variations in soil module occur along the pile length. The methods also suggest

approximate procedure to account for the pile-soil slip, hence can not bring accurate

results. The main deficiency of the numerical methods such as the finite element

method is that reiteration is required when input variables are changed. Moreover, any

mistakes by the user can be fatal.

Consequently, the reliability and accuracy of proposed methods for predicting pile

capacity and load-settlement are not guaranteed and the designer may rely on his or

her experience to make a selection between these methods using high factor of safety

to account for the uncertainty.

Considering the deficiencies in the aforementioned methods, a better alternative for

modelling the axial capacity and the load-settlement behaviour of piles is inevitable

and that can be the artificial intelligence techniques.

In the last two decades, several successful attempts have been made using artificial

intelligence techniques, artificial neural networks (ANNs) and genetic programming

(GP), for solving various problems in the field of geotechnical engineering. ANNs

have been used by (e.g. Abu-Kiefa 1998; Ardalan, Eslami, and Nariman-Zadeh 2009;

Shahin 2008) and the GP by (e.g. Javadi, Rezania, and Nezhad 2006; Rezania and

Javadi 2007) for modelling different geotechnical engineering problems. The

modelling advantage of the two techniques (ANNs and GP) over traditional methods

is their ability to capture the nonlinear and complex relationship between the problem

and factors affecting it without having to assume a priori formula of what could be

this relationship. They use the data alone to determine the structure and the unknown

parameters of the model, so that they are able to overcome the limitations of the

existing methods. The theme of this study is to apply the Gene Expression

Programming (GEP) which is a developed version of GP and the ANNs for modelling

bearing capacity and load settlement-behaviour of pile foundations embedded in sand

and mixed soils.

4

1.2 RESEARCH SIGNIFICANCE

1) The research highlights some of the shortcomings that exist in the commonly

used methods for predicting axial capacity and load-settlement relationship of

pile foundations and tries to obtain more accurate model. This will improve

the reliability of the design and the safety of the structure.

2) The research is economically important, as using accurate model requires a

low factor of safety. Consequently, wasted capacity will be minimised leading

to cost and effort reduction.

1.3 RSEARCH OBJECTIVES

The present work has been undertaken to investigate the feasibility of using two

artificial intelligence techniques, GEP and ANNs, for modelling the axial capacity

and simulating the full load-settlement behaviour of pile foundations embedded in

sand and mixed soils. The objectives of the proposed research can be summarised as

follow:

(1) To employ the GEP technique for determining a model that can accurately

predict the axial capacity of the piles.

(2) To evaluate the performance of the obtained model and compare it with the

most commonly used CPT based methods.

(3) To translate the model into mathematical expression applied easily.

(4) To explore the feasibility of using the GEP for simulation of the full load-

settlement behaviour of the piles.

(5) To utilize the ANNs for modelling the load-settlement behaviour of the piles

(6) To evaluate the performance of the obtained ANN model and compare it with

number of load-transfer methods

5

(7) To convert the ANN model into simple executable computer program.

1.4 OUTLINE OF THESIS

Chapter one introduces the studied problem and defines the scope and the objectives

of the research. A brief description of what will be covered in each chapter is

included.

Chapter two defines the basic concepts of the artificial intelligence techniques. Two

principal artificial intelligence techniques including genetic programming (GP) and

artificial neural networks (ANNs) are described. The main components of each

technique are explained. The necessary steps for the development of the artificial

intelligence model are discussed. Some of existing shortcomings in the two

techniques are listed.

Chapter three briefly describes pile foundations and the general bases of piles

classification. It also presents the general theories that have been developed for the

determining of piles’ axial capacity and reviews the main approaches for relating the

pile capacity to the cone penetration test data. The direct CPT methods which are

widely used are explained and their limitations are pointed out. The main approaches

that have been proposed for constructing the full load-settlement relationship are

defined and the load-transfer approach is explained. Three load transfer methods are

explained and comments on each method are pointed out.

Chapter four includes the development of the GEP model. The steps that are carried

out to develop the GEP model are explained. This includes data collection, selection

of input and output variables, data division and pre-processing and determination of

GEP model’s parameters. The translation of the model from expression tree into

mathematical expression is shown. The performance of the GEP model is evaluated

and the GEP model is compared with the widely used traditional CPT based methods.

Chapter five includes the simulation of the pile load-settlement behaviour. In the first

part, the load-settlement behaviour modelled using the GEP.

6

Several modelling attempts are carried out. The modelling attempt that brought the

best results is explained and the output model is evaluated. In the second part, the

ANNs are used to model the load-settlement. Modelling steps are explained. The

output results are shown and model evaluation is detailed. The ANN model is

compared with three load transfer methods and the results of comparison are

illustrated graphically and numerically.

Chapter six summarises the main conclusions of this work and presents the

conclusions and some suggestions for further research and development.

7

CHAPTER TWO

ARTIFICAL INTELLIGENCE TECHNIQUES

2.1 INTRODUCTION

In the 1940s, researchers realized the potential of the computer to perform repetitive

calculations and invented artificial intelligence as a problem’s solution techniques.

The two important elements of the artificial intelligence are: artificial neural networks

(ANNs) and evolutionary algorithms (including genetic algorithms, GAs, and genetic

programming, GP). In these techniques, the computer iterates using the problem’s

data input and outputs a solution. The techniques are inspired from nature mimicking

the principles of genetics (as with evolutionary algorithms) or the functions of the

human brain (as with artificial neural networks). The evolutionary algorithms try to

imitate the process of evolution that exist in living organisms and use evolutionary

tools such as mutation and crossover to evolve randomly created solutions to the

given problem. Artificial neural networks try to mimic the functions of human brain

by applying knowledge gained from experience on new unseen situations. In these

techniques, the computer is taught examples during the training phase to infer the

form of the relationship between independent input variables and targeted output

values.

Artificial intelligence techniques are very useful for the following reasons:

(i) They do not require prior knowledge on the form of the relationship between

the problem input variables, and hence are suitable for exploratory modelling.

(ii) They have a capability to model highly nonlinear complex problems.

(iii) They can handle noisy data efficiently and determine a useful solution.

(iv) Solutions obtained by these techniques can be improved by retraining when

new data is available.

ANNs, GAs and GP have been applied successfully on numerous occasions during

their existence. They have been applied to diverse problems in different fields of

science such as finance, medicine, engineering, geology physics and chemistry.

8

Recently, they have been applied across a range of areas including classification

estimation, prediction and function synthesis (Moselhi, Hegazy, and Fazio 1992).

They have also been introduced successfully to assist in solving problems of pattern

recognition, non-destructive testing, forecasting, data mining, bioengineering,

formulation, modelling of an industrial process, robotics, environment control and

mobile robotics.

In this chapter:

• A brief history is given about evolutionary algorithms and artificial neural

networks, which will be used in this study;

• The concepts that these techniques are based on, the main components and the

learning paradigms of the techniques are explained;

• The necessary steps that need to be followed for development of artificial

intelligence model are detailed; and

• Lastly, the shortcomings of artificial intelligence are listed.

2.2 GENETIC AND EVOLUTINOARY ALGORITHMS

2.2.1 Definition and brief history

The phrase “genetic and evolutionary algorithms” is used in the literature to describe

a variety of computational entities that borrow general principles from genetics and

from evolutionary biology in nature for the sake of engineering more powerful

problem solving systems (Lee 2007). The systems actually imitate the evolutionary

mechanism found in the nature such as selection, mutation, and crossover to solve a

function identification problem which is performed through a symbolic search on a set

of experimental data to obtain the function that fits the data.

Figure 2.1 illustrates the general structure of the problem solving strategy that many

forms of the evolutionary computation systems conform with. The solution of the

investigated problem starts with the creation of a random population of individuals

(i.e. chromosomes) each of which represents a candidate solution. The individuals

pass through fitness evaluation for selection.

9

The high fitness chromosomes are the candidates that perform well towards the target

solution meaning they have more opportunity to be selected. The low fitness

individuals are removed or have little chance of survival. The selected chromosomes

are exposed to further modifications to improve their performance. The new

generation of modified chromosomes are subjected to the same process which iterates

until a solution to the given problem is obtained.

Fitness check up

Selection Modifications

Random population

Solution

Figure 2.1 The common structure of problem solving strategy by evolutionary algorithms.

Genetic algorithms (GA) are the most straightforward widely used representatives of

evolutionary algorithms (Steeb, Hardy, and Stoop 2005). They were invented by

Holland (Holland 1960) and applied biological evolution theory to computer systems

(Holland 1975). A detailed description of GAs has been given by many authors (e.g.

Michalewicz 1996; Holland 1995; Goldberg 1989). In GAs, the chromosomes are

composed of genes which may take on a number of values (usually 0 and 1) called

alleles. That is, the chromosomes are represented as binary strings of fixed length.

Each chromosome encodes a potential solution to the target problem. The problem’s

solution is achieved through an evolutionary process as in Figure 2.1. Chromosomes

are selected according to their fitness and left to evolve through modifications

introduced by mutation, crossover and inversion until a solution is reached.

An important feature of GAs is that the chromosomes function simultaneously as

genotype and phenotype. This means that the chromosomes are the both the subject of

selection and the guardians of the genetic information that must be replicated and

transmitted with modifications to the next generation.

10

The dual functionality of the chromosomes and the structural organization (the

simple symbolic representation and their fixed length) are the main constraints that

have reduced the capability of GAs to deal with complex problems, hence they are

generally used in parameter optimisation to evolve the best values for a given set of

model parameters (Ferreira 2002).

Genetic programming (GP) is an extension of GAs and was invented by Cramer

(1985) and further developed by Koza (1992). Similar to the GAs, the GP employ the

evolution strategy described in Figure 2.1. However, the main difference between the

two algorithms is in the nature of the individuals and in the representation of the

solution. The GAs evolve individual programs of fixed length and expresses the

solution as a linear string of numbers (0s and 1s), whereas the GP evolve a population

of non-liner individuals that have different sizes and shapes and the solution of the

problem is expressed as parse trees rather than lines of code. The symbolic

representation in the GP consists of elements (nodes) known as functions such as (+, -

, ×) or terminals which can be constants like (2, 4) or variables like (d1, d2). The

variable terminals represent the input variable of the studied problem, while the

constant terminals represent constant values created randomly by the program to

achieve the best possible fitting. The functional set may take two arguments as in the

case of (+, -) or one argument like square root. The domain of the solution is created

through a repeated process of combining functional sets for any internal node with

terminal sets for any external node. Any time a functional node is created the number

of links equal to the number of the argument the function takes exist. Eventually, a set

of random trees of different shapes and sizes is generated and each tree exhibit

different fitness with the objective function. The trees are capable of representing

hierarchical programs of any complexity if the set of the assigned functions is

sufficient. The main shortcoming of the GP is that the size of parse trees increases

with the continuity of evolution. As a result, they require a lot of space for storing and

reproduction. If the problem is complex, it may require significant size of trees to

represent the solution which becomes impractical. Additionally, the mechanism of

genetic modifications is considerably restricted due to the execution of genetic

modifications on the parse trees.

11

Gene expression programming (GEP) that is used in the present work is a further

development of GP and was developed by Ferreira (2001). The GEP utilises the

evolution of computer programs (individuals or chromosomes) that are encoded

linearly in chromosomes of fixed length, and are expressed nonlinearly in the form of

expression trees (ETs) of different sizes and shapes.

The main strength of the GEP over the GP is the ability to deal with very complex

problems and develop solutions much quicker. For instance, the most complex

problem presented to the GEP is the evolution of cellular automata rules for the

density-classification task. The GEP was found to surpass the GP by more than four

orders of magnitude. This considerable improvement in the GEP performance is

actually based on two things. First, the GEP has overcome the limitation of the GAs

by utilizing the expression trees to present problem solutions and performing genetic

modifications at the chromosome level to overcome the shortcoming of GP. Secondly,

the GEP utilizes the multi-gene chromosomes which provide more space for genetic

variations and bring rapid evolution.

Evolutionary algorithms have been applied in numerous successful applications

during its existence. The GP, for instance, has been applied to a diverse range of

problems some of which include:

• Science-oriented applications such as biochemistry data mining, sequence

problems and image classification in geo-science and remote sensing.

• Computer science-oriented applications such as cellular encoding of artificial

neural networks, development and evolution of hardware behaviour, intrusion

detection and auto parallelization.

• Engineering-oriented applications such as on line control of real robot,

spacecraft attitude manoeuvres and design of electrical circuits.

Genetic and evolutionary computation methods require little prior knowledge of the

problems being solved or of the structure of the possible solution. As a result, they are

ideal for exploring domains about which we have little knowledge in advance (Lee

2007).

12

2.2.2 Biological genetic

To gain some insight into the natural genetics and evolution of living organisms, it is

important to understand the functions of the main players (DNA, RNA and protein) in

the cell. DNA is described as the carrier of the genetic information. The DNA

molecule is a double helix of strings which are complementary to each other. As

shown in Figure 2.2, the string consists of four lockable nucleotides known as A, T, C

and G, in which the sequence of the letters or the primary structure contains the

genetic information. The most important property of the DNA is incapability of

catalytic activity and structural diversity. That is the DNA functions as storage of

information. The role of DNA here corresponds to the role of the linear string in the

GAs and the chromosome in GEP.

Figure 2.2 Base pairing in the double stranded DNA (Source: Ferreira 2002).

The RNA functions as a working copy of the DNA; in terms of information the RNA

copy contains exactly the same information as the original DNA. The main property

of the RNA is it has unique three dimensional structures and therefore can exhibit

some degree of structural and functional diversity. The RNA molecule can function

simultaneously as genotype and phenotype. The function of RNA in the living cell is

imitated by parse trees in GEP. The protein function is to read and express the

information.

Living organisms reproduce and evolve via three important genetic operations:

genome replication, mutation and recombination. These operations are briefly

described here, and fully detailed elsewhere (e.g. Berg et al. 2002; Bruce 2002; Bruce

et al. 2004; Becker, Kleinsmith, and Hardin 2006; Devlin 2002).

13

Genome replication: In this operation, the complementary double-stranded DNA

molecule opens itself and each strand serves as a template for the synthesis of the

respective complementary strand. When copying is complete there will be two

daughter DNA molecules each identical in sequence to mother molecule (Berg et al.

2002).

Mutation: Occasionally, during replication the sequence of the mother molecule is

not copied exactly to the daughter molecule sequence due to some error in the

copying process. As a result, one small or large fragment of nucleotides in the

molecule of the daughter differs with the molecules of the mother. This kind of

change is referred to as mutation. The effects of the mutation on the structure and the

functionality of a protein depend on the region in the gene at which the mutation

exists. In the non coding region of the gene, the mutation has no effect on the

structure and the functionality of the protein. However, mutation may have drastic

effects if it takes place in the coding region. Mutation may occasionally have a lethal

effect, especially if the new protein is fundamental to the survival of the organism.

Nonetheless, on rare occasions mutation might give rise to new evolutionary traits

(Ferreira 2002).

Recombination: In this process, two distinct molecules pair and exchange some

fragments of genetic material forming two new daughters. The exchange of genetic

material between the recombining genes must take place in regions that correspond to

each other.

2.2.3 Gene expression programming structure and operation

Gene expression programming is a very simple imitation of natural genetics. In GEP,

chromosomes and expression trees are the main components. The GEP chromosomes

try to mimic the structure and function of DNA in nature. They are very simple strings

of single helix at which information is encoded and genetic variations occur.

Expression trees represent the counterpart of the RNA in the cell. The expression trees

represent the solution determined by GEP to the given problem. The GEP terms and

operation are explained next.

14

Chromosome

It is an individual program which represents one of the presumed solutions to the

given problem and has a fixed length and constant structure consisting of one or

several genes, as shown in Figure 2.3. The genes' heads can compose of functions like

(+, -, /) or functions and terminals like (+, d1, /). The gene's tails is composed of

terminals only like (d1, d2, d3).

+ - / d1 d2 d4 d3 d1 + / d4 d3 d2 d1

Gene head Gene tail

Gene 1 Gene 2

Figure 2.3 A chromosome composed of two genes

The gene's tail depends on its head size and thus it can be found from the expression:

t = h (n-1) +1 (2.1)

Where; t = tail size; h = head size; and n = arty.

Although the chromosome has a constant length, it can code expression trees of

different sizes and shapes.

The process of information translation from the chromosome to expression trees

involves using code and applying set of rules. The code represents one-to-one

relationship between the symbols of the chromosome and the functions or terminal

they represent. The rules determine the spatial organization (phenotype) of the

functions and terminals in the expression trees. The rules can also infer the gene

sequence (genotype) from the given expression trees. This bilingual system is called

karva (Ferreira 2002). The above chromosome (Figure 2.3) can be translated into

expression trees through the following steps:

(i) The symbol at the far left end of each of the gene’s heads will correspond to

the roots of the sub-expression trees.

(ii) In the next line, number of nodes equal to the number of arguments of the

previous step (functions may have more than one argument but terminals

have an arty of zero) are placed.

15

(iii) From left to right nodes are filled, in the same order, with the elements of the

gene. As illustrated Figure 2.4, this process continues until a line consisting

of terminals only is formed.

+ +

+ / -

d4 d3 d2 d1

Step 1: roots of sub-trees are established

Step 2: nodes equal to arguments of sub-trees roots are placed

d1 d2

d1

Gene 1 (sub-tree 1) Gene 2 (sub-tree 2)

Sub-tree root

Step 3: line of terminals only

/

Figure 2.4 The translation of the chromosome in Figure 1 into sub-expression trees

Fitness function

During simulated evolution, GEP uses a measure to evaluate the performance of the

evolving programs to determine how well each program has learned to predict the

output from the input. This measure is defined as the fitness function, which aims to

give feedback to the learning algorithm regarding which individuals have a higher

probability of being allowed to multiply and reproduce and which individuals should

have a higher probability of being removed from the population (Banzhaf et al. 1998).

Fitness can be measured in many ways including: (i) the amount of error between the

predicted output and the targeted output; (ii) the amount of time required to bring the

system to the desired output; (iii) program’s accuracy in object classification or

patterns recognition; (iv) the compliance of a structure with user-specified design

criteria (Poli, Langdon, and McPhee 2008). There are different types of fitness

functions (e.g. absolute error with selection range, absolute/hits, mean square error,

and mean absolute error) that are used depending on the application type.

Selection

After the fitness evaluation, individuals are selected for producing offspring. Each

individual receives a reproduction probability depending on its own fitness and the

fitness of all other individuals. There are several selection schemes such as roulette

wheel and tournament selection.

16

In GEP, selection is performed using the roulette-wheel sampling (Goldberg 1989) in

which individuals are mapped to contiguous slices of a line, such that every

individual’s slice is proportional in size to its fitness, as illustrated in Figure 2.5. The

wheel is spun a number of times (equivalent to the number of individuals) and every

time one individual is selected. This will keep the population level unchanged during

the run.

Chromosome 3

Chromosome 1

Chromosome 4

Chromosome 5

Chromosome 2

Figure 2.5 Roulette wheel selection

Genetic variations

During the evolution process, components of randomly selected individuals

(chromosomes) are subjected to genetic variations aiming to improve their

performance. The variations take place in two ways: first, within the chromosome by

the aid of genetic operators which include mutation, inversion, insertion sequence (IS)

and root insertion sequence (RIS); second, between two chromosomes by

recombination. A brief definition of each genetic variation and genetic operators is

provided below:

(i) Elitism (Replication): Cloning individuals that carry the best fitness and

placing them unchanged in the next generation is called elitism. Whenever

more than one individual shares the best fitness, the last one is cloned and

placed in the first order in the next generation. Elitism also plays another

role: it allows for the use of several genetic operators at relatively high rates

without the risk of causing mass extinction (Abraham, Nedjah, and Mourelle

2006).

(ii) Mutation: It is the operation by which any component of the gene's head, a

function or a terminal and the tail is replaced by either a function or a

17

terminal at the head but only by a terminal at the tail. A simple explanation

illustrating how the mutation works is indicated in Figure 2.6. The arrows

refer to the points at which mutation took place. It can be seen that at the

head of gene one the + function is replaced by the – function and at the tail

of gene 2 the d1 terminal replaces the d4 terminal.

+ - / d1 d2 d4 d3 d1 + / d4 d3 d2 d1

- - / d1 d2 d4 d3 d1 + / d1 d3 d2 d1

Before mutation

After mutation

Figure 2.6 One point mutation

(iii) Inversion: This is inverting a randomly chosen fragment within the genes

head only. For example, the fragment of two components of gene 1 in the

chromosome in Figure 2.3 is chosen for inversion. The result of that is the –

function moves to first place and the + moves to the second place. The rate

of this operator varies depending on the use of other operators such as

mutation.

(iv) Insertion sequence (IS): Any short fragment of the gene’s head can be

randomly chosen, copied and inserted in the first position of any other gene

within the chromosome except the root. As a result, an equivalent part of the

other genes head is deleted and usually taken away from the last elements.

For example, assume the fragment at position two and three of gene one (-,

/), in Figure 2.3, is selected for insertion. Then it will be copied and placed at

position one and two at gene one. The head of the new gene 1 will become (-

, /, +).

(v) Root insertion sequence (RIS): This operator can be activated, if there is a

function among the gene’s symbols. That is mainly because this

modification tool must start with a function. The rest of RIS performance is

exactly the same as IS.

(vi) Gene recombination: This is a trade in between two chromosomes which pair

and split exactly at the same point to exchange their ingredients beyond the

merging point.

18

When recombination takes place at one point in the chromosome, it is called

one point recombination and two point recombination when it happens at

two points. The third form of recombination is the gene recombination at

which the entire genes are exchanged between two chromosomes. An

example of one point recombination is shown in Figure 2.7.

+ - / d1 d2 d4 d3 d1 + / d1 d1 d2 d4

- - / d1 d2 d4 d3 d1 + / d3 d3 d2 d1

Before recombination

After recombination

+ - / d1 d2 d4 d3 d1 + / d3 d3 d2 d4

- - / d1 d2 d4 d3 d1 + / d1 d1 d2 d1

Figure 2.7 One point recombination

The modelling process by GEP, as illustrated in Figure 2.8, performed as follow:

• Random generation of chromosomes of the initial population are created.

• Then, each individual chromosome is expressed and its fitness is evaluated

through the fitness function.

• Individuals are subsequently based on fitness selected; the higher the fitness,

the more chance of being selected. The low fitness chromosomes, however,

are deleted or have a slim chance of selection.

• The selected chromosomes are then exposed to genetic variations which are

performed by the genetic operators such as mutation and recombination. Then,

new offspring of chromosomes with new traits are generated and replace the

existing population.

• The individuals of the new generation are then subjected to the same

developmental process which iterates until the stopping criteria are satisfied.

19

Create chromosomes of initial population

Express chromosomes & evaluate their fitness

Stopping criterion is satisfied

Select chromosomes & keep the fittest for next generation

Perform genetic variations via genetic operators (mutation, inversion, insertion sequence, root insertion sequence)

New generation of chromosomes

Designate results

End

Yes

No

Perform genetic variations via recombination (one point, two points and gene recombination)

Figure 2.8 Flow chart of gene expression algorithms

2.3 ARTTIFICIAL NEURAL NETWORKS

2.3.1 Definition and brief history

Neural networks are data processing techniques that mimic the structure and

functioning of the human brain. They do so by simulating the brain’s basic

components which include cell body, dendrites, synaptic connections and axons; they

apply the knowledge gained from past experience to find solutions to new problems

or situations.

20

McCulloch and Pitts (1943) are considered the first pioneers who proposed the single

nets neuron as a computational model of “nervous activity”. Their model defines the

neuron as linear threshold computing unit with multiple input and single output which

can be either 0 indicating the nerve cell is inactive or 1 indicating the nerve cell is

firing. Every time the sum of input exceeds the specified threshold, the cell fires. Few

years later, Hebb (1949) added a new feature to the networks by introducing the link

between the single neurons. His work represents the first mathematical rule to

implement learning of an artificial network. Based on the work of McCulloch and

Pitts (1943), Rosenblatt (1958) developed network utilizing a unit called perceptron

which produce scaled output range between (-1 and 1) depending upon the weighted

linear combination of input. During the 1960s further studies were curried out by

Rosenblatt (1962) and Widrow and Hoff (1960) to explore the perceptron-based

neural network. During the 1970s the researchers became less enthusiastic in perusing

more studies in neural networks because of two reasons. First, there are practical

difficulties in solving many real world problems. Second, the results of theoretical

study by Minsky and Papert (1969) revealed that the perceptrons suffered limitations

which can not be overcome by simply adding multiple layers of neurons. The study

also showed that the perceptron was incapable of representing simple functions that

were linearly inseparable such as in the famous case of the “exclusive or” (XOR)

problem. However, the research in the field gained momentum again when Hopefield

(1982) introduced two key concepts to overcome the limitations identified by Minsky

and Papert. He introduced the feedback between the input and output as well as the

nonlinearity between the total input received by a neuron and the output it produces

(Marini, Magri, and Bucci 2007). Since then, the neural networks have been applied

widely in different fields of science such as finance, medicine, engineering, geology

physics and chemistry. Recently, they have been applied across a range of areas

including classification estimation, prediction and function synthesis (Moselhi,

Hegazy, and Fazio 1992). They have also been introduced successfully to assist in

solving problems related to pattern recognition, non-destructive testing, forecasting,

data mining, bioengineering, formulation, modelling of an industrial process, robotics,

environment control and mobile robotics (Dreyfus 2005).

The reason behind the extraordinary success of neural networks can be attributed to

their capability to model highly non-linear complex problems. Artificial neural

21

networks are very arguably sophisticated nonlinear computational tools. They can

learn from examples and predict the form of the function that governs the relationship

between independent input variables and targeted output values. In the real world,

there are many problems in which the relationship between input and output is

complex and can not be easily identified using traditional statistical methods.

Alternativley, neural networks are employed to deal with such problems.

2.3.2 Natural neural networks

The brain has an enormous number of neurons with massive interconnection between

them. It is estimated that the cortex of the human brain has ten billion neurons with 60

trillion synapses or connections (Shepherd and Koch 1990). The basic components of

the biological neuron are shown in Figure 2.9. They include the cell body, dendrites,

synaptic connections and axon. The cell body is the component at which the incoming

signals from dendrites are processed. Dendrites are the recipients of electrical signals

and they are the carriers of the signals into the cell body. The synaptic connections are

the means by which neurons interact with each other. These units mediate the

interaction between neurons and interact with synapses from the axons of various

other neurons or from somewhere else in the central nervous system. Axons represent

the channels that carry the signals from the cell body out to other neurons.

Figure 2.9 The biological neuron (Source: Lee 1991).

The process of information flow into and out of the neuron begins with incoming

signals transfer through the synaptic connections. The signals are electronic impulses

22

that are transferred through the synaptic gaps to the dendrites by means of chemical

process (Fausett 1994). The strength of the synapses is a function of the signal

strength; the weaker the synapse the weaker the signal. The signals then transmit into

the cell body via the dendrites. The electrical energy of various signals is summed at

the cell membranes to activate the neuron which stay inactive if the charge of the

summed signals goes below threshold. The cell modifies the summed signal and

produces an output signal which is carried to the adjacent cells through the axon.

2.3.3 Artificial neural network structure and operation

Artificial neural networks are constructed in a way that imitates the construction of

the biological neural networks. The network consists of the following elements:

Artificial neurones

As with biological neurons, the artificial neurons are the core processing elements of

artificial neural networks. They receive one or more inputs and sum them to produce

an output. Usually the sums of each node are weighted, and the sum is passed through

a non-linear function known as an activation function or transfer function.

The information flow into and out of the artificial neuron is shown in Figure 2.10.

There are neurons labelled from x0 to xn that provide input to neuron j. The signal

from each neuron is multiplied by its connection weight with neuron j to produce an

input signal which enters into neuron j. There is also additional input signal comes

from the bias or threshold multiplied by its connection weight with neuron j. The bias

is always equal to 1. At neuron j, the incoming signals are summed and then the

activation function, Φ, is applied to the weighted sum, S, to produce an output signal.

In many applications, the neurons of these types of networks apply a sigmoid

activation function. The output of the neuron j provides input to the neurons in the

next layer.

The artificial neurons are arranged in layers and connected in a particular way to form

the structure of the ANN which can be composed of either two layers (i.e. input layer

and output layer) or multilayer when intermediate layers are added.

23

Figure 2.10 Information into and out of the artificial neuron.

Connection weights

The weight represents the counterpart of the synapse in the biological neural

networks. The scalar weights determine the strength of the connections between

interconnected neurons. The zero weight indicates that no connection exists between

two neurons whereas negative weight refers to a prohibitive relationship.

Activation functions

The activation function is also known as a squashing function, such that the output of

a neuron in a neural network is between certain values (usually 0 and 1, or -1 and 1)

(Graupe 1997). Generally, there are three types of activation functions, denoted by

f(.). The first type is the Threshold Function. This function takes a value of 0 if the

summed input is less than the certain threshold, and the value of 1 if the summed

input is greater than or equal to the threshold value, as in Eq.2.2.

( )

<≥

=0

0

0

1

i

i

i z

z

if

ifzf (2.2)

The piecewise-Linear function is the second type of activation function. This function

is similar to the previous one, but it can also take on values in between 0 and 1

depending on the amplification factor in a certain region of linear operation, as in

Eq.(2.3).

24

( )

−≤

>>−

≥

=

2

10

2

1

2

12

11

i

ii

i

i

z

zz

zif

zf (2.3)

The third type is the sigmoid function which is the most commonly used activation

function (Graupe 1997). The popular form of this function is the logistic sigmoid

function which is usually applied when the desired output range between 0 and 1, as

in Eq. 2.4.

jj zz

ef −+

=1

1 (2.4)

Out

Net

Out

Net

Out

Net

Out

Net

(a) Sigmoid function (b) tanh function

(c) Signum function (d) Step function

Figure 2.11 Common nonlinear activation functions

25

The hyperbolic tangent function is another popular sigmoid function. It is used when

the required output range between (-1 and 1), as in Eq. 2.5. The most commonly used

functions are shown in Figure 2.11.

jj

jj

j zz

zz

zee

eef −

−

+−= (2.5)

A simple structured ANN is the layered feed-forward network which is composed of

input neurons (processing elements) whose sole purpose is to supply input signals

from the outside world into the rest of the network. The neurons of input layer do no

processing of any sort and their activation (output) is defined by the network input

(Master 1993). One or more intermediate layers can come after the input layer. The

intermediate layers have no direct contact with the outside world, therefore they are

called hidden layers. The last layer is the output layer where the output of the

computation can be communicated to the outside world. The neurons of each layer are

not permitted to connect with each other. For this class of networks, the information

flow only in the forward direction from input layer to the output layer and the neurons

can have only one direction connection.

X1

X2

X3

Input layer Hidden layer

Output layer

Figure 2.12 Three layers feed forward neural network

An example of such a layered feed-forward network is shown in Figure 2.12. It should

be mentioned that this type of network is termed a static network since the time

26

necessary for the computation of the function of each neuron is usually negligibly

small (Dreyfus 2005).

The modelling process with ANNs can be easily understood by considering the

learning paradigm of the layered feed-forward network. In this network, the input is

weighted and processed to the nodes of hidden layer. The hidden nodes sum the

incoming input and add or subtract the bias unit which represents the threshold. The

hidden nodes then apply an activation function, which is generally a non-linear

function, on the summed input to produce output. These outputs are then fed into the

subsequent neurons of the networks where the same process is applied. The output at

the external neurons is compared with the targeted output and the error is measured.

The network adjusts its weight connections to minimize the error. The minimization

of error is carried out by implementing learning rules. This process continues until no

further error reduction is achieved and the end of this process defined as the training

of the network.

The feedback network is another type known as recurrent neural network. This

network distinguishes itself from the previous network in that it has at least one

feedback loop (Haykin 1994). The network may consist of single layer neurons with

each neuron feeding its output signal back to the inputs of all the other neurons, as

illustrated in Figure 2.13.

X1

X2

X3

Input layer

Output layer

Figure 2.13 Two layer feedback neural network

27

It can also consist of multiple layers with different settings of feedback loops. Some

recurrent networks have also connections between the nodes of the same layer. The

neurons of the network are either fully or partially connected. The fully connected

networks contain neurons with each of them have a feed back connection from every

neuron in the network, whereas the partially connected network may have one or

several neurons which have feed back connections. The architecture of recurrent

neural network does not only operate on an input space but also on an internal state-

space, a trace of what has already been proposed by the network (Boden 2001). The

main advantage of such architecture is that it allows for swapping of input vectors

with output vectors in the learning process to produce a model with minimal effort

(Basheer 1998). Depending on the nature of the problem, several researchers (e.g.

Elman 1990; Pineda 1989; Rumelhart, Hinton, and Williams 1986) have presented

training algorithms for recurrent networks. The feed back recurrent neural network

with one feed back loop from output layer to input layer proposed by Jordan (1986) is

selected for this study. This network has been found successful for solving several

geotechnical engineering problems (e.g. Ellis et al. 1995; Basheer 1998; Shahin and

Indraratna 2006) of similar nature to the studied problem in this work.

2.4 MODELING WITH ARTIFICIAL INTELLIGENCE (GEP & ANN)

There is no definite procedure or clearly identified steps that the user can follow to

determine the optimal artificial intelligence model. There are, however, important

steps and factors that the modeller can follow to obtain a robust model. The choice of

input variable, data division, program parameters, number of generations and training

are significant steps in developing the GEP model. Similarly, the choice of

performance criteria, division of data, data pre-processing, determination of model

inputs, determination of network architecture, optimization (training) and model

validation are the main steps in the development of an ANN (Maier and Dandy 2000).

The necessary steps for development artificial models are detailed in following

sections.

28

2.4.1 Input selection

Selecting an appropriate set of input variables is a vital step during development of an

artificial intelligence model, for the performance of the final model heavily depends

on the input variables. When selecting input variables, it is important to bear in mind

that the number of variables will need to be as small as possible because:

(i) The addition of new input variables will require the addition of more

parameters. In the GEP, the chromosome size can increase with increase of

number of input variables. This may drag the search for the solution. In the

ANNs, the number of hidden neurons rises as a result of the rise in the number

of input variables. Consequently, the processing speed decreases and network

efficiency reduces (Lachtermacher and Fuller 1994).

(ii) The inclusion of irrelevant variables whose contribution to the output is

smaller than the contribution of disturbances will lead to modeling errors

(Dreyfus 2005).

A large number of selection techniques have been proposed in the literature to assist

with the selection of input variables. The most popular techniques are briefly

described here.

The trial and error approach is a common input selection strategy. In this approach, as

many attempts as possible are carried out using different combinations of input

variables to train the GEP or the ANN. The set of the variables that produce the best

performing output is selected to be the model input. The disadvantage of this

approach is that it requires a large number of attempts which increase with an

increasing of number of variables.

Another common strategy is to produce a “complete model” including an oversize set

of candidate inputs. The performance of this model is compared with performances of

models whose inputs are subsets of the complete model. The best model is chosen

with respect to an appropriate selection criterion. The shortcoming of this approach is

its complexity increases with the increasing number of variables.

29

Another useful strategy is the constructive strategy which starts with a very simple

model whose output is equal to the mean of the measured output values in the data

set. This model is considered independent of the inputs, i.e. a model with zero

variables. The model is then compared with models consisting of one input variable.

The best model is chosen and the procedure is iterated with the addition of new input

variable. This process continues until the addition of a new input no longer improves

the performance of the model. The elimination strategy is the opposite of the

constructive strategy. The elimination method starts with a complete set of input

variable say n. Then the less significant variables are eliminated and new sub-models

with input n-1 are obtained. The best sub-model is selected and compared with the

complete model. If the best sub-model performs better than the complete model, the

sub-model is kept and the procedure is repeated. Both of the methods are time

consuming and difficult to apply with complex problems.

The mutual information (MI) is a useful method suggested by Fraser and Swinney

(1986). It has been used successfully to measure the dependencies between output and

input variables. The method is capable of measuring the dependencies based on both

linear and non linear relationships making it well suited for use with non complex

nonlinear systems. For variables X and Y, the mutual information function is defined

as:

( ) ( )( ) ( ) dxdy

yfxf

yxfLogyxfMI

YX

YXYX∫∫

=

,, ,

, (2.6)

Where: ( )xf X and ( )yfY are the marginal probability density functions of X and Y

respectively; ( )yxf YX ,, is the joint probability density function of X and Y.

If X and Y are independent of each other the MI is equal to zero. Otherwise, a high

value of MI would indicate a strong dependence between X and Y. The weakness of

the method is it can not measure the dependencies of multivariate data (Sharma 2000)

and is also difficult to apply to complex problems.

In ANNs, genetic algorithms can also be used to search for the best set of input

variables. This is performed by generating an initial population of chromosomes

which consist of a number of genes. One variable is randomly assigned to each gene

and the GA is then set in motion to let chromosomes compete, reproduce and die off.

30

The fittest chromosomes are selected and the sets of variables that are part of these

chromosomes are used to train several neural networks. The set of variables of the

best performing network is nominated as the model input. However, with this method

it will be difficult to select the input variables, if there are two or more chromosomes

that perform well but each consists of different set of variables.

The nature of the studied problem determines whether or not there is need for

systematic variable selection. When modeling problems of a very complex nature

(e.g. social, economic, financial or very complex physical problems), the real

variables that have influence on the problem are not well understood. Therefore, the

opinion of experts is sought first, to include every possible relevant variable, and one

of the above mentioned strategies can be adopted to reach the best possible solution.

On the other hand, in the case of physical or chemical process, the variables that have

influence on the output of the modeled quantity are generally analyzed in detail by

experts; that is systematic variable selection process is not necessary (Dreyfus 2005).

As the studied problem in this research falls into this category, a fixed number of

input variables are chosen to be the most effective input variables. This selection is

based on the extensive analysis of the geotechnical literature.

2.4.2 Data Division

Dividing the available data into subsets is a necessary step in modelling with artificial

intelligence techniques. The main aim of this step is to prevent the model from over

fitting which may happen during the training phase. The over fitting refers to the

ability of the model to memorise rather than generalise the form of the relationship

between input and output data. Artificial intelligence models usually involve a large

number of programs, in the case of GEP, or include many connection weights, in the

case of ANNs. Therefore, they have high tendency towards over fitting, particularly if

training data is noisy. Thus, in order to develop a model that has the ability of

generalisation, the data are generally divided into training set and validation set. The

other advantage of this step is that selection and preparation of suitable training data

sets can take up to 80% of the model development effort (Yale 1997).

The training data are used for the adjustment of the model parameters in order to

reduce the error between the model output and the corresponding targeted output.

31

The validation set is independent data not included in the training phase used to test

the generalisation ability of the model and verify its performance in the real world.

Some times, when sufficient data is available, it can be divided into three sets:

training, testing and validation. The training set is used for model parameter

adjustment. The testing set is used to monitor the performance of the model during

training stages and indicate when to stop training so as to avoid over-fitting. The

validation set is used to verify the performance of the developed model in the real

world. The advantage of this option is that it puts the performance of the developed

model under more scrutiny making the developed model more reliable (Stone 1974).

In the literature, there is no definite ratio of the used data to be assigned for each

subset, but in general 10-20% of the available data is suggested to be used as a

validation set and 80% for a training set (Ferreira 2002). Sometimes the size of the

available data is not large enough to permit for allocating a proper subset of validation

data. In this case, Master (1993) suggests the use of the leave-k-out method.

According to this method, a small portion of the available data is held as a validation

set and the remaining data is used for model calibration. After the completion of

training phase, the model performance is tested with the use of validation data. Then a

different subset of data is held back for validation and a new network is trained. The

performance of the new model is tested and compared with the performance of the

pervious model. This process is repeated many times until all the available data are

being used in the validation set. The best performing model is then selected as the

optimal one.

Several methods described in the literature use different strategies for data division.

The random selection of data sets is the popular method that is still been used widely

in the geotechnical field. This method is preferred over the other methods for its

simplicity. The method is suitable for a set of consistent data that has small variations

and the original distribution of data is adequate; an appropriate distribution of values

in the training set should be the same as in the whole data set (Kocjancic and Zupan

2000). However, the main setback of this method is that if the validation set includes

values outside the domain defined for training set, the developed model will show

weak performance. That is because, like other statistical and empirical models,

artificial intelligence models perform well within the range of data used for training

32

(interpolation) but are unreliable when they extrapolate beyond that range (Flood and

Kartam 1994). Therefore, in order to obtain a model with adequate generalisation

ability, given the available data, all of the patterns that are contained in the data need

to be represented in the calibration set (Bowden et al. 2006).

The weaknesses associated with arbitrary selection of data sets have encouraged

researchers to investigate better methods of data division on the base that all of the

patterns that are contained in the available data should be contained in the calibration

set. Likewise, all of the patterns in the available data should be contained in the

validation data, as this will provide the toughest evaluation of the generalisation

ability of the models (Bowden et al. 2006). To achieve this, several researchers

suggest that data subsets should be statistically consistent; training and validation sets

should possess similar statistical properties including mean, standard deviation,

maximum and minimum. Bowden et al. (2002) utilised the genetic algorithm (GA) for

selecting training, testing and validation sets. The GA selection is based on

minimising the mean and standard deviation between the data sets. However, this

approach does not provide guidelines on what ratios of the data should be used for

each subset (Shahin 2003).

The Kohonen neural network has also been used for selecting data sets. The data

subsets selection is performed in two steps:

(i) All the available data are processed by the Kohonen neural network. Data

processing continues until they are stabilised in the discrete two dimensional

top-map according to their similarity. The similar objects are grouped

topologically.

(ii) The top map is divided into several equal sub regions and an equal number

of objects are drawn from each of these regions to from the training set.

The shortcoming of this method is that if there are many similar objects, they tend to

occupy the majority of the space in the map making it difficult to choose

representative subset.

The fuzzy clustering method is also used for the selection of data subsets. Shi (2002)

and Shahin (2003) have used this approach to divide the data into training, testing and

33

validation sets. Although this approach provides better data division than the previous

methods, it is difficult to apply.

In this research, the data are divided according to a method recommended by Shahin,

Maier, and Jaska (2004) and detailed in Chapter 4.

2.4.3 Data Pre-processing

After completion of data division, ANNs models require data pre-processing before

starting the training phase. The pre-processing can vary from simple scaling or range-

compression to complex techniques such as polynomial expansion and Fourier

transformation (Prasad and Beg 2009). Data scaling is necessary step because it

makes all variables receive the same attention from the network during training phase

(Shahin 2003). Scaling of output data is also essential so that the range of the output

data matches the range of the transfer function in the output layer. If the transfer

function at the output layer is sigmoid, the output data is scaled between 0 and 1 and

if the transfer function is tanh, the output data is scaled to between -1 and 1.

As a pre-processing step, data transformation is sometimes preferable because the

output is a function of an explicit nonlinear combination of the input vectors rather

than original ones. Prasad and Beg (2009) used different methods of data

transformation and concluded that without transformation the accuracy of the ANN

output was very poor. However, with logarithmic transformation the accuracy of

ANN improved dramatically. In this study, scaling and transformation was tried

during the development of the GEP model, but has not improved the model

performance. However, in all modelling attempts using ANNs, data inputs were

scaled.

2.4.4 Choosing of model parameters

The success of the modelling process using artificial intelligence techniques depends

significantly on the design of the model structure. In this, the optimal model

parameters are determined to ensure that the best performing model is achieved. In

terms of the GEP technique, the number of chromosomes, chromosome structure,

functional set, fitness function, linking function and rates of genetic operators play

important role during modelling process and choosing suitable rates of these

34

parameters can reduce modelling time and effort and produce a robust solution. When

using the ANNs, the network size, learning rate, momentum term and initial weights

have strong influence on the success of modelling and the robustness of the developed

model.

The ways of determining GEP, and ANN model parameters are described below.

GEP model parameters

• Number of population and chromosome structure

The number of chromosomes greatly influences the performance of the GEP model

and the modelling time. Using a small number of chromosomes may not provide

enough variety of randomly created solutions which are required to solve the given

problem. If the number of competing individuals is small, nonviable ones may get

more opportunity for re-existing. As a result, weak solution is produced and the

evolution process is dragged. In addition, using a size of population less than required

may reduce the influence of the genetic operators, as the number of targeted

chromosomes by genetic operators becomes less. On the other hand, using too many

chromosomes may have a negative effect on the model performance, because too

many individuals compete against each other making it difficult to select between

them. Therefore, it is important to determine the number of chromosomes that is

necessary for problem solution.

No specific way has been recommended to determine the ideal number of

chromosomes, because this depends too much on the details of the application (Poli,

Langdon, and McPhee 2008). However, the easy way is to start with a small number

of chromosomes and gradually increase this number and monitor the fitness of the

output. When fitness starts decreasing, the number of chromosomes that correspond to

the best fitness is selected.

The chromosome structure also has an effect on the fitness of the output. Using

chromosomes that consist of one gene of small head size may not produce solution.

The same thing is applicable if the number of genes and gene head size exceeds the

required values. However, using multi gene chromosomes of sufficient head size can

35

produce a quick and robust solution as this gives more freedom for genetic variations

to take place.

The linking function which links between the genes of the chromosome also plays a

principal role during evolution. The correct choice of the linking function may have

two advantages: producing small size solution and less number of iterations are

required to achieve problem’s solution. Finding the optimal values of gene head size

and number of genes per-chromosome and linking function are more detailed in

Chapter 4.

• Selection set of functions

Inclusion of the required functions among the function set may expedite evolution and

produce the right solution for the studied problem. However, the choice of function

set is not so obvious and obtaining the proper set of mathematical operators may

require lots of effort, particularly for complex problems. In GEP, the suggested way to

determine the functions set is to start run with the basic mathematical operators (+, -,

×,÷) and in successive runs new functions are added until a satisfactory solution is

reached (Ferreira 2002). This procedure is adopted in this study.

• Rates of genetic operators

All evolutionary algorithms are based on the fact that evolution is based on genetic

variations which fundamentally depend on the rates of genetic operators. Using

genetic operators of very low rates will reduce the creation of enough genetic

diversity which is necessary for promoting evolution. On the other hand, high rates of

genetic operators can lead to lethal effects on evolved populations because already

evolved individuals may be targeted again by genetic operators and become unfit.

Therefore, the proper rates of genetic operators need to be determined to produce a

good solution.

Mutation is the most influential genetic operator. As shown in Figure 2.14, the

success rate significantly depends on the mutation rate. When this rate is below 0.01

the possibility of success is 50-60% and this reaches to 90-100% when mutation rate

36

is 0.05; however, the success rate drops dramatically if mutation rate is above than

0.1.

The mutation rate refers to the ratio of the targeted points by mutation to the whole

number of points of population. For example, for 10 chromosomes of size 30, the total

number of points is 300. If the mutation rate is 0.05, 15 randomly selected points

(15/300 = 0.05) will be targeted by mutation. There is no specific way to determine

the mutation rate, but good rule of thumb consists of using a mutation rate equivalent

to two one-point mutations per chromosome may be a good starting point (Ferreira

2002).

The rates of the other genetic operators have different levels of influence on evolving

solutions. Figure 2.14 reveals that the rates of these operators should not exceed 1.0.

Figure 2.14 Genetic operators and their power (Source: Ferreira 2002).

It should be mentioned that the rates of genetic operators, except the mutation rate,

refer to the probability of any of the operators (e.g. inversion, transposition and

recombination) evaluated relative to the number of chromosomes in the population.

Using each of these operators alone may not develop quick solution. However,

combining all of them along with gene recombination will accelerate evolution and

37

bring about a robust solution. To avoid the complexity, the values of mutation rate

and gene recombination can be varied and the rates of the other genetic operators

remain constant during the search for model. This approach is adopted in this work.

• Fitness function

The success of a problem solution greatly depends on the choice of fitness function

which its selection requires a clearly defined goal. For example, in the symbolic

regression or function finding applications the goal is to find expression which, when

applied, the error between the output given by the expression (predicted values) and

the real output (targeted values) is within acceptable level. In this case, a continuous

fitness function measures absolute error or relative error as in Eq. (2.7) can be used.

However, it is important to use a selection range that permits the potential solutions to

evolve. In this study, the mean square error fitness function (MSE) is used and

expressed as:

( )2

1.

1∑

=

−=n

jjjii TP

nE (2.7)

Where:

iE = the mean squared error of an of individual program i

Pi.j = the value returned by the individual program i for fitness case j out of n fitness

cases

Tj = is the target value for fitness case j.

ANN model parameters

• Network size

The network size includes the number of nodes per layer, number of layers in the

network and number of connections. Many researchers believe that the size of the

network has strong influence on the quality of problem solution, the network

complexity and the learning time (Bebis and Georgiopoulos 1994). The size of the

network also has a strong effect on the capability of the network to generalize.

38

Using a small size network can be beneficial because:

(i) It requires less computational time as well as less memory to store the

connection weights.

(ii) It can be implemented in hardware easier and more economically.

(iii) Using small networks may reduce the risk of having network that is able

to memorize rather than been able to generalize.

(iv) Bigger networks exhibit poor generalization if they are trained with limited

training data.

However, using smaller network may restrict the number of free parameters in the

network. As a result, the error surface of a smaller network will include more local

minima. Thus, despite the capability of the smaller network to generalize better, lots

of efforts is required to train them properly (Bebis and Georgiopoulos 1994).

Therefore, it is necessary to determine the network size that is appropriate for the

solution of the given problem.

In the literature, there is no general agreement on a specific method to be followed to

determine the optimum size of neural network. However, the results of most

theoretical studies concerning the number of layers show that a network with one

hidden layer is sufficient for approximation of any nonlinear function (Cybenko

1989). Moreover, it was shown that any Boolean function can be approximated with

the use of one hidden layer and any continuous function can be approximated with

arbitrary accuracy which is determined by the number of nodes in the hidden layer.

Hornik et al. (1989) have determined that a single hidden layer feed forward network

with arbitrary sigmoid hidden layer activation functions can approximate any arbitrary

mapping from one finite dimensional space to another; provide sufficiently many

hidden units are available. Accordingly, a one hidden layer network has been tried in

this study.

There are number of ways that can be followed to determine the number of hidden

nodes. Rule of thumb suggests that the number of hidden nodes be approximately

twice the number of input nodes for small number inputs (five inputs or less). The

ratio of the hidden layer nodes to the inputs decreases with increasing inputs (Priddy

and Keller 2005).

39

Pruning is another way of finding the number of hidden nodes. With these methods,

the size of the network starts large and reduces gradually in order to improve the

generalization capability of the network. The aim of using pruning approaches is to

encourage the learning algorithm to find solutions which use a minimum number of

connection weights. The pruning can be based on modifying the error function or

based on sensitivity measures. “Skeletonization” is another approach for pruning

proposed by Mozer and Smolensky (1989) as more heuristic. In this approach, the

relevance of the connection is computed according to information about the shape of

surface error near the minimum to which the network has currently settled. This is

performed using the partial derivative of the error with respect to the connection to be

removed. Connections with relevance below the certain threshold are then removed.

The key issue in the implementation of these techniques is finding a way to measure

how sensitive the solution is to the removal of a connection or a node. Moreover,

these approaches are extremely time consuming, especially when large network is

considered.

The constructive method is used to determine the number of hidden nodes. In this

approach the initial structure of the network includes a minimal number of hidden

nodes. Then new nodes are added during training until the optimum structure is

obtained. The problem associated with this approach is that the newly added nodes are

given arbitrary weights which are likely disturbing the approximate solution already

found.

Combining the pruning and the constructive approaches would overcome the setbacks

of each of them. This can be done by first letting the network grow by training until

the reasonable accuracy is found. Then the network structure is modified by pruning

until the optimum structure is obtained (Le Cun et al. 1990e). However, this approach

is difficult to implement and time consuming.

Genetic algorithms can also be used to determine the optimal size of the network. The

proposed structures are encoded in programs that are subjected to the evolution

process. During evolution, the programs compete against each other on the fitness

base. The programs of high fitness will have more chance to survive and be reselected

for further modifications. The highest fitness program is selected as the optimum

40

structure of the ANN. The key issue in using GA to find the optimum ANN structure

is how the architecture should be translated into a proper representation to be utilized

by the GA and how much information should be encoded into this representation

(Bebis and Georgiopoulos 1994).

An approach that relates the number of hidden nodes to the number of training

samples is another way of finding the optimum number of hidden nodes. Masters

(1993) indicated that using too many examples will prevent the network from learning

unique characteristics of the training set. Therefore, he suggested the minimum ratio

of the number of training samples to the number of connection weights to be 2. Amari

et al. (1997) showed that over-fitting is avoided if the ratio is 3 or more. Other

researchers such as Hush and Horne (1993) suggest the ratio to be 10.

Another way of determining the number of hidden nodes is the use of validation error.

In this way the network is trained with a varying number of hidden neurons and the

output error is observed as a function of the number of hidden neurons. The optimum

number of hidden nodes is the number of hidden nodes that correspond to the lowest

error in both of training and validation sets. The advantage of this approach is that the

over-fitting can be recognised easily and it brings reliable results (Priddy and Keller

2005). The use of this approach in geotechnical literature is common. It has, therefore,

been adopted in this research.

• Initial conditions

In ANN, the choice of initial weights has a significant effect on the modelling process

outcome. Depending on what values are given to the initial weights, the search for a

solution can be trapped in local minima or it can reach minimum global error.

Therefore, the initial weights need to be selected in a way that maintains a search

proceeding towards global minima. The values of the initial weights must not be too

large in order to avoid the neuron saturation, which results from the derivative of the

sigmoid function at neuron being too low. The weights also need not to be too samll

so as to avoid extremely slow learning, which results from very small net input into a

hidden or output unit (Fausett 1994).

41

The common way of weight initialization is to create values ranging between -1 and

+1 or -0.5 and +0.5 distributed randomly on connections between neurons. This way

is followed in this study. The connection weights of all trained networks were selected

in a range between -0.5 and +0.5.

The way in which the connection weights are updated in the network also affects the

performance of the network. During training, the connection weights of the network

are updated using either the online or per-epoch approach. The online approach

involves updating connection weights after presenting each training case to the

network. In the per-epoch approach, the connection weights are updated only after

presenting all training samples to the network. Although the two approaches are in

wide use, each of them has disadvantages. The shortcoming of the online approach is

that the network may just learn to generate an output for the current pattern, without

actually learning anything about the entire training set (Mehrotra, Mohan, and Ranka

1997). However, this can be overcome with the use of a momentum term which will

be explained later. The main limitation of the per-epoch approach is that the non-

convergence can occur if data is noisy. In this work the two approaches are tried and

the online using momentum was found to give better results.

• learning rate

The learning rate (η) controls the weight adjustment and the speed of weights

changing between successive training cycles. Using a high value of η may lead to

drastic change in the weight vector, w, form one cycle to another. Consequently, the

optimal w’s may be bypassed. On the other hand, using a low value of η may direct

the search path towards global minimum but with very slow convergence.

The value of η is commonly found using the trial and error approach. In each training

trial, the η is set to a new constant value. Training cycles continue until the lowest

global error is reached. In the literature, various ranges of η values were suggested

after being found successful in training of different networks. In general, the value of

learning rate depends on the type of the application as η range between 0.1-0.9 is used

in many applications (Mehrotra, Mohan, and Ranka 1997). Learning rate range of

0.05-0.6 was found successful in several geotechnical studies (e.g. Ellis et al. 1995;

Basheer 2001; Shahin 2010). This range (0.05-0.6) is adopted in this work.

42

The learning rate can be constant or adaptive. The constant η means that one learning

rate is employed for all weights during the whole learning process. On the other hand,

the adaptive learning rate means η is varying during the training phase. When the

optimal solution is far, the algorithm runs with high learning pace; however, the

algorithm runs with small pace near the optimal solution, so as to achieve low level of

mis-adjustment (Mandic and Chambers 2000). The advantage of this is that the

performance of the steepest descent algorithm can be improved, if the learning rate is

changing during the training process (Amini 2008). Many researchers (e.g. Battiti

1989; Chan and Fallside 1987; Vogl et al. 1988) have proposed different adjustable

learning rate algorithms. The two learning rates (constant and adaptive) were tried in

this study but the constant was found to give better results.

• Momentum term

This term means that the current gradient and weight change in the previous step

contribute to the modifications of the weight vector at the current time step. The

prime advantage of this arises when some training data are very different from the

majority of the data; in the case that abnormal training patterns exist among the

training data set, introducing the momentum term with use of a small learning rate

will avoid major disruption of the direction of the learning and maintain training at a

fairly rapid pace (Fausett 1994).

The momentum term can be set constant throughout the training phase or it can be set

to dynamically vary with training epochs. Different values of the constant momentum

term ranging between 0 and 1 are suggested in the literature. If the values are close to

0, this implies that the past history has an insignificant effect on the weight change.

On the other hand, if the values are close to 1 this implies the weight change depends

chiefly on the past history (Mehrotra, Mohan, and Ranka 1997). In this study the

constant momentum term is tried and found successful in giving good results.

2.4.5 Learning

With the use of artificial intelligence, learning can be performed in two ways. One

way is the unsupervised training, or self-organisation, in which an output unit is

trained to respond to clusters of pattern within the input. In this paradigm, the system

is supposed to discover statistically salient features of the input population. There is

43

no a priori set of categories into which the patterns are to be classified; rather, the

system must develop its own representation of the input stimuli.

The other way is via supervised learning. As with the GEP, the supervised learning

takes place when a set of input data is presented to the program to produce the desired

output. The data set includes a training set for model calibration and an independent

validation set to test the performance of the model in the real world. Each data set

consists of independent input variables (representing the terminals in the program)

and dependent output (representing the targeted values, i.e. fitness cases). After

completing the program setting which will be detailed in Chapter 4, the search for

solution begins with the creation of random individuals (chromosomes) using the

available set of functions and the terminals set. The individuals are expressed and

their error is determined by comparing the predicted and targeted output values. The

error is calculated using a suitable fitness function. For symbolic regression problems

(function finding), the mean squared error (MSE) as in Eq. 2.7 can be used. Then, the

individuals are ranked according to their fitness to pass through a selection process.

The selection is performed using one of the early mentioned methods. The selected

individuals are processed to the next step at which randomly selected ones are

subjected to genetic variations performed by genetic operators and recombination.

Subsequently, new offspring of individuals will appear. The new generation is

expressed again and this process iterates until the error reaches an acceptable level.

The learning is considered complete when the evolved solution meets the stopping

criteria.

In ANNs, learning is a process of weight modification that aims to configure a neural

network such that the application of a set of input produces the desired set of output.

In the supervised training, the ANN is fed with teaching patterns, a historical set of

model input and the corresponding output, and letting it change its weights according

to some learning rule. In this context of training, the network varies each weight in a

way that reduces the error between the targeted output and the network output. For

instance, if increasing a particular weight causes a larger error, then the weight is

decreased as the network is trained to perform better. In most networks, usually the

amount of change in weight is made very small in order to ensure the network does

not stray too far from its partially evolved state, and so that the network withstands

44

some mistakes made by the teacher, feedback, or performance evolution mechanism

(Mehrotra, Mohan, and Ranka 1997).

The networks use different learning techniques, the most common being back-

propagation. In this technique, the output values are compared with desired real

values to compute the global error which is determined by using a predefined error

function. The mean squared error (MSE) function is the most commonly used

function, for the simplicity of computing its derivative in the subsequent calculations.

Moreover, this function gives more attention to large errors and it lies close to the

heart of the normal distribution; if the error can be assumed to be normally

distributed, minimising the MSE is optimal (Master 1993). The amount of error

depends on several factors including initial weight, learning rate, momentum, number

of hidden layers and network structure. The most influential factor is the initial weight

therefore Rumelhart et al. (1986) proposed the back propagation algorithm to

minimise the error with respect to the initial weight. The weight adjustment starts with

the weights between the last hidden layer and the output layer. Then the weights

between the last hidden layer and the hidden layer before are adjusted etc.

To adjust weights properly, a general method is used for non-linear optimization that

is called gradient descent. For this, the derivative of the error function, E, with respect

to the network weights is calculated, and the weights are then changed such that the

error decreases. For this reason, back-propagation can only be applied on networks

with differentiable activation functions. The error at the node k, in Figure 2.15 can be

defined as the difference between the targeted output dk and the ANN output yk.

neuron

δ1 w1j wj1 δj ±δk kd

wji wkj ky

wjn wmj δm

k j i

n

1 1

m

Figure 2.15 Neuron j in a hidden layer.

45

kkk yd −=δ (2.8)

Where:

kδ = the global error

dk = targeted output; and

yk = predicted output

The mean square error is defined as the mean square value of the sum of squared

errors (Haykin 1994) and computed as follows:

∑=k

keE 2

2

1 (2.9)

Where: E = the global error function

Applying the gradient decent rule will lead to global error minimization as follow:

kj

kj w

Ew

∂∂−=∆ η (2.10)

Where:

kjw∆ = weight increment from node j to node k; and

η = learning rate which defines the step along the surface error.

Using delta rule Equation 2.10 can be rewritten as follows:

jkkj xw ηδ=∆ (2.11)

Where:

xj = input from node j, j = 0,1, …, n;

kδ = error value between the predicted and targeted output for node k.

Applying the delta rule at the output node, kδ can be calculated as in Eq. 2.12.

( ) kkkk Syd Φ′−=δ (2.12)

Where:

Φ′ = the derivative of the activation functionΦ with respect to the weight sum, S, at

node k.

46

Using the generalized rule of Rumelhart et al. (1986), the error value of hidden node j

is calculated in Eq. 2.13 and displayed in Figure 2.15.

( )j

m

mjmj Sw Φ′

= ∑1

δδ (2.13)

The weights are then adjusted as follows:

jijiji www ∆+=′ (2.14)

Where:

jiw′ = the value of new weight (after adjustment)

jiw = the value of weight between node j and node i before adjustment.

After repeating this process for a sufficiently large number of training cycles, the

network will usually converge and the error becomes small. In this case, it can be said

that the network has learned a certain target function.

2.4.6 Model performance measurements

After completing the learning phase, the ability of the developed model to predict is

evaluated through the model performance measurements. This will be detailed in

Chapter 4.

2.5 SHORTCOMINGS OF ARTIFICIAL INTELLIGENCE ALGORITHMS

1. Artificial intelligence techniques are data driven, so their accuracy and

robustness greatly depend on the accuracy of the given data. Moreover, these

techniques perform well in interpolation. However, they can not provide good

prediction beyond the range of the training data.

2. Artificial intelligence is a compute intensive process requiring a large amount

of machine time. The estimated machine time increases with the increasing

complexity of the problem.

3. Artificial intelligence models use a large number of model parameters, so

there is a high probability of model over-fitting take place.

4. Artificial intelligence does not guarantee an optimal solution in all runs

because they are a stochastic process that depends highly on the initial control

47

parameters setting. Therefore, several runs should be carried out to ensure that

the system has not fallen into local optima.

5. The size of the problem solution becomes larger with an increase in fitness as

in the case of GEP and with the increase in model parameters (e.g. number of

hidden layers) as in the case of ANNs. This means that although the model is

accurate, it is impractical.

6. With the use of artificial intelligence, for one problem, several answers that

are different but perform equally well can be determined. This can make the

selection of a single solution especially difficult when searching for a general

solution to the problem under consideration.

7. Artificial neural networks tend to be ‘black boxes’ as the relationship between

input and output variables are not developed by engineering judgement; the

problem solution by ANNs is represented as a set of weight matrices.

48

CHAPTER THREE

PILE FOUNDATIONS: CLASSIFICATION, BEARING

CAPACITY AND LOAD-SETTLEMENT BEHVIOUR

3.1 INTRODUCTION

Piles are deep foundations elements with the function of transferring the load that can

not be adequately supported at shallow depths to a depth where sufficient support is

available.

The Geotechnical Engineer may recommend the use of deep foundations for many

reasons, some of which are:

1. The top soil is soft, loose, expansive or subjected to erosion.

2. The foundation has to carry lateral or uplift loads which shallow foundations

can not carry.

3. Construction of shallow foundation is difficult due to site constraints such as

property lines.

4. When scour occurrence is probable.

5. Deep excavations next to the foundation are conducted in the future.

Bearing capacity and settlement are considered to be principal factors in the

design of pile foundations. The pile design must assure that the soil supporting the

pile is capable of carrying the pile ultimate load and the pile does not settle

beyond the permissible limits.

The ambiguity associated with the pile-soil interaction and the lack of a certain

interpretation of soil behaviour in pile vicinity has led many researchers to attempt

different techniques to model the pile behaviour. As a result, a large number of

theoretical and empirical methods have been proposed to predict the capacity and

the load-settlement behaviour of pile foundations.

49

In this chapter, the following points are presented:

• Pile classification and construction methods are briefly described.

• The design of pile foundation is discussed. Two important design

requirements including pile axial capacity and pile load-settlement behaviour

are considered.

• Methods for predicting pile capacity are briefly reviewed. The methods that

are relevant to this study are detailed.

• Three of load transfer procedures for constructing pile load-settlement

behaviour are discussed.

3.2 CLASSIFICATION OF PILE FOUNDATIONS

Pile foundations are classified based on material, load transfer, loading mode, size of

diameter and the installation method. Based on the material they are made of, piles are

classified e.g. timber, steel, concrete and polymer. The timber piles usually have

varying diameters and lengths range from 150 to 400 mm and 6 to 20 m, respectively.

The steel piles are fabricated in different shapes which are mostly pipe or H shapes.

The range of the pipe pile diameter and wall thickness is 50-4000 mm and 4-150 mm,

respectively. The range of H pile cross section area is 6562-21625 mm2. The concrete

piles are either prefabricated or cast-in-place. The precast piles can have square,

circular, hexagonal, and octagonal shape. The range of the precast pile diameter and

length is 250-450 mm and 12-25 m, respectively. The cast-in-place piles are installed

by digging a hole in the soil and then filling it with concrete. The polymer piles are a

rare type of piles which are usually tubular filled with concrete.

Based on load transfer, piles are classified into three categories. The bearing piles,

which are shown in Figure 3.1a, provide their load carrying capacity from the tip. The

pile tip situated in a strong stratum, while the shaft is surrounded by weak soil. The

second category is friction piles which develop their carrying capacity by friction with

surrounding soil, whereas the tip contribution is minor, Figure 3.1b. The third

category is the piles that their load carrying capacity results from both of point

resistance and skin friction, Figure 3.1c.

50

Strong soil

Strong soil

Weak soil

Weak soil Strong

soil

(a) (c) (b)

Qu Qu Qu

Rs Rs Rs

Rt Rt Rt

stuRRQ +=

suRQ ≈

tuRQ ≈

L L L

Figure 3.1 Pile categories based on load transfer.

Piles are classified based on loading mode into axially loaded piles which can be

subjected to axial compression or tension loads, laterally loaded piles which are

subjected to inclined loads and moment piles which are subjected to moment.

Based on diameter size, piles can also be categorised into small, large diameter piles

and mini-piles. Small diameter piles may have diameter equal to or less than 600 mm

whereas large diameter piles may have diameter larger than 600 mm. The mini-piles

usually have diameter less than 250 mm (Ng, Simons, and Menzies 2004).

Depending on the installation method, piles are classified into two groups: non-

displacement (bored) and displacement (driven) piles. The two insulation procedures

are defined as follows:

3.2.1 Non-displacement piles

Non-displacement piles are deep foundations that are installed after drilling a void in

the ground and then filling it with concrete. In Britain, this kind of foundations is

known as bored piles, whereas in the United States some refer to them as drilled piers

or drilled caissons.

51

Three excavation methods are generally used for constructing drilled shafts including

dry, wet and temporary casing. The choice between these methods depends on the

nature of the ground. Dry method usually used when excavations are carried out

above the water table on soils that exhibit cohesive nature such as stiff clay and

residual soils. The wet method is appropriate when excavations are curried out for

caving soils like sandy soils below the water table. The casing method is used when

dry method of excavation may result in unstable sidewalls for the excavation. This

method is useful when a layer of caving soil is underlain self supporting soil layer of

low permeability (Alsamman 1995). In this study, this type of piles will be referred to

as bored piles.

3.2.2 Displacement piles

The displacement piles are inserted into the soil without removing any soil prior to

insertion and the pile is commonly installed into the soil by jacking, vibratory driving

and driving. Jacking and vibratory driving are routinely used to drive sheet piles and

less frequently used to install relatively small steel H-piles. Driving piles by blows

into the ground is the most common method of installing this type piles. Piles

installed in this way are known as driven piles (Salgado 2006). In this study, this type

of piles will be referred to as driven piles.

3.3 DESIGN OF PILE FOUNDATIONS

In geotechnical literature, no definite procedure has been agreed for the design of pile

foundation, but generally pile design must satisfy safety, serviceability and economic

requirements. The design must assure:

• The pile must be strong enough to be installed into the ground and can carry

the design load during its service life.

• The pile settlement must not exceed the allowable limits.

• The supporting soil does not fail when the pile delivers its ultimate load.

The strength of the pile is verified during the structural design stage. At this stage pile

material, shape, dimensions and installation method are decided. Usually codes of

52

practice are referred to ensure the compliance of the design with standards. Pile

structural failure rarely occurs except in very long piles.

In order to satisfy serviceability requirements, the design must assure that the pile

settlement is within acceptable limits. This will be discussed later.

To avoid the failure in the soil supporting the pile, the load that the soil is capable to

carry must be determined. This load is defined as the bearing capacity of pile

foundation. In the geotechnical literature, numerous empirical and analytical methods

have been proposed to estimate the bearing capacity of pile foundations. A brief

description of these methods is given in the following section and the methods that are

relevant to this study are also detailed.

3.3.1 Pile capacity from static methods

The pile capacity calculated by static methods is based on soil strength determined

from laboratory or field measurements. The total bearing capacity is the sum of the tip

bearing resistance,tr , and side resistance along pile shaft, sr . The term “static” refers

to the use of static soil properties to determine the bearing capacity.

Unit tip resistance

The general expression for estimating unit tip resistance is written as follow:

γγγ DNLNcNr qct 2

1++= (3.1)

Where:

tr = unit tip resistance in kPa

c = soil cohesion in kPa

cN , qN , γN = non-dimensional bearing capacity factors

γ = unit weight of soil in kN/m3

L = embedded length of pile in m

D = diameter of pile base in m

In cohesive soil, the unit tip resistance is calculated considering the soil is in

undrained condition, which occurs when the rate of loading exceeds the rate of pore

53

water pressure dissipation. In most load tests, the rate of loading is faster than the rate

of pore water pressure dissipation, therefore the end bearing resistance is determined

under undrained condition, to account for the reduction in the capacity caused by pore

water pressure. In this case, the internal friction angle φ = 0 corresponding to qN = 1.

Hence, the second term of Equation 3.1 will become small. The third term of the

equation is also small. The two terms can be neglected and the unit tip resistance may

become:

ct cNr = (3.2)

In cohesionless soil, the pore water pressure dissipates rapidly due to the soil high

permeability. Consequently, the tip bearing resistance is computed under the drained

condition. As cohesionless soil does not exhibit any cohesion (i.e. c = 0), the first term

of the Equation (3.1) can be removed. The equation can be further simplified by

neglecting the third term, which is insignificant, and then the unit tip resistance

becomes:

qt LNr γ= (3.3)

Figure 3.2 Proposed functions of q

N vs φ (Source: Coduto 1994).

54

The shortcoming of the above procedure is that wide range values of q

N

corresponding to the same soil friction angle,φ , are suggested, as shown in Figure

3.2. This creates doubt about the reliability of these values and leaves unanswered

question on which of these values is the most accurate. Moreover, the values of φ can

be uncertain as they are based on laboratory test results of samples which usually

suffer a disruption as a result of sampling and transportation particularly in the case of

cohesionless soil.

Unit shaft resistance

The two common approaches for estimating unit shaft resistance are the α and the β

method. Theα method is widely used for piles installed in cohesive soil. As proposed

by Tomlinson (1971), the unit shaft resistance, rs, can be estimated as follows:

δσα tanKcrs

+= (3.4)

Where:

α = coefficient given in Figure 3.3 or Table 3.1.

c = average cohesion or undrained shear strength, u

S for each soil layer in kPa

σ = effective vertical stress at the soil layer of interest in kPa

K = coefficient of lateral earth pressure

δ = effective friction angle between soil and pile material ranging between 0 and 35.

The American Petroleum Institute (API 1984) also suggests the α method for

normally consolidated clay using the factors presented in Figure 3.3.

200

2

1.5

50 100 150

1.00

0.5

0

Adh

esio

n fa

cto

r, α

API

3

1

Undrained shear strength (uc ) kPa

3.3 Soil undrained strength and α (Source: Tomlinson 1971; API 1984).

55

The values of parameter α are uncertain because they depend on several factors

including undrained shear strength, embedment depth, effective overburden stress,

over consolidation ratio and L/D. The function between α and each of these factors is

not clearly identified. Consequently, the estimation given by this method may involve

wide range of error.

Table 3.1 Values of adhesion factor for piles driven into stiff to very stiff cohesive soils for design (Source: Tomlinson, 1971). Case Soil condition Penetration ratio٭ Adhesion factor, α

1 Sand or sandy gravel overlaying stiff to very stiff cohesive soil

<20

1.25

2 Soft clay or silts overlaying stiff to very stiff cohesive soil

8<PR≤ 20 0.4

3 Stiff to very stiff soils without overlaying strata

8<PR≤ 20 0.4

Penetration ration, PR = (depth of penetration into cohesive soil) / (diameter of pile) ٭

The β method is used to predict the unit shaft resistance of piles installed in

cohesionless soil as well as cohesive soil. According to Vesic (1967; 1969) the pile

soil interaction is governed by effective stress so that the unit side resistance can be

estimated from:

δσ tanvos

Kr = (3.5)

Where:

K = coefficient of earth pressure on the shaft

voσ = effective earth pressure on the shaft in kPa

δ = soil-shaft friction angle

There are difficulties in determining K and δ values, because they depend on several

factors such as pile type, construction method and friction angle. Burland (1973) tried

to overcome the difficulties by introducing the factor β which combines K andδ .

vosr σβ= (3.6)

Where:

β = skin friction factor, provided in Table 3.2

56

The shortcoming of the β method is that it does not pay attention to the influence of

factors like soil compressibility, strain softening, and nonlinearity in the failure

envelope. In fact these factors have significant influence on the development of unit

shaft resistance (Eslami 1996).

Table 3.2 Ranges of β coefficient (Source: Fellenius 1995) No. Soil type φ - angle β

1 Clay 25 - 30 0.25 - 0.35 2 Silt 28 - 34 0.27 - 0.50 3 sand 32 - 40 0.30 - 0.60 4 gravel 35 - 45 0.35 - 0.80

3.3.2 Pile capacity from pile load test

The pile load test is conducted to measure the actual resistance of soil on which

design can be based reliably and the test usually provides diagram showing the

relationship between applied load and the corresponding settlement. There are various

types of load tests which use different procedures, equipment, instrumentation and

load application methods. Pile load test is considered to be as the most reliable

method to estimate the load capacity of pile foundations (Bowles 1988). There are

several methods for obtaining pile capacity from load test some of which are:

1. The pile capacity is the plunging point from which the settlement increase

excessively with no or minimal increase the corresponding load. The

limitation of this method is that it may become inapplicable, if the settlement

that corresponds to the plunging load is higher than the allowable settlement.

2. The pile capacity is the load that corresponds to settlement equivalent to 10%

of pile diameter. For large diameter piles, this method may have the same

limitation of the previous method.

3. The failure load is the load that gives four times the movement of the pile head

as obtained for 80% of that load. This also called 80% Criterion which was

proposed by Hansen (1963).

4. The failure load is the load the corresponds to the movement which exceeds

the elastic compression of the pile by a value of 4 mm plus a factor equal to

pile diameter divided by 120. This is known as Davission (1972) Criterion.

More methods can be found in Ng, Simons, and Menzies (2004).

57

Undertaking pile load test is not always a desired option due to:

• Pile load tests are expensive, so they are not recommended for small projects.

• Site restrictions prevent from conducting load test, such as off shore piles.

• Pile diameter is too large, so it may be difficult to have equipment that can

load the pile up to failure.

• Unavailability of the technical skills to carry out the load test.

• Sufficient knowledge and experience is available from previous projects

executed adjacent to the site.

3.3.3 Pile capacity from dynamic methods

Dynamic methods determine the static load capacity based on the effort required to

drive the pile. They are categorised into theoretical, empirical and a combination of

the two. Dynamic Formulas and Wave Equation are the common methods for

estimating pile capacity on the basis of dynamic analysis. The Dynamic Formulas

evaluate the total resistance of the pile based on the work done by the pile during

penetration. Several researchers (e.g. Cummings 1940; Davisson 1979; Terzaghi

1942) have argued that the dynamic formulas are inaccurate; and statistical evaluation

of the methods, carried out by Hannigan et al. (1996), has shown a wide scatter when

compared with static load test results, therefore the Dynamic Formulas are not

suggested for practical use.

The main shortcoming of the Dynamic Formulas is that they involve uncertainties, as

the energy losses in a real pile driving situation can not be accounted for accurately

(Coduto 1994) and the capacity can not be estimated until the pile is driven (Eslami

1996).

The Wave Equation is another approach to estimate pile capacity using dynamic

analysis. Smith (1960) proposed a numerical solution applying the wave equation

theory to pile design. In this solution, the passage of stress wave down the pile would

be represented through the idealization of the hammer-pile-soil system as in Figure

3.4. The pile and driving system are represented by a series of rigid masses connected

by springs. Shaft and tip resistance are represented by bi-linear springs and the

increased resistance of the soil is represented by a series of dashpots. According to

58

Smith, the instantaneous soil resistance force, R, acting on adjacent rigid mass can be

computed as follows:

( )JVRRs

+= 1 (3.7)

Where:

Rs = static soil resistance

J = damping constant

V = instantaneous velocity of the adjacent mass

Figure 3.4 Discrete elements of the pile soil system (Sourcr: Smith 1960).

The main limitations of the Wave Equation approach are:

• The Wave Equation analysis significantly depends on the input assumptions

which include hammer performance, hammer and pile cushion parameters, the

soil resistance distribution, the quake and damping characteristics. If input

59

data are not real, the results are only useful for qualitative assessment, not for

quantitative (Fellenius 1983; Eslami 1996).

• The method encounters two difficulties: (1) The total resistance is time

dependent and different variations in the method produce different results; (2)

The dimensionless damping coefficient have questionable correlation to soil

type and need to be calibrated for the specific pile, soil and site condition (Ng,

Simons, and Menzies 2004; Paikowsky 1982; Thompson and Glob 1988).

3.3.4 Pile capacity from in-situ tests

Cone penetration test (CPT) and standard penetration test (SPT) are mainly used for

providing information about penetration resistance of soil, shear strength and pore

water pressure. The data obtained from CPT or SPT are used to predict pile capacity

in two methods: (1) The CPT or SPT data are correlated with conventional strength

parameters of soil, such as φ or Su, and then static methods used to predict the

capacity, (2) the tests’ results are directly correlated with the end bearing and side

resistance of pile.

The SPT has been used for pile design for over than 50 years. It has been used

extensively in North and South America, UK and Japan (Coduto 1994). However, its

major weakness is that it is affected by many factors like operator, drilling, hammer

efficiency and rate of blows. As a result, high variability and uncertainty associate

with SPT data. On the other hand, the CPT is simple, fast, provides direct readings of

soil resistance and allows for considerable data to be obtained in short time. The data

provided by the CPT can be interpreted empirically or analytically, so it has become

preferable test for pile design. Hence, this study will focus on the methods that use the

CPT data to predict pile capacity.

Brief historical background of the Cone penetration test

The CPT is an in-situ testing method involves pushing instrumented pentrometer into

the ground at a constant rate, normally 2 centimetres per second, and recording

multiple measurements continuously (Lunne, Robertson, and Powell 1997). There are

two types of cones available: the mechanical cone and the electrical cone.

60

The mechanical cone was initially invented by P. Barenteson, an engineer at the

Department of Public Work, in Holland, in 1932. Since then several researchers

(Vermeiden 1948; Begemann 1953; Sanglerat 1972) have introduced developments

on the initial design of the cone to improve its accuracy and increase number of

measurements (i.e. in addition to the cone resistance, sleeve friction can be measured

as well).

Figure 3.5 Begemann cone pentrometer (Source: Sanglerat 1972).

The late configuration is the Begemann’s cone as shown in Figure 3.5, which

composes of inner rods moves freely inside steel outer rods. The cone tip is connected

to the inner rode. The cone operates in this way: the cone is advanced ahead of the

outer rod to measure the cone resistance; then the cone and outer rods are advanced

61

together to measure the total load. The sleeve friction is the difference between the

total load and cone resistance.

Because of their low cost, simplicity and robustness, the mechanical cones are still

used widely. However, the accuracy of the data depends significantly on the

experience of the operator (Lunne, Robertson, and Powell 1997). In addition,

mechanical cones are slow and less effective in soft soils.

The electrical cone was developed in 1948 by the Delft Soil Mechanic Laboratory.

This version of cone offered successive measurements of tip resistance with depth

plus direct strip chart plotting off the sounding record (Vlasblom 1985). Electrical

cone with tip resistance and sleeve friction readings became available in 1960

(Roberston 2001). In this kind of cone pentrometer, there is no relative movement

between the cone and the friction sleeve. The cone pentrometer contains of strain gage

load cells mounted on the cone and friction sleeve to monitor the cone resistance and

sleeve friction during test. The signals are transmitted via cables passing through the

centre of the hollow push rods to a field computer at the surface for automated data

acquisition. The electric cone may also contain inclinometer electronics to measure

the deviation from the vertical.

The electric cone that was developed by Fugro in co-operation with the Dutch State

Research Institute (TNO) is shown in Figure 3.6. The shape and dimensions of this

cone represent the base on which the International Reference Test Procedures are

formed (Lunne, Robertson, and Powell 1997).

Figure 3.6 Electrical friction cone pentrometer (Source: DeRuiter 1971).

62

The advantages of the electrical cone relative to the mechanical cone are:

• The problems associated with poor load readings acquired by the mechanical

cone systems which results from frictional force build-ups between the inner

and the outer rods caused by rusting and bending do not exist in the electrical

cone because there is no relative movement between the cone and the friction

sleeve.

• The electrical CPTs are faster than the mechanical CPTs, because they are

conducted at a constant rate of push rather than stepped increments.

Piezometer elements are incorporated to the ordinary electric cone so that,

during the same sounding, the cone can be used to provide three independent

readings including tip resistance, sleeve friction and pore water pressure

(Tumay and Fakhroo 1981).

• Additional features have been added to the electrical cone to enable it to give

additional measurements including temperature, electrodes, geophones, stress

cells, full displacement pressure meter, vibrator, radio-isotope detectors for

density and water content determination, microphones for monitoring

acoustical sounds, and dielectric electric permittivity measurements

(Jamiolkowski et al. 1985).

Advantages of CPT

The cone penetration test has been used in Europe for many years and has also been

gaining more popularity in North America and other parts of the world. The main

advantage of the CPT are summarised in the following points.

• The CPT provides reliable information not subject to operator interpretation

with minimal need for on-site supervision.

• It can be used to assess engineering properties of the soil through the use of

empirical correlations. Those correlations are generally more accurate when

intended for use in chohesionless soil (Coduto 1994).

• The test provides continuous measurements of density and strength with

immediate charting of results.

• The CPT is relatively cheaper than alternative borehole drilling, sampling and

in-situ testing.

• Stratification depths can be measured accurately.

63

• The CPT enables recording thin layers which often missed in borehole

investigations.

Methods for estimating pile bearing capacity from CPT data

Because of the above mentioned advantages and the similarities between the CPT and

pile, estimation of pile capacity from CPT has been one of the earliest applications of

cone penetrometer (Eslami 1996).

There are mainly two methods (indirect methods and direct methods) used to correlate

pile capacity and CPT results. The methods are explained below.

The indirect methods

Based on these methods, the pile capacity is predicted from cone results as follows:

Firstly, the cone results are correlated with fundamental soil properties such as soil

friction angle, φ , relative density, Dr, and earth pressure coefficient, K0. Secondly, the

static methods described in Section 3.2 are used to determine the unit tip and shaft

resistances of pile. Several researchers (e.g. Mesri 1991; Schmertmann 1978; Masood

1988; Meigh 1987; Baldi et al. 1982) have proposed methods based on indirect

correlations of CPT results to predict pile capacity.

Currently, the indirect methods are undesirable because of their specific applicability

and the lack of accuracy. The methods that are applied in sand require certain criteria

in order to be applicable. The sand must be clean normally consolidated and

incompressible. Otherwise, the correlation between cone tip resistance, qc, and sand

relative density, Dr, may overestimate the Dr, if the sand is over-consolidated. In

addition, the correlation between qc and soil friction angle, φ , would provide only

lower limits for φ (Meigh 1987). The methods that are applied in clay lack the

accuracy because they are derived from the correlation of undrained shear strength

with cone results and cone factor Nk. The suggested values for Nk are approximate or

unreliable particularly in soft clay (Mesri 1991). There is also uncertainty in the

indirect methods resulting from the intermediate steps and correlations. Consequently,

the accuracy of these methods is questionable (Jamiolkowski et al. 1982).

64

Indirect methods are not considered in this study and the focus will be on the direct

methods.

Direct methods

The majority of these methods are initially derived for driven piles and then applied

on bored piles with reduction factors considering the difference between the

installation methods.

The direct methods employ direct correlation between pile tip and side friction

resistances with the CPT results. All of the methods use an average cone resistance qc

near the elevation of the pile tip to estimate the unit tip resistance, r t. The averaging

zone, which is known as the influence zone, is a function of the pile diameter. The

extents of the influence zone represent the failure envelope, and may vary form 0-8 to

1-4 pile diameter, D, above and below the pile tip, respectively. There are several

patterns of failure zone suggested by researchers as illustrated in Figure 3.7.

The unit shaft resistance, rs, is correlated with cone point resistance along pile shaft or

with local side friction of the cone. Currently, several direct methods have been

proposed to predict the pile capacity from CPT data. The widely used methods and

relevant to this study are discussed in the following sections.

Figure 3.7 Assumed failure patterns under pile foundations (Source: Vesic 1976).

65

Schmertmann method

The Schmertmann procedure is based on the work done by Nodingham (1975) who

used 108 load test results on model piles to develop an equation to predict the

capacity of driven piles in sand. Schmertmann proposed the following procedure to

calculate unit tip resistance:

1. qc values are filtered to trace the “minimum-path” as shown in Figure 3.8.

2. 1c

q is determined by computing the average qc value along the line abcd.

Note that the point b is at a depth x below the proposed pile tip and

DxD 47.0 ≤≤ . The x that produces the minimum 1c

q is selected.

3. 2c

q is determined by computing the average qc along the line defgh as shown

in the Figure 3.8.

4. A reduction factor,w , is introduced to account for gravel content and over

consolidation ratio, as given in Table 3.3.

5. The end bearing capacity is computed by applying:

+=

221 cc

t

qqwr (3.8)

Figure 3.8 Dutch method for calculating end bearing from CPT (Source: Schmertmann 1978).

66

Table 3.3 wvalues for use in Equation 3.8 (Source: Deruiter and Beringen 1979) Soil condition w Sand with OCR = 1 1.00 Very gravelly coarse sand; sand with OCR = 2 to 4 0.67 Fine gravel; sand with OCR = 6 to 10 0.50 OCR = Overconsolidation ratio

The unit shaft resistance, rs, is computed by dividing the pile into segments and

assigning appropriate local side friction fs to each segment. The fs of segments are

summed and the total is multiplied by a coefficient to give rs as:

ss Kfr = (3.9)

Where; K is a dimensionless coefficient related with pile shape and material, cone

type and embedment length ratio. K values range between 0.8-2.0 in sand and

between 0.2-1.25 in clay.

If the sleeve friction values are not available, rs can be determined from cone tip

resistance as follows:

cs Cqr = (3.10)

Where; C is a dimensionless coefficient which depends on pile type and ranges from

0.008-0.018. rs must not exceed 120 kPa.

Schmertmann introduced a 25% reduction factor to be applied on Eq. 3.10 when is

used to predict the capacity of bored piles. The method imposes an upper limit on the

unit tip resistance to not exceed 25 MPa in sand and 9.5 MPa in very silty clay.

Remarks:

1- The method does not explain from which ground was derived the 25%

reduction factor applied on bored piles.

2- Imposing an upper limit on qc may result in under-estimate of pile capacity.

3- The failure zone may not extend to 8D above the pile tip particularly in

layered soil when the pile tip is located in weak soil underneath strong soil.

4- Evaluating pile side resistance from cone tip resistance, qc, may not prove

accurate.

5- In sand, the pile unit tip resistance can not be estimated properly, since the

over-consolidation ratio is difficult to obtain (Eslami 1996).

67

Bustamante & Gianeselli method

Bustamante and Gianeselli (1982) proposed a method, which is also known as the

LCPC (Laboratoire Central des Ponts et Chausees), to predict pile capacity from CPT

results. The method was developed based on the analysis of 197 pile load tests with a

variety of pile types and soil condition. Only the measured CPT qc values are used for

the calculation of both of unit tip and shaft resistance. The unit tip resistance is

estimated as follows:

1- qca is determined by averaging qc over the influence zone which extending to

1.5D below and above pile tip.

2- Eliminating qc values higher than 1.3 qca along the length –a to +a, and

eliminating all qc values lower than 0.7 qca along the length –a, which create

the thick curve shown in Figure 3.9.

Figure 3.9 LCPC method to calculate equivalent cone resistance at pile tip (Source: Bustamante and Gianesellie 1982).

3- The equivalent average cone tip resistance, qeq, is determined by averaging the

remaining cone tip resistance (qc) values over the thick curve.

4- The unit tip resistance can be then estimated from Eq. 3.11.

68

eqct

qkr = (3.11)

Where:

kc = the end bearing coefficient, shown in Table 3.4.

The unit shaft resistance rs is determined from:

s

c

s k

qr = (3.12)

Where:

ks = friction coefficient, provided in Table 3.4.

Maximum values of rs, ranging from 15 kPa through 120 kPa, are recommended

based on pile type, soil type, and installation method, see Table 3.4.

Table 3.4 Empirical coefficients for LCPC method (Source: Bustamante & Gianeselli 1982)

Driven Piles Bored Piles Ks Upper limit

of rs (kPa) Ks Upper limit

of rs (kPa)

Nature of soil qc

(MPa) Kc

A B A B A B A B Soft clay and

mud <1 0.5 30 30 15 15 30 30 15 15

Moderately compact clay

1-5 0.45 40 80 35 (80)

35 (80)

40 80 35 (80)

35 (80)

Compact to stiff clay and compact silt

>5 0.55 60 120 35 (80)

35 (80)

60 120 35 (80)

35 (80)

Silt and loose sand

<5 0.5 60 120 35 35 60 150 35 35

Moderately compact sand

gravel

5-12 0.5 100 200 80 (120)

80 100 200 80 35 (80)

Compact to very compact

sand and gravel

>12 0.4 150 200 120 (150)

120 150 300 120 (150)

80 (120)

A: Driven pre-cast piles, prestressed tubular piles, and jacked concrete piles B: Driven metal piles, and jacked metal piles Note: Bracket values for rs apply to carful execution and minimum disturbance of soil due to disturbance. Remarks:

1- The method neglects sleeve friction which would represent an important

component of CPT data and soil properties.

69

2- The extents of the influence zone 1.5D below and above the pile tip may be too

conservative.

3- The method was developed based on local experience.

Alsamman Method

Alsamman (1995) proposed two different models to predict the capacity of drilled

piles: a model for piles embedded in cohesive soil and another model for piles

embedded in cohesionless soil. He developed the models based on data comprising of

95 pile load test and CPT results collected from all over the world. Alsamman has

introduced justifications to the coefficients used by the LCPC method and suggested

the following expressions for estimating pile capacity.

For a pile embedded in cohesive soil, the unit tip resistance, r t, is estimated from:

( )votipct

qr σ−=)(

27.0 (3.13)

Where:

( )tipcq = the average of cone resistance over a zone extending to one pile diameter

below the pile tip

σvo = the total vertical stress at the elevation of the shaft base

The unit shaft resistance rs is estimated from (3.14), which is inferred from the graphs

provided by Alsamman. If the pile is embedded in a layered soil, Equation (3.14) is

applied for each layer and the total unit shaft resistances will be the sum of the unit

shaft resistance of the layers.

( )voshaftcs

qr σ−=)(80

75.1 (3.14)

Where:

( )shaftcq = average of the cone tip resistance along the pile side

σvo = total vertical stress at mid-depth of the soil layer

The total pile tip resistance, t

R , and side resistance, s

R , are calculated from:

( ) ( )bbtt

ALArR ** γ+= (3.15)

70

( )∑=

=n

iiss

SArR1

* (3.16)

Where:

Ab = area of the shaft base

γ = soil unit weight

L = pile embedded length

SA = surface area of the shaft for each sub-layer

n = number of layers.

For piles in cohesionless soil, Alsamman also suggested graphs to be used to estimate

the pile capacity. Equations (3.17-3.23) are inferred from the graphs. The unit tip

resistance is calculated from:

( ))(

15.0tipct

qr = ( )tipcq ≤ 9.5 MPa (3.17)

( )5.9075.044.1)(−+=

tipctqr ( )tipc

q > 9.5 MPa (3.18)

r t must not exceed 2.87 MPa.

The unit side resistance is determined as follows:

in sand and silty sand,

( ))(

015.0shaftcs

qr = ( )shaftcq ≤ 4.75 MPa (3.19)

( )( )79.410*67.1072.0 3 −+= −

shaftcsqr ( )shaftc

q ≥ 4.75 MPa (3.20)

rs must not exceed 95 kPa

in gravelly sand and gravel,

( ))(

02.0shaftcs

qr = ( )shaftcq ≤ 4.75 MPa (3.21)

( )75.4105.2095.0)(

3 −×+= −

shaftcsqr ( )shaftc

q ) ≥ 4.75 MPa (3.22)

rs must not exceed 130 kPa.

The total pile tip resistance is then obtained from:

btt

ArR *= (3.23)

The total side resistance Rs is obtained from 3.16.

71

Remarks:

1- The depth at which cone tip resistance is averaged (one pile diameter blow the

pile tip) may be too conservative.

2- The method neglects sleeve friction values; only the cone point resistance is

employed to estimate pile tip and side resistance.

3- Imposing upper limits on rs and r t may lead to inaccurate estimate of pile

capacity.

4- The method employs total stress calculations to estimate pile behaviour,

however the effective stress governs the pile behaviour in long term

(Fellenous 1996).

DeRuiter and Beringen method

DeRuiter and Beringen (1979) developed a method based on the experience which

they gained from the North Sea offshore construction. The method utilises the same

model obtained by Schmertmann to estimate the unit tip resistance of a pile in sand.

In clay, the method relies on total stress analysis and the determination of undrained

shear strength, Su, to estimate the unit tip resistance as follows:

( )

k

tipc

u N

qS = (3.24)

uct SNr = (3.25)

Where:

kN = the cone factor ranging from 15-20 depending on local experience

( )tipcq = the average cone point resistance computed similar to Schmertmann method.

Nc = 9

The method imposes 15 MPa as an upper limit of the unit tip resistance.

The unit shaft resistance is obtained from Eq.3.26-3.27 using the correlation between

the undrained shear resistance for each soil layer along pile shaft, ( )shaftuS , and the

adhesion factor, α, which is taken equal to 1.0 for normally consolidated clay and 0.5

for over-consolidated clay. An upper limit of 120 kPa is imposed on the unit shaft

resistance.

72

k

shaftc

shaftu N

qS )(

)(= (3.26)

)(

*shaftus

Sr α= (3.27)

Remarks:

1- More than one correlation is applied to determine pile capacity in clay, so the

determined results can be unjustifiable.

2- Imposing limits on the unit tip and shaft resistances may lead to inaccurate

prediction especially in dense sand and very stiff clay.

3- The method is derived from local experience in a particular site which is not

necessarily representing all types of soil.

4- Total stress analysis and undrained shear strength are used to determine the

unit tip and shaft resistances. However, the long term behaviour of the pile is

actually governed by the effective stress rather than the total stress particularly

in cohesive soil.

Eslami and Fellenius method

Eslami and Fellenius (1997) proposed a method to predict pile capacity based on

pizocone results. Unlike the aforementioned methods, the cone tip resistance and

sleeve friction are not filtered. The influence of peaks and troughs is reduced through

the utilization of the geometric mean, which is used to calculate the average cone

point resistance within the influence zone. The method also accounts for the pore

water pressure, as it considers the effective stress as the long term governing factor of

the pile behaviour.

Eslami and Felleniuse recommend the following steps to estimate unit tip resistance:

• Defining the extents of the influence zone in the vicinity of pile tip. When pile

is installed in a homogeneous soil the influence zone extends 4D below and

above the pile tip. The zone extends 4D below to 8D above the pile tip when

pile tip is situated in strong soil layer underneath weak soil layer or 4D below

to 2D above the pile tip when pile is installed through a dense soil into a weak

soil.

73

• Subtracting the pore water pressure u2 from the measured total cone resistance,

qc, to determine effective cone resistance, E

q .

• The pile unit tip resistance is determined from:

Egtt

qCr = (3.28)

Where:

t

C = tip correlation coefficient assumed equal to one

Eg

q = geometric average of the cone point resistance over the influence zone

The unit shaft resistance is determined from the modified effective cone point

resistance as follow:

Ess qCr = (3.29)

Where:

Cs = shaft correlation coefficient given in Table 3.5

qE = cone point resistance after correction for pore pressure

Table 3.5 Shaft correlation coefficient Cs (Source: Eslami 1996). Soil type Cs %

Very soft clay and soft sensitive soil 8

Soft clay 5

Stiff clay, and mixture of clay and silt 2.5

Mixture of silt and sand 1.0

Sand, gravely sand 0.4

Remarks:

1- The geometric mean not always reflects a good representation of qc values. If

qc values are very low for a segment of the pile length and then become much

higher for another segment, the geometric mean provides poor representation.

2- The assumptions of the influence zone may not be applicable if the plie length

to diameter ratio (L/D) is less than 8, as can be found in many cases of drilled

shafts.

74

3- The method does not refer to the construction method. Driven and bored piles

interact with soil differently. Therefore the bearing capacities of the piles can

not be predicted by the same model.

4- The method does not refer to the pile material which has been proved to have

influence on pile capacity.

3.4 SETTLEMENT PREDICTION

Generally, design methods still treat the estimation of pile settlement as a secondary

issue, and concentrate on providing adequate axial capacity from the piles to carry the

structural load (Randolph 1994). However, limiting settlements to an acceptable level

is one of the main reasons for using pile foundations and settlement and differential

settlement are perhaps the most important features in pile design (Fleming 1992).

Pooya Nejad et al. (2009) pointed out that pile design must not only meet strength

criteria but also must meet serviceability requirements which essentially demand a

reliable estimate of pile settlement to be available. Hence, plotting load settlement

relationship is a necessary step for meeting design criteria; the designer can decide the

allowable loads that can be applied and adhere to serviceability requirements.

Plotting the load settlement may have another advantage that is it provides more

insight to the behaviour of pile, as the full picture of the pile behaviour under loading

is simulated. Moreover, it gives the designer a freedom to choose the failure criterion

(he may choose the Hansen 80% Criterion, for instance, or the 10% pile diameter or

whichever criterion he thinks appropriate for design).

The most reliable method for obtaining the load-settlement relationship is to carry out

in-situ pile load test. However, this approach is not always available due to the

aforementioned limitations (see Section 3.3.2). As a result, pile load settlement is

predicted and used for design.

Numerous procedures have been proposed to predict the load settlement behaviour of

single axially loaded pile foundations, and they are mainly categorised into closed

form solutions, numerical solutions and load transfer solutions.

75

The closed form solutions were initially proposed for estimating the behaviour of

single pile embedded in homogenous linear elastic half space (Murff 1975; Satou

1965). These solutions were extended to predict the pile behaviour in layered systems

of Gibson soil profile (Guo 2000). However, the main limitation of these methods is

that the closed form solution models can not accurately model the behaviour of a pile

embedded in an arbitrarily non-homogenous soil profile, which has been found to

have great influence in pile settlement (Guo and Randolph 1997; Pando 2003).

Numerical solutions [e.g. Finite Element Method (FEM); Boundary Element Method

(BEM); Variation Elements (VE)] can also be employed to estimate the load

settlement behaviour of single axially loaded piles. Details of FEM are available in

Zienkiewicz (1971) and the application of the method in geotechnical engineering is

covered in Desai (1977). The BEM is fully detailed in Butterfield and Banerjee (1971)

and the application of VE in piles is available in Rajapakse (1990).

The load-transfer method of analysis (Coyle and Reese 1966) is another approach for

modelling the load settlement behaviour of a single pile. Based on this approach,

several theoretical models (e.g. Kraft, Ray, and Kagawa 1981; Randolph and Wroth

1978; Verbrugge 1986) and empirical models (e.g. API 1993; Coyle and Reese 1966;

Vijayvergiya 1977) have been proposed.

The load-transfer has been widely used for prediction of load-settlement behaviour of

single piles subjected to axial load because of its simplicity and capability

incorporating nonlinear soil behaviour (Zhu and Chang 2002). Therefore, this

approach has been detailed and three methods including Verburgge (1986), Fleming

(1992) and American Petroleum Institute (API) 1993 have been selected for the

purpose of comparison with results of this study. This choice is made because the

Verburgge (1986) is a theoretical model based on CPT data; the Fleming (1992)

model is well known analytical approach; and the API (1993) is well known method

and is based on practical ground. The description of the load-transfer concept and the

three selected methods are discussed in the following section.

76

3.4.1 The load transfer approach

The load-transfer model was primarily proposed by Seed and Rees (1957) to calculate

the local load-displacement relation of piles. Since then, many researchers (e.g. Coyle

and Reese 1966; Randolph and Wroth 1978; Guo and Randolph 1997; Pando 2003;

Zhu and Chang 2002) have involved in the subject and as a result several load-transfer

procedures have been proposed.

The load transfer approach includes modelling the piles as a series of discrete

elements. Each element is connected to the following element by a spring

representing the axial stiffness of the pile and supported from the side by nonlinear

spring representing the resistance of the soil in skin friction (T-Z spring). There is

also a nonlinear spring at the pile base representing the end bearing (Q-Z spring). The

nonlinear soil springs represent the soil reaction versus displacement as shown

schematically in Figure 3.10.

Figure 3.10 Idealized model used in load-transfer analyses (Source: Pando 2003).

The load transfer models are mainly categorised into two groups: the empirical and

the theoretical models. The empirical models are developed based on the

measurements of load and local displacement obtained from load tests of

77

instrumented piles. The models represent the functions that can achieve the best

possible fit with the measured data. Several types of these functions are available in

the literature such as the empirical functions (e.g. Vijayvergiya 1977; API 1993), the

exponential functions (e.g. Kezdi 1975; Liu and Meyerhof 1987; Vaziri and Xie

1990), the polygonal functions (e.g. Zhao 1991; Kodikara and Johnston 1994),

Romberg-Osgood functions (e.g. Abendroth and Greimann 1988; O'Neill and Raines

1991) and hyperbolic function (e.g. Hirayama 1990).

The other approach for constructing the load-settlement relationship of pile is the

theoretical model. In this approach, the soil is divided into two layers. The

deformations in the upper layer (Z) are caused by the pile shaft load (T) whereas the

deformations in the lower layer (Z) are caused by base load (Q). The deformations in

the soil around the pile shaft can be idealized as shearing of concentric cylinders

(Randolph and Wroth 1978); they are predominantly vertical while the radial

deformations are negligible. The deformations below the pile base can be estimated

using the elastic solution for the punch of rigid body acting on a half space. The

solutions proposed by Mindlin (1936) and Boussinseq (1885) are used to drive the

load transfer function for the pile base. This approach is further detailed in Randolph

and Worth (1978). In the following subsections, the load transfer methods that have

been selected for comparison are summarised and discussed.

Verbrugge Method

Verbrugge (1986) suggested that the pile load-settlement behaviour can be

represented as in the Figure 3.11. At the initial stage (OA) of loading, the pile load-

settlement behaviour is fully elastic. At point A plasticity commences on the pile shaft

and develops until point B, where ultimate pile capacity is reached.

78

O

A

B

C

Q Qult.

w

Figure 3.11 Assumed pile load-settlement behaviour (Source: Verburgge 1986).

For construction of load-settlement behaviour for a pile subjected to axial load, the

pile is divided into n elements as shown in Figure 3.12. The length of elements can

vary but each must be within the same soil layer.

i

3

2

1

n

D

Q

h1

Figure 3.12 Pile division to n elements

The settlement at the lower face of element (1) at the pile tip is calculated from:

o

o

o E

DRw σλ= (3.30)

Where:

0w = tip settlement

79

0E = soil modulus under the tip (the mean value between pile tip and 3D below it)

λ = shape coefficient: (circular pile = 1; square pile = 1.12)

R = point coefficient for cylindrical pile = 1

0σ = stress at soil-pile tip interface

D = pile diameter

Soil modulus can be calculated from:

6.32.20

+=c

qE (MPa) c

q > 0.4 MPa (3.31)

Based on the evident by Sanglerat (1972), Formula 3.31 accounts for the probable

increase of c

qE0

with depth up to 30%. For driven piles, values given in 3.31 have

to be multiplied by 3.

The settlement of the upper face of element 1 or any element i is computed as follows:

1. The shear stress along the sides of element i is computed from:

( )max1. ssii

i

irrw

D

EB ≤≤= −λ

τ (3.32)

Where:

iτ = mobilised soil-shaft friction

iE = soil modulus around element i

D = pile diameter

1−iw = vertical displacement at the lower face of element i

B = shaft coefficient ≅ 0.22

sir = unit shaft resistance for element i

( )maxsr = maximum unit shaft resistance for element i

2. As shown in Figure 3.13, element i is in equilibrium condition, so the normal

stress at the top of the element can be expressed as:

D

h iiii

τσσ 41 += − (3.33)

Where:

iσ = normal stress at the top of element i

1−iσ = normal stress at the bottom of element i

ih = height of the element i

80

1−iw

iw

iσ

1−iσ

iz

Figure 3.13 Stresses acting on element i as a result of pile loading

3. With the use of Hooke’s low the upper displacement can be calculated from

Eq. 3.34.

++= −− D

hh

Eww ii

iip

ii

2

11

21 τσ (3.34)

Where:

pE = modulus of pile material

The plot of the full load-settlement curve can be obtained by implementing the

following steps.

1. Start from the pile tip and assume a value of oσ between 0 and the allowable

pile base capacity.

2. Calculate ow with (3.30), 1τ with (3.32), 1σ with (3.33) and 1w with (3.34) for

the bottom element.

3. Move upward until i = n

4. Calculate the load 4

2DQ n

πσ= that corresponds to the settlement of the pile

head, nw .

5. Vary the value of oσ and repeat steps 1-4 and so on to complete the load-

settlement curve.

81

Remarks:

1. The method relies on the conventional CPT methods to determine the shear

stress along pile shaft and tip resistance. Comparative studies of the available

CPT based methods carried out by a number of researchers (Briaud 1988;

Roberston et al. 1988; Abu-Farsakh and Titi 2004; Cai et al. 2009) have

shown that the capacity predictions can be very different for the same case

depending on the method employed. It is also found that these methods can

not provide consistent and accurate prediction of pile capacity.

2. The method assumes that at the initial stage of loading the soil behaviour is

fully elastic; however, the elastic-plastic behaviour is the most probable.

3. After reaching pile capacity, the method assumes the pile behaviour is fully

plastic. This may not be applicable in most of cohesionless soils as strain

hardening continues until failure.

4. The method considers soil deformation along pile shaft is due to shear stress

and does not refer to the influence of other stresses.

5. Soil modulus is evaluated from same equation below the pile tip and around

the shaft.

Fleming method

Fleming (1992) presented a method to model the load-settlement relationship for a

single pile subjected to maintained loading. His method is summarised as follows:

1. Hyperbolic functions to describe individual shaft and base performance are

determined.

2. The shaft and base functions are combined.

3. Elastic pile shortening is calculated.

4. The load settlement relationship is determined by adding pile shortening to the

combined function.

The shaft friction settlement is calculated from:

ss

sss PR

DPM

−=∆ (3.35)

G

M s

s 2

ζτ=

Where:

s∆ = settlement of pile shaft under applied load

82

sM = flexibility factor representing movement of pile relative to the soil when

transferring load by friction

D = pile diameter

sP = applied load to pile carried by friction

sR = ultimate shaft friction load which can be estimated with the use of conventional

methods for calculating pile capacity.

G = shear modulus of soil

ζ = ln(rm/rc)

rm = radius at which shear stress becomes negligible

rc = radius of pile

sτ = mobilised shear stress

For estimating tip settlement the following expression is proposed:

( )ttB

ttB PRDE

PR

−=∆ 6.0

(3.36)

Where:

B∆ = settlement of pile tip under applied load

tP = load applied at pile tip

tR = ultimate pile tip load

BE = deformation secant modulus for soil under pile base at 25% of ultimate stress

D = pile diameter

If the pile is assumed purely rigid, the shaft, the base and the total settlement can be

set equal and the total load is

St PPQ += (3.37)

Substituting (3.35) and (3.36) in (3.37) will result a relationship between total load

and total settlement expressed as:

T

T

T

T

ed

b

c

aQ

∆+∆+

∆+∆= (3.38)

Equation 3.38 can be rearranged and simplified. This yields an expression

representing the total settlement as a function of the applied load.

( )

f

fhggT 2

42 −±−=∆ (3.39)

83

Negative results of Equation 3.34 are ignored.

Where: T

∆ = total settlement; a = sR ; b = tBRDE ; c = DMs

; d = tR6.0 and e = B

DE ;

f = baeeQ −− ; bcadecQdQg −−+= and cdQh =

For calculation of pile shortening and to avoid the complexities associated with using

the analytical methods, Fleming suggests a simplified method, as indicated in Figure

3.14. The pile elastic shortening is calculated in three stages:

Centroid of friction transfer

L0

Lf KELf

Friction free or low friction zone

Frictional load Transfer length

Mobilized tip load (Q-Rs) for Q > Rs

Q

Figure 3.14 Simplified method of calculating elastic shortening (Source: Fleming 1992)

In the first stage, the pile deformation along zone extends to 0

L is calculated. In this

zone, the pile is assumed to have neglected or minimal friction with surrounding soil.

0L is estimated as the portion of the pile length that penetrates through fill or soft

alluvial deposits. Pile shortening for a length of 0

L can be given by:

c

ED

QL2

0

1

4

π=∆ (3.40)

Where:

c

E = Young’s modulus for the pile material under compression

In the second stage, pile shortening is estimated for a length F

L over which friction is

transferred. This can be expressed as Eq. 3.41.

84

c

FE

ED

QLK22

4=∆ (3.41)

Where:

EK = effective column length of shaft transferring friction divided by

FL , ranging

between 0.4 to 0.67 depending on soil type and stage of loading.

In the third stage, the pile shortening is calculated when the ultimate shaft friction has

been reached.

Any additional applied load exceeding the s

R will be carried by the full length F

L

and the shortening of F

L becomes:

( )

c

Fs

ED

LRQ23

4

π−=∆ (3.42)

The total elastic shortening is the sum of the elemental shortenings caused by load Q

up to the ultimate shaft load sR and can be estimated as follows:

( )

c

FE

E ED

LKLQ2

04

π+=∆ (3.43)

For loads greater than sR

( ) ( )[ ]EsFFc

E KRLLLQED

−−+=∆ 14

02π (3.44)

By combining equations (3.39), and (3.43) or (3.44) the load-settlement relationship

for any load up to the ultimate load can be constructed.

Remarks:

1. The method uses hyperbolic lows for both of shaft and base. Using two

hyperbolic relations may violate the original assumptions that the load and

settlement conform to hyperbolic low (Poskitt 1993).

2. The method relies on the conventional pile capacity methods to calculate the

ultimate shear and tip resistance. As mentioned earlier the conventional

methods provide inaccurate and inconsistent estimate to the pile capacity.

3. The method suggests number of correlations to determine the G. Applying the

correlations on single case show different results.

85

4. In layered soil, the method does not suggest clear procedures to calculate the

effective length.

5. In calculating the effective length, the upper soil layer is assumed weaker than

the lower soil. This is not always the case, as the pile some times penetrates

through a strong soil layer into a weaker soil layer.

API (1993) method

For the construction of the load-settlement t-z curves for piles in non-carbonate soils

API (1993) has recommended the values shown in Table 3.6, in the absence of more

definitive criteria.

Table 3.6 The recommended values for constructing the t-z curve for axially loaded single pile (Source: API 1993).

z/D t/tmax 0.0016 0.3 0.0031 0.5 0.0057 0.75 0.008 0.9 0.01 1.00 0.02 0.70-0.90

Clays

∞ 0.70-0.90 z (mm) t/tmax 0.000 0.00

25 1.00 Sands

∞ 1.00 z = local pile deflection; D = pile diameter (mm); t = mobilized soil pile adhesion (kPa); tmax = total shear resistance

The API (1993) recommends the values shown in Table 3.7 for the construction of the

load-settlement q-z curve (for the pile base) for piles in sand or clay.

Table 3.7 The recommended values for constructing the q-z curve for axially loaded single pile (Source: API 1993).

z/D Q/Qp 0.002 0.25 0.013 0.50 0.042 0.75 0.73 0.90 0.100 1.00

z = local pile deflection; D = pile diameter (mm); Q = mobilised end bearing capacity (kN); Qp = total end bearing (kN).

86

Remarks:

1. The method represents an approximate solution based on local practical

experience.

2. For constructing q-z curve same values are suggested for sand and clay. The

sand and clay deform differently and their behaviour under load can not be

similar.

3. The method suggests using the conventional methods to calculate the ultimate

shaft and tip resistance. In addition to what have been mentioned previously,

the conventional methods assume that the ultimate base and shaft resistance

are reached simultaneously. In fact, this assumption is not always correct,

because the pile tip may deliver its full capacity at the load much higher than

what is considered by the conventional methods as the ultimate load.

87

CHAPTER FOUR

DEVELOPMENT OF GEP MODEL

4.1 INTRODUCTION

In this chapter, a new approach, which is based on the recent developments in

artificial intelligence techniques, i.e. the gene expression programming (GEP), is

investigated for predicting the capacity of bored and driven piles embedded in sand or

layered soils. GEP models are developed using the commercial available software

package GeneXproTools 4.0 (Gepsoft 2002). The necessary steps for model

development including data collection, input variables selection, data division and

model parameters are explained. Model formulation and performance measurements

are discussed. The performance of the GEP model is examined via:

• Examining the predictions of the model in training and validation sets

• Conducting sensitivity analysis

• Carrying out statistical analysis by comparing the GEP model with number of

currently used CPT-based methods.

4.2 DATA COLLECTION

4.2.1 Description of piles

The database of this work comprises 50 bored piles and 58 driven piles of two

categories (steel and concrete piles). The bored piles have different sizes and round up

shapes, with diameter ranging from 320 mm to 1800 mm and lengths from 6 to 27 m.

The driven piles also have different sizes and shapes (i.e. circular, square and

hexagonal), with diameters ranging from 250 to 660 mm and lengths from 8 to 36 m.

Since the piles considered in the current study have a wide range of diameters, they

are classified as small-diameter piles (diameter ≤ 600 mm) and large-diameter piles

(diameter > 600 mm).

88

This classification is in accordance with Ng et al. (2004), and based on large-diameter

piles may show different behaviour in comparison with small-diameter piles.

Detailed information of case records is presented in the Appendix A, B and C which

include the CPT profile, schematic soil profile along and beneath the pile, pile

geometry, installation method and types of pile load test. The CPT profile includes the

cone point resistance, c

q , for bored piles and c

q and sleeve friction, fs, for driven

piles. The load- settlement diagram is also provided.

4.2.2 Source of data

The compiled database consists of case records collected from the literature, mainly

in-situ tests, and CPT results reported by Alsamman (1995) and Eslami (1996). The

cases were obtained from all over the world. The summary of the data of each case

record used to develop the models are presented in Tables 4.1- 4.3.

4.2.3 Pile load tests

The bored piles in the database are subjected to axial compression load tests. The

driven piles are also tested under axial compression or tension loads. The load tests

vary in their procedure, equipment, instrumentation, and load application method. The

load test type of each case record is shown in the case record details in Appendix A, B

and C.

4.2.4 Cone penetration test results

The cone penetration tests were performed to a depth of at least four times the pile

diameter below the pile tip and at a distance close enough to the load test location so

as to be representative; the distance between the CPT location and the load test was at

least greater than five shaft diameter.

Records of cone point resistance, c

q , versus depth are available in all load tests in the

database; however the sleeve friction, s

f , is only available in the driven piles case

records.

89

Table 4.1 Summary of data used for developing GEP model for bored piles Test No. D (mm) L (m) tipcq − (MPa) shaftcq − (MPa) Qu (kN) Soil profile Site Location

1 1100 13.0 16.2 4.0 2624 Mud, peat, sand Not available 2 421 5.8 22.9 11.8 912 Silt, peat, sand Berlin, Germany 3 320 10.2 22.0 7.2 712 Silty clay, medium sand Hamburg, Germany 4 457 15.2 1.6 8.1 1423 Sand, clay Evanston, U.S.A 5 393 6.5 10.1 12.8 738 Sand California, U.S.A 6 410 5.6 16.7 15.8 560 Sand California, U.S.A 7 320 10.2 14.6 4.5 832 Silty clay, medium sand Hamburg, Germany 8 320 7.7 8.3 2.6 445 Silty clay, medium sand Hamburg, Germany 9 403 9.2 13.1 10.3 1352 Sand California, U.S.A 10 814 24.2 6.5 9.6 5872 Sandy clay, sand Houston, U.S.A 11 320 10.2 21.9 7.1 818 Silty clay, medium sand Hamburg, Germany 12 671 13.0 25.6 17.2 4270 Gravelly sand, sandy gravel Dusseldorf, Germeny 13 1000 9.5 29.3 5.1 2358 Fine sand Not available 14 1000 9.0 35.9 8.5 3692 Sand Not available 15 840 24.4 47.6 9.2 9653 Silty clay, sand Kuala Lumpur 16 600 7.2 10.9 7.6 1437 Clay, silty sand Guimaraes, Portugal 17 1100 9.0 15.4 5.4 3247 Sand Not available 18 500 10.2 8.9 2.2 1005 Sand, gravelly sand Berlin, Germany 19 329 6.2 20.7 10.6 605 Sandy silt, medium sand Berlin, Germany 20 408 5.8 17.6 8.2 765 Medium sand, fine sand Berlin, Germany 21 521 8.2 12.9 9.6 1334 Gravelly sand Berlin, Germany

22 1800 11.5 36.6 7.6 7651 Fine sand Not available 23 405 8.4 33.4 11.5 1019 Silt & sand, gravelly sand California, U.S.A

D, pile diameter; L, pile embedment length; tipcq − , average cone point resistance within tip influence zone; shaftcq − , average cone point resistance

along shaft; Qu, measured pile capacity.

90

Table 4.1 (continued) Test No. D (mm) L (m) tipcq − (MPa) shaftcq − (MPa) Qu (kN) Soil profile Site Location

24 405 10.4 8.9 11.3 1019 Sand California, U.S.A 25 399 7.8 12.8 4.4 667 Sandy clay, medium sand Berlin, Germany 26 671 10.2 13.7 20.1 4697 Gravelly sand, sandy gravel Dusseldorf, Germeny 27 430 8.7 31.7 14.5 516 Gravel, coarse sand Berlin, Germany 28 320 7.7 7.9 2.6 356 Medium sand Hamburg, Germany 29 399 10.0 24.6 12.7 756 Medium sand Berlin, Germany 30 600 12.0 21.4 10.8 2687 Clayey sand, fine sand Kallo, Belgium 31 600 12.0 21.3 11.1 2406 Clayey sand, fine sand Kallo, Belgium 32 1100 27.0 7.0 9.4 8207 Sand & clay Shandong, China 33 320 7.7 8.2 2.6 391 Silty clay, medium sand Hamburg, Germany 34 400 9.4 2.4 1.4 480 Clay and silt, silty sand Sao Poulo, Brazil 35 1085 25.1 32.0 9.0 7695 Sand & clay Shandong, China 36 350 15.8 5.1 5.5 840 Sand Seattle, U.S.A 37 500 10.2 14.7 3.2 1299 Sand, gravelly sand Berlin, Germany 38 405 7.9 6.2 12.8 792 Silty sand, sandy silt California, U.S.A 39 1100 6.0 21.0 7.8 2469 Fine sand & silt Not available 40 631 18.3 30.0 11.7 1770 Clay, sand Nertherland 41 521 8.2 12.8 9.5 1263 Gravelly sand Berlin, Germany 42 405 7.0 17.8 14.3 1294 Sand California, U.S.A 43 399 7.8 13.1 4.1 578 Sandy clay, medium sand Berlin, Germany 44 1500 6.0 10.4 8.5 2669 Sand Not available 45 400 7.8 10.6 3.6 543 Sandy clay, medium sand Berlin, Germany 46 320 7.7 8.5 2.6 409 Silty clay, medium sand Hamburg, Germany



91

Table 4.1 (continued) Test No. D (mm) L (m) tipcq − (MPa) shaftcq − (MPa) Qu (kN) Soil profile Site Location

47 762 16.8 5.9 5.2 3425 Residual silty sand Atlanta, U.S.A 48 430 8.7 26.8 11.7 627 Gravel, sand Berlin, Germany 49 329 6.3 25.9 15.6 756 Medium sand Berlin, Germany 50 1078 13.0 31.0 19.0 8825 Gravelly sand, sandy gravel Dusseldorf, Germeny



Table 4.2 Summary of the data used for developing the GEP model for concrete driven piles

Test No. D (mm) L (m) tipcq − (MPa) sf (kPa) shaftcq − (MPa) Qu (kN) Soil profile Site Location

1 250 21.3 8.0 33 5.6 810 Sand, silty sand Blount Island, U.S.A 2 400 11.3 10.8 105 5.0 870 Clay, sand Washnigton, U.S.A 3 450 10.3 4.1 47 2.5 1250 Sand, clay Wathall, U.S.A 4 350 8.6 5.7 25 4.6 600 Sand, clay Perry, MS U.S.A 5 450 8 7.9 205 3.0 1140 Silty sand West P Beach, U.S.A 6 285 15 7.7 56 5.0 1600 Silty sand, uniform sand Baghdad, Iraq 7 450 14.9 5.3 38 6.3 1755 Sand Blount Island, U.S.A 8 400 12.5 3.2 35 3.3 620 Sand Hinds, MS U.S.A 9 350 15.85 6.0 50 5.6 1485 Silty sand Blount Island, U.S.A 10 450 9.15 11.7 150 15.7 1845 Sand & clay Jefferson County, U.S.A 11 610 18.2 10.5 43 9.6 3600 Sand, silty clay Oklohama, U.S.A 12 400 11.2 7.0 88 8.4 1020 Sand Hinds, MS U.S.A

D, pile diameter; L, pile embedment length; tipcq − , average cone point resistance within tip influence zone; sf , average sleeve friction along

shaft; shaftcq − , average cone point resistance along shaft; Qu, measured pile capacity.

92

Table 4.2 (continued) Test No. D (mm) L (m) tipcq − (MPa)

sf (kPa) shaftcq − (MPa) Qm (kN) Soil profile Site Location 13 250 9.25 3.8 104 2.8 700 Clay, silty sand Almere, Netherland 14 400 12.5 4.1 43 3.6 1170 Sand Hinds, MS U.S.A 15 285 11 3.1 47 3.4 1000 Silty sand, uniform sand Baghdad, Iraq 16 400 8.8 7.6 36 5.6 1140 Clay, sand Smith, MS U.S.A 17 355 10.2 7.8 80 5.0 1300 Silt, sand, dens sand Victoria, Australia 18 400 11.4 9.8 52 5.7 1140 Clay, sand Madison, U.S.A 19 350 20.4 5.0 86 5.4 1260 Sand, silt Florida, U.S.A 20 500 11 6.8 60 13.9 2070 Sand Florida, U.S.A 21 350 16 7.5 60 7.3 1070 Clay, sand Washnigton, U.S.A 22 350 16 7.6 154 7.5 1350 Sand Florida, U.S.A 23 625 25.8 18.6 139 8.6 5455 Clay, sand Los Angeles, U.S.A 24 450 15 10.3 46 6.0 1420 Sand Harrison, MS U.S.A 25 400 13.4 8.8 48 4.4 1170 Clay, sand Yazoo, MS U.S.A 26 450 11.3 1.1 195 2.5 830 Silty sand West P Beach, U.S.A 27 350 9.5 4.5 124 6.6 900 Sand, clay Louisiana, U.S.A 28 500 13.8 11.8 125 10.9 4250 Dense sand, lime stone Victoria, Australia



93

Table 4.3 Summary of the data used for developing the GEP model for steel driven piles

Test No. D (mm) L (m) tipcq − (MPa) sf (kPa) shaftcq − (MPa) Qm (kN) Soil profile Site Location

1 300 11.0 0.0 66 15.2 560 Sand Lock & Dam 26, U.S.A 2 455 12.0 0.0 65 15.9 1170 Sand ″″ 3 455 11.3 0.0 67 15.8 870 Sand ″″ 4 273 22.5 23.9 46 8.1 1620 Sand, dense sand Blount Island, U.S.A 5 660 18.2 10.2 46 9.5 3650 Sand, silty clay shale Oklohama, U.S.A 6 609 34.3 13.3 48 9.5 4460 Sand, clay, sand Taiwan 7 330 10.0 2.3 38 3.0 625 Clay, silty sand, clay Milano, Italy 8 300 28.4 1.3 24 3.2 1240 Peat, sand, soft clay Rnerto Rico, U.S.A 9 273 22.5 0.0 27 2.1 765 Sand, dense sand Blount Island, U.S.A 10 455 16.2 0.0 67 9.8 1170 Sand Lock & Dam 26, U.S.A 11 300 16.2 20.0 64 16.9 1310 Sand ″″ 12 450 15.2 0.5 50 6.2 1020 Sand, clay Evanston, U.S.A 13 455 16.8 0.0 66 17.5 1260 Sand Lock & Dam 26, U.S.A 14 350 14.4 21.6 72 17.6 1300 Sand ″″ 15 400 14.6 20.0 74 17.0 1800 Sand ″″ 16 400 14.6 0.0 50 15.5 945 Sand ″″ 17 273 9.2 6.5 18 5.4 490 fill, sand S Farncisco, U.S.A 18 273 15.2 5.4 36 6.4 675 Sand, dense sand Blount Island, U.S.A 19 455 16.2 15.5 89 9.7 3600 Sand Lock & Dam 26, U.S.A 20 392 36.3 14.0 131 11.7 2130 Sand, silty clay, sand Albama, U.S.A

Deq, equivalent pile diameter; L, pile embedment length; tipcq − , average cone point resistance within tip influence zone; sf , average sleeve

friction along shaft; shaftcq − , average cone point resistance along shaft; Qu, measured pile capacity.

94

Table 4.3 (continued)

Test No. Deq

(mm) L (m) tipcq − (MPa)

sf (kPa) shaftcq − (MPa) Qm (kN) Soil profile Site Location

21 490 14.0 15.6 32 11.2 3500 Soft soil, dense sand Kallo, Belgium 22 385 19.0 2.8 82 2.0 1370 Clay, sand Washington DC, U.S.A 23 385 12.4 1.8 48 1.7 520 Clay, sand ″″ 24 455 15.2 0.3 55 6.1 1010 Sand, clay Evanston, U.S.A 25 321 8.5 5.0 70 1.5 590 Clay, sand Launderdale, U.S.A 26 350 31.1 5.6 19 1.4 1710 Clay, sand, clay Louisiana, U.S.A 27 609 34.3 8.7 33 4.5 4330 Sand, clay, sand Taiwan 28 455 11.3 0.0 65 15.5 817 Sand Lock & Dam 26, U.S.A 29 350 11.1 0.0 60 15.5 630 Sand ″″ 30 300 31.4 1.2 35 3.1 1690 Peat, sand, soft clay, sand Ruerto Rico U.S.A

Deq, equivalent pile diameter; L, pile embedment length; tipcq − , average cone point resistance within tip influence zone; sf , average sleeve

friction along shaft; shaftcq − , average cone point resistance along shaft; Qu, measured pile capacity.

95

Several pile load tests include mechanical rather than electric CPT data and thus, it

was necessary to transform the mechanical CPT readings into equivalent electric CPT

values. This is carried out using the correlation proposed by Kulhway and Mayne

(1990) as follows:

19.1

47.0Mechanicala

c

Electrica

c

p

q

p

q

=

(4.1)

Where; a

p = atmospheric pressure in kPa; c

q = cone point resistance in kPa.

For fs values, the mechanical cones give higher readings than the electric cones in all

soils. Kulhway and Mayne (1990) suggested a ratio of 2 for sand and 2.5–3.5 for clay.

In the present study, a ratio of 2 is adopted for sand and 3 for clay.

4.2.5 Soil profile

Soil profiles are mainly classified into two categories: sand soil profiles consisting of

dens to loose sand; mixed soil profiles consisting of layers of cohesionless soil (sand

or gravel) and layers of cohesive soil (clay).

Although in number of case records soil profiles include a portion of cohesive soils,

the cases can be considered as piles embedded in chohesionless soil for these reasons:

1. For most of the cases, the pile tip is situated in sand. It is believed that the

sand provides most of its resistance at the pile tip (Eslami 1996). Therefore,

the expected behaviour of these piles is to be seen as piles in cohesionless

soil.

2. For few cases, the pile tip is situated in clay. In these cases, the tip

participation in the total capacity would be minimal, because the clay provides

most of its resistance at the pile shaft. Hence, these piles can also be

considered as piles in cohesionless soil.

4.3 SELECTION OF INPUT VARIABLES

A proper estimation of bearing capacity of pile foundation requires the identification

of the factors that influence the pile soil interaction. These factors include pile

geometry and material, soil properties, construction method and testing procedure. As

these factors have different degrees of influence on pile capacity, they can be

classified into two categories: primary and secondary factors.

96

The primary factors will have significant effect on the pile capacity, whereas the

secondary factors will have insignificant effect.

4.3.1 The primary factors

Pile geometry

All geotechnical engineering sources confirm that pile diameter and length have

significant influence on bearing capacity of pile foundation. Therefore, these factors

are selected to represent pile geometry for input of GEP model.

Pile material

The adherence or friction between the pile and the surrounding soil depends

significantly on the pile’s surface roughness which varies with pile material.

Consequently, piles made of different materials (e.g. steel or concrete) have different

capacities. As the data base of this work includes two types of piles (steel and

concrete), the pile material must be considered. However, there is a difficulty

obtaining a proper representation to pile material that the GEP model can handle. Two

approaches can be adopted to tackle the difficulty. The first approach is to combine

the two pile groups in one model. In this case, the GEP require that the pile material to

be translated from text format into numerical format. This can be done by

representing the steel as 1 and the concrete as 2. The issue with this approach is that

the used numbers do not carry any physical meaning and it is hard to prove that this

representation will reflect the real contribution of the pile material. Moreover,

swapping the numbers (2 for steel and 1 for concrete) or using different numbers will

produce models of different performance. This will leave unanswered questions of

which of the selected numbers is really representing the pile material. The other

approach is to model the capacity of each of pile groups separately. The two

approaches were attempted but the second approach was favoured to avoid the

uncertainty that would exist in the first approach. Two different models are

developed: A model for steel piles and a model for concrete piles.

97

Average cone point resistance within tip influence zone

All current CPT based methods apply a correlation factor to the average cone point

resistance,c

q , over a certain zone identified as the tip influence zone, to estimate the

unit tip resistance. Hence, the average of c

q over the tip influence zone is included as

primary input variable. The depth over which the c

q is averaged and the averaging

procedure are discussed as follows:

The term of influence zone refers to the region that may extend for a distance upwards

and downwards of the pile tip, and in which the failure envelope may reside when the

pile delivers its ultimate tip resistance. The extents and the form of the influence zone

around the tip of loaded pile depend on many factors such as angle of shearing

resistance, the stiffness, the volumetric strain, and the mean effective stress of the pile

tip and the local heterogeneity (Yang 2006). The interaction between the factors is

very complicated and not entirely understood. As a result, researchers have suggested

several patterns of influence zone as shown in Chapter 3, Figure 3.7.

There is no common agreement among the researchers on the extents of the influence

zone. Results of experimental and numerical study on two concrete piles in medium

dense sand, carried out by Altaee and Fellenius (1992) have shown that the tip

influence zone extends from 5D below to 5D above the pile tip. A theoretical analysis

by Eslami (1996) indicates that in a homogeneous soil, the zone may reach to 1.5D

below the pile tip to 4 through 9D above the tip. Horizontally, the zone may reaches

to 5D. A study by Yang (2006) has revealed that for piles in clean sand the influence

zone above the pile tip is between 1.5D to 2.5D and the zone below the pile tip ranges

between 3.5 to 5.5D. There is also no agreement on the boundaries of the zone among

the current CPT based methods which are discussed in Chapter 3.

Considering the theoretical definitions and the current practice, it can be concluded

that, in this study and for small diameter piles, the extents of the influence zone can be

assumed according to the definition given by Esalmi (1996) which is detailed in

Chapter 3. This choice is made because for piles in homogeneous soil the definition

given by the method consistent with the definition driven from the theoretical

analysis, and for piles in non-homogenous soil where no theoretical analysis are

98

applied the definition is based on what has been adopted in current practice.

Moreover, the definition that is given by the method accounts for the soil

heterogeneity which has an effect on the extents of the tip influence zone.

For large diameter piles the pattern of the rapture zone is likely to be similar to the

influence zone of shallow foundations. In this case, the definition recommended by

Alsamman (1995) is adopted.

All CPT based methods consider determining a representative value for the cone point

resistance,tipc

q − , within the tip influence zone is necessary for calculating the pile unit

tip resistance. When the unit tip resistance approaches to its ultimate value, the points

along the rupture surface, located at different depths, may have different friction angle

and/or mobilised c

q value resulting from soil variations and confining stress. Hence, a

representing cone resistance is required for pile design to account for the variations of

soil characteristics particularly, for unit tip resistance (Eslami 1996). The representing

cq is determined by averaging the

cq values within the tip rupture zone.

Three types of averaging c

q values can be considered: the arithmetic average the

geometric average and the weighted average. The arithmetic average is determined

from:

n

qqqq cncc

arthc

+++=−

...21 (4.2)

Where:

arthcq − = arithmetic average of

cq values which range from

1cq to

cnq

The geometric average is determined from:

ncnccgeoc

qqqq ×××=− ...21

(4.3)

Where:

=−geocq geometric average of values which range from

1cq to

cnq .

99

The weighted average is determined from:

∑−=∆

=∆

−−

−

∆

∆

+++∆

++∆

+

=1

1

11

232

121

2...

22nl

l

ncncncccc

wetdc

l

lqq

lqq

lqq

q (4.4)

Where:

=−wetdcq weighted average of values which range from

1cq to

cnq

=∆l length of the depth segment between two consecutive c

q values

The arithmetic average is useful when peaks and troughs are removed from the data

and also useful in homogenous soils where values are uniform.

The arithmetic average is not considered in this study because most of the cases in the

database include piles installed in cohesionless soil. The CPT results of this type of

soil usually involve large number of peaks and troughs which make the arithmetic

average inappropriate for averagingc

q .

The geometric average is useful when many sharp peaks and troughs are available in

the data, as can be found for many sand deposits, and when a dominant value exists

among the collected values. However, the setback of the geometric average is that, if

the collected values are low for a segment of the depth and then become much higher

for another segment, the geometric average provides unsatisfactory averaging results.

In this case, the weighted average method may be better, as it accounts for the depth

over which values are averaged. This can be clearly seen in the following example

which illustrates the geometric average and the weighted average of c

q values

computed within the tip influence zone for a bored pile installed in cohesionless soil

(Case record 13) selected from the database. The extents of the pile tip influence zone

are assumed to extend for a zone which is shown in Figure 4.1. It can be seen that the

cq values within the influence zone remain low (range between 1 to 5 MPa) for a

distance of 6 meter of the zone and then become much higher (range between 5 to 25

MPa) for a distance of 8 meters of the zone. The geometric average of c

q values

within the tip influence zone is 5.6 MPa, whereas the weighted average is 10.3 MPa.

Obviously, the geometric average is low and resides near the lower range of c

q

100

values, although there is a significant amount of large c

q values involved. The

weighted average on the other hand lay near the middle range of c

q values and it

accounts for the low and the high range c

q values. Hence, for this kind of problem,

weighted average provides more appropriate representation to the c

q values than the

geometric average. As many cases in the database of this study are similar to this case,

the weighted average method has been adopted.

-16

-14

-12

-10

-8

-6

-4

-2

0

0 5 10 15 20 25 30

Cone point resistance (MPa)

Depth (m

)

Geo. Av

Wetd. Av

Tip

influ

en

ce zo

ne

Figure 4.1 Comparison of averaging methods for cone point resistance within tip

influence zone.

Average cone point resistance along pile shaft

Several CPT based methods (e.g. Alsamman 1995; Aoki and De Alencar 1975; De

Ruiter and Beringen 1979; Philipponnat 1980) have proposed correlations to estimate

the unit shaft resistance from the average cone point resistance along pile shaft. The

methods consider qc values more reliable for estimating pile shaft resistance.

Accordingly, this factor is used as input variable.

Average sleeve friction along pile shaft

A numbers of CPT based methods (e.g. Clisby et al. 1978; Schmertmann 1978) have

proposed models to predict unit shaft resistance based on average sleeve friction

measurements sf along pile shaft. On the other hand, other methods (e.g. Alsamman

1995; Bustamante and Gianeselli 1982) consider sleeve friction more variable

101

measurement than the cone point resistance and ignore it. In this study, the sleeve

friction measurements were available in the driven piles database. Therefore, sf has

been included among input variables and its influence on the pile capacity is verified

in the sensitivity analyses which are detailed later.

Measured pile capacity

The pile capacity, Qu, is the single model output variable. For driven piles, the pile

capacity, Qu, is estimated according to Eslami (1996) as the plunging failure, for the

well defined failure cases, and the 80% Criterion of Hansen (1963), for the cases that

the failure load is not clearly defined. For bored piles, the pile capacity, Qu, is taken in

accordance with Alsamman (1995) as the axial load measured at 5% of pile diameter

displacement plus the elastic compression of the pile (i.e. PL/EA where; P is the

applied load, L is the pile embedded length, E is the pile elastic modulus and A is the

pile cross sectional area). Figures 4.2- 4.4 present how pile capacity is interpreted

from load test results.

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30

Cone tip resistance (MPa)

De

pth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32

Sleeve friction (MPa)

Dep

th (

m)

0

400

800

1200

1600

2000

0 18 36 54 72 90

Movement (mm)

Axi

al l

oad

(kN

)

Pile geometry Soil profile CPT profile

400 mm14.6 m

sand

0

Failure load = 1800 kN taken according to 80% - criterion

Figure 4.2 Summary sheet for driven steel pile Case record 15, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load-movement plot.

102

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


De

pth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dep

th (

m)

0

150

300

450

600

750

0 14 28 42 56 70

Movement (mm)

Axi

al lo

ad (

kN)


300 mm11 m

sand

0

Fialure load = 560 kN taken as a plunging load

Figure 4.3 Summary sheet for driven steel pile Case record 1, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load-movement plot.

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 4 8 12 16 20 24 28 32


Depth

(m

)

0

30

60

90

120

150

180

0 1000 2000 3000 4000 5000

Axial load (kN)

Move

ment (m

m)

mud & peat

fine sand

2.3

12.2

Soil profileShaft geometry

CPT profile

0

1500 mm6 m

Head deflection = 0.05 * pile diameter + PL/AE

Failure load

Figure 4.4 Summary sheet for the bored pile Case record 45, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load-movement plot.

103

4.3.2 The secondary factors

These factors have less degree of contribution among the factors that influence the

bearing capacity of pile. They include pile shape, pile tip (closed or open), pile

construction procedure and the depth of the water table.

Most of the currently available CPT based methods do not incorporate any parameters

to represent the effect of pile shape. A recent study to predict pile settlement has

shown that pile shape has insignificant influence on pile performance; the study has

also shown that the open or closed ended tip has similar and minor influence on the

pile settlement (Pooya Nejad et al. 2009). Therefore these factors have not been

included among input variables.

Because bored and driven piles show different behaviour, two separate GEP model

are developed: A model for bored piles and the other model for driven piles.

The depth of water table was not available in the bored piles data but in several cases

of driven piles the water table was provided with CPT profile. The influence of water

table already exists, because the total qc is included. As a result, the GEP model will

account for the effect of water table and there is no need to include variable

representing water table.

4.4 DATA DIVISION

The next step in development of the GEP models is the data division. As explained in

Chapter 2, the aim of this step is to use the available data for obtaining a GEP model

that is able to generalize the solution. To achieve this, the available data is divided

into two sets: training and validation. In total, 41 data records (82%) of the available

50 bored pile cases are used for training and 9 cases (18%) for validation. For

concrete driven piles, 23 data records (82%) of the available 28 cases are used for

training and 5 cases (18%) for validation; for steel driven piles 25 data records (80%)

of the available 30 cases are used for training and 5 cases (20%) for validation. As has

been discussed in Chapter 2, a proper data division can be achieved by dividing the

data into two statistically consistent sets Master (1993).

104

The statistical consistency of the data sets is achieved by applying the method that is

detailed by Shahin at al. (2004). In this method, the data are divided by the trail-and-

error process and statistical parameters including mean, standard deviation, minimum,

maximum and range are used as indicators to show whether or not the data sets are

statistically consistent. The statistics of the training and testing sets are shown in

Table 4.4.

Table 4.4 GEP models input and output statistics.

Statistical parameters Piles group

Model variables and data sets Mean SD* Minimum Maximum Range Pile diameter, D (mm) Training set 602 325 320 1800 1480 Validation set 624 412 320 1500 1180 Pile embedment length, L (m) Training set 11 5 6 27 21 Validation set 9 4 6 17 11 Weighted average cone point resistance, along pile tip influence zone, tipcq −

(MPa) Training set 18 10 2 48 46 Validation set 17 9 6 31 24 Weighted average cone point resistance along pile shaft, shaftcq − (MPa)

Training set 9 4 1 20 19 Validation set 9 5 2 19 16 Pile capacity, Qu (kN) Training set 2235 2393 356 9653 9297

Bored

Validation set 2125 2727 409 8825 8416 Pile diameter, Deq (mm) Training set 402 92 250 625 375 Validation set 430 57 350 500 150 Pile embedment length, L (m) Training set 13 4 8 26 18 Validation set 13 2 9 15 6 Weighted average cone point resistance along pile tip influence zone, tipcq −

(MPa) Training set 7 4 3 19 16 Validation set 7 4 1 12 11 Weighted average sleeve friction along shaft length, sf (kPa)

Training set 77 48 25 205 180

Driven concrete

Validation set 107 62 46 195 149 *SD indicates standard deviation

105

Table 4.4 GEP models input and output statistics (continued).

Statistical parameters Piles group

Model variables and data sets Mean SD* Minimum Maximum Range

Weighted average cone point resistance along pile shaft shaftcq −

Training set 3 4 0.7 14 13 Validation set 4 4 0.7 11 10 Pile capacity, Qu (kN) Training set 1489 1066 600 5455 4855

Driven concrete Validation set 1714 1436 830 4250 3420

Pile diameter, Deq (mm) Training set 396 102 273 660 387 Validation set 413 123 300 609 309 Pile embedment length, L (m) Training set 17 7 9 36 28 Validation set 24 12 11 34 23 Weighted average cone point resistance along pile tip influence zone, tipcq −

Training set 8 10 0 38 38 Validation set 3 4 0 9 9 Weighted average sleeve friction along shaft length, sf (kPa)

Training set 57 24 18 131 113 Validation set 42 19 19 65 46 Weighted average cone point resistance along pile shaft, shaftcq −

Training set 9 6 1.5 18 16 Validation set 8 7 1.4 16 14 Pile capacity, Qu (kN) Training set 1506 1110 490 4460 3970

Driven steel

Validation set 1835 1479 630 4330 3700 *SD indicates standard deviation

It should be noted that, like all empirical models, GEP performs best in interpolation

rather than extrapolation, thus, the extreme values of the data used are included in the

training sets.

To ensure that the statistical consistency of the data sets (training and validation) has

been achieved, t-and F-tests are carried out. The t-test is used to determine wether

there is a significant difference between the means of the two data sets and the F-test

is used to determine wether there is a significant difference between the standard

deviation of the data sets. To run the tests, the level of significance which indicates to

the confidence level in the consistency in the two data sets must be chosen.

106

For instance, if a level of confidence is selected to be 5%, there is a confidence level

of 95% that the training and validation sets are statistically consistent.

A level of significance equal to 5% is used in this study, as it has been the traditional

level of significance (Levine et al. 2002). The results of the t- and F-tests are indicated

in Table 4.5, which shows that the validation and training sets are statistically

consistent.

Table 4.5 t-and F-tests to examine the statistical consistency of the training and validation data sets of the GEP model input and output variables.

Piles group Variable

t-value

Lower critical value

Upper critical value

t-test F-

value

Lower critical value

Upper critical value

F-test

tipcq − 0.306 -2.106 2.106 Accept 1.34 0.286 3.51 Accept

shaftcq − -0.402 -2.106 2.106 Accept 0.518 0.286 3.51 Accept

L 1.098 -2.106 2.106 Accept 2.36 0.286 3.51 Accept

D -0.181 -2.106 2.106 Accept 0.621 0.286 3.51 Accept

Bored piles

Qu 0.122 -2.106 2.106 Accept 0.769 0.286 3.51 Accept

Deq -0.759 -2.056 2.506 Accept 2.802 0.16 6.29 Accept

L 0.384 -2.056 2.506 Accept 4.44 0.16 6.29 Accept


sf -1.307 -2.056 2.506 Accept 0.576 0.16 6.29 Accept

shaftcq − 0.101 -2.056 2.506 Accept 1.137 0.16 6.29 Accept D

riven concrete piles

Qu -0.403 -2.056 2.506 Accept 0.551 0.16 6.29 Accept

Deq -0.331 -2.048 2.048 Accept 0.68 0.16 6.26 Accept

L -1.78 -2.048 2.048 Accept 0.37 0.16 6.26 Accept


sf 1.29 -2.048 2.048 Accept 1.52 0.16 6.26 Accept

shaftcq − 0.536 -2.048 2.048 Accept 0.66 0.16 6.26 Accept

Driven steel piles

Qu -0.574 -2.048 2.048 Accept 0.56 0.16 6.26 Accept

D, Deq, pile diameter and equivalent pile diameter; L, pile embedment length; tipcq − ,

average cone point resistance within tip influence zone; sf , average sleeve friction

along shaft; shaftcq − , average cone point resistance along shaft; Qu, pile capacity.

107

4.5 DERMINATION OF SETTING PARAMETERS AND GEP MODEL SELECTION

The search for the optimum model settings and the selection process of the GEP

models for bored and driven piles is carried out in three stages detailed next.

4.5.1 Determination of the optimum values of setting parameters

As mentioned in Chapter 2, in GEP, values of setting parameters have significant

influence on the fitness of the output model. These include the number of

chromosomes, number of genes and gene’s head size, functions set, linking function

and the rate of genetic operators. In this work, the trial-and-error approach is used to

determine the optimum values of setting parameters. This approach involved using

different settings and conducting runs in steps. During each step, runs are carried out

and the values of one of the above mentioned parameters (with its optimal value being

searched) are varied, whereas the values of the other parameters are set constant (i.e.

number of chromosomes = 30, number of genes = 3, gene’s head size = 8, functions

set = +, -, *, and /, fitness function = mean squared error (MSE), linking function = +,

mutation = 0.04, and gene recombination = 0.1). The runs are stopped after fifty

thousand generations, which was found sufficient to evaluate the fitness of the output.

At the end of each run, the MSE for both training and validation sets are recorded in

order to identify the optimal values that give the least MSE.

In the first step, the optimum number of chromosomes was determined. Several runs

were conducted varying the number of chromosomes (i.e. 20, 21, 22, …36), whereas

the other parameters are set constants. The number of chromosomes that was found to

correspond to the least MSE in both of the training and the validation sets was

selected as the optimal.

In the same way, the optimum chromosome architecture, i.e. the head size and number

of genes per chromosome, are determined. Several runs are carried out by using the

gene’s head size = 6, 7, 8, …,14, and number of genes per chromosome = 1, 2, 3,… 5.

The fitness of the output of the runs was then compared to determine the optimum

chromosome’s architecture.

108

In the following step the best set of functions was determined. The initial run began

with the use of the four basic arithmetic operators (+,-,*,/). Then in the subsequent run

an additional function such as root square was added to the set and so on. Then the

addition and the multiplication linking functions were used in different runs to

determine which of these functions best suits this problem.

The last step was to search for the best rates of each of the genetic operators. The

focus was more on mutation and gene recombination, as they are the main gene

modifiers. The results of finding the optimum values of model setting parameters for

bored piles model are shown in Figures 4.5 - 4.9. The Figure 4.5 shows that the model

performs best when the number of chromosomes is 24, indicating that this number of

chromosomes is optimal. It can also be seen that, in Figures 4.6 and 4.7, the optimum

chromosome structure consists of 3 genes of head size = 9. Above these values the

fitness of the model decreases. This can be because of using too long gene; the genetic

variations may take place in regions where they have minor effect on the fitness of the

chromosome.

0

1

2

3

4

5

6

7

8

9

10

20 22 24 26 28 30 32 34 36 38

Number of chromosomes

Mea

n s

qu

ared

err

or tr

ain

ing

0

1

2

3

4

5

6

7

8

9

Mea

n sq

uar

ed e

rror

val

idat

ion

Training set

Validation set

Optimum number of chromosomes

×10

5

×10

6

Figure 4.5 Effect of number of chromosomes on the performance of the GEP

model.

109

0

1

2

3

4

5

5 7 9 11 13 15

Gene head size

Mea

n sq

uare

d e

rror

trai

nin

g

0

1

2

3

4

5

6

Mea

n e

qua

red

err

or v

alid

atio

n

Training set

Validation set

Optimum head size

×10

5

×10

6

Figure 4.6 Effect of gene’s head size on the performance of the GEP model.

0

2

4

6

8

10

0 1 2 3 4 5 6

Number of genes

Mea

n sq

uar

ed e

rror

trai

nin

g

0

1

2

3

4

5

6M

ean

sq

uare

d e

rror

val

idat

ion

Training set

Validation set

Optimum number of genes

×10

5

×10

6

Figure 4.7 Effect of number of genes per chromosome on the performance of the

GEP model.

110

0

1

2

3

4

5

6

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Mutation rate

Mea

n sq

uar

ed e

rror

trai

nin

g

0

1

2

3

4

5

6

Mea

n sq

uar

ed e

rror

val

idat

ion

Training set

Validation set

Optimum mutation rate

×105

×106

Figure 4.8 Effect of mutation rate on the performance of the GEP model.

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5

Gene recombination rate

Mea

n s

qu

ared

err

or tr

ain

ing

2

3

4

5

6

Mea

n s

qu

ared

err

or v

alid

atio

nTraining set

Validation set

Optimum gene recombination rate

×10

5

×10

6

Figure 4.9 Effect of the gene recombination rate on the performance of the GEP

model.

111

The functions group that produced the best output fitness includes functions (+, -, /,× ,

2x , 3x , , 3 ). The presence of a function such as the among the functions

group is recognizable in the models of the evolutionary algorithms. During the

evolution process, this function is selected randomly by the program to improve the

fitness of the solution. The results also showed that the model performs better when

the addition is used as a linking function. Figures 4.8 and 4.9 present the influence of

the rates of the genetic operators (mutation and gene recombination) on the

performance of the GEP model. It can be seen that the GEP model performs best

when mutation and gene recombination rates are 0.05 and 0.2, respectively. For

brevity the graphical representation of the driven piles’ results are not shown, but the

optimum setting parameters for the driven piles model are provided in Table 4.6.

Table 4.6 Optimum GEP models parameters Driven piles GEP parameter Bored piles

Concrete Steel Number of

chromosomes 24 21 23

Number of genes 3 3 3

Chromosome head size

9 9 9

Functions set +, -, × , /, 2x , 3x ,

, 3 +, -, × , /, 2x , 3x ,

, 3 +, -, × , /, 2x , 3x ,

, 3 , Ln

Linking function + + +

Fitness function aMSE MSE MSE

Mutation rates 0.05 0.05 0.04

Gene recombination rate

0.2 0.2 0.2

aMSE indicates mean squared error

4.5.2 Selection of the GEP model

After finding the optimum values of setting parameters, the GEP model was

determined by conducting several runs using the optimum setting parameters. The

outputs of these runs were several chromosomes (models) which represent potential

112

solutions to the problem. The best model was determined by screening these solutions

through selection criteria which are defined as follows: First, the model has to have

correlation coefficient, r ≥ 0.90, for both of the training and validation sets. Second, it

must have mean values within 10%. Third, it must give results that agree with what is

expected in the sensitivity analysis, which is explained later. The desirable criteria of

the model are to be short and simple expressions.

4.5.3 Optimization and simplification of the GEP model

The third stage was to develop the model that is selected from the previous stage. The

model that satisfied selection criteria is further developed with the optimization and

simplification procedures, which are available in the program. The model is then

formulated and its performance is analysed further.

Figure 4.10 Expression tree (ET) of the GEP model formulation for bored piles d0 = D; d1= L; d2 = tipcq − ; d3= shaftcq − ; Sqrt = Square root; 3Rt = Cubic root; Sub-ET 1, c3 = 250.80;

Sub-ET 2, c0 = 52; Sub-ET 3, c0 = 1171, c3 = 265

113

4.6 MODELS FORMULATION

The expression trees of the GEP models are shown in Figure 4.10 for bored piles

and Figures 4.11 and 4.12 for driven piles. As mentioned earlier, one of the

advantages of the GP techniques is that the relationship between model inputs and

the corresponding outputs is automatically formulated in a mathematical equation

that is accessible to the users.

Figure 4.11 Expression tree (ET) of the GEP model formulation for driven concrete piles. d0 = Deq; d1 = L; d2 = tipcq − ; d3 = shaftcq − ; d4 = sf ; Sqrt = Square root; 3Rt =

Cubic root; X2, X3 = X to power 2 and 3, respectively; Sub-ET 1 c1 = -86.04; Sub-ET 2 c0 = 4, c1 = 18.58; Sub-ET 3 c1= 17.7

114

Figure 4.12 Expression tree (ET) of the GEP model formulation for driven steel piles. d0 = Deq; d1 = L; d2 = tipcq − ; d3 = shaftcq − ; d4 = sf ; Sqrt = Square root; 3Rt = Cubic root; X2,

X3 = X to power 2 and 3, respectively; Sub-ET 1 c0 = 208.14; Sub-ET 2 c0 = 325.59

The expression trees of the models are easily translated into mathematical

formulations which are given in Eqns. (4.5), (4.6) and (4.7) for bored, concrete

driven-piles and steel driven-piles, respectively.

521251265

11711 33.1

25.1

−++

+−+

−+= −−− LqDqLD

qD

LQ tipctipcshaftcp (4.5)

( ) ( ) ( ) 16587.17

5.1014.103.885

2

5.1 +

++−−−−= −−−

eqshaftctipcshaftcp

DLqLLqLqQ (4.6)

( )[ ] ( ) )(59.325214.208 325.0

sseqtipctipceqpfLnLnfLDqqDLQ +−+−= −−

(4.7)

Where; D, Deq, pile diameter and equivalent pile diameter; L, pile embedment length;

tipcq − , average cone point resistance within tip influence zone; sf , average sleeve

friction along shaft; shaftcq − , average cone point resistance along shaft; Ln, natural

logarithm; Qp, predicted pile capacity.

115

4.7 MODEL VALIDATION

The robustness of the GEP model is evaluated through examining the model

performance in the following three steps:

4.7.1 Evaluating the model performance in training and validation sets

The performance of the GEP models is shown numerically in Table 4.7 and depicted

graphically in Figure 4.13.

Table 4.7 Performance of the GEP models in the training and validation sets Coefficient of correlation, r Mean, µ Pile type

Training Validation Training Validation Bored 0.96 0.96 1.04 0.99 Driven concrete 0.96 0.97 1.05 1 Driven steel 0.96 0.97 1.05 0.9

It can be seen from the Table 4.7 that two performance measures are used, namely the

coefficient of correlation, r, between the measured pile capacity, Qu, and the predicted

pile capacity, Qp, and the mean, µ, which measures the bias between Qu and Qp. The

mean is calculated according to Long and Wysockey (1999) as follows:

Lneµµ = (4.8)

and

∑=

=

n

iu

p

Ln Q

QLn

n 1

1µ (4.9)

Where; n is the number of observations.

A mean value equal to unity (i.e. µ = 1) indicates that, on average, Qp equals to Qu. If

µ < 1, this means that the method, on average, under-predicts pile capacity, and if µ >

1, the method, on average, over-predicts the pile capacity. The Table 4.7 indicates that

the GEP models perform well with high coefficients of correlation and good mean

prediction values in the training and validation sets.

116

Figure 4.13 also indicates that the models - (a), (b1) and (b2) - have minimum scatter

around the line of equality between the measured and predicted pile capacities for the

training and validation sets. The above results demonstrate that the developed GEP

models are reliable and perform well.

4.7.2 Conducting sensitivity analysis

To examine further the generalization ability (robustness) of the developed GEP

models, sensitivity analyses were carried out to demonstrate the response of each

model to a set of hypothetical input data that lay within the range of the data used for

model training. For example, the effect of one input variable, such as the pile

diameter, D, was investigated in the bored pile model by allowing it to change while

all other input variables were set to selected constant values. The inputs were then

accommodated in the GEP model and the predicted pile capacity was calculated. This

process was repeated for the next input variable and so on, until the model response

had been examined for all inputs. The robustness of the GEP model was determined

by examining its predictions and comparing that with what is available geotechnical

knowledge and experimental data.

The results of the sensitivity analyses are shown in Figures 4.14 and 4.15 for the

bored piles and driven piles, respectively.

Visual inspections to the figures may conclude that: For bored piles, the Figure 4.14

shows that the pile diameter and average of cone point resistance, tipcq − , are the most

influential variables on the pile capacity. This means that the piles’ tip contribute in

significant part of pile capacity. This can be because 95 percent of the studied cases

have the tip in sand; it is known in the geotechnical engineering that the piles

embedded in sand provide most of its resistance from the tip. The figure also shows

that there is steady increase in the pile capacity with increase of shaft length and

weighted average of cone point resistance along shaft length.

117

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

Measured pile capacity (kN)

Pre

dicte

d p

ile c

apac

ity (kN

)

Training set (r = 0.96)

Validation set r = 0.97)

(b2)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000


Pre

dicte

d p

ile c

apac

ity (kN

)

Training Set (r = 0.96)

Validation Set (r = 0.97)

(b1)

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000Measured pile capacity (kN)

Pre

dicte

d p

ile c

apac

ity (kN

)

Training Set (r = 0.96)

Validatoin Set (r = 0.99)

(a)

Figure 4.13 Performance of the GEP models in the training and validation sets: (a) bored piles; (b1) concrete driven piles; (b2) steel driven piles.

118

In the case of driven piles, the Figure 4.15 shows that the sleeve friction has no

influence on the capacity of concrete piles and minor influence on steel piles capacity.

Therefore this variable can be considered as a secondary variable. The figure also

shows that the variations of pile length have insignificant influence on the pile

capacity of steel piles. On the other hand, the variations of the pile length show great

influence on the capacity of concrete piles. This can be because the concrete piles

have stronger adherence with soil than the steel piles. Thus when pile length increases

the surface area of the pile increases leading to more adherence with the soil. Similar

conclusion can be reached when considering the influence of shaftcq − on the capacities

of the two piles groups (concrete and steel). It can also be seen that the capacities of

the two piles group increase in the same rate with the tipcq − increase. The Figure 4.15

also indicates that concrete piles are higher capacity than the steel piles.

In all cases, the results of sensitivity analysis prove an incremental relationship

between each of the input variables and the output, Qu. This agrees with what is

available in the geotechnical knowledge and experimental data. Hence, the sensitivity

analyses provide an additional confirmation that the developed GEP models perform

well.

119

500

750

1000

1250

1500

1750

2000

2250

2500

0 10 20 30 40 50

Average cone point resistance (MPa)

Pile

ca

paci

ty (

KN

)

700

900

1100

1300

1500

1700

1900

2100

2300

4 8 12 16 20 24 28

Average cone point resistance along shaft (MPa)

Pile

ca

paci

ty (

kN)

300

800

1300

1800

2300

2800

3300

3800

4300

0 400 800 1200 1600 2000

Pile diameter (mm)

Pile

ca

paci

ty (

kN)

500

750

1000

1250

1500

1750

2000

0 10 20 30 40 50

Pile embedded length (m)

Pile

ca

paci

ty (

kN)

Figure 4.14 Sensitivity analyses to test the robustness of the GEP bored piles model

120

0

500

1000

1500

2000

2500

3000

3500

250 350 450 550 650

Pile diameter (mm)

Pile

ca

paci

ty (

kN)

Concrete piles

Steel piles0

500

1000

1500

2000

2500

3000

3500

4000

10 15 20 25

Pile embedded length (m)

Pile

ca

paci

ty (

kN)

Concrete piles

Steel piles

0

500

1000

1500

2000

2500

3000

3500

9 11 13 15 17 19

Average cone point resistance (MPa)

Pile

ca

paci

ty (

kN)

Concrete piles

Steel piles

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100

Average sleeve friction (kPa)

Pile

ca

paci

ty (

kN)

Concret piles

Steel piles

0

500

1000

1500

2000

2500

3000

0 5 10 15

Average cone point resistance along shaft (MPa)

Pile

ca

paci

ty (

kN)

Concrete piles

Steel piles

Figure 4.15 Sensitivity analyses to test the robustness of the GEP driven piles models

121

4.7.3 Comparing GEP model with number of CPT-based methods

A comparison between the GEP models and number of currently used CPT-based

methods is carried out aiming to examine the accuracy of the GEP models further.

The methods used for comparison with the GEP bored piles model include

Schmertmann (1978), LCPC (1982) and Alsamman (1995). The methods selected for

comparison with the GEP driven piles model are De Ruiter and Beringen (1979),

LCPC (1982) and Eslami and Fellenius (1997). Statistical evaluation is made to assess

the performance of the GEP models and traditional CPT-based methods, in relation to

the available 50 case records of bored piles and 58 case records of driven piles. For

this purpose, the ranking index method, RI, proposed by Abu-Farsakh and Titi (2004)

is used. According to this method, different statistical criteria are utilized to measure

the performance of each method and then the criteria are summed to calculate the

ranking index RI (RI = R1+R2+R3). The lower the ranking index the better the

predicting performance of the method.

The first criterion, R1, is the equation of the best fit line of predicted versus measured

capacity (Qp/Qu) with the corresponding coefficient of correlation, r. According to the

criterion, the closer the ratio of Qp/Qu and the correlation coefficient, r, to one the

better the method performs.

The results of bored piles are indicated numerically in Table 4.8 (columns 3, 4 and 5)

and graphically in Figure 4.16. Inspection of the results may conclude that the GEP

model has the best fit equation Qfit/Qu = 0.91 with r = 0.96. Figure 4.16 also illustrates

that the GEP model has the minimum scatter around the line of equality between

measured and predicted pile capacities, therefore GEP is given R1 = 1. According to

this criterion, the GEP model tends to under-predict the pile measured capacity by an

average of 9%. It can also be seen the LCPC method ranks second (R1 = 2) with

Qfit/Qu = 1.1 which means that this method tends to over-predict the pile capacity by

an average of 10%. The results also show that the Schmertmann method tends to over-

predict the measured pile capacity by an average of 12%, whereas the Alsamman

method tends to under-predict the pile capacity by an average of 11%. Therefore, the

Alsamman method is given R1 = 3 and the Schmertmann method is given R1 = 4.

122

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000


Pre

dict

ed p

ile c

apac

ity (

kN)

Schmertmann

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000


Pre

dict

ed p

ile c

apac

ity (

kN)

Bustamante & Gianeselli

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000


Pre

dict

ed p

ile c

apac

ity (

kN)

GEP (This tsudy)

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000


Pre

dict

ed p

ile c

apac

ity (

kN)

Alsamman

Figure 4.16 Performance comparison of GEP bored piles model and CPT based

methods

Table 4.8 Performance of the GEP models versus available CPT-based methods.

Best fit calculations Arithmetic calculations

Cumulative probability

Overall rank P

iles

Method Qfit/Qu r R1 µ σ R2 P50 R3 RI

Final rank

GEP 0.91 0.96 1 1.01 0.3 1 0.98 1 3 1 Schmertmann 1.12 0.87 4 1.40 0.5 4 1.30 4 12 4 LCPC 1.09 0.91 2 1.04 0.3 3 0.96 2 7 2

Bored

Alsamman 0.89 0.95 3 0.98 0.3 2 0.92 3 8 3 GEP 0.92 0.92 2 1.04 0.3 1 1.01 1 4 1

De Ruiter 0.77 0.90 4 0.79 0.3 4 0.82 2 10 4

LCPC 0.99 0.85 1 1.16 0.3 2 1.25 4 7 2

Driven C

o.

Eslami 1.13 0.96 3 1.2 0.2 3 1.2 3 9 3

Co., Concrete piles; St., Steel piles; Qfit, fit capacity; Qu, measured capacity; r, coefficient of correlation; µ, mean; σ, standard deviation; P50, 50% cumulative probability; R1, R2, and R3, ranking criteria; RI, ranking index.

123

Table 4.8 Continued

Best fit calculations Arithmetic calculations

Cumulative probability

Overall rank

Piles group

Method Qfit/Qu r R1 µ σ R2 P50 R3 RI

Final rank

GEP 0.91 0.95 2 1.02 0.3 1 1.01 1 4 1

De Ruiter 0.89 0.95 3 0.70 0.4 4 0.75 4 11 4

LCPC 0.82 0.92 4 0.80 0.3 3 0.84 3 10 3

Driven S

t.

Eslami 1.05 0.95 1 1.05 0.2 2 1.04 2 5 2

Co., Concrete piles; St., Steel piles; Qfit, fit capacity; Qu, measured capacity; r, coefficient of correlation; µ, mean; σ, standard deviation; P50, 50% cumulative probability; R1, R2, and R3, ranking criteria; RI, ranking index.

The results of driven piles are indicated numerically in Table 4.8 (columns 3, 4 and 5)

and graphically in Figures 4.17 and 4.18.

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000


Pre

dic

ted p

ile c

apac

ity (

kN)

Eslami & Fellenius

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000


Pre

dic

ted p

ile c

apac

ity (

kN)

GEP (This study)

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000


Pre

dic

ted p

ile c

apac

ity (

kN)

Bustamante & Gineselli

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000


Pre

dict

ed p

ile c

apac

ity (

kN)

De Ruiter & Beringen

Figure 4.17 Performance comparison of GEP driven concrete piles model and CPT based methods.

124

It can be seen that the GEP model, for concrete piles, has fit equation Qfit/Qu = 0.92

with r = 0.92 and ranks second (R1 = 2), while the LCPC method has Qfit/Qu = 0.99

with r = 0.86 and ranks first (R1 = 1). According to this criterion, the LCPC and the

GEP model tends to under-predict the measured pile capacity by an average of 1%

and 9%, respectively. The results also show that the Eslami and Fellenius method

tends to over-predict the measured capacity by an average of 13% and ranks third (R1

= 3), whereas the DeRuiter & Beringen method tends to under-predict the pile

capacity by an average of 23% and ranks last (R1 = 4).

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

Meaured pile capacity (kN)

Pre

dict

ed p

ile c

apac

ity (

kN)

GEP (This study)

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000


Pre

dict

ed p

ile c

apac

ity (

kN)

Eslami & Fellenius

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000


Pre

dict

ed p

ile c

apac

ity (

kN)

De Ruiter & Bernigen

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000


Pre

dict

ed p

ile c

apac

ity (

kN)

LCPC

Figure 4.18 Performance comparison of GEP driven steel piles model and CPT based methods.

For steel piles, the GEP model has fit equation Qfit/Qu = 0.91 with r = 0.95, whereas

the Eslami and Fellenius method has Qfit/Qu = 1.05 with r = 0.95. Therefore, the GEP

model is given R1 = 2 and the Eslami and Fellenius method is given R1= 1. According

to this criterion, the Eslami and Fellenius method tends to over-predict the pile

capacity by an average of 5%, while the GEP model tends to under-predict the pile

capacity by an average of 9%.

125

The results also show that the LCPC is given (R1 = 3) and De Ruiter and Beringen

methods is given (R1 = 4) and the methods tend to under-predict the pile capacity by

an average of 15% and 16%, respectively.

The second criterion is to undertake mathematical calculations to obtain the arithmetic

mean, µ, and standard deviation, σ, for each method. The arithmetic mean, µ, is

calculated as in (4.9).

The σ is calculated according to Long and Wysockey (1999) as follows:

2

1

2

1

1∑

=

−

−=

n

iLn

u

p

Ln Q

QLn

nµσ (4.10)

(8)

Where; n is the number of observations; Qp is predicted pile capacity; Qu is measured

pile capacity; and µLn is logarithmic mean.

According to this criterion, the best method is the one that gives µ (Qp/Qu) closer to

one with σ (Qp/Qu) nearer to zero. The results of bored piles are given in Table 4.8

(columns 6, 7 and 8). As can be seen, the GEP model ranks first (R2 = 1) with µ =

1.01 and σ = 0.3 and the Alsamman method ranks second (R2 = 2) with µ = 0.98 and σ

= 0.3. This suggests that the GEP model tend to over-predict the measured pile

capacity by an average of 1%, whereas the Alsamman method tends to under-predict

the measured pile capacity by average of 2%. It can also be seen that the

Schmertmann method ranks last (R2 = 4) with µ = 1.3 and σ = 0.4 and the LCPC

method ranks third (R2 = 3) with µ = 1.04 and σ = 0.3.

The results of driven piles are given in Table 4.8 (column 6, 7 and 8) for each method.

According to the criterion, the GEP model, for concrete piles, ranks first (R2 = 1) with

µ = 1.04 and σ = 0.3. On the other hand, the De Ruiter and Beringen method ranks last

(R2 = 4) with µ = 0.79 and σ = 0.3. This means that the GEP model tends to over-

predict the measured pile capacity by an average of 4%, whereas the De Ruiter and

Beringen method tends to under-predict the measured pile capacity by an average of

21%.

126

The table also shows that both of the LCPC and Esalmi and Fellenius methods tend to

over-predict the capacity by an average of 16% and 20%, respectively. Therefore, the

LCPC methods ranks second (R2 = 2), whereas the Eslami and Fellenius method ranks

third (R2 = 3). The GEP model for steel piles also ranks first with µ = 1.02 and σ = 0.3,

whereas the DeRuiter method ranks fourth (R2 = 4) with µ = 0.7 and σ = 0.4.

According to this criterion, the GEP model tends to over-predict the pile capacity by

an average of 2%, while and the DeRuiter method tend to under-predict the pile

capacity by an average of 30%. The table also shows that the Eslami and Fellenius

method tends to over-predict the pile capacity by an average of 5% and ranks second

(R2 = 4). On the other had, the LCPC method tends to under-predict the pile capacity

by an average of 20% and ranks third (R2 = 3).

The third ranking criterion is the 50% cumulative probability, P50, as given in

Equation 4.11. P is obtained by sorting Qp/Qu in an ascending order for each method.

The smallest Qp/Qu is given number i = 1 and the largest is given i = n.

( )1+=

n

iP (4.11)

Where; i is order number for the corresponding ratio; and n is number of pile load

tests. The value of Qp/Qu that corresponds the P = 50% is chosen for comparison. The

nearer the P50 to unity the better the method performs. The results of bored piles

model are given in Table 4.8 (columns 9 and 10) for each method. It can be seen that

the GEP model ranks first (R3 = 1) with P50 = 0.98. On the other hand, the

Schmertmann method ranks last (R3 = 4) with P50 = 1.30. According to this criterion,

the GEP tends to under-predict measured pile capacity by an average of 2%, whereas

the Schmertmann method tends to over-predict the measured pile capacity by an

average of 30%. The table also shows that the LCPC method ranks second (R3 = 2)

and the Alsamman method ranks third (R3 = 3). The LCPC and Alsamnan methods

tend to under-predict measured pile capacity by an average of 4% and 8%,

respectively.

The results of the concrete driven piles model are given in Table 4.8 (columns 9 and

10) for each method. The GEP model with P50 = 1.01 ranks first (R3 = 1), whereas the

DeRuiter method with P50 = 0.80 ranks last (R3 = 4).

127

Based on this criterion, the GEP model tends to over-predict the measured pile

capacity by an average of 1%, whereas the DeRuiter method, tends to under-predict

the measured pile capacity by an average of 20%. The table also shows that the

Eslami and Fellenius and LCPC methods tend to over-predict the measured pile

capacity by an average of 20% and 25%, respectively. Hence, the Eslami and

Fellenius ranks second (R3 = 2) and the method LCPC ranks third (R3 = 4). The results

of the steel piles model show that the GEP ranks first with P50 = 1.01, whereas the

DeRutier and method ranks last with P50 = 0.64. It can also be seen that the Eslami

method ranks second with P50 = 1.04 and the LCPC method ranks third with P50 =

0.84.

The overall results, as seen in Table 4.8 (column 12), indicate that the developed GEP

models for bored and driven piles have achieved the lowest RI with minimum score

(RI = 3 for bored and RI = 4 for driven piles). This gives additional evidence to the

reliability and the accuracy of the obtained GEP models.

128

CHAPTER FIVE

SIMULATION OF LOAD-SETTLEMET BEHAVIOUR

5.1 INTRODUCTION

This chapter composed of two parts. In the first part, the load-settlement behaviour of

axially loaded piles has been simulated using the GEP technique. Several attempts are

carried out to model the load-settlement behaviour of bored piles. The results have

revealed that the GEP model has performed satisfactorily in a number of case records;

however, in the majority of the case records the model has shown weak performance.

Therefore, another technique has been attempted namely artificial neural networks

(ANNs). Part two of this chapter details the simulation of the load-settlement

behaviour using the ANNs.

5.2 SIMULATION OF LOAD-SETTLEMENT BEHAVIOUR USING GEP

In this part of the study, modelling the load-settlement behaviour of axially loaded

bored piles has been attempted. All modelling steps that are required to develop the

GEP model are carried out in similar fashion to the steps detailed in Chapter 4. The

additional steps are detailed as follows:

5.2.1 Including additional input variables

In addition to the input variables used in Chapter 4, the settlement, εi, the settlement

increment, ∆ εi, and the current state load, Pi, are incorporated into the input variables.

Because the data needed for the GEP model at the selected settlement increments

were not recorded in the original experiments of the pile load-settlement tests, the

curves of the available tests are digitized to obtain the required data. On average, a set

of 50 training patterns is used to represent a single load-settlement curve.

5.2.2 Modelling approach

In this work, the available commercial software package GeneXproTools 4.0 (Gepsoft

2002) is used for modelling. Several modelling attempts have been carried out to

129

model the load-settlement behaviour of bored piles using different input settings. The

summary of the input settings of those attempts is included in the Appendix D. The

modelling approach that brought the best results is discussed in this sub-section.

As there is interdependency in the load-settlement relationship, which means the

current state of load-settlement influence the next state, the current state load was

incorporated into the input variables and the GEP model is trained to predict the next

state of load-settlement by learning the current state of load-settlement. The

settlement and the settlement increment are normalised (= settlement/pile diameter),

because there is a wide range of non-uniformity of the settlement domain of the

modelled load-settlement cases. As mentioned in Chapter two, this may assist with

improving the GEP model performance. The settlement increment is chosen to be

incremental (0.01, 0.02, 0.03…), as recommended by Penumadu and Zhao (1999) The

advantage of using varying settlement increment is improving the modelling

capability without the need for large size of training data and also reducing the time

required for model evolution. A sample of the input setting is presented in Table 5.1.

Table 5.1 Sample of data input setting used to develop the GEP model

tipcq −

(MPa) shaftc

q −

(MPa) L (m) D (mm) i

ε % i

ε∆ % Pi (kN) Pi+1 (kN)

47.6 9.2 24.4 840 0.01 0.02 0 197 47.6 9.2 24.4 840 0.03 0.03 197 395 47.6 9.2 24.4 840 0.06 0.04 395 592 47.6 9.2 24.4 840 0.1 0.05 592 823 47.6 9.2 24.4 840 0.15 0.06 823 1119 47.6 9.2 24.4 840 0.21 0.07 1119 1448 47.6 9.2 24.4 840 0.28 0.08 1448 1843 47.6 9.2 24.4 840 0.36 0.09 1843 2238 47.6 9.2 24.4 840 0.45 0.1 2238 2573 47.6 9.2 24.4 840 0.55 0.11 2573 2918 47.6 9.2 24.4 840 0.66 0.12 2918 3263 47.6 9.2 24.4 840 0.78 0.13 3263 3652 47.6 9.2 24.4 840 0.91 0.14 3652 4034 47.6 9.2 24.4 840 1.05 0.15 4034 4401 47.6 9.2 24.4 840 1.2 0.16 4401 4775

D, pile diameter; L, pile embedment length; tipcq − , average cone point resistance

within tip influence zone; shaftcq − , average cone point resistance along shaft; i

ε =

normalized settlement; i

ε∆ = normalized settlement increment; Pi = current load state;

Pi+1 = future load state

130

Table 5.1 (continued)

tipcq −

(MPa) shaftc

q −


ε % i

ε∆ % Pi (kN) Pi+1 (kN)

47.6 9.2 24.4 840 1.36 0.17 4775 5185 47.6 9.2 24.4 840 1.53 0.18 5185 5499 47.6 9.2 24.4 840 1.71 0.19 5499 5839 47.6 9.2 24.4 840 1.9 0.2 5839 6156 47.6 9.2 24.4 840 2.1 0.21 6156 6417 47.6 9.2 24.4 840 2.31 0.22 6417 6687 47.6 9.2 24.4 840 2.53 0.23 6687 6972 47.6 9.2 24.4 840 2.76 0.24 6972 7255 47.6 9.2 24.4 840 3 0.25 7255 7522 47.6 9.2 24.4 840 3.25 0.26 7522 7762 47.6 9.2 24.4 840 3.51 0.27 7762 8009 47.6 9.2 24.4 840 3.78 0.28 8009 8235 47.6 9.2 24.4 840 4.06 0.29 8235 8479 47.6 9.2 24.4 840 4.35 0.3 8479 8726 47.6 9.2 24.4 840 4.65 0.31 8726 8935 47.6 9.2 24.4 840 4.96 0.32 8935 9125 47.6 9.2 24.4 840 5.28 0.33 9125 9263 47.6 9.2 24.4 840 5.61 0.34 9263 9397 47.6 9.2 24.4 840 5.95 0.35 9397 9538 47.6 9.2 24.4 840 6.3 0.36 9538 9680 14.6 4.5 10.2 320 0.01 0.02 0 13 14.6 4.5 10.2 320 0.03 0.03 13 28 14.6 4.5 10.2 320 0.06 0.04 28 47 14.6 4.5 10.2 320 0.1 0.05 47 70 14.6 4.5 10.2 320 0.15 0.06 70 99 14.6 4.5 10.2 320 0.21 0.07 99 131 14.6 4.5 10.2 320 0.28 0.08 131 169 14.6 4.5 10.2 320 0.36 0.09 169 210 14.6 4.5 10.2 320 0.45 0.1 210 238 14.6 4.5 10.2 320 0.55 0.11 238 262 14.6 4.5 10.2 320 0.66 0.12 262 288 14.6 4.5 10.2 320 0.78 0.13 288 317 14.6 4.5 10.2 320 0.91 0.14 317 337 14.6 4.5 10.2 320 1.05 0.15 337 355 14.6 4.5 10.2 320 1.2 0.16 355 376 14.6 4.5 10.2 320 1.36 0.17 376 399 14.6 4.5 10.2 320 1.53 0.18 399 425 14.6 4.5 10.2 320 1.71 0.19 425 451 14.6 4.5 10.2 320 1.9 0.2 451 478 14.6 4.5 10.2 320 2.1 0.21 478 507



ε =


ε∆ = normalized settlement increment; Pi = current state load;

Pi+1 = future state load

131

5.2.3 Results

The results have revealed a strong correlation between the targeted and predicted

load-settlement behaviour of the studied cases in training and validation sets.

However, after formulating the model, it has shown weak performance when applied.

To explain this, the Case record 42 is selected from the validation set, as an example.

As illustrated in Figure 5.1 (a), when applying the model on the validation set the

model performed very well and for this case the MSE was 411. After model

formulation and application on the same case, as shown in Figure 5.1 (b), the results

appeared different and the MSE became 67755.

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5 6

(Settlement / diameter)%

Load

(kN

)

Measured

GEP

(a)

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5 6

(Settlement / diameter)%

Load

(kN

)

Measured

GEP

(b)

Figure 5.1 Performance of the GEP model applied on Case 42. (a) in validation set; and (b) after formulation.

132

The reason is that in (a) the model used the values provided in column 7 of Table 5.1

as a current state of load-settlement to predict the output. In (b) the model is required

to utilize its predicted output in step one, for instance, to predict the output for step

two, which is the real situation that the model suppose to perform in practice. As a

result, the amount of error between the targeted and the predicted values have

accumulated and caused a shift in the trend of the load-settlement relationship from its

initial condition. Table 5.2 shows the results of this case.

Table 5.2 Results of GEP model predictions for case 42 after formulation

tipcq −

(MPa) shaftc

q −

(MPa) L

(m) D

(mm) i

ε %

iε∆

%

Pi

(kN) (a)

Pi+1 (kN) Measured

Pi+1 (kN) GEP (a)

Pi (kN) (b)

Pi+1 (kN) GEP (b)

17.8 14.3 7 405 0.01 0.02 0 38 29 0 29 17.8 14.3 7 405 0.03 0.03 38 76 73 29 64 17.8 14.3 7 405 0.06 0.04 76 122 113 64 101 17.8 14.3 7 405 0.1 0.05 122 183 160 101 140 17.8 14.3 7 405 0.15 0.06 183 259 222 140 179 17.8 14.3 7 405 0.21 0.07 259 351 298 179 218 17.8 14.3 7 405 0.28 0.08 351 442 390 218 257 17.8 14.3 7 405 0.36 0.09 442 551 481 257 296 17.8 14.3 7 405 0.45 0.1 551 587 589 296 335 17.8 14.3 7 405 0.55 0.11 587 623 625 335 373 17.8 14.3 7 405 0.66 0.12 623 662 660 373 410 17.8 14.3 7 405 0.78 0.13 662 708 699 410 446 17.8 14.3 7 405 0.91 0.14 708 757 744 446 482 17.8 14.3 7 405 1.05 0.15 757 810 792 482 517 17.8 14.3 7 405 1.2 0.16 810 860 844 517 551 17.8 14.3 7 405 1.36 0.17 860 895 893 551 584 17.8 14.3 7 405 1.53 0.18 895 933 927 584 617 17.8 14.3 7 405 1.71 0.19 933 965 964 617 648 17.8 14.3 7 405 1.9 0.2 965 999 996 648 679 17.8 14.3 7 405 2.1 0.21 999 1026 1029 679 708 17.8 14.3 7 405 2.31 0.22 1026 1047 1055 708 737 17.8 14.3 7 405 2.53 0.23 1047 1070 1075 737 766 17.8 14.3 7 405 2.76 0.24 1070 1093 1097 766 793 17.8 14.3 7 405 3 0.25 1093 1119 1120 793 819 17.8 14.3 7 405 3.25 0.26 1119 1146 1145 819 845 17.8 14.3 7 405 3.51 0.27 1146 1165 1171 845 870



ε =


ε∆ = normalized settlement increment; Pi = current state load;

Pi+1 = future state load

133

It is concluded that although the model may perform well in number of cases, it

performs unsatisfactorily in many other cases and therefore can not be relied on.

Consequently, better artificial intelligence technique is sought and that is the artificial

neural network. The development of ANN model is described in the following sub-

section.

5.3 SIMULATION OF LOAD-SETTLEMENT BEHAVIOUR USIG ANNs

ANNs have been applied for modelling the load-settlement behaviour of the piles

using same data set used for the development of the GEP model. The steps that are

required to develop the ANN models are the same steps that carried out to develop the

GEP model in Chapter 4. The new and different steps are detailed as follows:

5.3.1 Modelling approach

In this work, ANN models are developed using the commercial available software

package Neuroshell 2, release 4.0 (Ward 2000). Three ANN models are developed for

piles installed in sand and mixed soil: a model for bored piles and two models for

driven piles (i.e. a model for each of steel and concrete piles).

As the pile load-settlement relationship involves interdependency between the current

and next states of load-settlement points, the sequential (recurrent) neural network is

used. The sequential neural network implies an extension of the MLPs and was first

proposed by Jordan (1986). It includes two sets of input units; i.e. plan units and

current state units. The role of the plan units is to present a set of independent input

variables to the network, whereas the role of the current state units is to remember the

past activity during training. In the first iteration, patterns of input data are presented

to the plan units while the current state units are set to zero and the network is allowed

to predict the output which in turn is copied back to the current state units for the next

training epoch. The actual output is used to modify the weights of the network using

the back-propagation learning laws. In the next epoch, the network is presented with

input from plain units and the current state units and this process continues until the

end of the training phase. The performance of the trained network is then tested using

an independent validation set.

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The sequential neural network that is used to develop bored piles model is depicted in

Figure 5.2. Similar network is used to develop the ANN models for driven piles but

with additional plane input node representing the average sleeve friction, s

f , along

shaft.

D Hidden units L tipcq −

Output unit shaftcq − Pi+1

εi ∆εi Pi

Plan units

Current state units

Figure 5.2 Schematic representation of the structure of ANN model for bored piles

5.3.2 Input setting

A sample of data input setting which are used to develop the ANN models is shown in

Table 5.3.

Table 5.3 A sample of data input setting used to develop the ANN models

tipcq −

(MPa) shaftc

q −


ε % i

ε∆ % Pi+1 (kN)

47.6 9.2 24.4 840 0.01 0.02 197 47.6 9.2 24.4 840 0.03 0.03 395 47.6 9.2 24.4 840 0.06 0.04 592 47.6 9.2 24.4 840 0.1 0.05 823 47.6 9.2 24.4 840 0.15 0.06 1119 47.6 9.2 24.4 840 0.21 0.07 1448 47.6 9.2 24.4 840 0.28 0.08 1843 47.6 9.2 24.4 840 0.36 0.09 2238 47.6 9.2 24.4 840 0.45 0.1 2573



ε =



Pi+1 = future load state

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Table 5.3 A sample of data input setting used to develop the ANN model (continued)

tipcq −

(MPa) shaftc

q −


ε % i

ε∆ % Pi+1 (kN)

47.6 9.2 24.4 840 0.55 0.11 2918 47.6 9.2 24.4 840 0.66 0.12 3263 47.6 9.2 24.4 840 0.78 0.13 3652 47.6 9.2 24.4 840 0.91 0.14 4034 47.6 9.2 24.4 840 1.05 0.15 4401 47.6 9.2 24.4 840 1.2 0.16 4775 47.6 9.2 24.4 840 1.36 0.17 5185 47.6 9.2 24.4 840 1.53 0.18 5499 47.6 9.2 24.4 840 1.71 0.19 5839 47.6 9.2 24.4 840 1.9 0.2 6156 47.6 9.2 24.4 840 2.1 0.21 6417 47.6 9.2 24.4 840 2.31 0.22 6687 47.6 9.2 24.4 840 2.53 0.23 6972 47.6 9.2 24.4 840 2.76 0.24 7255



ε =



Pi+1 = future load state 5.3.3 Data pre-processing

After completion of data division, a pre-processing step is carried out by scaling the

input and output variables so that all variables receive equal attention during training.

For input variables, the range of the scaling is selected to be between -1 to 1 to

coincide with ultimate limits of the transfer function (tanh) in the hidden layer and for

output variable 0 to 1 to coincide with the ultimate limits of the transfer function

(logistic) in the output layer. The commonly scaling method (Master 1993) for

calculating a scaled value n

x for a variable x with minimum value min

x and maximum

value max

x is adopted as follows:

minmax

min

xx

xxx

n −−= (5.1)

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5.3.4 Network geometry and model parameters

Network geometry

The search for optimum network began with determining the model architecture (that

is the number of hidden layers and nods). A network with one hidden layer is used in

this study. Hornik et al. (1989) recommended that one hidden layer can approximate

any continuous function provided that sufficient connection weights are used. The

trial-and-error approach is used to determine the optimum values of network

parameters. In the first stage, the number of hidden nodes was determined by

assuming the following neural network parameters: initial connection weights of 0.3,

learning rate of 0.1, momentum term of 0.1, tanh transfer function in the hidden layer

and sigmoidal transfer function in the output layer.

During training phase, it is important to decide when training stop. This in fact is a

challenging task on which the successful application of ANN depends (Das and

Basudhar 2006-2008). Therefore it is necessary adopting training strategy so that to

avoid model over-fitting which usually takes palace if training is excessive; on the

other hand sufficient training should be given to the network in order not to get under-

trained model. In this work, the mean squared error, MSE, between the actual and the

predicted values of the pile loads in the validation set was used as stopping criterion to

terminate the training. Whenever the MSE of the validation set has reached the lowest

value with no improvement in the performance of the training set, training is stopped

and the output is examined. Several neural networks were trained assuming the

following number of hidden nodes: 2, 3, 4, …, (2I+1); where I is the number of

inputs, as recommended by Caudill (1988). The geometry of the neural network that

had the lowest MSE for both of training and validation set is considered as the

optimum.

Model parameters

To achieve best weight optimization, the optimal model parameters including learning

rate, momentum term and initial weights need to be determined. The optimum model

parameters is achieved by training the network with different combinations of

learning rates (i.e. 0.05, 0.06, 0.07, … 0.1, 0.15, 0.2, …, and 0.6) and momentum

terms (i.e. 0.05, 0.1, 0.15, … and 0.6). In each of training attempts, when MSE

reached minimum value in the validation set the training stopped.

137

This continued until all of the above values were investigated. The values of the

parameters (learning rate and momentum term) that produced a model with lowest

MES are considered as the optimal. It should be mentioned, that the optimum number

of hidden nodes, which was obtained in the previous step, is used in all of the training

attempts of this step. The model is then retrained with different initial weights to

investigate a better performance model.

Results

The results of training attempts, which have aimed to find the best model architecture,

are shown in Figure 5.3. For brevity, the figures for driven piles are not shown. It can

be seen that the performance of the ANN model improves with increasing numbers of

hidden nodes. The performance improved rapidly when number of hidden nodes is

changed from 1 to 4; however, there is a little improvement in the performance of the

model beyond 6 hidden layer nodes. The Figure 5.3 also shows that the network with

12 hidden nodes has the lowest MSE. Hence, it has the best performance. Although

this network has the lowest prediction error, the network with 6 hidden nodes can be

considered as optimal. This is due to there is not much difference between the

performances of the two networks, and also because the network with 6 hidden nodes

has a smaller size.

0

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Sca

led

MS

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Figure 5.3 Influence of number of hidden nodes on ANN model performance in validation set. MSE: mean squared error.

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The influence of learning rate on the performance of the ANN model can be seen on

Figure 5.4. The ANN model performs best when learning rate is 0.08. Hence, this

learning rate can be considered as optimal. The Figure also shows that the

performance of the ANN model reduces when the learning rate increases. This is

possibly due to the presence of local minima.

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Figure 5.4 Influence of learning rate on ANN model performance in validation set. MSE: mean squared error.

The effect of momentum term on the performance of the ANN model is illustrated in

Figure 5.5. It can be seen that the momentum term has insignificant influence on the

performance of the ANN model in the range of 0.1-0.25; however, the best

performance was obtained when momentum term is 0.3. Thus the model that was

found to perform best for bored piles composed of six hidden layer nodes, learning

rate of 0.08 and momentum term of 0.3.

For driven piles, the model that is found to perform best, for steel piles, is composed

of eleven hidden layer nodes, learning rate of 0.3 and momentum term of 0.2. The

model that is found to perform best for concrete piles includes eleven hidden layer

nodes, learning rate of 0.3 and momentum term of 0.3.

139

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Sca

led

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Figure 5.5 Influence of momentum term on ANN model performance in validation set. MSE: mean squared error.

5.3.5 Results and model validation

The obtained Run Code of each developed ANN model are provided in the Appendx

E.

Evaluating the model performance in training and validation sets

The performance and the predictive ability of the developed ANN models in the

training and validation sets is shown graphically in Figures 5.6-5.14, for bored piles;

in Figures 5.15-5.19, for concrete driven piles; and in Figures 5.20-5.25, for steel

driven piles. The solid line in the figures represents the experimental data while the

dotted lines are for the ANN model predictions.

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Figure 5.13 Simulation results in validation set of the developed ANN model for

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Figure 5.14 Simulation results in validation set of the developed ANN model for

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Figure 5.15 Simulation results in training set of the developed ANN model for concrete driven piles.

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Figure 5.19 Simulation results in validation set of the developed ANN model for concrete driven piles.

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Figure 5.20 Simulation results in training set of the developed ANN model for steel driven piles.

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Figure 5.25 Simulation results in validation set of the developed ANN model for steel driven piles.

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A visual inspection the figures may conclude:

For bored piles, the ANN model performs well and is capable in simulating the

measured load-settlement behaviour of the piles. For most of the training cases, there

is an excellent correlation between ANN and measured load-settlement curve.

Examining the predictive ability of the ANN model in the validation set indicate that

the ANN model is able to forecast the load-settlement behaviour accurately.

It can also be seen that, in few training cases records, the ANN model may not

perform as good as in the other cases. This cannot be considered as a shortcoming, as

in most of these cases (e.g. 9, 19, 23 and 36) the ANN model under-predicts the load-

settlement relationship and as a result this may assist with achieving safe design.

For driven piles, both of the ANN models that are developed for concrete and steel

piles perform well in training and validation sets. There is an excellent correlation can

be seen between measured and simulated load-settlement relationship of the modelled

piles. The figures also show that the complex nonlinear relationship of pile load-

settlement is well simulated by the ANN models including the strain hardening

behaviour.

The developed ANN models are also evaluated numerically using two performance

measure that are the coefficient of correlation, r, between the measured and the

predicted load-settlement and the mean which calculated from: Equations (4.8, 4.9)

Chapter 4. The results are shown in Table 5.4.

Table 5.4 Performance of the ANN models in the training and validation sets. Piles group Data set Coefficient of correlation, r Mean, µ

Training 0.98 0.89 Bored

Validation 1.00 0.91 Training 0.99 1.18

Driven concrete Validation 1.00 0.96 Training 0.99 1.06

Driven steel Validation 1.00 0.96

The results indicate that the developed ANN models perform well in both of training

and validation sets with high values of coefficient of correlation and low mean values.

161

These results demonstrate that the ANN models are able to accurately predict the

nonlinear behaviour of pile load settlement for bored and driven piles in sand and

mixed soils and therefore can be used with confidence for routine design practice.

Comparing ANN models and selected load-transfer methods

A comparison between the ANN models and number of load-transfer methods is

carried out to examine the accuracy of the developed ANN models further. The

methods used for comparison include Verburrge (1986), Fleming (1991) and API

(1993). The predicted load-settlement curves given by the ANN models and the load-

transfer methods are compared with experimental load-settlement curves provided in

validation cases records.

It should be mentioned that the API (1993) method requires the determination of pile

unit shaft and tip resistance for constructing the load-settlement behaviour. The

method depends on calculations of undrained shear strength for determining pile unit

shaft and tip resistances in cohesive soils. The undrained shear strength is correlated

with CPT data using the correlation which is provided in Lunne (1997) as follows:

0

. σ+=ucc

SNq (5.2)

Where; c

q = measured cone resistance; c

N = theoretical cone factor, taken as 9.9

according to DeBeer (1977); u

S = undrained shear strength; 0

σ = total stress.

The Fleming method also requires the calculations of pile unit shaft and base

resistance for simulating the load-settlement curve. The method suggests using

conventional methods to calculate the pile unit shaft and base resistance. For this

purpose and in this study, the Bustamante and Gianeselli (1982) method is used.

Moreover, Fleming suggests number of correlations to be used to calculate the soil

initial shear modulus,0

G . The following correlation that was recommended by Imai

and Tonouchi (1982) is adopted.

162

6.0

0 50

=

a

c

ap

q

p

G (5.3)

Where; 0

G = initial shear modulus; a

p = atmospheric pressure; c

q = measured cone

resistance.

The results of comparison are illustrated graphically in Figures 5.26 and 5.27 for

bored piles and in Figures 5.28 and 5.29 for driven piles. The figures illustrate that the

predicted load-settlement curves by ANN models are in close agreement or, in a

number of cases, coincide with the experimental curves, whereas the predicted curves

by load-transfer methods are, in several cases, far from the experimental curves. It can

also be seen that the ANN models are capable to simulate the nonlinear behaviour of

the soil more accurately than the load-transfer methods. Moreover, the ANN models

are able to simulate the load-settlement behaviour beyond the point that is described

by the compared methods as pile capacity, whereas the load-transfer methods are not.

163

0

2000

4000

6000

8000

10000

12000

0 5 10 15


Loa

d (k

N)

MeasuredANNVerburgge

Case record 45

0

1000

2000

3000

4000

5000

0 5 10 15


Loa

d (k

N)

MeasuredANNVerburgge

Case record 42

0

200

400

600

800

1000

1200

0 5 10 15


Loa

d (k

N)

Measured ANN

Verburgge Fleming

Case record 44

0

2000

4000

6000

8000

10000

12000

0 5 10 15


Loa

d (k

N)

Measured ANNVerburgge FlemingAPI

Case record 43

0

200

400

600

800

0 2 4 6 8


Loa

d (k

N)

Measured ANNVerburgee FlemingAPI

Case record 46

0

100

200

300

400

500

600

0 2 4 6 8 10


Loa

d (k

N)


Case record 47

Figure 5.26 Comparison performance of ANN bored piles model and load-

transfer methods.

164

0

200

400

600

800

1000

1200

1400

0 10 20 30 40


Loa

d (k

N)


Case record 50

0

1000

2000

3000

4000

5000

0 5 10 15 20 25


Loa

d (k

N)


Case record 48

0

400

800

1200

1600

0 5 10 15 20

(settlement/diameter)%

Loa

d (k

N)

Measured ANNVeburgge FlemingAPI

Case record 49

Figure 5.27 Comparison performance of ANN bored piles model and load-

transfer methods.

165

0

700

1400

2100

0 2 4 6 8


Loa

d (k

N)


Case record 24

0

400

800

1200

1600

0 2 4 6 8


Loa

d (k

N)


Case record 25

0

1000

2000

3000

4000

5000

0 2 4 6 8


Loa

d (k

N)


Case record 28

0

200

400

600

800

1000

0 1 2 3


Loa

d (k

N)


Case record 27

Figure 5.28 Comparison performance of ANN concrete driven piles model and

load-transfer methods.

166

0

800

1600

2400

3200

0 1 2 3 4


Loa

d (k

N)


Case record 28

0

900

1800

2700

3600

4500

0 1 2 3 4 5


Loa

d (k

N)


Case record 26

0

300

600

900

1200

1500

1800

0 5 10 15 20


Loa

d (k

N)

Measured ANNVerburgge Fleming

Case record 27

0

400

800

1200

0 2 4 6 8 10


Loa

d (k

N)


Case record 29

0

200

400

600

800

1000

0 5 10 15


Loa

d (k

N)


Case record 30

Figure 5.29 Comparison performance of ANN steel driven piles model and load-

transfer methods.

167

Statistical evaluation is made to assess the performance of the ANN models and load-

transfer methods, in relation to the available case records. Coefficient of correlation,

r, and mean absolute percentage error (MAPE) are used for comparison. The mean

absolute percentage error is calculated from:

−=

m

prm

P

PP

nMAPE

1 (5.4)

Where:

mP = measured value

prP = predicted value

n = number of values

Table 5.5 Performance of the ANN models versus the load-transfer methods

Piles group

Prediction method

Coefficient of correlation, r R1

Mean absolute percentage error, MAPE

R2 Final rank RI

ANN 0.99 1 12 1 2 Verburgge 0.97 2 70 2 4 Fleming 0.94 3 70 2 5

Bored piles

API 0.87 4 66 3 7 ANN 0.96 1 6 1 2 Verburgge 0.64 4 27 2 6 Fleming 0.80 2 28 3 5

Driven piles (concrete)

API 0.69 3 31 4 7 ANN 0.99 1 15 1 2 Verburgge 0.76 4 84 4 8 Fleming 0.89 3 61 3 6

Driven piles (steel)

API 0.90 2 57 2 4 R1, R2, ranking criteria; RI, ranking index.

Using the ranking method which was detailed in Chapter 4, the compared methods are

ranked based on their scores. Two ranking criteria are used: the best fitting criterion

(R1) which employs the coefficient of correlation between predicted and measured

values as a measure of fitting and the error criterion (R2) which utilizes the mean

absolute percentage error between predicted and measured values as a measure of

error. The method that achieves nearest r to unity and least MAPE will be given R1 =

1 and R2 = 1. The results of comparison are indicated in Table 5.5.

168

For bored piles, with r = 0.99 the ANN model ranks first (R1 = 1) based on the first

criterion. The Verburgge method ranks second (R1 = 2), whereas the Fleming and the

API methods rank third (R1 = 3). With the lowest MAPE (MAPE = 12) among the

compared methods and according to the second criterion the ANN model also ranks

first (R2 = 1) and the API method ranks second (R2 = 2). The Fleming and Verburgge

methods on the other hand rank third (R2 = 3).

For concrete driven piles, the ANN model ranks first (R1 = 1) with r = 0.96, whereas

the Verburgge method ranks last (R1 = 4) with r = 0.64. The Fleming and API

methods rank third and fourth, respectively. Based on the second criterion and with

lowest MAPE (MAPE = 6) the ANN model ranks first (R2 = 1), whereas the API

method with the highest MAPE (MAPE = 31) ranks last (R2 = 4). The Verburgge and

Fleming methods rank second and third, respectively.

For steel driven piles, according to the first criterion the ANN model, with r = 0.99,

ranks first (R1 = 1). On the other hand, the Verburgge method, with r = 0.76, ranks

last (R1 = 4). The API and Fleming methods rank second and third, respectively.

Based on the second criterion the ANN model scored the lowest MAPE (MAPE = 15),

therefore it ranks first (R2 = 1). The API, the Fleming and the Verburgge methods

rank second, third and fourth, respectively.

The overall results, as seen in Table 5.5 (column 7), indicate that the developed ANN

models for bored and driven piles have achieved the lowest RI with minimum score

(RI = 2 for bored driven piles). This gives additional evidence to the reliability and the

accuracy of the obtained ANN models.

5.3.6 Output computer program

The developed ANN models are coded in an executable program which can be run

easily. A Fusioncharts software (FusionCharts Technologies 2009) was incorporated

to assist with program execution. At the beginning, the program asks the user to select

the piles group (bored, driven concrete or driven steel). Then the input variables are

required to be entered and the user have the option to choose the percentage ratio of

settlement/pile diameter (e.g. 5, 10, 15). The program is then ready for execution and

calculating the load versus (settlement/diameter)%. The output is the plot of load-

169

settlement diagram. The user then has the option to exit or carry out another attempt.

A simple flowchart of the program is shown in Figure 5.28. The program can be

further developed to be a complete package for using artificial intelligence technique

for modelling the pile foundation behaviour.

Select piles group

Enter input variables

Enter (settlement/diameter)%

Calculate

Try another

Exit

Figure 5.30 The flowchart of the ANN models computer program

170

CHPTER SIX

CONCLUSIONS AND RECOMMENDATIONS 6.1 CONCLUSIONS The evidence, analysis and discussion produced in the course of this study have

allowed the folloing conclusions to be drawn:

• The factors that have significant influence on the bearing capacity of pile

foundations include the pile embedded length and diameter, the average cone

point resistance within tip influence zone and weighted average cone point

resistance along shaft. The weighted average sleeve friction has a minor effect

and can be considered as a secondary factor.

• The weighted average method for calculating the average of cone point

resistance within tip influence zone or along pile shaft provides better

averaging results than the mathematic and geometric averages. The weighted

average proved useful particularly when many peaks and troughs are available

in measured values and when extreme changes exist in the values of cone

point resistance from one segment of the pile length to another.

• The parameters of the GEP model have different levels of influence on the

fitness of the output. The head size and number of genes per chromosome are

the most influential parameters.

• Learning rate and number of hidden nodes have significant effect on the

performance of the ANN model.

• Dividing data into statistically consistent sets is a necessary step for

developing the artificial intelligence models.

• The GEP is able to deal with noisy data efficiently and produce a model of

high performance.

171

• The GEP model has the ability to determine a solution which demonstrates the

interaction between the factors that affect the bearing capacity.

• The developed GEP model has an excellent predictive capability and provides

results that agree with what is available in the geotechnical knowledge.

• The GEP model is able to perform well in comparison with the traditional CPT

based methods.

• The results of the evaluation of the performance of the GEP model have

shown that the model performs well and can be used as an alternative for

predicting the axial capacity of piles embedded in sand and mixed soils.

• The GEP technique requires additional tools in order to be able to deal with

constitutive models. The technique lacks the facility that can utilize the output

of the current sate as an input for the next state.

• The ANN model is successfully and accurately able to model the load-

settlement behaviour of the piles. It has high ability to simulate the nonlinear

load-settlement relationship and strain hardening.

• The ANN model shows excellent performance in training and validation sets

with a high coefficient of correlation and low mean values.

• The ANN model performs well in predicting the load-settlement behaviour of

the piles compared with the load-transfer methods. Hence, the ANN can be

used as an alternative to predict the load-settlement of piles embedded in sand

and mixed soils.

172

6.2 RECOMMENDATIONS

• The GEP and the ANNs can be applied to develop models to predict the axial

capacity of piles group.

• The two techniques can be also applied to determine the bearing capacity and

the load-settlement behaviour of piles subjected to lateral loads.

• The two techniques also can be applied to predict the capacity of the piles

using the input of dynamic methods.

• Introducing additional tools to the GEP like the option of using more than a

linking function for the multi-gene chromosome may improve the ability of

the technique to achieve more accurate results.

• The capability of the GEP to model the constitutive behaviour of soil may

significantly be improved, if the technique is made capable to perform a

feedback task in which the predicted output in the current stat is fed back to

be an input for the next state.

• We recommend designers to consider the developed models as alternative for

for predicting the axial capacity and load-settlement behaviour of piles

embedded in sand and mixed soils.

173

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Every reasonable affort has been made to acknowledge the owners of copyright

material. I would be pleased to hear from any copyright owner who has been ommited

or incorrectly acknowledged.

191

APPENDIX A

Table A.1 Bored piles case records summary

Piles grou

p

Case record number

Reference

Case number at

the reference

Shape

Tip, closed or

open Ac (m

2) Acir

(m2/m) D or Deq

(mm) L (m) Type of load test

Type of cone

1 Alsamman (1995) LTN 89 round closed 0.951 3.458 1100 13.0 na M 2 ˝˝ LTN 894 ˝˝ ˝˝ 0.139 1.322 421 5.8 ˝˝ ˝˝ 3 ˝˝ LTN 865 ˝˝ ˝˝ 0.080 1.006 320 10.2 ˝˝ ˝˝ 4 ˝˝ LTN 652 ˝˝ ˝˝ 0.164 1.437 457 15.2 ˝˝ E 5 ˝˝ LTN 928 ˝˝ ˝˝ 0.121 1.236 393 6.5 CYC ˝˝ 6 ˝˝ LTN 923 ˝˝ ˝˝ 0.132 1.289 410 5.6 ˝˝ ˝˝ 7 ˝˝ LTN 870 ˝˝ ˝˝ 0.080 1.006 320 10.2 SML M 8 ˝˝ LTN 869 ˝˝ ˝˝ 0.080 1.006 320 7.7 ˝˝ ˝˝ 9 ˝˝ LTN 938 ˝˝ ˝˝ 0.128 1.267 403 9.2 CYC E 10 ˝˝ LTN 742 ˝˝ ˝˝ 0.520 2.558 814 24.2 QML ˝˝ 11 ˝˝ LTN 866 ˝˝ ˝˝ 0.080 1.006 320 10.2 SML M 12 ˝˝ LTN 911 ˝˝ ˝˝ 0.353 2.107 671 13.0 ˝˝ ˝˝ 13 ˝˝ LTN 860 ˝˝ ˝˝ 0.785 3.142 1000 9.5 na ˝˝ 14 ˝˝ LTN 861 ˝˝ ˝˝ 0.785 3.142 1000 9.0 ˝˝ ˝˝ 15 ˝˝ LTN 857 ˝˝ ˝˝ 0.554 2.640 840 24.4 CYC ˝˝ 16 ˝˝ LTN 302 ˝˝ ˝˝ 0.283 1.887 600 7.2 IE ˝˝

Bored piles

17 ˝˝ LTN 859 ˝˝ ˝˝ 0.951 3.457 1100 9.0 na ˝˝ Ac = cross section area, Acir = unit circumferential area; D = diameter; Deq = equivalent diameter; L = embedment length; SML = slow maintained load test; na = not available; CYC = cyclic load test; QML = quick maintained load test; CRP = constant rate of penetration; IE = incremental equilibrium; M = Mechanical; E = Electrical

192

Table A.1 Case records summary (continued)

Piles group

Case record

number Reference

Case number at the

reference

Shape

Tip, closed or

open Ac (m

2) Acir (m2/m)

D or Deq (mm)

L (m) Type of

load test

Type of cone

18 Alsamman (1995) LTN 886 ˝˝ ˝˝ 0.196 1.571 500 10.2 SML ˝˝ 19 ˝˝ LTN 896 ˝˝ ˝˝ 0.085 1.035 329 6.2 ˝˝ ˝˝ 20 ˝˝ LTN 895 ˝˝ ˝˝ 0.131 1.284 408 5.8 ˝˝ ˝˝ 21 ˝˝ LTN 881 round closed 0.213 1.638 521 8.2 CRP M 22 ˝˝ LTN 862 ˝˝ ˝˝ 2.546 5.657 1800 11.5 na ˝˝ 23 ˝˝ LTN 937 ˝˝ ˝˝ 0.129 1.274 405 8.4 CYC E 24 ˝˝ LTN 936 ˝˝ ˝˝ 0.129 1.274 405 10.4 ˝˝ E 25 ˝˝ LTN 893 ˝˝ ˝˝ 0.125 1.255 399 7.8 SML M 26 ˝˝ LTN 912 ˝˝ ˝˝ 0.353 2.107 671 10.2 ˝˝ ˝˝ 27 ˝˝ LTN 887 ˝˝ ˝˝ 0.145 1.351 430 8.7 CRP ˝˝ 28 ˝˝ LTN 871 ˝˝ ˝˝ 0.080 1.006 320 7.7 SML ˝˝ 29 ˝˝ LTN 872 ˝˝ ˝˝ 0.125 1.255 399 10.0 CRP ˝˝ 30 ˝˝ LTN 406 ˝˝ ˝˝ 0.283 1.887 600 12.0 SML ˝˝ 31 ˝˝ LTN 407 ˝˝ ˝˝ 0.283 1.887 600 12.0 ˝˝ ˝˝ 32 ˝˝ LTN 159 ˝˝ ˝˝ 0.951 3.458 1100 27.0 ˝˝ ˝˝ 33 ˝˝ LTN 868 ˝˝ ˝˝ 0.080 1.006 320 7.7 ˝˝ ˝˝

Bored piles

34 Eslami (1996) USPB2 ˝˝ ˝˝ 0.126 1.257 400 9.4 ˝˝ E Ac = cross section area, Acir = unit circumferential area; D = diameter; Deq = equivalent diameter; L = embedment length; SML = slow maintained load test; na = not available; CYC = cyclic load test; QML = quick maintained load test; CRP = constant rate of penetration; IE = incremental equilibrium; M = Mechanical; E = Electrical

193

Table A.1 Case records summary (continued)

Piles group

Case record

number Reference

Case number at the

reference

Shape

Tip, closed or

open Ac (m

2) Acir (m2/m)

D or Deq (mm)

L (m) Type of load test

Type of cone

35 Alsamman (1995) LTN 158 ˝˝ ˝˝ 0.925 3.410 1085 25.1 ˝˝ M 36 Eslami (1996) SEATW ˝˝ ˝˝ 0.096 1.100 350 15.8 ˝˝ E 37 Alsamman (1995) LTN 885 ˝˝ ˝˝ 0.196 1.571 500 10.2 SML M 38 ˝˝ LTN 925 ˝˝ ˝˝ 0.129 1.274 405 7.9 CYC E 39 ˝˝ LTN 93 ˝˝ ˝˝ 0.951 3.458 1100 6.0 CRP M 40 ˝˝ LTN 404 ˝˝ ˝˝ 0.313 1.983 631 18.3 CYC ˝˝ 41 ˝˝ LTN 880 round closed 0.213 1.638 521 8.2 CRP M 42 ˝˝ LTN 935 ˝˝ ˝˝ 0.129 1.274 405 7.0 ˝˝ ˝˝ 43 ˝˝ LTN 910 ˝˝ ˝˝ 0.915 3.391 1079 13.0 ˝˝ ˝˝ 44 ˝˝ LTN 892 ˝˝ ˝˝ 0.125 1.255 399 7.8 ˝˝ ˝˝ 45 ˝˝ LTN 95 ˝˝ ˝˝ 1.768 4.714 1500 6.0 ˝˝ ˝˝ 46 ˝˝ LTN 891 ˝˝ ˝˝ 0.126 1.257 400 7.8 ˝˝ ˝˝ 47 ˝˝ LTN 867 ˝˝ ˝˝ 0.080 1.006 320 7.7 ˝˝ ˝˝ 48 ˝˝ LTN 941 ˝˝ ˝˝ 0.456 2.395 762 16.8 ˝˝ ˝˝ 49 ˝˝ LTN 888 ˝˝ ˝˝ 0.145 1.351 430 8.7 ˝˝ ˝˝

Bored piles

50 ˝˝ LTN 897 ˝˝ ˝˝ 0.085 1.035 329 6.3 ˝˝ ˝˝ Ac = cross section area, Acir = unit circumferential area; D = diameter; Deq = equivalent diameter; L = embedment length; SML = slow maintained load test; na = not available; CYC = cyclic load test; QML = quick maintained load test; CRP = constant rate of penetration; IE = incremental equilibrium; M = Mechanical; E = Electrical

194

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30


Dep

th (

m)

0

40

80

120

160

200

0 1000 2000 3000 4000 5000

Load (kN)

Hea

d de

flect

ion

(mm

)


Failure load= 2624 kN

0

1100 mm

mud

peat

medium sand

7.6

10.3

13.0 m


CPT profile

Figure A.1 Summary sheet for Case record 1, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot

195

(a)

(b)

(c)

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35


Dep

th (

m)

silt

peat

sandy silt

medium sand

fine sand

0

1.2

1.8

2.8

4.2

420 mm4.2 m


CPT profile

0

20

40

60

80

100

0 300 600 900 1200 1500

Load (kN)

Hea

d de

flect

ion

(m

m)




196

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30


Dep

th (

m)


CPT profile

silty clay

medium sand

sandy gravel

medium sand

0

4.6

8.2

9.6

320 mm

10.2 m

12.8

0

7

14

21

28

35

0 200 400 600 800 1000

Load (kN)

Hea

d d

efle

ctio

n (

mm

)




197

(a)

(b)

(c)

0

3

6

9

12

15

18

21

0 5 10 15 20 25 30 35


Dep

th (

m)

SP

soft to medium clay

MI


CPT profile

00.3

7

455 mm15.3 m

0

13

26

39

52

65

78

0 400 800 1200 1600 2000

Load (kN)

Hea

d de

flect

ion

(mm

)




198

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35


Dep

th (

m)

0

6

12

18

24

30

0 200 400 600 800 1000

Load (kN)

Hea

d d

efle

ctio

n (m

m)



silt

fine to medium sand

clayey silt + silty fine sand

silty sand0

1

2.3

10.2

393 mm6.5 m


CPT profile

3.5


199

(a)

(b)

(c)

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30 35


Dep

th (

m)

0

5

10

15

20

25

30

0 150 300 450 600 750

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



clayey fine sand

gravel + sand

fine sand

micaceous silt+ fine sand

26

0

7.5

13.5

405 mm5.6 m


CPT profile


200

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 3 6 9 12 15 18 21


Dep

th (

m)

0

5

10

15

20

25

0 200 400 600 800 1000

Load (kN)

Hea

d d

efle

ctio

n (

mm

) Failure load= 830 kN


silty clay

medium sand

0

4.4

12.4

320 mm10.2 m


CPT profile


201

(a)

(b)

(c)

0

1.5

3

4.5

6

7.5

9

10.5

12

0 2 4 6 8 10 12 14


Dep

th (

m)

0

6

12

18

24

30

0 150 300 450 600 750

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



medium sand

silty clay

320 mm

7.7 m

4.6

0


CPT profile


202

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28


Dep

th (

m)

0

6

12

18

24

30

0 300 600 900 1200 1500

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



10.2 m320 mm

clayey silt

silty sand

fine sand

silt & silty sand

fine sand

0 0.5

2.3

5.6

9.3

11


CPT profile


203

(a)

(b)

(c)

0

12

24

36

48

60

0 1500 3000 4500 6000 7500

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



0

4

8

12

16

20

24

28

0 6 12 18 24 30 36 42


Dep

th (

m)

24.2 m814 mm

v. stiff sandy clay

sand & sandy silt

v. stiff sandy clay

27.5

13.4

4.5

0


CPT profile


204

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28


Dep

th (

m)

0

7

14

21

28

35

0 200 400 600 800 1000

Load (kN)

Hea

d d

efle

ctio

n (m

m)



medium sand

medium sand

silty clay

sandy gravel

0

4.6

8.2

9.6

320 mm 10.2 m


CPT profile


205

(a)

(b)

(c)

0

3

6

9

12

15

18

21

0 8 16 24 32 40 48 56


Dep

th (

m)

0

20

40

60

80

100

0 1500 3000 4500 6000 7500

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



sandy gravel

sandy gravel

gravelly sand

gravelly sand

0

5.2

10.2

13.4670 mm 13 m


CPT profile


206

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 4 8 12 16 20 24 28


Dep

th (

m)

0

26

52

78

104

130

0 800 1600 2400 3200 4000

Load (kN)

Hea

d de

flect

ion (

mm

)



fine sand

fine sand

0

5

6 peat

15.3

1000 mm 9.5 m


CPT profile


207

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 4 8 12 16 20 24 28 32


Dep

th (

m)

0

15

30

45

60

75

0 1000 2000 3000 4000 5000

Load (kN)

Hea

d d

efle

ctio

n (m

m)



sand

sand

0

3.3

6.7

peat

15.3

1000 mm 9 m


CPT profile


208

(a)

(b)

(c)

0

5

10

15

20

25

30

35

0 7 14 21 28 35 42 49


Dep

th (

m)

0

15

30

45

60

75

0 2500 5000 7500 10000 12500

Load (kN)

Hea

d d

efle

ctio

n (m

m)



fine sand

silty fine sand

clayey silt

fill

silty clay

0

4 5.5 7.3

21.7

28.9


CPT profile

840 mm 24.4 m


209

(a)

(b)

(c)

0

1.5

3

4.5

6

7.5

9

10.5

0 2 4 6 8 10 12 14 16


Dep

th (

m)

0

13

26

39

52

65

0 500 1000 1500 2000 2500

Load (kN)

Hea

d d

efle

ctio

n (m

m)



silty sand

clay

0

3.5

9.8

600 mm 7.2 m


CPT profile


210

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 4 8 12 16 20 24 28


Dep

th (

m)

0

20

40

60

80

100

120

0 1500 3000 4500 6000 7500

Load (kN)

Hea

d d

efle

ctio

n (m

m)



sand

sand

peat

1100 mm 7.2 m


CPT profile

0

5

6

15.3


211

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35


Dep

th (

m)

0

8

16

24

32

40

0 300 600 900 1200 1500

Load (kN)

Hea

d de

flect

ion

(mm

)



2.7 3.9

4.6

6.2

10.2

13.6

0

fill

peat

fine sand

medium sand

gravelly sand

silt

500 mm

10.2 m


CPT profile


212

(a)

(b)

(c)

0

1.5

3

4.5

6

7.5

9

10.5

12

0 3 6 9 12 15 18 21


Dep

th (

m)

0

30

60

90

120

150

0 300 600 900 1200 1500

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



0

1.5

8

silt

2.8

peat

medium sand


CPT profile

6.2 m 329 mm

2sandy silt


213

(a)

(b)

(c)

0

1

2

3

4

5

6

7

8

0 3 6 9 12 15 18 21 24


Dep

th (

m)

0

50

100

150

200

250

0 300 600 900 1200 1500

Load (kN)

Hea

d de

flect

ion

(mm

)



silt

peat

sandy silt

medium sand

fine sand

1.2

1.8

2.8

4.2

0

5.8 m 408 mm


CPT profile


214

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28 32


Dep

th (

m)

0

40

80

120

160

200

0 700 1400 2100 2800 3500

Load (kN)

Hea

d de

flect

ion

(mm

)



medium sand

gravelly sand

fill

0

5.3

10.2


CPT profile

521 mm

8.2 m


215

(a)

(b)

(c)

0

3

6

9

12

15

18

21

0 4 8 12 16 20 24 28 32


Dep

th (

m)

0

20

40

60

80

100

120

0 2000 4000 6000 8000 10000

Load (kN)

Hea

d de

flect

ion

(mm

)



fine sand

sand

mud & peat

clay

6

18

14.5

1800 mm 11.5 m

0


CPT profile


216

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 6 12 18 24 30 36 42


Dep

th (

m)

0

5

10

15

20

25

30

0 250 500 750 1000 1250

Load (kN)

Hea

d de

flect

ion

(mm

)



405 mm 8.4 m gravelly fine

sand

7

10.7

0

4.3

6.4 clayey silt

silt & sandy silt

silt & silty sand with thin

clay lenses


CPT profile


217

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 6 12 18 24 30 36 42


Dep

th (

m)

0

5

10

15

20

25

30

0 250 500 750 1000 1250

Load (kN)

Hea

d de

flect

ion

(mm

)



sandsandy silt

fine sand

silty fine sand

sand & gravel

clayey silt

0

0.9

1.8

3.4

9.2

10.2 11.4 12.2

405 mm10.4 m


CPT profile


218

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28


Dep

th (

m)

0

10

20

30

40

50

60

0 250 500 750 1000 1250

Load (kN)

Hea

d de

flect

ion

(mm



sandy clay

medium sand

peat

11.4

3

2.1

0


CPT profile

400 mm7.8m


219

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 7 14 21 28 35 42 49


Dep

th (

m)

0

12

24

36

48

60

72

0 1500 3000 4500 6000 7500

Load (kN)

Hea

d d

efle

ctio

n (

mm



gravelly sand

gravelly sand

sandy gravel

sandy gravel

0

5.2

10.2

670 mm

10.2 m


CPT profile


220

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35


Dep

th (

m)

0

14

28

42

56

70

84

0 200 400 600 800 1000

Load (kN)

Hea

d d

efle

ctio

n (

mm



mud

fill

fine sand

gravel

coarse sand

1.3

3.1

5.2

7.3

12.5


CPT profile

0

430 mm

8.7 m


221

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 3 6 9 12 15 18 21


Dep

th (

m)

0

6

12

18

24

30

36

0 150 300 450 600 750

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



medium sand

silty clay

4.3

0

12.4

430 mm 7.7 m


CPT profile


222

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28


Dep

th (

m)

0

40

80

120

160

200

240

0 300 600 900 1200 1500

Load (kN)

Hea

d d

efle

ctio

n (

mm



medium sand

fill1.4

0


CPT profile

400 mm 10 m


223

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 4 8 12 16 20 24 28


Dep

th (

m)

0

60

120

180

240

300

360

0 1250 2500 3750 5000 6250

Load (kN)

Hea

d d

efle

ctio

n (

mm



stiff clay

600 mm 12 m

1

11

fill

peat & sandy clay

clayey sand

fine sand

5

0

16.4


CPT profile


224

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 4 8 12 16 20 24 28


Dep

th (

m)

0

60

120

180

240

300

360

0 1250 2500 3750 5000 6250

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



fill

peat & sandy clay

clayey sand

fine sand

5

0

11


CPT profile

1

600 mm 12 m


225

(a)

(b)

(c)

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35


Dep

th (

m)

0

9

18

27

36

45

54

0 2000 4000 6000 8000 10000

Load (kN)

Hea

d d

efle

ctio

n (

mm



SP

7.6 SP

SP

SP

CL

CL

CL

CL

CL

6.1

9.1 10.6 12.2

16

24.8

26.2

32

0


CPT profile

1100 mm

27 m


226

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 3 6 9 12 15 18 21


Dep

th (

m)

0

5

10

15

20

25

30

0 150 300 450 600 750

Load (kN)

Dea

d def

lect

ion (

mm

)



medium sand

silty clay

0

4.6

7.6


CPT profile

7.7 m 320 mm


227

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8


Dep

th (

m)

0

40

80

120

160

200

240

0 150 300 450 600 750

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



clay & silty clay

silty sand

0

6.8


CPT profile

400 mm 9.4 m


228

(a)

(b)

(c)

0

5

10

15

20

25

30

35

0 4 8 12 16 20 24 28 32


Dept

h (m

)

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000

Load (kN)

Hea

d d

efle

ctio

n (

mm

)



SP

SP

SP

CL

CL

CL

CL

CL

6.1

9.1 10.6 12.2

16

24.8

26.2

32

0

7.6

1085 mm 25.1 m


CPT profile


229

(a)

(b)

(c)

0

3

6

9

12

15

18

21

0 3 6 9 12 15 18 21 24


Dep

th (

m)

0

7

14

21

28

35

42

0 200 400 600 800 1000

Load (kN)

Hea

d de

flect

ion

(mm

)



350 mm 15.8 m

sand

0


CPT profile


230

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28 32


Dep

th (

m)

0

10

20

30

40

50

60

0 400 800 1200 1600 2000

Load (kN)

Hea

d d

efle

ctio

n (

mm



10.2 m

silt

peat

medium sand

fine sand

gravelley sand

4.6 5.3

8

13.7


CPT profile

500 mm

fill

2.7

0

6.2


231

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28 32


Dept

h (m

)

0

5

10

15

20

25

30

0 200 400 600 800 1000

Load (kN)

Head

defle

ctio

n (m

m)

Failure load= 791 kN Head deflection =

0.05 * pile diameter + PL/AE

6.7

0

11.6

silty sand

clayey silt & sandy silt

405 mm 7.9 m


CPT profile


232

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28 32


Dept

h (m

)

0

30

60

90

120

150

180

0 1000 2000 3000 4000 5000

Load (kN)

Head

defle

ctio

n (m

m) Failure load

= 2468 kN


2.7

0

1100 mm 6 m

mud & peat

fine sand + silt


CPT profile


233

(a)

(b)

(c)

0

4

8

12

16

20

24

28

0 5 10 15 20 25 30 35


Dep

th (

m)

0

20

40

60

80

100

120

0 600 1200 1800 2400 3000

Load (kN)

Hea

d d

efle

ctio

n (m

m)



clayey sand

sand

sand

sand

clay

clay

peat

peat

1.2

6.2 7.2

12.2 13.2

15.7

17

24.4

631 mm 18.3 m


CPT profile

0


234

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24 28 32


Depth

(m

)

0

30

60

90

120

150

180

0 700 1400 2100 2800 3500

Load (kN)

Head d

efle

ctio

n (

mm



gravelley sand

medium sand

fill

5.3

10.2

521 mm 8.2 m


CPT profile

0


235

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 6 12 18 24 30 36 42 48


Dep

th (

m)

0

5

10

15

20

25

30

0 300 600 900 1200 1500

Load (kN)

Head d

efle

ctio

n (

mm

)



silt

fine to medium sand

silt

4.3

7.6

9.1

405 mm 7 m

0


CPT profile


236

(a)

(b)

(c)

0

3

6

9

12

15

18

21

0 7 14 21 28 35 42 49 56


Depth

(m

)

0

30

60

90

120

150

180

0 2000 4000 6000 8000 10000

Load (kN)

Head d

efle

ctio

n (

mm



gravelly sand

gravelly sand

sandy gravel

sandy gravel

0

5.2

10.2

13.4 1078 mm 13 m


CPT profile


237

(a)

(b)

(c)

0

2

4

6

8

10

12

0 4 8 12 16 20 24 28


Depth

(m

)

0

20

40

60

80

100

120

0 150 300 450 600 750

Load (kN)

Head

def

lect

ion (

mm

)



medium sand

peat

sandy clay

2.1

3

11.4


CPT profile

0

400 mm 7.8 m


238

(a)

(b)

(c)

0

2

4

6

8

10

12

14

16

0 4 8 12 16 20 24 28 32


Depth

(m

)

0

30

60

90

120

150

180

0 1000 2000 3000 4000 5000

Load (kN)

Head

defle

ctio

n (

mm

)

mud & peat

fine sand

2.3

12.2


CPT profile

0

1500 mm6 m


Failure load= 2668


239

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18


Dep

th (

m)

0

5

10

15

20

25

30

0 150 300 450 600 750

Load (kN)

Hea

d de

flect

ion

(mm

)



sandy clay

peat

medium sand

2.1

3

0

11.4

400 mm7.8 m


CPT profile


240

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18


Dep

th (

m)

0

5

10

15

20

25

30

0 150 300 450 600 750

Load (kN)

Head

defle

ctio

n (

mm

)



320 mm7.7 m

11

4.6

0

medium sand

silty clay


CPT profile


241

(a)

(b)

(c)

0

3

6

9

12

15

18

21

24

0 1.5 3 4.5 6 7.5 9 10.5 12


Depth

(m

)

0

30

60

90

120

150

180

0 1000 2000 3000 4000 5000

Load (kN)

Head

defle

ctio

n (

mm



1.8

0 fill

residual silty sand

762 mm16.8 m


CPT profile

20.1


242

(a)

(b)

(c)

0

2

4

6

8

10

12

14

0 3 6 9 12 15 18 21 24 27


Dept

h (

m)

0

14

28

42

56

70

84

0 200 400 600 800 1000 1200

Load (kN)

Head

defle

ctio

n (

mm

)



coarse sand

fine sand

gravel

fill

mud1.3

3.1

5.2

0

7.3

12.6


CPT profile

430 mm8.7 m


243

(a)

(b)

(c)

0

1.5

3

4.5

6

7.5

9

10.5

12

0 3 6 9 12 15 18 21 24 27


Depth

(m

)

0

25

50

75

100

125

150

0 250 500 750 1000 1250

Load (kN)

Hea

d d

efle

ctio

n (m

m)

Failure load= 756 kN Head deflection =

0.05 * pile diameter + PL/AE

medium sand

sandy silt

peat

silt

1.6

0

2

3

8.2

6.3 m 329 mm


CPT profile


244

APPENDIX B Table B.1 Concrete driven piles case records summary

Piles group

Case record number

Reference

Case number at

the reference

Shape

Tip, closed or open

Ac (m2)

Acir (m2/m)

D or Deq (mm)


Type of cone

1 Eslami (1996) N&SB1-215 ˝˝ ˝˝ 0.049 0.785 250 21.3 ˝˝ ˝˝ 2 ˝˝ A&M38 ˝˝ ˝˝ 0.16 1.6 400 11.3 ˝˝ ˝˝ 3 ˝˝ A&M22 ˝˝ ˝˝ 0.203 1.8 450 10.3 ˝˝ ˝˝ 4 ˝˝ A&M26 ˝˝ ˝˝ 0.123 1.4 350 8.6 ˝˝ ˝˝ 5 ˝˝ N&SWPB1 ˝˝ ˝˝ 0.203 1.8 450 8.0 ˝˝ ˝˝ 6 ˝˝ POLA1 ˝˝ ˝˝ 0.081 1.14 285 15.0 ˝˝ ˝˝ 7 ˝˝ N&SB1348 ˝˝ ˝˝ 0.202 1.8 450 14.9 ˝˝ ˝˝ 8 ˝˝ A&M48 ˝˝ ˝˝ 0.16 1.6 400 12.5 ˝˝ ˝˝ 9 ˝˝ N&SB1316 ˝˝ ˝˝ 0.123 1.4 350 15.9 ˝˝ ˝˝ 10 ˝˝ N&SJC1 ˝˝ ˝˝ 0.203 1.8 450 9.2 ˝˝ ˝˝ 11 ˝˝ OKLACO round closed 0.292 1.92 610 18.2 QML E

12 ˝˝ A&M47 square ˝˝ 0.16 1.6 400 11.2 SML M

13 ˝˝ NETH2 ˝˝ ˝˝ 0.83 1.0 250 9.3 ˝˝ ˝˝

14 ˝˝ A&M49 ˝˝ ˝˝ 0.16 1.6 400 12.5 SML ˝˝

15 ˝˝ BGHD1 ˝˝ ˝˝ 0.081 1.14 285 11.0 ˝˝ ˝˝

16 ˝˝ A&M1 ˝˝ ˝˝ 0.16 1.6 400 8.8 ˝˝ ˝˝

Driven piles (con

crete)

17 ˝˝ A&N3 round ˝˝ 0.292 1.92 355 10.2 QML E

Ac = cross section area, Acir = unit circumferential area; D = diameter; Deq = equivalent diameter; L = embedment length; SML = slow maintained load test; na = not available; CYC = cyclic load test; QML = quick maintained load test; CRP = constant rate of penetration; IE = incremental equilibrium; M = Mechanical; E = Electrical

245

Table B.1 Concrete driven piles case records summary (continued)

Piles grou

p

Case record numbe

r

Reference

Case number at

the reference

Shape

Tip, closed

or open Ac (m

2) Acir (m2/m)

D or Deq (mm)


Type of cone

18 Eslami (1996) A&M46 square ˝˝ 0.16 1.6 400 11.4 SML M

19 ˝˝ UFL53 ˝˝ ˝˝ 0.123 1.4 350 20.4 ˝˝ E

20 ˝˝ UFL52 square ˝˝ 0.25 2 500 11.0 ˝˝ E

21 ˝˝ A&M40 ˝˝ ˝˝ 0.123 1.4 350 16.0 ˝˝ M

22 ˝˝ UFL22 ˝˝ ˝˝ 0.096 1.1 350 16.0 ˝˝ E

23 ˝˝ POLA1

octagonal

˝˝ 0.308 2.02 625 25.8

QML ˝˝

24 ˝˝ A&M30 square ˝˝ 0.203 1.8 450 15.0 SML M

25 ˝˝ A&M24 ˝˝ ˝˝ 0.16 1.6 400 13.4 ˝˝ ˝˝

26 ˝˝ N&SWPB2 ˝˝ ˝˝ 0.203 1.8 450 11.3 ˝˝ ˝˝

27 ˝˝ LSUA1 ˝˝ ˝˝ 0.096 1.1 350 9.5 ˝˝ E

Driven piles (con

crete)

28 ˝˝ A&N2 ˝˝ ˝˝ 0.203 1.8 500 13.8 ˝˝ ˝˝

Ac = cross section area, Acir = unit circumferential area; D = diameter; Deq = equivalent diameter; L = embedment length; SML = slow maintained load test; na = not available; CYC = cyclic load test; QML = quick maintained load test; CRP = constant rate of penetration; IE = incremental equilibrium; M = Mechanical; E = Electrical

246

(a)

(b) (c)

(d)

0

5

10

15

20

25

30

0 5 10 15 20 25


Depth

(m

)

0

5

10

15

20

25

30

0 0.05 0.1 0.15 0.2


Depth

(m

)

0

200

400

600

800

1000

0 5 10 15 20 25 30 35 40 45

Head deflection (mm)

Load (kN

)

250 mm21.3 m

13

sand

silty sand

0


Fialure load = 810 kN

Figure B.1 Summary sheet for case record 1, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot

247

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 5 10 15 20 25


Depth

(m

)

0

4

8

12

16

20

0 0.15 0.3 0.45 0.6


Depth

(m

)

0

200

400

600

800

1000

0 7 14 21 28 35


Load (kN

)

400 mm11.3 m

0


sand

clay2

Failure load = 870 kNtaken according to 80%-Criterion


248

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

0 3 6 9 12 15


Depth

(m

)

0

3

6

9

12

15

18

21

0 0.06 0.12 0.18 0.24


Depth

(m

)

0

300

600

900

1200

1500

0 6 12 18 24 30


Load (kN

)



450 mm10.3 m

0

8

sand

clay


249

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

0 4 8 12 16 20


Depth

(m

)

0

3

6

9

12

15

0 0.09 0.18 0.27 0.36


Depth

(m

)

0

200

400

600

800

1000

0 25 50 75 100 125


Load (kN

)



350 mm8.6 m

0

2

8

sand (SM)

sand (SP)

clay


250

(a)

(b) (c)

(d)

0

2

4

6

8

10

12

0 4 8 12 16 20


Depth

(m

)

0

2

4

6

8

10

12

0 0.06 0.12 0.18 0.24


Depth

(m

)

0

300

600

900

1200

1500

0 5 10 15 20 25


Load (kN

)

Failure load = 1140 kN


450 mm8 m

0

silty sand


251

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

0 3 6 9 12 15


Depth

(m

)

0

3

6

9

12

15

18

0 0.06 0.12 0.18 0.24


Depth

(m

)

0

400

800

1200

1600

2000

0 8 16 24 32 40


Load (kN

)



285 mm15 m

0

6

silty sand

sand


252

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

0 4 8 12 16 20


Depth

(m

)

0

3

6

9

12

15

18

21

0 0.06 0.12 0.18 0.24


Depth

(m

)

0

400

800

1200

1600

2000

0 12 24 36 48 60


Load (kN

) Failure load = 1755 kNtaken as 80% Craterion


450 mm14.9 m

0

sand

loose sand

8

13

dense sand


253

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

0 2 4 6 8 10


Depth

(m

)

0

3

6

9

12

15

18

0 0.06 0.12 0.18 0.24


Depth

(m

)

0

150

300

450

600

750

0 6 12 18 24 30


Load (kN

)



400 mm12.5 m

0

sand


254

(a)

(b) (c)

(d)

0

4

8

12

16

20

24

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

24

0 0.07 0.14 0.21 0.28


Depth

(m

)

0

400

800

1200

1600

2000

0 5 10 15 20 25


Load (kN

)

Failure load = 1485 kNtaken as 80% Criterion


350 mm9.3 m

0

3

silty sand

fill


255

(a)

(b) (c)

(d)

0

2

4

6

8

10

12

0 5 10 15 20 25


Depth

(m

)

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8


Depth

(m

)

0

400

800

1200

1600

2000

0 8 16 24 32 40


Load (kN

) Failure load = 1845 kN


450 mm9.2 m

0

sand

clay

10


256

(a)

(b) (c)

(d)

0

4

8

12

16

20

24

0 4 8 12 16 20


Depth

(m

)

0

4

8

12

16

20

24

0 0.04 0.08 0.12 0.16


Depth

(m

)

0

800

1600

2400

3200

4000

0 15 30 45 60 75


Load (kN



610 mm18.2 m

0

sand

silty clay

20


257

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

0 5 10 15 20 25


Depth

(m

)

0

3

6

9

12

15

18

0 0.2 0.4 0.6 0.8


Depth

(m

)

0

250

500

750

1000

1250

0 6 12 18 24 30


Load (kN

)



400 mm11.2 m

sand

0


258

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

0 4 8 12 16 20


Depth

(m

)

0

3

6

9

12

15

18

0 0.03 0.06 0.09 0.12


Depth

(m

)

0

200

400

600

800

1000

0 25 50 75 100 125


Load (kN

)



250 mm9.3 m

fill

clay

silty sand

01

6


259

(a)

(b) (c)

(d)

0

3

6

9

12

15

18

21

0 2 4 6 8 10


Depth

(m

)

0

3

6

9

12

15

18

21

0 0.05 0.1 0.15 0.2


Depth

(m

)

0

250

500

750

1000

1250

0 6 12 18 24 30


Load (kN



400 mm12.5 m

sand

0


260

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 2 4 6 8 10


Depth

(m

)

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2


Depth

(m

)

0

250

500

750

1000

1250

0 10 20 30 40 50 60 70 80 90


Load (kN

)



285 mm11 m

silty sand

uniform sand

0

3


261

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 5 10 15 20 25


Depth

(m

)

0

3

6

9

12

15

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

250

500

750

1000

1250

0 5 10 15 20 25 30 35 40 45


Load (kN



400 mm8.8 m

sand

clay

4

0


262

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 5 10 15 20 25


Depth

(m

)

0

3

6

9

12

15

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

300

600

900

1200

1500

0 15 30 45 60 75


Load (kN



355 mm10.2 m

2

0silt

sand

dense sand


263

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 5 10 15 20 25


Depth

(m

)

0

3

6

9

12

15

18

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

300

600

900

1200

1500

0 7 14 21 28 35


Load (kN

)



400 mm11.4 m

5

0

clay

sand


264

(a)

(b) (c)

(d)

0

5

10

15

20

25

30

0 3 6 9 12 15


Depth

(m

)

0

5

10

15

20

25

30

0 0.08 0.16 0.24 0.32


Depth

(m

)

0

300

600

900

1200

1500

0 8 16 24 32 40


Load (kN

)



350 mm20.4 m

10

0

sand

silt


265

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 5 10 15 20 25


Depth

(m

)

0

4

8

12

16

20

0 0.03 0.06 0.09 0.12


Depth

(m

)

0

500

1000

1500

2000

2500

0 8 16 24 32 40


Load (kN

)

Failure load = 2070 kNtaken according to 80% Criterion


500 mm11.0 m

sand

0


266

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 5 10 15 20 25


Depth

(m

)

0

4

8

12

16

20

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

250

500

750

1000

1250

0 8 16 24 32 40


Load (kN

)



350 mm16 m

sand

clay3

0


267

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 5 10 15 20 25


Depth

(m

)

0

4

8

12

16

20

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

300

600

900

1200

1500

0 8 16 24 32 40


Load (kN

)



350 mm16 m

sand

0


268

(a)

(b) (c)

(d)

0

6

12

18

24

30

0 7 14 21 28 35


Depth

(m

)

0

6

12

18

24

30

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

1200

2400

3600

4800

6000

0 16 32 48 64 80


Load (kN

)

Failure load = 5455 kNtaken according to 80%-Criterion


625 mm25.8 m

sand

0


269

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 4 8 12 16 20


Depth

(m

)

0

4

8

12

16

20

0 0.3 0.6 0.9 1.2


Depth

(m

)

0

300

600

900

1200

1500

0 8 16 24 32 40


Load (kN



450 mm15 m

sand

0


270

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 4 8 12 16 20


Depth

(m

)

0

4

8

12

16

20

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

300

600

900

1200

1500

0 8 16 24 32 40


Load

(kN

)



400 mm13.4 m

sand

clay

0

6


271

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 3 6 9 12 15


Dept

h (m

)

0

3

6

9

12

15

0 0.07 0.14 0.21 0.28


Dept

h (m

)

0

200

400

600

800

1000

0 4 8 12 16 20


Load

(kN

)



400 mm11.3 m

sand

0


272

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 5 10 15 20


Depth

(m

)

0

3

6

9

12

15

0 0.07 0.14 0.21 0.28


Depth

(m

)

0

200

400

600

800

1000

0 6 12 18 24 30


Load (kN



350 mm9.5 m

sand

0

9

clay


273

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 8 16 24 32 40


Depth

(m

)

0

4

8

12

16

20

0 0.1 0.2 0.3 0.4


Depth

(m

)

0

1000

2000

3000

4000

5000

0 8 16 24 32 40


Load (kN

)



500 mm13.8 m

sand

9

dense sand

0


274

APPEDIX C Table C.1 Steel driven piles case records summary

Piles group

Case record number

Reference

Case number at the

reference

Shape

Tip, closed or

open Ac (m

2) Acir (m2/m)

D or Deq (mm)


Type of cone

1 Eslami (1996) L&D32 pipe closed 0.071 0.94 300 11.0 SML (T) E 2 ˝˝ L&D314 H-pile open 0.014 1.43 455 12 ˝˝ ˝˝ 3 ˝˝ L&D316 ˝˝ ˝˝ 0.014 1.43 455 11.3 ˝˝ ˝˝ 4 ˝˝ N&SBI43 pipe closed 0.059 0.858 273 22.5 SML M 5 ˝˝ OKLAST ˝˝ ˝˝ 0.342 2.07 660 18.2 ˝˝ E 6 ˝˝ TWNTP6 ˝˝ ˝˝ 0291 1.91 609 34.25 ˝˝ ˝˝ 7 ˝˝ MILANO ˝˝ ˝˝ 0.066 1.037 330 10.0 ˝˝ ˝˝ 8 ˝˝ PRICOS ˝˝ ˝˝ 0.071 0.942 300 28.4 ˝˝ ˝˝ 9 ˝˝ N&SBI44 ˝˝ ˝˝ 0.059 0.858 273 22.5 SML (T) M 10 ˝˝ L&D12 H-pile open 0.014 1.43 455 16.2 ˝˝ E 11 ˝˝ L&D31 pipe closed 0.071 0.94 300 16.2 SML ˝˝ 12 ˝˝ NWUP ˝˝ ˝˝ 0.159 1.41 450 15.2 ˝˝ ˝˝ 13 ˝˝ L&D21 H-pile open 0.014 1.43 455 16.8 QML (T) ˝˝ 14 ˝˝ L&D34 pipe closed 0.096 1.1 350 14.4 SML ˝˝ 15 ˝˝ L&D37 ˝˝ ˝˝ 0.126 1.26 400 14.6 ˝˝ ˝˝ 16 ˝˝ L&D38 ˝˝ ˝˝ 0.126 1.26 400 14.6 SML (T) ˝˝ 17 ˝˝ FHWASF ˝˝ ˝˝ 0.059 0.858 273 9.2 SML ˝˝


18 ˝˝ N&SBI42 ˝˝ ˝˝ 0.059 0.858 273 15.2 ˝˝ M Ac = cross section area, Acir = unit circumferential area; D = diameter; Deq = equivalent diameter; L = embedment length; SML = slow maintained load test; na = not available; CYC = cyclic load test; QML = quick maintained load test; CRP = constant rate of penetration; IE = incremental equilibrium; T = tension; M = Mechanical; E = Electrical

275

Table C.1 Steel driven piles case records summary (continued)

Piles group

Case record number

Reference

Case number at the

reference

Shape

Tip, closed or

open Ac (m

2) Acir (m2/m)

D or Deq (mm)


Type of cone

19 Eslami (1996) L&D16 H-pile open 0.014 1.43 455 16.2 QML E 20 ˝˝ ALABA ˝˝ ˝˝ 0.014 1.23 392 36.3 SML ˝˝ 21 ˝˝ KP1 ˝˝ ˝˝ 0.046 1.54 490 14.0 SML (T) ˝˝ 22 ˝˝ A&M39 ˝˝ ˝˝ 0.01 1.21 385 19 SML M 23 ˝˝ A&M41 ˝˝ ˝˝ 0.01 1.21 385 12.4 ˝˝ ˝˝ 24 ˝˝ NWUH H-pile open 0.128 1.43 455 15.2 SML E 25 ˝˝ A&M14 ˝˝ ˝˝ 0.008 1.01 321 8.5 ˝˝ M 26 ˝˝ LSUN215 pipe closed 0.096 1.01 350 31.1 QML E 27 ˝˝ TWNTP4 ˝˝ ˝˝ 0.291 1.91 609 34.3 SML ˝˝ 28 ˝˝ L&D315 H-pile open 0.014 1.43 455 11.3 SML (T) ˝˝ 29 ˝˝ L&D35 pipe closed 0.096 1.1 350 11.1 ˝˝ ˝˝


30 ˝˝ PRICOL ˝˝ ˝˝ 0.71 0.942 300 31.4 SML ˝˝ Ac = cross section area, Acir = unit circumferential area; D = diameter; Deq = equivalent diameter; L = embedment length; SML = slow maintained load test; na = not available; CYC = cyclic load test; QML = quick maintained load test; CRP = constant rate of penetration; IE = incremental equilibrium; T = tension; M = Mechanical; E = Electrical

276

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

150

300

450

600

750

0 14 28 42 56 70


Load (kN

)


300 mm11 m

sand

0

Fialure load = 560 kN taken as a plunging load

Figure C.1 Summary sheet for case record 1, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot

277

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

250

500

750

1000

1250

0 6 12 18 24 30


Load (kN

)


455 mm12 m

sand

0



278

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30

Cone tip resistance (MPa)Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Depth

(m

)

0

250

500

750

1000

1250

0 11 22 33 44 55


Load (kN

)



455 mm11.3

sand

0


279

(a)

(b) (c)

(d)

0

5

10

15

20

25

0 6 12 18 24 30


Depth

(m

)

0

5

10

15

20

25

0 0.08 0.16 0.24 0.32


Depth

(m

)

0

400

800

1200

1600

2000

0 8 16 24 32 40


Load (kN

)



455 mm12 m

sand

0


280

(a)

(b) (c)

(d)

0

5

10

15

20

25

0 5 10 15 20 25


Depth

(m

)

0

5

10

15

20

25

0 0.06 0.12 0.18 0.24


Dept

h (m

)

0

1000

2000

3000

4000

5000

0 18 36 54 72 90


Load (kN

)



660 mm18.2 m

sand

0

20

silty clay


281

(a)

(b) (c)

(d)

0

8

16

24

32

40

0 6 12 18 24 30


Depth

(m

)

0

8

16

24

32

40

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

1000

2000

3000

4000

5000

0 6 12 18 24 30


Load

(kN

)



609 mm34.3 m

sand0

6

20

clay

sand


282

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 3 6 9 12 15


Depth

(m

)

0

3

6

9

12

15

0 0.04 0.08 0.12 0.16


Dept

h (m

)

0

200

400

600

800

1000

0 6 12 18 24 30


Load (kN

)



330 mm10 m

silty sand

4

clay

10

clay

0


283

(a)

(b) (c)

(d)

0

7

14

21

28

35

0 4 8 12 16 20


Depth

(m

)

0

7

14

21

28

35

0 0.04 0.08 0.12 0.16


Depth

(m

)

0

300

600

900

1200

1500

0 8 16 24 32 40


Load (kN

)



300 mm28.4 m

sand

peat

19

7

0

soft clay


284

(a)

(b) (c)

(d)

0

6

12

18

24

30

0 6 12 18 24 30

Cone tip resistance (MPa)Depth

(m

)

0

6

12

18

24

30

0 0.08 0.16 0.24 0.32


Depth

(m

)

0

200

400

600

800

1000

0 9 18 27 36 45


Load (kN

)



455 mm22.5 m

sand

4 fill

18

dense sand

0


285

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

250

500

750

1000

1250

0 12 24 36 48 60


Load (kN

)



455 mm16.2 m

sand

0


286

(a)

(b) (c)

(d)

0

5

10

15

20

25

0 6 12 18 24 30


Depth

(m

)

0

5

10

15

20

25

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

300

600

900

1200

1500

0 18 36 54 72 90


Load (kN

)

Failure load = 1310 kNtaken according to 80% Criterion


300 mm16.2 m

sand

0


287

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 7 14 21 28 35


Depth

(m

)

0

4

8

12

16

20

0 0.09 0.18 0.27 0.36


Depth

(m

)

0

250

500

750

1000

1250

0 15 30 45 60 75


Load (kN

)



455 mm12 m

sand

0


288

(a)

(b) (c)

(d)

0

5

10

15

20

25

0 6 12 18 24 30


Depth

(m

)

0

5

10

15

20

25

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

300

600

900

1200

1500

0 12 24 36 48 60


Load (kN

)



455 mm16.8 m

sand

0


289

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

300

600

900

1200

1500

0 18 36 54 72 90


Load (kN

)



350 mm14.4 m

sand

0


290

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

400

800

1200

1600

2000

0 18 36 54 72 90


Load (kN

)


400 mm14.6 m

sand

0

Failure load = 1800 kN taken according to 80% Criterion


291

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 6 12 18 24 30


Depth

(m

)

0

3

6

9

12

15

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

250

500

750

1000

1250

0 12 24 36 48 60


Load (kN

)



400 mm

14.6 m

sand

0


292

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 4 8 12 16 20


Depth

(m

)

0

3

6

9

12

0 0.03 0.06 0.09 0.12


Dept

h (m

)

0

150

300

450

600

750

0 18 36 54 72 90


Load (kN

)



273 mm9.2 m

hydraulic sand

0

2 fill

13


293

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 3 6 9 12 15

cone tip resistance (MPa)

Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32

sleeve friction (MPa)

Dept

h (m

)

0

200

400

600

800

1000

0 8 16 24 32 40


load (kN

)



273 mm15.2 m

sand

fill

15

4

0

dense sand


294

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Depth

(m

)

0

800

1600

2400

3200

4000

0 8 16 24 32 40


Load (kN

)



455 mm16.2 m

sand

0


295

(a)

(b) (c)

(d)

0

8

16

24

32

40

0 7 14 21 28 35


Depth

(m

)

0

8

16

24

32

40

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

500

1000

1500

2000

2500

0 8 16 24 32 40


Load (kN

)



392 mm36.3 m

sand

0

4

8

sand

silty clay


296

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.02 0.04 0.06 0.08


Dept

h (m

)

0

800

1600

2400

3200

4000

0 18 36 54 72 90


Load (kN

)



490 mm14 m

dense sand

soft soil

0

5

17


297

(a)

(b) (c)

(d)

0

5

10

15

20

25

0 6 12 18 24 30


Depth

(m

)

0

5

10

15

20

25

0 0.11 0.22 0.33 0.44


Dept

h (m

)

0

300

600

900

1200

1500

0 10 20 30 40 50


Load (kN

)



385 mm19 m

sand

0

3 clay


298

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 3 6 9 12 15


Depth

(m

)

0

3

6

9

12

15

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

120

240

360

480

600

0 8 16 24 32 40


Load (kN

)



385 mm12.4 m

sand

0

3

clay


299

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 7 14 21 28 35


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

250

500

750

1000

1250

0 14 28 42 56 70


Load (kN

)



455 mm15.2 m

sand

0

7

clay


300

(a)

(b) (c)

(d)

0

3

6

9

12

15

0 5 10 15 20 25


Depth

(m

)

0

3

6

9

12

15

0 0.16 0.32 0.48 0.64


Depth

(m

)

0

180

360

540

720

0 18 36 54 72 90


Load

(kN

)



321 mm8.5 m

sand

clay 0

1.5


301

(a)

(b) (c)

(d)

0

8

16

24

32

40

0 3 6 9 12 15


Depth

(m

)

0

8

16

24

32

40

0 0.04 0.08 0.12 0.16


Dept

h (m

)

0

400

800

1200

1600

2000

0 3 6 9 12 15


Load (kN

)



350 mm31.3 m

silty sand

0

clay

24

35


302

(a)

(b) (c)

(d)

0

8

16

24

32

40

0 5 10 15 20 25


Depth

(m

)

0

8

16

24

32

40

0 0.05 0.1 0.15 0.2


Dept

h (m

)

0

1000

2000

3000

4000

5000

0 18 36 54 72 90


Load

(kN

)



609 mm34.4 m

sand

sand

clay

0

6

19


303

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.08 0.16 0.24 0.32


Dept

h (m

)

0

200

400

600

800

1000

0 10 20 30 40 50


Load (kN

)



455 mm11.3 m

sand

0


304

(a)

(b) (c)

(d)

0

4

8

12

16

20

0 6 12 18 24 30


Depth

(m

)

0

4

8

12

16

20

0 0.06 0.12 0.18 0.24


Dept

h (m

)

0

160

320

480

640

800

0 9 18 27 36 45


Load (kN

)



350 mm

11.1 m

sand

0


305

(a)

(b) (c)

(d)

0

7

14

21

28

35

0 3 6 9 12 15


Depth

(m

)

0

7

14

21

28

35

0 0.04 0.08 0.12 0.16


Dept

h (m

)

0

400

800

1200

1600

2000

0 12 24 36 48 60


Load (kN

)



300 mm31.4 m

sand

peat7

0

19

sand

soft clay21


306

APPENDIX D In setting attempt 1, the GEP is presented with input variables including weighted average cone point resistance within pile tip influence zone, weighted average cone point resistance along shaft, pile embedded length, pile diameter and the total load is the output variable as presented in Table D1. Table. D1 Input setting attempt 1

tipcq − (MPa)

shaftcq − (MPa) L (m) D (mm) ɛi (mm) Pi (kN)

47.6 9.2 24.4 840 0.0 0 47.6 9.2 24.4 840 4.7 2332 47.6 9.2 24.4 840 9.5 3894 47.6 9.2 24.4 840 14.2 5173 47.6 9.2 24.4 840 18.9 6100 47.6 9.2 24.4 840 23.6 6760 47.6 9.2 24.4 840 28.4 7420 47.6 9.2 24.4 840 33.1 7906 47.6 9.2 24.4 840 37.8 8364 47.6 9.2 24.4 840 42.6 8822 47.6 9.2 24.4 840 47.3 9143 47.6 9.2 24.4 840 52.0 9360 47.6 9.2 24.4 840 56.7 9577 47.6 9.2 24.4 840 61.5 9794

In setting attempt 2, the GEP is presented with same input variables as in attempt 1, however the settlement is replaced with settlement increment as presented in table D2. Table D2 input setting attempt 2

tipcq − (MPa)

shaftcq − (MPa) L (m) D (mm) ∆ɛi (mm) Pi (kN)

47.6 9.2 24.4 840 0 0 47.6 9.2 24.4 840 0.6 298 47.6 9.2 24.4 840 1.2 940 47.6 9.2 24.4 840 1.8 1881 47.6 9.2 24.4 840 2.5 2899 47.6 9.2 24.4 840 3.1 3848 47.6 9.2 24.4 840 3.7 4885 47.6 9.2 24.4 840 4.4 5867 47.6 9.2 24.4 840 5.0 6632 47.6 9.2 24.4 840 5.6 7442 47.6 9.2 24.4 840 6.3 8132 47.6 9.2 24.4 840 6.9 8713 47.6 9.2 24.4 840 7.5 9176 47.6 9.2 24.4 840 8.1 9585 47.6 9.2 24.4 840 8.8 10010

307

In setting attempt 3, the GEP is presented with same input variables as in attempt 1, however the settlement and the output load are replaced with settlement and load increments as presented in Table D3. Table D3 Input setting attempt 3

tipcq − (MPa)

shaftcq − (MPa) L (m) D (mm) ∆ɛi (mm) ∆Pi (kN)

47.6 9.2 24.4 840 0 0 47.6 9.2 24.4 840 0.63 298.6 47.6 9.2 24.4 840 1.26 642 47.6 9.2 24.4 840 1.89 940.7 47.6 9.2 24.4 840 2.52 1017.8 47.6 9.2 24.4 840 3.15 949.5 47.6 9.2 24.4 840 3.78 1036.8 47.6 9.2 24.4 840 4.41 982 47.6 9.2 24.4 840 5.04 764 47.6 9.2 24.4 840 5.67 810 47.6 9.2 24.4 840 6.3 689 47.6 9.2 24.4 840 6.93 580 47.6 9.2 24.4 840 7.56 463 47.6 9.2 24.4 840 8.19 408 47.6 9.2 24.4 840 8.82 410

In attempt 4, the GEP is presented with same input variables as in attempt 1, however the load is included as input variable while the settlement is the predicted output as shown in Table D4. Table D4 input setting attempt 4

tipcq − (MPa)

shaftcq − (MPa) L (m) D (mm) Pi (kN) ∆ɛi (mm)

47.6 9.2 24.4 840 0 0 47.6 9.2 24.4 840 715 1.4 47.6 9.2 24.4 840 1430 2.8 47.6 9.2 24.4 840 2145 4.3 47.6 9.2 24.4 840 2860 6.3 47.6 9.2 24.4 840 3575 8.5 47.6 9.2 24.4 840 4290 10.9 47.6 9.2 24.4 840 5005 13.5 47.6 9.2 24.4 840 5720 16.9 47.6 9.2 24.4 840 6435 21.2 47.6 9.2 24.4 840 7150 26.4 47.6 9.2 24.4 840 7865 32.7 47.6 9.2 24.4 840 8580 40.0 47.6 9.2 24.4 840 9295 50.6 47.6 9.2 24.4 840 10010 66.2

308

In attempt 5, the GEP is presented with same input variables as in attempt 1, but the input variables are scaled in this attempt as presented in Table D5. Table D5 Input setting attempt 5

tipcq − (MPa)

shaftcq − (MPa) L (m) D (mm) ɛi (mm) Pi (kN)

1 0.43 0.88 0.35 0.00 0 1 0.43 0.88 0.35 0.01 0.23 1 0.43 0.88 0.35 0.03 0.39 1 0.43 0.88 0.35 0.04 0.52 1 0.43 0.88 0.35 0.06 0.61 1 0.43 0.88 0.35 0.07 0.68 1 0.43 0.88 0.35 0.09 0.74 1 0.43 0.88 0.35 0.10 0.79 1 0.43 0.88 0.35 0.12 0.84 1 0.43 0.88 0.35 0.13 0.88 1 0.43 0.88 0.35 0.15 0.91 1 0.43 0.88 0.35 0.16 0.94 1 0.43 0.88 0.35 0.18 0.96 1 0.43 0.88 0.35 0.19 0.98 1 0.43 0.88 0.35 0.20 1.00

In attempt 6, the input is presented to the GEP as shown in Table D6. The attempt is more detailed in Chapter Five. Table D6 Input setting attempt 6

tipcq −

(MPa) shaftc

q −

(MPa) L (m) D (mm) ɛi % ∆ɛi% Pi (kN)

Pi+1 (kN)

47.6 9.2 24.4 840 0.01 0.02 0 197 47.6 9.2 24.4 840 0.03 0.03 197 395 47.6 9.2 24.4 840 0.06 0.04 395 592 47.6 9.2 24.4 840 0.1 0.05 592 823 47.6 9.2 24.4 840 0.15 0.06 823 1119 47.6 9.2 24.4 840 0.21 0.07 1119 1448 47.6 9.2 24.4 840 0.28 0.08 1448 1843 47.6 9.2 24.4 840 0.36 0.09 1843 2238 47.6 9.2 24.4 840 0.45 0.1 2238 2573 47.6 9.2 24.4 840 0.55 0.11 2573 2918 47.6 9.2 24.4 840 0.66 0.12 2918 3263 47.6 9.2 24.4 840 0.78 0.13 3263 3652 47.6 9.2 24.4 840 0.91 0.14 3652 4034 47.6 9.2 24.4 840 1.05 0.15 4034 4401

309

APPENDIX E Bored Piles Run Code: ' Insert this code into your VB program to fire the G:\Bored in Sand & mixed selected model\LS ANN 2 network ' This code is designed to be simple and fast for porting to any machine. ' Therefore all code and weights are inline without looping or data storage ' which might be harder to port between compilers. Sub Fire_LS ANN 2 (inarray(), outarray()) Dim netsum as double Static feature2(6) as double Static feature4(1) as double ' inarray(1) is qc_(Mpa) ' inarray(2) is qc-shaft_(Mpa) ' inarray(3) is L_(m) ' inarray(4) is D_(mm) ' inarray(5) is ei_% ' inarray(6) is ?_ei_% ' outarray(1) is Pi+1_(kN) if (inarray(1)<1.58) then inarray(1) = 1.58 if (inarray(1)>47.58) then inarray(1) = 47.58 inarray(1) = (inarray(1) - 1.58) / 46 if (inarray(2)<1.4) then inarray(2) = 1.4 if (inarray(2)>20.1) then inarray(2) = 20.1 inarray(2) = (inarray(2) - 1.4) / 18.7 if (inarray(3)<5.6) then inarray(3) = 5.6 if (inarray(3)>27) then inarray(3) = 27 inarray(3) = (inarray(3) - 5.6) / 21.4 if (inarray(4)<320) then inarray(4) = 320 if (inarray(4)>1800) then inarray(4) = 1800 inarray(4) = (inarray(4) - 320) / 1480 if (inarray(5)<0.01) then inarray(5) = 0.01 if (inarray(5)>48.51) then inarray(5) = 48.51 inarray(5) = (inarray(5) - 0.01) / 48.5 if (inarray(6)<0.02) then inarray(6) = 0.02 if (inarray(6)>0.99) then inarray(6) = 0.99 inarray(6) = (inarray(6) - 0.02) / 0.97 netsum = -1.222157 netsum = netsum + inarray(1) * 3.281758 netsum = netsum + inarray(2) * -4.071105

310

netsum = netsum + inarray(3) * 3.119632 netsum = netsum + inarray(4) * -9.348659 netsum = netsum + inarray(5) * -2.382426 netsum = netsum + inarray(6) * 2.056843 netsum = netsum + -1.461063 netsum = netsum + feature4(1) * 0.6642534 feature2(1) = tanh(netsum) netsum = -0.7781836 netsum = netsum + inarray(1) * 1.555902 netsum = netsum + inarray(2) * -0.432686 netsum = netsum + inarray(3) * 2.120256 netsum = netsum + inarray(4) * -6.144647 netsum = netsum + inarray(5) * -2.093086 netsum = netsum + inarray(6) * 2.694094 netsum = netsum + -0.9365909 netsum = netsum + feature4(1) * 0.8826105 feature2(2) = tanh(netsum) netsum = 0.7509452 netsum = netsum + inarray(1) * -0.518931 netsum = netsum + inarray(2) * -0.4358304 netsum = netsum + inarray(3) * -0.9757731 netsum = netsum + inarray(4) * -0.4252531 netsum = netsum + inarray(5) * 1.926874 netsum = netsum + inarray(6) * -2.70438 netsum = netsum + 1.082544 netsum = netsum + feature4(1) * -1.699769 feature2(3) = tanh(netsum) netsum = 1.687351 netsum = netsum + inarray(1) * 2.549266 netsum = netsum + inarray(2) * 0.5941773 netsum = netsum + inarray(3) * -6.13457 netsum = netsum + inarray(4) * -2.964279 netsum = netsum + inarray(5) * 3.460182 netsum = netsum + inarray(6) * 0.2949941 netsum = netsum + 2.092655 netsum = netsum + feature4(1) * 2.33162 feature2(4) = tanh(netsum) netsum = 2.637428 netsum = netsum + inarray(1) * -1.623992 netsum = netsum + inarray(2) * -1.573576 netsum = netsum + inarray(3) * -0.9629161 netsum = netsum + inarray(4) * -1.22856 netsum = netsum + inarray(5) * 1.35493 netsum = netsum + inarray(6) * -3.552577 netsum = netsum + 3.421926 netsum = netsum + feature4(1) * -2.159666

311

feature2(5) = tanh(netsum) netsum = 0.8694988 netsum = netsum + inarray(1) * -0.2648007 netsum = netsum + inarray(2) * -0.2166335 netsum = netsum + inarray(3) * -0.6479651 netsum = netsum + inarray(4) * -0.3693971 netsum = netsum + inarray(5) * -1.42069 netsum = netsum + inarray(6) * 9.07458 netsum = netsum + 1.110248 netsum = netsum + feature4(1) * -0.7345452 feature2(6) = tanh(netsum) netsum = -1.053944 netsum = netsum + feature2(1) * 4.703946 netsum = netsum + feature2(2) * -1.090795 netsum = netsum + feature2(3) * -1.343496 netsum = netsum + feature2(4) * -0.3335546 netsum = netsum + feature2(5) * -0.9552888 netsum = netsum + feature2(6) * 5.174768 outarray(1) = 1 / (1 + exp(-netsum)) feature4(1) = feature4(1) + feature4(1) * -0.8 feature4(1) = feature4(1) + outarray(1) * 0.8 outarray(1) = 9970 * (outarray(1) - .1) / .8 + 4 if (outarray(1)<4) then outarray(1) = 4 if (outarray(1)>9974) then outarray(1) = 9974 End Sub Concrete Driven Piles Run Code: ' Insert this code into your VB program to fire the G:\Load settlement ANN files\LS concrete piles in sand selected model\concrete piles load settlement model 1 network ' This code is designed to be simple and fast for porting to any machine. ' Therefore all code and weights are inline without looping or data storage ' which might be harder to port between compilers. Sub Fire concrete piles load settlement model 1 (inarray(), outarray()) Dim netsum as double Static feature2(11) as double Static feature4(1) as double ' inarray(1) is Deq_(mm) ' inarray(2) is L_(m) ' inarray(3) is qc'_(MPa) ' inarray(4) is fs'_(kPa) ' inarray(5) is qc-sh

312

' inarray(6) is ? ' inarray(7) is e ' outarray(1) is Q if (inarray(1)<250) then inarray(1) = 250 if (inarray(1)>625) then inarray(1) = 625 inarray(1) = (inarray(1) - 250) / 375 if (inarray(2)<8) then inarray(2) = 8 if (inarray(2)>25.8) then inarray(2) = 25.8 inarray(2) = (inarray(2) - 8) / 17.8 if (inarray(3)<1.1) then inarray(3) = 1.1 if (inarray(3)>18.55) then inarray(3) = 18.55 inarray(3) = (inarray(3) - 1.1) / 17.45 if (inarray(4)<25.1) then inarray(4) = 25.1 if (inarray(4)>205) then inarray(4) = 205 inarray(4) = (inarray(4) - 25.1) / 179.9 if (inarray(5)<2.5) then inarray(5) = 2.5 if (inarray(5)>15.7) then inarray(5) = 15.7 inarray(5) = (inarray(5) - 2.5) / 13.2 if (inarray(6)<0.02) then inarray(6) = 0.02 if (inarray(6)>0.83) then inarray(6) = 0.83 inarray(6) = (inarray(6) - 0.02) / 0.81 if (inarray(7)<0.01) then inarray(7) = 0.01 if (inarray(7)>34.03) then inarray(7) = 34.03 inarray(7) = (inarray(7) - 0.01) / 34.02 netsum = -1.045789 netsum = netsum + inarray(1) * -2.562945 netsum = netsum + inarray(2) * 0.4342159 netsum = netsum + inarray(3) * 1.297501 netsum = netsum + inarray(4) * -0.1989307 netsum = netsum + inarray(5) * -0.1905069 netsum = netsum + inarray(6) * 3.046128 netsum = netsum + inarray(7) * -1.089958 netsum = netsum + -0.9867942 netsum = netsum + feature4(1) * 0.6174999 feature2(1) = tanh(netsum) netsum = 0.1894704 netsum = netsum + inarray(1) * -3.695792 netsum = netsum + inarray(2) * -1.898238 netsum = netsum + inarray(3) * 1.321143 netsum = netsum + inarray(4) * 2.695451 netsum = netsum + inarray(5) * 4.998773

313

netsum = netsum + inarray(6) * -7.121385 netsum = netsum + inarray(7) * 6.416268 netsum = netsum + 0.3434364 netsum = netsum + feature4(1) * 0.7211493 feature2(2) = tanh(netsum) netsum = -2.758353 netsum = netsum + inarray(1) * 2.030766 netsum = netsum + inarray(2) * 0.9762658 netsum = netsum + inarray(3) * 1.506516 netsum = netsum + inarray(4) * -0.1191566 netsum = netsum + inarray(5) * 1.430223 netsum = netsum + inarray(6) * 1.930591 netsum = netsum + inarray(7) * 0.1888873 netsum = netsum + -2.779031 netsum = netsum + feature4(1) * 2.962754 feature2(3) = tanh(netsum) netsum = 0.6224663 netsum = netsum + inarray(1) * -1.39882 netsum = netsum + inarray(2) * -0.5977075 netsum = netsum + inarray(3) * -0.5061968 netsum = netsum + inarray(4) * -0.2363005 netsum = netsum + inarray(5) * -0.3197615 netsum = netsum + inarray(6) * 4.284199 netsum = netsum + inarray(7) * -2.384323 netsum = netsum + 0.6610048 netsum = netsum + feature4(1) * 1.643592 feature2(4) = tanh(netsum) netsum = 0.67422 netsum = netsum + inarray(1) * -1.235994 netsum = netsum + inarray(2) * -3.290738 netsum = netsum + inarray(3) * 3.320049 netsum = netsum + inarray(4) * 4.797752 netsum = netsum + inarray(5) * 3.836853 netsum = netsum + inarray(6) * -1.016855 netsum = netsum + inarray(7) * 0.9489809 netsum = netsum + 0.7173474 netsum = netsum + feature4(1) * -0.9606945 feature2(5) = tanh(netsum) netsum = -1.001559 netsum = netsum + inarray(1) * -2.096237 netsum = netsum + inarray(2) * -0.675222 netsum = netsum + inarray(3) * 2.063347 netsum = netsum + inarray(4) * -4.930504 netsum = netsum + inarray(5) * 3.444701 netsum = netsum + inarray(6) * 3.121217 netsum = netsum + inarray(7) * -1.900178

314

netsum = netsum + -1.071634 netsum = netsum + feature4(1) * 1.400324 feature2(6) = tanh(netsum) netsum = -1.132636 netsum = netsum + inarray(1) * -1.867166 netsum = netsum + inarray(2) * 2.123487 netsum = netsum + inarray(3) * -1.53077 netsum = netsum + inarray(4) * 1.731936 netsum = netsum + inarray(5) * -2.619829 netsum = netsum + inarray(6) * 3.745813 netsum = netsum + inarray(7) * -1.108461 netsum = netsum + -1.101934 netsum = netsum + feature4(1) * 0.7111958 feature2(7) = tanh(netsum) netsum = 0.84042 netsum = netsum + inarray(1) * 9.011703E-02 netsum = netsum + inarray(2) * 4.906503 netsum = netsum + inarray(3) * -5.974189 netsum = netsum + inarray(4) * 1.633194 netsum = netsum + inarray(5) * -2.858086 netsum = netsum + inarray(6) * 0.1218291 netsum = netsum + inarray(7) * 1.454938 netsum = netsum + 0.5100222 netsum = netsum + feature4(1) * 2.051457 feature2(8) = tanh(netsum) netsum = 1.133188 netsum = netsum + inarray(1) * -2.268884 netsum = netsum + inarray(2) * 2.908233 netsum = netsum + inarray(3) * 1.885508 netsum = netsum + inarray(4) * 3.116997 netsum = netsum + inarray(5) * -2.209796 netsum = netsum + inarray(6) * -4.790582 netsum = netsum + inarray(7) * 3.074495 netsum = netsum + 1.189659 netsum = netsum + feature4(1) * 0.1757697 feature2(9) = tanh(netsum) netsum = -0.3034642 netsum = netsum + inarray(1) * 0.9293773 netsum = netsum + inarray(2) * 5.297246 netsum = netsum + inarray(3) * -4.215946 netsum = netsum + inarray(4) * 2.300442 netsum = netsum + inarray(5) * -0.1804721 netsum = netsum + inarray(6) * 0.9830358 netsum = netsum + inarray(7) * -2.165698 netsum = netsum + -0.3288558 netsum = netsum + feature4(1) * 0.281

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feature2(10) = tanh(netsum) netsum = -2.01309 netsum = netsum + inarray(1) * 2.790639 netsum = netsum + inarray(2) * -0.7972183 netsum = netsum + inarray(3) * 6.816371E-02 netsum = netsum + inarray(4) * 2.329911 netsum = netsum + inarray(5) * 1.207308 netsum = netsum + inarray(6) * 2.100281 netsum = netsum + inarray(7) * -2.881017 netsum = netsum + -2.020616 netsum = netsum + feature4(1) * -3.728518 feature2(11) = tanh(netsum) netsum = -0.844494 netsum = netsum + feature2(1) * 3.927204 netsum = netsum + feature2(2) * -0.6243812 netsum = netsum + feature2(3) * 1.068827 netsum = netsum + feature2(4) * 2.147272 netsum = netsum + feature2(5) * 2.670998 netsum = netsum + feature2(6) * -2.79193 netsum = netsum + feature2(7) * -1.529014 netsum = netsum + feature2(8) * -1.237962 netsum = netsum + feature2(9) * -2.057312 netsum = netsum + feature2(10) * 1.109439 netsum = netsum + feature2(11) * 1.631509 outarray(1) = 1 / (1 + exp(-netsum)) feature4(1) = feature4(1) + feature4(1) * -0.5 feature4(1) = feature4(1) + outarray(1) * 0.5 outarray(1) = 5702 * (outarray(1) - .1) / .8 + 3 if (outarray(1)<3) then outarray(1) = 3 if (outarray(1)>5705) then outarray(1) = 5705 End Sub Steel Driven Piles Run Code: ' Insert this code into your VB program to fire the G:\Load settlement ANN files\LS steel driven in sand selected model\LS Driven in sand & mixed 2 network ' This code is designed to be simple and fast for porting to any machine. ' Therefore all code and weights are inline without looping or data storage ' which might be harder to port between compilers. Sub Fire_LS Driven in sand & mixed 2 (inarray(), outarray()) Dim netsum as double Static feature2(11) as double Static feature4(1) as double

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' inarray(1) is Deq_(mm) ' inarray(2) is L_(m) ' inarray(3) is qc'_(MPa) ' inarray(4) is fs'_(kPa) ' inarray(5) is qc-sh ' inarray(6) is ? ' inarray(7) is e_(mm) ' outarray(1) is Q_(kN) if (inarray(1)<273) then inarray(1) = 273 if (inarray(1)>660) then inarray(1) = 660 inarray(1) = (inarray(1) - 273) / 387 if (inarray(2)<8.5) then inarray(2) = 8.5 if (inarray(2)>36.3) then inarray(2) = 36.3 inarray(2) = (inarray(2) - 8.5) / 27.8 if (inarray(3)<0) then inarray(3) = 0 if (inarray(3)>23.9) then inarray(3) = 23.9 inarray(3) = inarray(3) / 23.9 if (inarray(4)<18) then inarray(4) = 18 if (inarray(4)>131) then inarray(4) = 131 inarray(4) = (inarray(4) - 18) / 113 if (inarray(5)<1.4) then inarray(5) = 1.4 if (inarray(5)>17.6) then inarray(5) = 17.6 inarray(5) = (inarray(5) - 1.4) / 16.2 if (inarray(6)<0.02) then inarray(6) = 0.02 if (inarray(6)>0.78) then inarray(6) = 0.78 inarray(6) = (inarray(6) - 0.02) / 0.76 if (inarray(7)<0.01) then inarray(7) = 0.01 if (inarray(7)>30.03) then inarray(7) = 30.03 inarray(7) = (inarray(7) - 0.01) / 30.02 netsum = -0.9323793 netsum = netsum + inarray(1) * 0.4911428 netsum = netsum + inarray(2) * 2.743531E-02 netsum = netsum + inarray(3) * 5.947673E-02 netsum = netsum + inarray(4) * -0.1430892 netsum = netsum + inarray(5) * -0.3271712 netsum = netsum + inarray(6) * 0.3842645 netsum = netsum + inarray(7) * -0.1044744 netsum = netsum + -0.7185783 netsum = netsum + feature4(1) * 5.785269E-02 feature2(1) = tanh(netsum)

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netsum = 1.630296 netsum = netsum + inarray(1) * -1.698268 netsum = netsum + inarray(2) * 1.134722 netsum = netsum + inarray(3) * -0.5377055 netsum = netsum + inarray(4) * 2.827256 netsum = netsum + inarray(5) * -2.853436 netsum = netsum + inarray(6) * -2.52688 netsum = netsum + inarray(7) * 3.112499 netsum = netsum + 1.542801 netsum = netsum + feature4(1) * 1.210193 feature2(2) = tanh(netsum) netsum = -2.028322 netsum = netsum + inarray(1) * 2.808855 netsum = netsum + inarray(2) * -0.2579687 netsum = netsum + inarray(3) * 0.5094767 netsum = netsum + inarray(4) * 1.61997 netsum = netsum + inarray(5) * -1.257184 netsum = netsum + inarray(6) * 2.399192 netsum = netsum + inarray(7) * -0.4056424 netsum = netsum + -1.69525 netsum = netsum + feature4(1) * 0.2867941 feature2(3) = tanh(netsum) netsum = 0.6882428 netsum = netsum + inarray(1) * -1.427858 netsum = netsum + inarray(2) * -1.575278 netsum = netsum + inarray(3) * -0.6227902 netsum = netsum + inarray(4) * 0.2133883 netsum = netsum + inarray(5) * 5.786179E-02 netsum = netsum + inarray(6) * 4.010863 netsum = netsum + inarray(7) * 0.3318986 netsum = netsum + 0.6445944 netsum = netsum + feature4(1) * 1.142488 feature2(4) = tanh(netsum) netsum = -0.2623035 netsum = netsum + inarray(1) * -1.104266 netsum = netsum + inarray(2) * 1.418248 netsum = netsum + inarray(3) * 1.832693 netsum = netsum + inarray(4) * 0.4068221 netsum = netsum + inarray(5) * 2.663873 netsum = netsum + inarray(6) * 1.03975 netsum = netsum + inarray(7) * -0.9028041 netsum = netsum + -0.1324384 netsum = netsum + feature4(1) * -2.859479 feature2(5) = tanh(netsum) netsum = -0.715117 netsum = netsum + inarray(1) * -0.1785652

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netsum = netsum + inarray(2) * -2.252809 netsum = netsum + inarray(3) * 2.389553 netsum = netsum + inarray(4) * -0.8242859 netsum = netsum + inarray(5) * 2.544415 netsum = netsum + inarray(6) * -2.329354 netsum = netsum + inarray(7) * -0.1863263 netsum = netsum + -0.681648 netsum = netsum + feature4(1) * -2.153968 feature2(6) = tanh(netsum) netsum = -1.111591 netsum = netsum + inarray(1) * -0.5484812 netsum = netsum + inarray(2) * -1.209893 netsum = netsum + inarray(3) * 0.2186301 netsum = netsum + inarray(4) * 0.8334771 netsum = netsum + inarray(5) * -0.8743395 netsum = netsum + inarray(6) * 1.480538 netsum = netsum + inarray(7) * -0.4376018 netsum = netsum + -0.8616403 netsum = netsum + feature4(1) * 0.2429457 feature2(7) = tanh(netsum) netsum = 4.927373E-02 netsum = netsum + inarray(1) * -4.921978 netsum = netsum + inarray(2) * 1.57961 netsum = netsum + inarray(3) * 1.231455 netsum = netsum + inarray(4) * 1.416331 netsum = netsum + inarray(5) * 5.683895 netsum = netsum + inarray(6) * 0.0355361 netsum = netsum + inarray(7) * -0.2970401 netsum = netsum + -0.4088985 netsum = netsum + feature4(1) * -4.944896 feature2(8) = tanh(netsum) netsum = 2.931603 netsum = netsum + inarray(1) * -1.964484 netsum = netsum + inarray(2) * -3.09814 netsum = netsum + inarray(3) * -0.5542416 netsum = netsum + inarray(4) * 2.086954 netsum = netsum + inarray(5) * 1.242634 netsum = netsum + inarray(6) * -1.996533 netsum = netsum + inarray(7) * 0.6923131 netsum = netsum + 2.476298 netsum = netsum + feature4(1) * -1.198801 feature2(9) = tanh(netsum) netsum = 1.095533 netsum = netsum + inarray(1) * -1.114782 netsum = netsum + inarray(2) * -0.1259929 netsum = netsum + inarray(3) * -1.922172

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netsum = netsum + inarray(4) * -5.054327E-02 netsum = netsum + inarray(5) * -1.104949 netsum = netsum + inarray(6) * -1.226637 netsum = netsum + inarray(7) * -1.532847 netsum = netsum + 0.8667034 netsum = netsum + feature4(1) * -0.1618561 feature2(10) = tanh(netsum) netsum = -1.578137 netsum = netsum + inarray(1) * 0.6978155 netsum = netsum + inarray(2) * 1.263638 netsum = netsum + inarray(3) * 3.364008 netsum = netsum + inarray(4) * 1.052766 netsum = netsum + inarray(5) * 0.5841 netsum = netsum + inarray(6) * 3.998873 netsum = netsum + inarray(7) * -1.305039 netsum = netsum + -1.318058 netsum = netsum + feature4(1) * -2.202004 feature2(11) = tanh(netsum) netsum = 0.9382805 netsum = netsum + feature2(1) * -0.36071 netsum = netsum + feature2(2) * -2.994854 netsum = netsum + feature2(3) * 1.159189 netsum = netsum + feature2(4) * 1.458748 netsum = netsum + feature2(5) * 1.421714 netsum = netsum + feature2(6) * -0.6684889 netsum = netsum + feature2(7) * -1.770883 netsum = netsum + feature2(8) * -0.9634265 netsum = netsum + feature2(9) * -2.247745 netsum = netsum + feature2(10) * 0.7148361 netsum = netsum + feature2(11) * 1.028298 outarray(1) = 1 / (1 + exp(-netsum)) feature4(1) = feature4(1) + feature4(1) * -0.2 feature4(1) = feature4(1) + outarray(1) * 0.2 outarray(1) = 4519.5 * (outarray(1) - .1) / .8 + 4.5 if (outarray(1)<4.5) then outarray(1) = 4.5 if (outarray(1)>4524) then outarray(1) = 4524 End Sub

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