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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.
iii
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 ………………………………….
iv
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.
vi
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.
vii
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
ix
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
x
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
xi
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
xii
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
xiii
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
Figure 5.8 Simulation results in training set of the developed ANN model for bored piles
142
Figure 5.9 Simulation results in training set of the developed ANN model for bored piles
143
Figure 5.10 Simulation results in training set of the developed ANN model for bored piles
144
Figure 5.11 Simulation results in training set of the developed ANN model for bored piles
145
Figure 5.12 Simulation results in training set of the developed ANN model for bored piles
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
Figure 5.16 Simulation results in training set of the developed ANN model for driven concrete piles
150
Figure 5.17 Simulation results in training set of the developed ANN model for driven concrete piles
151
Figure 5.18 Simulation results in training set of the developed ANN model for driven concrete piles
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
Figure 5.21 Simulation results in training set of the developed ANN model for driven steel piles
155
Figure 5.22 Simulation results in training set of the developed ANN model for driven steel piles
156
Figure 5.23 Simulation results in training set of the developed ANN model for driven steel piles
157
Figure 5.24 Simulation results in training set of the developed ANN model for driven steel piles
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
xiv
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
xvi
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
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.
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
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.
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
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.
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
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
150
300
450
600
750
0 14 28 42 56 70
Movement (mm)
Axi
al lo
ad (
kN)
Pile geometry Soil profile CPT profile
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
Cone tip resistance (MPa)
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
tipcq − 0.046 -2.056 2.506 Accept 0.604 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
tipcq − 1.08 -2.048 2.048 Accept 4.44 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
Measured pile capacity (kN)
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
Measured pile capacity (kN)
Pre
dict
ed p
ile c
apac
ity (
kN)
Schmertmann
0
2000
4000
6000
8000
10000
0 2000 4000 6000 8000 10000
Measured pile capacity (kN)
Pre
dict
ed p
ile c
apac
ity (
kN)
Bustamante & Gianeselli
0
2000
4000
6000
8000
10000
0 2000 4000 6000 8000 10000
Measured pile capacity (kN)
Pre
dict
ed p
ile c
apac
ity (
kN)
GEP (This tsudy)
0
2000
4000
6000
8000
10000
0 2000 4000 6000 8000 10000
Measured pile capacity (kN)
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
Measured pile capacity (kN)
Pre
dic
ted p
ile c
apac
ity (
kN)
Eslami & Fellenius
0
1000
2000
3000
4000
5000
0 1000 2000 3000 4000 5000
Measured pile capacity (kN)
Pre
dic
ted p
ile c
apac
ity (
kN)
GEP (This study)
0
1000
2000
3000
4000
5000
0 1000 2000 3000 4000 5000
Measured pile capacity (kN)
Pre
dic
ted p
ile c
apac
ity (
kN)
Bustamante & Gineselli
0
1000
2000
3000
4000
5000
0 1000 2000 3000 4000 5000
Measured pile capacity (kN)
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
Measured pile capacity (kN)
Pre
dict
ed p
ile c
apac
ity (
kN)
Eslami & Fellenius
0
1000
2000
3000
4000
5000
6000
0 1000 2000 3000 4000 5000
Measured pile capacity (kN)
Pre
dict
ed p
ile c
apac
ity (
kN)
De Ruiter & Bernigen
0
1000
2000
3000
4000
5000
0 1000 2000 3000 4000 5000
Measured pile capacity (kN)
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 −
(MPa) L (m) D (mm) i
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
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 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
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 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.
134
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 −
(MPa) L (m) D (mm) i
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
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
135
Table 5.3 A sample of data input setting used to develop the ANN model (continued)
tipcq −
(MPa) shaftc
q −
(MPa) L (m) D (mm) i
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
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 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)
136
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
50
100
150
200
250
300
350
0 2 4 6 8 10 12 14 16
Number of hidden nodes
Sca
led
MS
E (
E-5
)
learning rate = 0.1momentum term = 0.1
Figure 5.3 Influence of number of hidden nodes on ANN model performance in validation set. MSE: mean squared error.
138
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.
0
50
100
150
200
250
300
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Learning rate
Sca
led
MS
E (
E-5
)
number of hidden nodes = 6momentum term = 0.1
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
0
50
100
150
200
250
300
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Momentum term
Sca
led
MS
E (
E-5
)
number of hidden nodes = 6learning rate = 0.08
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.
140
0
200
400
600
800
1000
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 3 Measured▲ ANN
0
200
400
600
800
1000
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 5 Measured▲ ANN
0
200
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800
1000
1200
1400
1600
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 2 Measured▲ ANN
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1000
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3000
4000
5000
6000
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 1 Measured▲ ANN
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800
1000
1200
1400
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 6 Measured▲ ANN
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400
800
1200
1600
2000
0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 4 Measured▲ ANN
Figure 5.6 Simulation results in training set of the developed ANN model for
bored piles.
141
0
200
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600
800
1000
1200
1400
0.00 2.00 4.00 6.00
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 9 Measured▲ ANN
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1000
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 7 Measured▲ ANN
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500
600
700
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900
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 11 Measured▲ ANN
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600
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 8 Measured▲ ANN
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4000
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6000
7000
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 10 Measured▲ ANN
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3000
4000
5000
6000
0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 12 Measured▲ ANN
Figure 5.7 Simulation results in training set of the developed ANN model for
bored piles.
142
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6000
8000
10000
12000
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 15 Measured▲ ANN
0
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1200
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 18 Measured▲ ANN
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5000
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 14 Measured▲ ANN
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6000
0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 13 Measured▲ ANN
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5000
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 17 Measured▲ ANN
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400
800
1200
1600
2000
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 16 Measured▲ ANN
Figure 5.8 Simulation results in training set of the developed ANN model for
bored piles.
143
0
200
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600
800
1000
1200
0 10 20 30 40
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 20 Measured▲ ANN
0
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4000
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8000
0 1 2 3 4 5
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 22 Measured▲ ANN
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700
1400
2100
2800
3500
0 10 20 30
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 21 Measured▲ ANN
0
300
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900
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1500
0 10 20 30 40
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 19 Measured▲ ANN
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300
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1200
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 24 Measured▲ ANN
0
300
600
900
1200
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 23 Measured▲ ANN
Figure 5.9 Simulation results in training set of the developed ANN model for
bored piles.
144
0
200
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800
1000
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1400
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 27 Measured▲ ANN
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5000
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 26 Measured▲ ANN
0
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500
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 28 Measured▲ ANN
0
200
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800
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 25 Measured▲ ANN
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5000
6000
0 20 40 60
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 30 Measured▲ ANN
0
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900
1200
1500
0 10 20 30
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 29 Measured▲ ANN
Figure 5.10 Simulation results in training set of the developed ANN model for
bored piles.
145
0
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6000
8000
10000
0 1 2 3 4
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 32 Measured▲ ANN
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5000
0 10 20 30 40 50
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 31 Measured▲ ANN
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600
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 33 Measured▲ ANN
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8000
0 1 2 3 4 5
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 35 Measured▲ ANN
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800
0 5 10 15 20 25
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 34 Measured▲ ANN
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800
1000
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 36 Measured▲ ANN
Figure 5.11 Simulation results in training set of the developed ANN model for
bored piles.
146
0
200
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600
800
1000
1200
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 38 Measured▲ ANN
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0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 39 Measured▲ ANN
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3000
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 40 Measured▲ ANN
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2500
0 10 20 30
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 41 Measured▲ ANN
0
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1200
1600
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 37 Measured▲ ANN
Figure 5.12 Simulation results in training set of the developed ANN model for
bored piles.
147
0
400
800
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 46 Measured▲ ANN
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800
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 43 Measured▲ ANN
0
800
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2400
3200
4000
4800
0 3 6 9 12
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 44 Measured▲ ANN
0
100
200
300
400
500
600
700
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 45 Measured▲ ANN
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1600
2400
3200
4000
4800
0 5 10 15 20 25
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 47 Measured▲ ANN
0
200
400
600
800
1000
1200
1400
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 42 Measured▲ ANN
Figure 5.13 Simulation results in validation set of the developed ANN model for
bored piles.
148
0
2000
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6000
8000
10000
12000
0 3 6 9 12 15
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 50 Measured▲ ANN
0
300
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1200
0 10 20 30 40
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 49 Measured▲ ANN
0
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600
800
1000
1200
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 48 Measured ▲ ANN
Figure 5.14 Simulation results in validation set of the developed ANN model for
bored piles.
149
0
200
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800
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1400
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 5 Measured ▲ ANN
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2000
0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 6 Measured▲ ANN
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1000
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 1 Measured▲ ANN
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1600
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2400
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Case record 2 Measured▲ ANN
Training set
0
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800
1000
1200
1400
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 3 Measured▲ ANN
0
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800
0 5 10 15 20 25
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 4 Measured▲ ANN
0
300
600
900
1200
1500
0 0.5 1 1.5 2 2.5
(Settlement/diameter)%
Loa
d (k
N)
Measured
ANN
Case record 2
Figure 5.15 Simulation results in training set of the developed ANN model for concrete driven piles.
150
0
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1800
2700
3600
4500
0 3 6 9 12
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 11 Measured ▲ ANN
0
400
800
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1600
0 1 2 3 4 5 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 12 Measured▲ ANN
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0 3 6 9 12 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 7 Measured▲ ANN
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200
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800
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Case record 8 Measured▲ ANN
Training set
0
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2000
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 9 Measured▲ ANN
0
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1500
2000
2500
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 10 Measured▲ ANN
Figure 5.16 Simulation results in training set of the developed ANN model for concrete driven piles.
151
0
300
600
900
1200
1500
0 3 6 9 12 15 18
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 17 Measured ▲ ANN
0
400
800
1200
1600
0 1 2 3 4 5 6 7
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 18 Measured ▲ ANN
0
300
600
900
1200
0 6 12 18 24 30 36
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 13 Measured ▲ ANN
0
400
800
1200
1600
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Case record 14 Measured▲ ANN
Training set
0
400
800
1200
1600
0 3 6 9 12
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 15 Measured ▲ ANN
0
300
600
900
1200
1500
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 16 Measured ▲ ANN
Figure 5.17 Simulation results in training set of the developed ANN model for concrete driven piles.
152
0
1100
2200
3300
4400
5500
6600
0 3 6 9 12
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 23 Measured ▲ ANN
0
300
600
900
1200
1500
0 1 2 3
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 19 Measured ▲ ANN
0
500
1000
1500
2000
2500
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Case record 20 Measured ▲ ANN
Training set
0
400
800
1200
0 3 6 9
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 21 Measured ▲ ANN
0
300
600
900
1200
1500
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 22 Measured ▲ ANN
Figure 5.18 Simulation results in training set of the developed ANN model for concrete driven piles.
153
0
300
600
900
1200
1500
0 1 2 3 4 5 6 7
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 25 Measured ▲ ANN
0
200
400
600
800
1000
0 1 2 3
(Settlement / diameter) %
Loa
d (k
N)
Case record 26 Measured ▲ ANN
Validation set
0
200
400
600
800
1000
1200
0 3 6 9
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 27 Measured ▲ ANN
0
1000
2000
3000
4000
5000
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Validat ion set
Case record 28 Measured ▲ ANN
0
300
600
900
1200
1500
1800
0 1 2 3 4 5 6 7
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 24 Measured ▲ ANN
Figure 5.19 Simulation results in validation set of the developed ANN model for concrete driven piles.
154
0
500
1000
1500
2000
2500
3000
3500
4000
0 3 6 9 12 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 5 Measured ▲ ANN
0
800
1600
2400
3200
4000
4800
0 1 2 3 4
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 6 Measured▲ ANN
0
100
200
300
400
500
600
700
0 5 10 15 20 25
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 1 Measured ▲ ANN
0
300
600
900
1200
1500
0 1 2 3 4 5
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 2 Measured ▲ ANN
0
200
400
600
800
0 0.5 1 1.5 2
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 3 Measured▲ ANN
0
400
800
1200
1600
2000
0 3 6 9 12 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 4 Measured ▲ ANN
Figure 5.20 Simulation results in training set of the developed ANN model for steel driven piles.
155
0
300
600
900
1200
1500
0 3 6 9 12 15 18 21 24
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 11 Measured ▲ ANN
0
200
400
600
800
1000
1200
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 12 Measured ▲ ANN
0
100
200
300
400
500
600
700
0 2 4 6
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 7 Measured ▲ ANN
0
300
600
900
1200
1500
0 3 6 9 12
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 8 Measured ▲ ANN
0
200
400
600
800
1000
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 9 Measured ▲ ANN
0
400
800
1200
1600
0 3 6 9 12
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 10 Measured ▲ ANN
Figure 5.21 Simulation results in training set of the developed ANN model for steel driven piles.
156
0
200
400
600
800
0 5 10 15 20 25 30 35
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 17 Measured ▲ ANN
0
200
400
600
800
0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 18 Measured ▲ ANN
0
300
600
900
1200
1500
0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 13 Measured ▲ ANN
0
300
600
900
1200
1500
0 5 10 15 20 25
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 14 Measured ▲ ANN
0
400
800
1200
1600
2000
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 15 Measured ▲ ANN
0
300
600
900
1200
0 3 6 9 12 15 18
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 16 Measured ▲ ANN
Figure 5.22 Simulation results in training set of the developed ANN model for steel driven piles.
157
0
600
1200
1800
2400
3000
3600
0 2 4 6 8
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 19 Measured ▲ ANN
0
200
400
600
800
1000
1200
0 3 6 9 12 15 18
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 24 Measured ▲ ANN
0
600
1200
1800
2400
3000
3600
4200
0 5 10 15 20
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 21 Measured ▲ ANN
0
400
800
1200
1600
0 5 10 15
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 22 Measured ▲ ANN
0
100
200
300
400
500
600
0 3 6 9
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 23 Measured ▲ ANN
0
400
800
1200
1600
2000
2400
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 20 Measured ▲ ANN
Figure 5.23 Simulation results in training set of the developed ANN model for steel driven piles.
158
0
200
400
600
800
0 5 10 15 20 25
(Settlement / diameter) %
Loa
d (k
N)
Training set
Case record 25 Measured ▲ ANN
Figure 5.24 Simulation results in training set of the developed ANN model for steel driven piles.
159
0
400
800
1200
1600
2000
0 3 6 9 12 15 18
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 30 Measured ▲ ANN
0
400
800
1200
1600
2000
0 1 2 3 4
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 26 Measured ▲ ANN
0
800
1600
2400
3200
4000
4800
0 1 2 3 4 5
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 27 Measured ▲ ANN
0
200
400
600
800
1000
0 2 4 6 8 10
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 28 Measured▲ ANN
0
200
400
600
800
0 3 6 9 12
(Settlement / diameter) %
Loa
d (k
N)
Validation set
Case record 29 Measured ▲ ANN
Figure 5.25 Simulation results in validation set of the developed ANN model for steel driven piles.
160
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
(Settlement/diameter)%
Loa
d (k
N)
MeasuredANNVerburgge
Case record 45
0
1000
2000
3000
4000
5000
0 5 10 15
(Settlement/diameter)%
Loa
d (k
N)
MeasuredANNVerburgge
Case record 42
0
200
400
600
800
1000
1200
0 5 10 15
(Settlement/diameter)%
Loa
d (k
N)
Measured ANN
Verburgge Fleming
Case record 44
0
2000
4000
6000
8000
10000
12000
0 5 10 15
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 43
0
200
400
600
800
0 2 4 6 8
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgee FlemingAPI
Case record 46
0
100
200
300
400
500
600
0 2 4 6 8 10
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
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
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 50
0
1000
2000
3000
4000
5000
0 5 10 15 20 25
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
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
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 24
0
400
800
1200
1600
0 2 4 6 8
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 25
0
1000
2000
3000
4000
5000
0 2 4 6 8
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 28
0
200
400
600
800
1000
0 1 2 3
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
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
(settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 28
0
900
1800
2700
3600
4500
0 1 2 3 4 5
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 26
0
300
600
900
1200
1500
1800
0 5 10 15 20
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge Fleming
Case record 27
0
400
800
1200
0 2 4 6 8 10
(settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
Case record 29
0
200
400
600
800
1000
0 5 10 15
(Settlement/diameter)%
Loa
d (k
N)
Measured ANNVerburgge FlemingAPI
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
Cone tip resistance (MPa)
Dep
th (
m)
0
40
80
120
160
200
0 1000 2000 3000 4000 5000
Load (kN)
Hea
d de
flect
ion
(mm
)
Head deflection = 0.05 * pile diameter + PL/AE
Failure load= 2624 kN
0
1100 mm
mud
peat
medium sand
7.6
10.3
13.0 m
Soil profileShaft geometry
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
Cone tip resistance (MPa)
Dep
th (
m)
silt
peat
sandy silt
medium sand
fine sand
0
1.2
1.8
2.8
4.2
420 mm4.2 m
Soil profileShaft geometry
CPT profile
0
20
40
60
80
100
0 300 600 900 1200 1500
Load (kN)
Hea
d de
flect
ion
(m
m)
Head deflection = 0.05 * pile diameter + PL/AE
Failure load= 911 kN
Figure A.2 Summary sheet for Case record 2, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
196
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30
Cone tip resistance (MPa)
Dep
th (
m)
Soil profileShaft geometry
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
)
Failure load= 711 kN
Head deflection = 0.05 * pile diameter + PL/AE
Figure A.3 Summary sheet for Case record 3, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
197
(a)
(b)
(c)
0
3
6
9
12
15
18
21
0 5 10 15 20 25 30 35
Cone tip resistance (MPa)
Dep
th (
m)
SP
soft to medium clay
MI
Soil profileShaft geometry
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
)
Failure load= 1423 kN
Head deflection = 0.05 * pile diameter + PL/AE
Figure A.4 Summary sheet for Case record 4, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
198
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35
Cone tip resistance (MPa)
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)
Failure load= 738 kN
Head deflection = 0.05 * pile diameter + PL/AE
silt
fine to medium sand
clayey silt + silty fine sand
silty sand0
1
2.3
10.2
393 mm6.5 m
Soil profileShaft geometry
CPT profile
3.5
Figure A.5 Summary sheet for Case record 5, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
199
(a)
(b)
(c)
0
1
2
3
4
5
6
7
8
9
0 5 10 15 20 25 30 35
Cone tip resistance (MPa)
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
)
Failure load= 560 kN
Head deflection = 0.05 * pile diameter + PL/AE
clayey fine sand
gravel + sand
fine sand
micaceous silt+ fine sand
26
0
7.5
13.5
405 mm5.6 m
Soil profileShaft geometry
CPT profile
Figure A.6 Summary sheet for Case record 6, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
200
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 3 6 9 12 15 18 21
Cone tip resistance (MPa)
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
Head deflection = 0.05 * pile diameter + PL/AE
silty clay
medium sand
0
4.4
12.4
320 mm10.2 m
Soil profileShaft geometry
CPT profile
Figure A.7 Summary sheet for Case record 7, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
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
Cone tip resistance (MPa)
Dep
th (
m)
0
6
12
18
24
30
0 150 300 450 600 750
Load (kN)
Hea
d d
efle
ctio
n (
mm
)
Failure load= 444 kN
Head deflection = 0.05 * pile diameter + PL/AE
medium sand
silty clay
320 mm
7.7 m
4.6
0
Soil profileShaft geometry
CPT profile
Figure A.8 Summary sheet for Case record 8, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
202
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
Dep
th (
m)
0
6
12
18
24
30
0 300 600 900 1200 1500
Load (kN)
Hea
d d
efle
ctio
n (
mm
)
Failure load= 1352 kN
Head deflection = 0.05 * pile diameter + PL/AE
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
Soil profileShaft geometry
CPT profile
Figure A.9 Summary sheet for Case record 9, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
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
)
Failure load= 5871 kN
Head deflection = 0.05 * pile diameter + PL/AE
0
4
8
12
16
20
24
28
0 6 12 18 24 30 36 42
Cone tip resistance (MPa)
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
Soil profileShaft geometry
CPT profile
Figure A.10 Summary sheet for Case record 10, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
204
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
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)
Failure load= 818 kN
Head deflection = 0.05 * pile diameter + PL/AE
medium sand
medium sand
silty clay
sandy gravel
0
4.6
8.2
9.6
320 mm 10.2 m
Soil profileShaft geometry
CPT profile
Figure A.11 Summary sheet for Case record 11, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
205
(a)
(b)
(c)
0
3
6
9
12
15
18
21
0 8 16 24 32 40 48 56
Cone tip resistance (MPa)
Dep
th (
m)
0
20
40
60
80
100
0 1500 3000 4500 6000 7500
Load (kN)
Hea
d d
efle
ctio
n (
mm
)
Failure load= 4270 kN
Head deflection = 0.05 * pile diameter + PL/AE
sandy gravel
sandy gravel
gravelly sand
gravelly sand
0
5.2
10.2
13.4670 mm 13 m
Soil profileShaft geometry
CPT profile
Figure A.12 Summary sheet for Case record 12, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
206
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
Dep
th (
m)
0
26
52
78
104
130
0 800 1600 2400 3200 4000
Load (kN)
Hea
d de
flect
ion (
mm
)
Failure load= 2357 kN
Head deflection = 0.05 * pile diameter + PL/AE
fine sand
fine sand
0
5
6 peat
15.3
1000 mm 9.5 m
Soil profileShaft geometry
CPT profile
Figure A.13 Summary sheet for Case record 13, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
207
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
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)
Failure load= 3692 kN
Head deflection = 0.05 * pile diameter + PL/AE
sand
sand
0
3.3
6.7
peat
15.3
1000 mm 9 m
Soil profileShaft geometry
CPT profile
Figure A.14 Summary sheet for Case record 14, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
208
(a)
(b)
(c)
0
5
10
15
20
25
30
35
0 7 14 21 28 35 42 49
Cone tip resistance (MPa)
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)
Failure load= 9652 kN
Head deflection = 0.05 * pile diameter + PL/AE
fine sand
silty fine sand
clayey silt
fill
silty clay
0
4 5.5 7.3
21.7
28.9
Soil profileShaft geometry
CPT profile
840 mm 24.4 m
Figure A.15 Summary sheet for Case record 15, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
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
Cone tip resistance (MPa)
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)
Failure load= 1436 kN
Head deflection = 0.05 * pile diameter + PL/AE
silty sand
clay
0
3.5
9.8
600 mm 7.2 m
Soil profileShaft geometry
CPT profile
Figure A.16 Summary sheet for Case record 16, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
210
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
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)
Failure load= 3247 kN
Head deflection = 0.05 * pile diameter + PL/AE
sand
sand
peat
1100 mm 7.2 m
Soil profileShaft geometry
CPT profile
0
5
6
15.3
Figure A.17 Summary sheet for Case record 17, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
211
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35
Cone tip resistance (MPa)
Dep
th (
m)
0
8
16
24
32
40
0 300 600 900 1200 1500
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 1005 kN
Head deflection = 0.05 * pile diameter + PL/AE
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
Soil profileShaft geometry
CPT profile
Figure A.18 Summary sheet for Case record 18, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
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
Cone tip resistance (MPa)
Dep
th (
m)
0
30
60
90
120
150
0 300 600 900 1200 1500
Load (kN)
Hea
d d
efle
ctio
n (
mm
)
Failure load= 604 kN
Head deflection = 0.05 * pile diameter + PL/AE
0
1.5
8
silt
2.8
peat
medium sand
Soil profileShaft geometry
CPT profile
6.2 m 329 mm
2sandy silt
Figure A.19 Summary sheet for Case record 19, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
213
(a)
(b)
(c)
0
1
2
3
4
5
6
7
8
0 3 6 9 12 15 18 21 24
Cone tip resistance (MPa)
Dep
th (
m)
0
50
100
150
200
250
0 300 600 900 1200 1500
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 765 kN
Head deflection = 0.05 * pile diameter + PL/AE
silt
peat
sandy silt
medium sand
fine sand
1.2
1.8
2.8
4.2
0
5.8 m 408 mm
Soil profileShaft geometry
CPT profile
Figure A.20 Summary sheet for Case record 20, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
214
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
Dep
th (
m)
0
40
80
120
160
200
0 700 1400 2100 2800 3500
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 1334 kN
Head deflection = 0.05 * pile diameter + PL/AE
medium sand
gravelly sand
fill
0
5.3
10.2
Soil profileShaft geometry
CPT profile
521 mm
8.2 m
Figure A.21 Summary sheet for Case record 21, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
215
(a)
(b)
(c)
0
3
6
9
12
15
18
21
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
Dep
th (
m)
0
20
40
60
80
100
120
0 2000 4000 6000 8000 10000
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 7650 kN
Head deflection = 0.05 * pile diameter + PL/AE
fine sand
sand
mud & peat
clay
6
18
14.5
1800 mm 11.5 m
0
Soil profileShaft geometry
CPT profile
Figure A.22 Summary sheet for Case record 22, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
216
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 6 12 18 24 30 36 42
Cone tip resistance (MPa)
Dep
th (
m)
0
5
10
15
20
25
30
0 250 500 750 1000 1250
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 1018 kN
Head deflection = 0.05 * pile diameter + PL/AE
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
Soil profileShaft geometry
CPT profile
Figure A.23 Summary sheet for Case record 23, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
217
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 6 12 18 24 30 36 42
Cone tip resistance (MPa)
Dep
th (
m)
0
5
10
15
20
25
30
0 250 500 750 1000 1250
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 1018 kN
Head deflection = 0.05 * pile diameter + PL/AE
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
Soil profileShaft geometry
CPT profile
Figure A.24 Summary sheet for Case record 24, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
218
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
Dep
th (
m)
0
10
20
30
40
50
60
0 250 500 750 1000 1250
Load (kN)
Hea
d de
flect
ion
(mm
) Failure load= 667 kN
Head deflection = 0.05 * pile diameter + PL/AE
sandy clay
medium sand
peat
11.4
3
2.1
0
Soil profileShaft geometry
CPT profile
400 mm7.8m
Figure A.25 Summary sheet for Case record 25, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
219
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 7 14 21 28 35 42 49
Cone tip resistance (MPa)
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
) Failure load= 4697 kN
Head deflection = 0.05 * pile diameter + PL/AE
gravelly sand
gravelly sand
sandy gravel
sandy gravel
0
5.2
10.2
670 mm
10.2 m
Soil profileShaft geometry
CPT profile
Figure A.26 Summary sheet for Case record 26, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
220
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35
Cone tip resistance (MPa)
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
) Failure load= 515 kN
Head deflection = 0.05 * pile diameter + PL/AE
mud
fill
fine sand
gravel
coarse sand
1.3
3.1
5.2
7.3
12.5
Soil profileShaft geometry
CPT profile
0
430 mm
8.7 m
Figure A.27 Summary sheet for Case record 27, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
221
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 3 6 9 12 15 18 21
Cone tip resistance (MPa)
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
)
Failure load= 355 kN
Head deflection = 0.05 * pile diameter + PL/AE
medium sand
silty clay
4.3
0
12.4
430 mm 7.7 m
Soil profileShaft geometry
CPT profile
Figure A.28 Summary sheet for Case record 28, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
222
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
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
) Failure load= 756 kN
Head deflection = 0.05 * pile diameter + PL/AE
medium sand
fill1.4
0
Soil profileShaft geometry
CPT profile
400 mm 10 m
Figure A.29 Summary sheet for Case record 29, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
223
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
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
) Failure load= 2686 kN
Head deflection = 0.05 * pile diameter + PL/AE
stiff clay
600 mm 12 m
1
11
fill
peat & sandy clay
clayey sand
fine sand
5
0
16.4
Soil profileShaft geometry
CPT profile
Figure A.30 Summary sheet for Case record 30, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
224
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
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
)
Failure load= 2406 kN
Head deflection = 0.05 * pile diameter + PL/AE
fill
peat & sandy clay
clayey sand
fine sand
5
0
11
Soil profileShaft geometry
CPT profile
1
600 mm 12 m
Figure A.31 Summary sheet for Case record 31, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
225
(a)
(b)
(c)
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
Cone tip resistance (MPa)
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
) Failure load= 8206 kN
Head deflection = 0.05 * pile diameter + PL/AE
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
Soil profileShaft geometry
CPT profile
1100 mm
27 m
Figure A.32 Summary sheet for Case record 32, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
226
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 3 6 9 12 15 18 21
Cone tip resistance (MPa)
Dep
th (
m)
0
5
10
15
20
25
30
0 150 300 450 600 750
Load (kN)
Dea
d def
lect
ion (
mm
)
Failure load= 391 kN
Head deflection = 0.05 * pile diameter + PL/AE
medium sand
silty clay
0
4.6
7.6
Soil profileShaft geometry
CPT profile
7.7 m 320 mm
Figure A.33 Summary sheet for Case record 33, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
227
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6 7 8
Cone tip resistance (MPa)
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
)
Failure load= 480 kN
Head deflection = 0.05 * pile diameter + PL/AE
clay & silty clay
silty sand
0
6.8
Soil profileShaft geometry
CPT profile
400 mm 9.4 m
Figure A.34 Summary sheet for Case record 34, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
228
(a)
(b)
(c)
0
5
10
15
20
25
30
35
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
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
)
Failure load= 7695 kN
Head deflection = 0.05 * pile diameter + PL/AE
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
Soil profileShaft geometry
CPT profile
Figure A.35 Summary sheet for Case record 35, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
229
(a)
(b)
(c)
0
3
6
9
12
15
18
21
0 3 6 9 12 15 18 21 24
Cone tip resistance (MPa)
Dep
th (
m)
0
7
14
21
28
35
42
0 200 400 600 800 1000
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 840 kN
Head deflection = 0.05 * pile diameter + PL/AE
350 mm 15.8 m
sand
0
Soil profileShaft geometry
CPT profile
Figure A.36 Summary sheet for Case record 36, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
230
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
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
) Failure load= 1298 kN
Head deflection = 0.05 * pile diameter + PL/AE
10.2 m
silt
peat
medium sand
fine sand
gravelley sand
4.6 5.3
8
13.7
Soil profileShaft geometry
CPT profile
500 mm
fill
2.7
0
6.2
Figure A.37 Summary sheet for Case record 37, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
231
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
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
Soil profileShaft geometry
CPT profile
Figure A.38 Summary sheet for Case record 38, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
232
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
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
Head deflection = 0.05 * pile diameter + PL/AE
2.7
0
1100 mm 6 m
mud & peat
fine sand + silt
Soil profileShaft geometry
CPT profile
Figure A.39 Summary sheet for Case record 39, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
233
(a)
(b)
(c)
0
4
8
12
16
20
24
28
0 5 10 15 20 25 30 35
Cone tip resistance (MPa)
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)
Failure load= 1770 kN
Head deflection = 0.05 * pile diameter + PL/AE
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
Soil profileShaft geometry
CPT profile
0
Figure A.40 Summary sheet for Case record 40, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
234
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
Depth
(m
)
0
30
60
90
120
150
180
0 700 1400 2100 2800 3500
Load (kN)
Head d
efle
ctio
n (
mm
) Failure load= 1263 kN
Head deflection = 0.05 * pile diameter + PL/AE
gravelley sand
medium sand
fill
5.3
10.2
521 mm 8.2 m
Soil profileShaft geometry
CPT profile
0
Figure A.41 Summary sheet for Case record 41, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
235
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 6 12 18 24 30 36 42 48
Cone tip resistance (MPa)
Dep
th (
m)
0
5
10
15
20
25
30
0 300 600 900 1200 1500
Load (kN)
Head d
efle
ctio
n (
mm
)
Failure load= 1294 kN
Head deflection = 0.05 * pile diameter + PL/AE
silt
fine to medium sand
silt
4.3
7.6
9.1
405 mm 7 m
0
Soil profileShaft geometry
CPT profile
Figure A.42 Summary sheet for Case record 42, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
236
(a)
(b)
(c)
0
3
6
9
12
15
18
21
0 7 14 21 28 35 42 49 56
Cone tip resistance (MPa)
Depth
(m
)
0
30
60
90
120
150
180
0 2000 4000 6000 8000 10000
Load (kN)
Head d
efle
ctio
n (
mm
) Failure load= 8825 kN
Head deflection = 0.05 * pile diameter + PL/AE
gravelly sand
gravelly sand
sandy gravel
sandy gravel
0
5.2
10.2
13.4 1078 mm 13 m
Soil profileShaft geometry
CPT profile
Figure A.43 Summary sheet for Case record 43, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
237
(a)
(b)
(c)
0
2
4
6
8
10
12
0 4 8 12 16 20 24 28
Cone tip resistance (MPa)
Depth
(m
)
0
20
40
60
80
100
120
0 150 300 450 600 750
Load (kN)
Head
def
lect
ion (
mm
)
Failure load= 578 kN
Head deflection = 0.05 * pile diameter + PL/AE
medium sand
peat
sandy clay
2.1
3
11.4
Soil profileShaft geometry
CPT profile
0
400 mm 7.8 m
Figure A.44 Summary sheet for Case record 44, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
238
(a)
(b)
(c)
0
2
4
6
8
10
12
14
16
0 4 8 12 16 20 24 28 32
Cone tip resistance (MPa)
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
Soil profileShaft geometry
CPT profile
0
1500 mm6 m
Head deflection = 0.05 * pile diameter + PL/AE
Failure load= 2668
Figure A.45 Summary sheet for Case record 45, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
239
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18
Cone tip resistance (MPa)
Dep
th (
m)
0
5
10
15
20
25
30
0 150 300 450 600 750
Load (kN)
Hea
d de
flect
ion
(mm
)
Failure load= 542 kN
Head deflection = 0.05 * pile diameter + PL/AE
sandy clay
peat
medium sand
2.1
3
0
11.4
400 mm7.8 m
Soil profileShaft geometry
CPT profile
Figure A.46 Summary sheet for Case record 46, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
240
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18
Cone tip resistance (MPa)
Dep
th (
m)
0
5
10
15
20
25
30
0 150 300 450 600 750
Load (kN)
Head
defle
ctio
n (
mm
)
Failure load= 409 kN
Head deflection = 0.05 * pile diameter + PL/AE
320 mm7.7 m
11
4.6
0
medium sand
silty clay
Soil profileShaft geometry
CPT profile
Figure A.47 Summary sheet for Case record 47, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
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
Cone tip resistance (MPa)
Depth
(m
)
0
30
60
90
120
150
180
0 1000 2000 3000 4000 5000
Load (kN)
Head
defle
ctio
n (
mm
) Failure load= 3425 kN
Head deflection = 0.05 * pile diameter + PL/AE
1.8
0 fill
residual silty sand
762 mm16.8 m
Soil profileShaft geometry
CPT profile
20.1
Figure A.48 Summary sheet for Case record 48, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
242
(a)
(b)
(c)
0
2
4
6
8
10
12
14
0 3 6 9 12 15 18 21 24 27
Cone tip resistance (MPa)
Dept
h (
m)
0
14
28
42
56
70
84
0 200 400 600 800 1000 1200
Load (kN)
Head
defle
ctio
n (
mm
)
Failure load= 627 kN
Head deflection = 0.05 * pile diameter + PL/AE
coarse sand
fine sand
gravel
fill
mud1.3
3.1
5.2
0
7.3
12.6
Soil profileShaft geometry
CPT profile
430 mm8.7 m
Figure A.49 Summary sheet for Case record 49, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
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
Cone tip resistance (MPa)
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
Soil profileShaft geometry
CPT profile
Figure A.50 Summary sheet for Case record 50, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) load deflection plot
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)
L (m) Type of load test
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)
L (m) Type of load test
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
Cone tip resistance (MPa)
Depth
(m
)
0
5
10
15
20
25
30
0 0.05 0.1 0.15 0.2
Sleeve friction (MPa)
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
Pile geometry Soil profile CPT profile
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
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.15 0.3 0.45 0.6
Sleeve friction (MPa)
Depth
(m
)
0
200
400
600
800
1000
0 7 14 21 28 35
Head deflection (mm)
Load (kN
)
400 mm11.3 m
0
Pile geometry Soil profile CPT profile
sand
clay2
Failure load = 870 kNtaken according to 80%-Criterion
Figure B.2 Summary sheet for case record 2, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
248
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
0 3 6 9 12 15
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
21
0 0.06 0.12 0.18 0.24
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 6 12 18 24 30
Head deflection (mm)
Load (kN
)
Fialure load = 1250 kN
Pile geometry Soil profile CPT profile
450 mm10.3 m
0
8
sand
clay
Figure B.3 Summary sheet for case record 3, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
249
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.09 0.18 0.27 0.36
Sleeve friction (MPa)
Depth
(m
)
0
200
400
600
800
1000
0 25 50 75 100 125
Head deflection (mm)
Load (kN
)
Fialure load = 600 kN
Pile geometry Soil profile CPT profile
350 mm8.6 m
0
2
8
sand (SM)
sand (SP)
clay
Figure B.4 Summary sheet for case record 4, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
250
(a)
(b) (c)
(d)
0
2
4
6
8
10
12
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
2
4
6
8
10
12
0 0.06 0.12 0.18 0.24
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 5 10 15 20 25
Head deflection (mm)
Load (kN
)
Failure load = 1140 kN
Pile geometry Soil profile CPT profile
450 mm8 m
0
silty sand
Figure B.5 Summary sheet for case record 5, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
251
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
0 3 6 9 12 15
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
0 0.06 0.12 0.18 0.24
Sleeve friction (MPa)
Depth
(m
)
0
400
800
1200
1600
2000
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 1600 kN
Pile geometry Soil profile CPT profile
285 mm15 m
0
6
silty sand
sand
Figure B.6 Summary sheet for case record 6, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
252
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
21
0 0.06 0.12 0.18 0.24
Sleeve friction (MPa)
Depth
(m
)
0
400
800
1200
1600
2000
0 12 24 36 48 60
Head deflection (mm)
Load (kN
) Failure load = 1755 kNtaken as 80% Craterion
Pile geometry Soil profile CPT profile
450 mm14.9 m
0
sand
loose sand
8
13
dense sand
Figure B.7 Summary sheet for case record 7, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
253
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
0 2 4 6 8 10
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
0 0.06 0.12 0.18 0.24
Sleeve friction (MPa)
Depth
(m
)
0
150
300
450
600
750
0 6 12 18 24 30
Head deflection (mm)
Load (kN
)
Failure load = 620 kN
Pile geometry Soil profile CPT profile
400 mm12.5 m
0
sand
Figure B.8 Summary sheet for case record 8, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
254
(a)
(b) (c)
(d)
0
4
8
12
16
20
24
0 6 12 18 24 30
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
24
0 0.07 0.14 0.21 0.28
Sleeve friction (MPa)
Depth
(m
)
0
400
800
1200
1600
2000
0 5 10 15 20 25
Head deflection (mm)
Load (kN
)
Failure load = 1485 kNtaken as 80% Criterion
Pile geometry Soil profile CPT profile
350 mm9.3 m
0
3
silty sand
fill
Figure B.9 Summary sheet for case record 9, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
255
(a)
(b) (c)
(d)
0
2
4
6
8
10
12
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
2
4
6
8
10
12
0 0.2 0.4 0.6 0.8
Sleeve friction (MPa)
Depth
(m
)
0
400
800
1200
1600
2000
0 8 16 24 32 40
Head deflection (mm)
Load (kN
) Failure load = 1845 kN
Pile geometry Soil profile CPT profile
450 mm9.2 m
0
sand
clay
10
Figure B.10 Summary sheet for case record 10, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
256
(a)
(b) (c)
(d)
0
4
8
12
16
20
24
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
24
0 0.04 0.08 0.12 0.16
Sleeve friction (MPa)
Depth
(m
)
0
800
1600
2400
3200
4000
0 15 30 45 60 75
Head deflection (mm)
Load (kN
) Failure load = 3600 kN
Pile geometry Soil profile CPT profile
610 mm18.2 m
0
sand
silty clay
20
Figure B.11 Summary sheet for case record 11, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
257
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
0 0.2 0.4 0.6 0.8
Sleeve friction (MPa)
Depth
(m
)
0
250
500
750
1000
1250
0 6 12 18 24 30
Head deflection (mm)
Load (kN
)
Failure load = 1020 kN
Pile geometry Soil profile CPT profile
400 mm11.2 m
sand
0
Figure B.12 Summary sheet for case record 12, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
258
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
0 0.03 0.06 0.09 0.12
Sleeve friction (MPa)
Depth
(m
)
0
200
400
600
800
1000
0 25 50 75 100 125
Head deflection (mm)
Load (kN
)
Failure load = 700 kN
Pile geometry Soil profile CPT profile
250 mm9.3 m
fill
clay
silty sand
01
6
Figure B.13 Summary sheet for case record 13, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
259
(a)
(b) (c)
(d)
0
3
6
9
12
15
18
21
0 2 4 6 8 10
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
21
0 0.05 0.1 0.15 0.2
Sleeve friction (MPa)
Depth
(m
)
0
250
500
750
1000
1250
0 6 12 18 24 30
Head deflection (mm)
Load (kN
) Failure load = 1170 kN
Pile geometry Soil profile CPT profile
400 mm12.5 m
sand
0
Figure B.14 Summary sheet for case record 14, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
260
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 2 4 6 8 10
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.05 0.1 0.15 0.2
Sleeve friction (MPa)
Depth
(m
)
0
250
500
750
1000
1250
0 10 20 30 40 50 60 70 80 90
Head deflection (mm)
Load (kN
)
Failure load = 1000 kN
Pile geometry Soil profile CPT profile
285 mm11 m
silty sand
uniform sand
0
3
Figure B.15 Summary sheet for case record 15, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
261
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
250
500
750
1000
1250
0 5 10 15 20 25 30 35 40 45
Head deflection (mm)
Load (kN
) Failure load = 1140 kN
Pile geometry Soil profile CPT profile
400 mm8.8 m
sand
clay
4
0
Figure B.16 Summary sheet for case record 16, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
262
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 15 30 45 60 75
Head deflection (mm)
Load (kN
) Failure load = 1300 kN
Pile geometry Soil profile CPT profile
355 mm10.2 m
2
0silt
sand
dense sand
Figure B.17 Summary sheet for case record 17, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
263
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
18
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 7 14 21 28 35
Head deflection (mm)
Load (kN
)
Failure load = 1140 kN
Pile geometry Soil profile CPT profile
400 mm11.4 m
5
0
clay
sand
Figure B.18 Summary sheet for case record 18, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
264
(a)
(b) (c)
(d)
0
5
10
15
20
25
30
0 3 6 9 12 15
Cone tip resistance (MPa)
Depth
(m
)
0
5
10
15
20
25
30
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 1260 kN
Pile geometry Soil profile CPT profile
350 mm20.4 m
10
0
sand
silt
Figure B.19 Summary sheet for case record 19, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
265
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.03 0.06 0.09 0.12
Sleeve friction (MPa)
Depth
(m
)
0
500
1000
1500
2000
2500
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 2070 kNtaken according to 80% Criterion
Pile geometry Soil profile CPT profile
500 mm11.0 m
sand
0
Figure B.20 Summary sheet for case record 20, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
266
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
250
500
750
1000
1250
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 1070 kN
Pile geometry Soil profile CPT profile
350 mm16 m
sand
clay3
0
Figure B.21 Summary sheet for case record 21, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
267
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 1350 kN
Pile geometry Soil profile CPT profile
350 mm16 m
sand
0
Figure B.22 Summary sheet for case record 22, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
268
(a)
(b) (c)
(d)
0
6
12
18
24
30
0 7 14 21 28 35
Cone tip resistance (MPa)
Depth
(m
)
0
6
12
18
24
30
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
1200
2400
3600
4800
6000
0 16 32 48 64 80
Head deflection (mm)
Load (kN
)
Failure load = 5455 kNtaken according to 80%-Criterion
Pile geometry Soil profile CPT profile
625 mm25.8 m
sand
0
Figure B.23 Summary sheet for case record 23, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
269
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.3 0.6 0.9 1.2
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 8 16 24 32 40
Head deflection (mm)
Load (kN
) Failure load = 1420 kN
Pile geometry Soil profile CPT profile
450 mm15 m
sand
0
Figure B.24 Summary sheet for case record 24, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
270
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 8 16 24 32 40
Head deflection (mm)
Load
(kN
)
Failure load = 1170 kN
Pile geometry Soil profile CPT profile
400 mm13.4 m
sand
clay
0
6
Figure B.25 Summary sheet for case record 25, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
271
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 3 6 9 12 15
Cone tip resistance (MPa)
Dept
h (m
)
0
3
6
9
12
15
0 0.07 0.14 0.21 0.28
Sleeve friction (MPa)
Dept
h (m
)
0
200
400
600
800
1000
0 4 8 12 16 20
Head deflection (mm)
Load
(kN
)
Failure load = 830 kN
Pile geometry Soil profile CPT profile
400 mm11.3 m
sand
0
Figure B.26 Summary sheet for case record 26, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
272
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 5 10 15 20
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.07 0.14 0.21 0.28
Sleeve friction (MPa)
Depth
(m
)
0
200
400
600
800
1000
0 6 12 18 24 30
Head deflection (mm)
Load (kN
) Failure load = 900 kN
Pile geometry Soil profile CPT profile
350 mm9.5 m
sand
0
9
clay
Figure B.27 Summary sheet for case record 27, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
273
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 8 16 24 32 40
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.1 0.2 0.3 0.4
Sleeve friction (MPa)
Depth
(m
)
0
1000
2000
3000
4000
5000
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 4250 kN
Pile geometry Soil profile CPT profile
500 mm13.8 m
sand
9
dense sand
0
Figure B.28 Summary sheet for case record 28, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
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)
L (m) Type of load test
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 ˝˝
Driven piles (steel)
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)
L (m) Type of load test
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 ˝˝ ˝˝
Driven piles (steel)
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
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
150
300
450
600
750
0 14 28 42 56 70
Head deflection (mm)
Load (kN
)
Pile geometry Soil profile CPT profile
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
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
250
500
750
1000
1250
0 6 12 18 24 30
Head deflection (mm)
Load (kN
)
Pile geometry Soil profile CPT profile
455 mm12 m
sand
0
Failure load = 1170 kN
Figure C.2 Summary sheet for case record 2, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
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
Sleeve friction (MPa)
Depth
(m
)
0
250
500
750
1000
1250
0 11 22 33 44 55
Head deflection (mm)
Load (kN
)
Failure load = 870 kN
Pile geometry Soil profile CPT profile
455 mm11.3
sand
0
Figure C.3 Summary sheet for case record 3, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
279
(a)
(b) (c)
(d)
0
5
10
15
20
25
0 6 12 18 24 30
Cone tip resistance (MPa)
Depth
(m
)
0
5
10
15
20
25
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Depth
(m
)
0
400
800
1200
1600
2000
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 1620 kN
Pile geometry Soil profile CPT profile
455 mm12 m
sand
0
Figure C.4 Summary sheet for case record 4, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
280
(a)
(b) (c)
(d)
0
5
10
15
20
25
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
5
10
15
20
25
0 0.06 0.12 0.18 0.24
Sleeve friction (MPa)
Dept
h (m
)
0
1000
2000
3000
4000
5000
0 18 36 54 72 90
Head deflection (mm)
Load (kN
)
Failure load = 3650 kN
Pile geometry Soil profile CPT profile
660 mm18.2 m
sand
0
20
silty clay
Figure C.5 Summary sheet for case record 5, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
281
(a)
(b) (c)
(d)
0
8
16
24
32
40
0 6 12 18 24 30
Cone tip resistance (MPa)
Depth
(m
)
0
8
16
24
32
40
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Dept
h (m
)
0
1000
2000
3000
4000
5000
0 6 12 18 24 30
Head deflection (mm)
Load
(kN
)
Failure load = 4460 kN
Pile geometry Soil profile CPT profile
609 mm34.3 m
sand0
6
20
clay
sand
Figure C.6 Summary sheet for case record 6, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
282
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 3 6 9 12 15
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.04 0.08 0.12 0.16
Sleeve friction (MPa)
Dept
h (m
)
0
200
400
600
800
1000
0 6 12 18 24 30
Head deflection (mm)
Load (kN
)
Failure load = 625 kN
Pile geometry Soil profile CPT profile
330 mm10 m
silty sand
4
clay
10
clay
0
Figure C.7 Summary sheet for case record 7, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
283
(a)
(b) (c)
(d)
0
7
14
21
28
35
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
7
14
21
28
35
0 0.04 0.08 0.12 0.16
Sleeve friction (MPa)
Depth
(m
)
0
300
600
900
1200
1500
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 1240 kN
Pile geometry Soil profile CPT profile
300 mm28.4 m
sand
peat
19
7
0
soft clay
Figure C.8 Summary sheet for case record 8, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
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
Sleeve friction (MPa)
Depth
(m
)
0
200
400
600
800
1000
0 9 18 27 36 45
Head deflection (mm)
Load (kN
)
Failure load = 765 kN
Pile geometry Soil profile CPT profile
455 mm22.5 m
sand
4 fill
18
dense sand
0
Figure C.9 Summary sheet for case record 9, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
285
(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
Sleeve friction (MPa)
Dept
h (m
)
0
250
500
750
1000
1250
0 12 24 36 48 60
Head deflection (mm)
Load (kN
)
Failure load = 1170 kN
Pile geometry Soil profile CPT profile
455 mm16.2 m
sand
0
Figure C.10 Summary sheet for case record 10, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
286
(a)
(b) (c)
(d)
0
5
10
15
20
25
0 6 12 18 24 30
Cone tip resistance (MPa)
Depth
(m
)
0
5
10
15
20
25
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Dept
h (m
)
0
300
600
900
1200
1500
0 18 36 54 72 90
Head deflection (mm)
Load (kN
)
Failure load = 1310 kNtaken according to 80% Criterion
Pile geometry Soil profile CPT profile
300 mm16.2 m
sand
0
Figure C.11 Summary sheet for case record 11, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
287
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 7 14 21 28 35
Cone tip resistance (MPa)
Depth
(m
)
0
4
8
12
16
20
0 0.09 0.18 0.27 0.36
Sleeve friction (MPa)
Depth
(m
)
0
250
500
750
1000
1250
0 15 30 45 60 75
Head deflection (mm)
Load (kN
)
Failure load = 1020 kN
Pile geometry Soil profile CPT profile
455 mm12 m
sand
0
Figure C.12 Summary sheet for case record 12, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
288
(a)
(b) (c)
(d)
0
5
10
15
20
25
0 6 12 18 24 30
Cone tip resistance (MPa)
Depth
(m
)
0
5
10
15
20
25
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Dept
h (m
)
0
300
600
900
1200
1500
0 12 24 36 48 60
Head deflection (mm)
Load (kN
)
Failure load = 1260 kN
Pile geometry Soil profile CPT profile
455 mm16.8 m
sand
0
Figure C.13 Summary sheet for case record 13, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
289
(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
Sleeve friction (MPa)
Dept
h (m
)
0
300
600
900
1200
1500
0 18 36 54 72 90
Head deflection (mm)
Load (kN
)
Failure load = 1300 kNtaken as 80% Criterion
Pile geometry Soil profile CPT profile
350 mm14.4 m
sand
0
Figure C.14 Summary sheet for case record 14, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
290
(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
Sleeve friction (MPa)
Dept
h (m
)
0
400
800
1200
1600
2000
0 18 36 54 72 90
Head deflection (mm)
Load (kN
)
Pile geometry Soil profile CPT profile
400 mm14.6 m
sand
0
Failure load = 1800 kN taken according to 80% Criterion
Figure C.15 Summary sheet for case record 15, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
291
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 6 12 18 24 30
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Dept
h (m
)
0
250
500
750
1000
1250
0 12 24 36 48 60
Head deflection (mm)
Load (kN
)
Failure load = 945 kN
Pile geometry Soil profile CPT profile
400 mm
14.6 m
sand
0
Figure C.16 Summary sheet for case record 16, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
292
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 4 8 12 16 20
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
0 0.03 0.06 0.09 0.12
Sleeve friction (MPa)
Dept
h (m
)
0
150
300
450
600
750
0 18 36 54 72 90
Head deflection (mm)
Load (kN
)
Failure load = 490 kN
Pile geometry Soil profile CPT profile
273 mm9.2 m
hydraulic sand
0
2 fill
13
Figure C.17 Summary sheet for case record 17, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
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
Head deflection (mm)
load (kN
)
Failure load = 675 kNtaken as 80% Criterion
Pile geometry Soil profile CPT profile
273 mm15.2 m
sand
fill
15
4
0
dense sand
Figure C.18 Summary sheet for case record 18, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
294
(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
Sleeve friction (MPa)
Depth
(m
)
0
800
1600
2400
3200
4000
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 3600 kN
Pile geometry Soil profile CPT profile
455 mm16.2 m
sand
0
Figure C.19 Summary sheet for case record 19, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
295
(a)
(b) (c)
(d)
0
8
16
24
32
40
0 7 14 21 28 35
Cone tip resistance (MPa)
Depth
(m
)
0
8
16
24
32
40
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Dept
h (m
)
0
500
1000
1500
2000
2500
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 2130 kN
Pile geometry Soil profile CPT profile
392 mm36.3 m
sand
0
4
8
sand
silty clay
Figure C.20 Summary sheet for case record 20, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
296
(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 0.02 0.04 0.06 0.08
Sleeve friction (MPa)
Dept
h (m
)
0
800
1600
2400
3200
4000
0 18 36 54 72 90
Head deflection (mm)
Load (kN
)
Failure load = 3500 kN
Pile geometry Soil profile CPT profile
490 mm14 m
dense sand
soft soil
0
5
17
Figure C.21 Summary sheet for case record 21, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
297
(a)
(b) (c)
(d)
0
5
10
15
20
25
0 6 12 18 24 30
Cone tip resistance (MPa)
Depth
(m
)
0
5
10
15
20
25
0 0.11 0.22 0.33 0.44
Sleeve friction (MPa)
Dept
h (m
)
0
300
600
900
1200
1500
0 10 20 30 40 50
Head deflection (mm)
Load (kN
)
Failure load = 1370 kN
Pile geometry Soil profile CPT profile
385 mm19 m
sand
0
3 clay
Figure C.22 Summary sheet for case record 22, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
298
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 3 6 9 12 15
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.08 0.16 0.24 0.32
Sleeve friction (MPa)
Dept
h (m
)
0
120
240
360
480
600
0 8 16 24 32 40
Head deflection (mm)
Load (kN
)
Failure load = 520 kN
Pile geometry Soil profile CPT profile
385 mm12.4 m
sand
0
3
clay
Figure C.23 Summary sheet for case record 23, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
299
(a)
(b) (c)
(d)
0
4
8
12
16
20
0 7 14 21 28 35
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
250
500
750
1000
1250
0 14 28 42 56 70
Head deflection (mm)
Load (kN
)
Failure load = 1010 kN
Pile geometry Soil profile CPT profile
455 mm15.2 m
sand
0
7
clay
Figure C.24 Summary sheet for case record 24, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
300
(a)
(b) (c)
(d)
0
3
6
9
12
15
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
3
6
9
12
15
0 0.16 0.32 0.48 0.64
Sleeve friction (MPa)
Depth
(m
)
0
180
360
540
720
0 18 36 54 72 90
Head deflection (mm)
Load
(kN
)
Failure load = 590 kN
Pile geometry Soil profile CPT profile
321 mm8.5 m
sand
clay 0
1.5
Figure C.25 Summary sheet for case record 25, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
301
(a)
(b) (c)
(d)
0
8
16
24
32
40
0 3 6 9 12 15
Cone tip resistance (MPa)
Depth
(m
)
0
8
16
24
32
40
0 0.04 0.08 0.12 0.16
Sleeve friction (MPa)
Dept
h (m
)
0
400
800
1200
1600
2000
0 3 6 9 12 15
Head deflection (mm)
Load (kN
)
Failure load = 1710 kN
Pile geometry Soil profile CPT profile
350 mm31.3 m
silty sand
0
clay
24
35
Figure C.26 Summary sheet for case record 26, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
302
(a)
(b) (c)
(d)
0
8
16
24
32
40
0 5 10 15 20 25
Cone tip resistance (MPa)
Depth
(m
)
0
8
16
24
32
40
0 0.05 0.1 0.15 0.2
Sleeve friction (MPa)
Dept
h (m
)
0
1000
2000
3000
4000
5000
0 18 36 54 72 90
Head deflection (mm)
Load
(kN
)
Failure load = 4330 kN
Pile geometry Soil profile CPT profile
609 mm34.4 m
sand
sand
clay
0
6
19
Figure C.27 Summary sheet for case record 27, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
303
(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
Sleeve friction (MPa)
Dept
h (m
)
0
200
400
600
800
1000
0 10 20 30 40 50
Head deflection (mm)
Load (kN
)
Failure load = 817 kN
Pile geometry Soil profile CPT profile
455 mm11.3 m
sand
0
Figure C.28 Summary sheet for case record 28, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
304
(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 0.06 0.12 0.18 0.24
Sleeve friction (MPa)
Dept
h (m
)
0
160
320
480
640
800
0 9 18 27 36 45
Head deflection (mm)
Load (kN
)
Failure load = 630 kN
Pile geometry Soil profile CPT profile
350 mm
11.1 m
sand
0
Figure C.29 Summary sheet for case record 29, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
305
(a)
(b) (c)
(d)
0
7
14
21
28
35
0 3 6 9 12 15
Cone tip resistance (MPa)
Depth
(m
)
0
7
14
21
28
35
0 0.04 0.08 0.12 0.16
Sleeve friction (MPa)
Dept
h (m
)
0
400
800
1200
1600
2000
0 12 24 36 48 60
Head deflection (mm)
Load (kN
)
Failure load = 1690 kN
Pile geometry Soil profile CPT profile
300 mm31.4 m
sand
peat7
0
19
sand
soft clay21
Figure C.30 Summary sheet for case record 30, (a) pile geometry and soil profile, (b) cone tip resistance profile, (c) sleeve friction profile, (d) load deflection plot
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
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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
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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
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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
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' 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
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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
315
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
316
' 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)
317
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
319
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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