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Predicting the Side Resistance of Piles Using a

Genetic Algorithm and SPT N-Values

Markus Jesswein & Jinyuan Liu

Department of Civil Engineering – Ryerson University, Toronto, ON, Canada

Minkyung Kwak

Ministry of Transportation of Ontario, Toronto, ON, Canada

ABSTRACT

A genetic algorithm (GA) was developed to predict the side resistance of piles in Ontario with the standard penetration test

blowcounts (SPT N-values). Pile foundations commonly support structures by transferring loads deeper into the ground;

unfortunately, the soil characteristics, such as the strength and grain-size distribution, are rarely consistent at a site. Due

to the spatial variability of the soil, challenges arise to accurately predict the ultimate axial capacity of piles. This research

aims to mitigate this problem by implementing genetic programming. Since the 1950s, the Ministry of Transportation of

Ontario has gathered approximately 100 pile load tests in various soil conditions, and a total of 23 piles were selected for

this study. These piles were either H piles or pipe piles and were subjected to extension load tests. A GA was created to

correlate the side resistances to the SPT N-values, and the developed relationships were compared to existing design

methods for different soil types. In all, the ultimate goal of this research was to improve local pile design in Ontario’s

practice.

RÉSUMÉ

Un algorithme génétique (AG) a été développé pour prédire la résistance au cisaillement des pieux en Ontario avec les

compteurs d'essai de pénétration standard (valeurs N du SPT). Les fondations de pieux soutiennent généralement les

structures en transférant les charges plus profondément dans le sol; Malheureusement, les caractéristiques du sol, telles

que la force et la distribution granulométrique, sont rarement constantes sur un site. En raison de la variabilité spatiale du

sol, il est difficile de prédire avec précision la capacité axiale ultime des piles. Cette recherche vise à atténuer ce problème

en mettant en œuvre la programmation génétique. Depuis les années 1950, le ministère des Transports de l'Ontario a

recueilli environ 100 essais de chargement de pieux dans diverses conditions de sol, et un total de 23 piles ont été

sélectionnées pour cette étude. Ces piles étaient des piles H ou des pieux tubulaires et ont été soumises à des essais de

charge d'extension. Un AG a été créé pour corréler les résistances au cisaillement aux valeurs N du SPT, et les relations

développées ont été comparées aux méthodes de conception existantes pour différents types de sols. Dans l'ensemble,

le but ultime de cette recherche était d'améliorer la conception locale des piles dans la pratique ontarienne.

1 INTRODUCTION

Deep foundations are designed to support bridges and

buildings, but accurately predicting the capacity of a pile is

a challenge due to the influences from the installation

method, pile geometry, and soil properties. Especially

since glacial tills are commonly found in Ontario, the site

conditions are rarely consistent as the soil strength and

contents can vary spatially. In addition, the standard

penetration test (SPT) is unreliable because it lacks

accuracy. Yet, it is commonly used in site investigations

because it is a cheap and simple measurement technique

and can be applied in various soil conditions, including

gravel and cobble rich soils. Numerous correlations have

been proposed to predict the pile capacity with SPT N-

values, but many of the design methods were developed

by averaging or generalizing the soil conditions. Also, a

limited number of design methods have been proposed for

soils with stiff clays and glacial tills, especially for Ontario.

This investigation addresses the uncertainty in design

by developing a genetic algorithm (GA) to correlate SPT N-

values to the side resistance of driven piles. The Ministry

of Transportation of Ontario (MTO) accumulated a

database with over 100 pile load tests, and results from 23

high-quality extension load tests were selected for this

study. GAs can efficiently correlate several variables

compared to traditional statistical approaches, and a GA

was developed to predict the frictional resistance with

multiple N-values and soil types along the length of a pile.

2 RESEARCH BACKGROUND

2.1 Current Design Methods

A pile subjected to axial compressive loading can

experience two mechanisms: the side resistance () and

the tip resistance (). The side resistance is the friction

between the soil and pile walls, while the tip resistance is

developed by the strength of the soil at the pile base. As a

pile reaches its maximum load, these mechanisms

contribute towards the ultimate pile resistance, or capacity

():

[1]

In this paper, the focus is on the side resistance, which

depends on the unit side resistance (), pile perimeter ()

and embedment length ().

[2]

Usually, the side resistance is directly predicted by the

average SPT N-value (

) along the pile length. As shown

in Table 1, many empirical correlations have been

proposed for various soil conditions. Unfortunately, the

average soil conditions may not accurately represent the

soil behaviour.

Table 1. Existing Design Methods for Pile Side Resistance

Soil Type

Reference

Equation for (kPa)

Cohesive

Shioi & Fukui

(1982)

Noncohesive

Meyerhof (1956)

Pipe Piles:

H Piles:

Shioi & Fukui

(1982)

All

Brown (2001)1

Decourt (1982)2

1 Recommended SPT range is and 2 .

Several references also report various influences on

the capacity with the pile length (Meyerhof 1976; Vesic

1977; Poulos et al. 2001). This relationship can be due to

load dissipation along the pile length; events related to the

pile installation process, such as whipping; or the

confinement of the effective stress with noncohesive soils.

In all, the side resistance is influenced by many

variables, including the soil type, soil strength, pile

geometry, and installation process. The complex and

nonlinear relationship between the pile and soil can be

predicted with a GA.

2.2 An Introduction to Genetic Algorithms

Genetic algorithms are an optimization approach inspired

by Darwin’s theory of evolution (Banzhaf et al. 1998). In

nature, chromosomes give an organism its attributes to

survive and succeed in an environment. Through

reproduction, organisms can adapt and evolve to their

environment. A GA represents the problem domain as a

chromosome. In this case, a GA was developed to conduct

symbolic regression and predict the side resistance. For

symbolic regression, the genes of a chromosome

represented the components of a function: a variable,

constant, or operator.

A generic GA searches for a solution through five

general steps: chromosome creation, evaluation, selection,

crossover, and mutation. First, multiple attempts for a

problem are made at once in a trial, or generation, by

generating a population of chromosomes with different

attributes. The performance or fitness of a single

chromosome is measured by an objective function. From

the population of chromosomes, potential parents are

selected for the creation of offspring. Typically, during

selection, a preference is given to chromosomes with a

higher fitness. The population size remains constant

throughout every generation, and the previous

chromosomes, or at least a majority, are replaced by new

offspring. The population then evolves through several

generations by reproduction mechanisms, such as

crossover and mutation.

A GA is a stochastic method. If a regression analysis

was repeated with multiple trials and had the same initial

conditions, the GA can complete the analysis with a similar

level of fitness but provide a different solution. A GA is also

data-driven and, depending on the complexity of a

problem, may not find an exact solution or global minimum,

but it is an efficient optimization approach, especially if

aspects of a problem are unknown.

3 RESEARCH METHODOLOGY AND RESULTS

3.1 Overview of the Methodology

For driven piles in heterogeneous soils, the goal was to

improve the predictability of the side resistance. A new

design method was developed by following four steps. (1)

Results from pile load tests and soil measurements were

collected from a database by MTO. (2) For every pile, the

measured side resistance was obtained from load-

displacement responses that were measured at the pile

top. (3) A GA was then developed to nonlinearly correlate

the side resistance in heterogeneous soils with SPT N-

values. (4) In the end, the accuracy of the GA was

compared to existing design methods.

3.2 Testing Sites and Pile Load Tests

For this investigation, borehole logs for the soil conditions

and records on the pile load tests were collected from

MTO. Driven piles were either H piles or steel pipe piles,

and they were subjected to static axial-tension loads to

measure the side resistance. The pile properties and

Figure 1. Location of Studied Sites

Table 2. Details on the Studied Piles

Site

No.

Pile

No.

Pile Type1

Length2

(m)

Embedded Soil

Type3

(kN)

22

3

324 OD Pipe

15.30

Clayey Silt

118

22

4

324 OD Pipe

30.15

Clayey Silt

340

23

2

324 OD Pipe

3.02

Silty Clay

209

23

3

HP 310x110

3.05

Silty Clay

236

24

2

324 OD Pipe

15.39

Sand

372

24

3

324 OD Pipe

22.40

Sand

401

24

4

HP 310x79

22.40

Sand

403

24

5

HP 310x79

15.39

Sand

263

35

1

HP 310x110

14.69

Layered Clayey Silt

and Silty Sand

506

35

4

324 OD Pipe

14.69

Layered Clayey Silt

and Silty Sand

730

35

5

HP 310x110

27.58

Layered Clayey Silt

and Silty Sand

1493

37

3

HP 310x79

14.48

Sand to Silty Sand

333

37

4

HP 310x79

38.94

Sand to Silty Sand

1394

37

5

HP 310x79

31.24

Sand to Sandy Silt

420

37

6

HP 310x110

14.48

Sand to Silty Sand

383

37

7

HP 310x110

45.29

Sand to Silty Sand

1524

37

8

HP 310x110

30.92

Sand to Silty Sand

699

39

2

HP 310x110

25.50

Silty Sand; Layered

Clay and Silt

614

39

3

324 OD Pipe

25.40

Silty Sand; Layered

Clay and Silt

470

40

2

HP 310x110

24.50

Layered Sand and

Silty Clay

598

40

3

324 OD Pipe

17.20

Sandy Silt to Sand

505

41

2

HP 310x110

19.50

Sand

1052

41

3

324 OD Pipe

16.00

Sand

664

1 Steel H pile designations are depth (mm) by weight (kg/m). Steel

pipe piles were filled with concrete before testing, and OD is the

outside diameter (mm); 2 Embedment Length; 3 Classifications

according to MTO standards.

ultimate side resistances are in Table 2. From the 23 piles,

9 were pipe piles, and 14 were H piles. The embedment

lengths varied from 3 m to 45 m, but most of the piles were

between 12 to 25 m long.

Figure 1 shows the locations of the sites. The soils were

generally compact or stiff, but some loose sands were

found. Noncohesive soils were common in the database.

For the pipe piles, two were mainly in cohesive soils, four

dominated in noncohesive soils, and the remaining had

mixed soil conditions. One H pile was fully embedded in

cohesive soils, while nine H piles were in noncohesive

soils. Borehole logs contained the soil type, SPT N-values,

and occasionally, the unit weights at the sites. SPT N-

values were corrected according to CGS (2006) for a

hammer efficiency of 60% and the overburden conditions.

3.3 Measured Side Resistance ()

The load-displacement response was measured with dial

gauges at the top of the piles during the load tests. The

failure load was determined by the criteria from De Beer

(Fellenius 1980). De Beer recommends plotting both axes

of the load-displacement curves with a log-scale, and the

failure load is indicated by the largest change in slope on

the plot (Fellenius 1980).

3.4 Construction of the Genetic Algorithm

3.4.1 Introduction

Each pile was divided into 50 segments to consider the

varying side resistance along their length. The variables in

the analysis included the corrected SPT N-values (), the

soil type (), effective stress (), and pile slenderness ratio

( ). N-values were corrected for the hammer

efficiency () for cohesive soils, and the overburden

correction was also applied () for noncohesive soils.

The soil type was a binary variable equal to 1 for

noncohesive soils or 2 for cohesive soils. The slenderness

ratio was modified to determine the side resistance at any

depth. It was composed of the embedment length (),

depth to the centre of a pile segment (), and maximum

width or diameter of a pile (). The side resistance of a H

pile will be influenced if the soil creates an unplugged, fully

plugged, or partially plugged condition. If a pile is assumed

to be fully plugged, illogical results may be provided,

especially for noncohesive soils. Since the actual perimeter

of the pile is known, H piles were assumed to be unplugged

for the analysis. The database was divided for H piles and

pipe piles, and the GA performed 5 trials for each pile type

(a total of 10 runs) to regress the variables and test results.

Figure 2. Process of the Genetic Algorithm

As displayed in Figure 2, the GA in this investigation

evolved the chromosomes with the following steps:

creation, evaluation, selection, crossover, mutation, and

constant refinement. The GA was created with Matlab

(Mathworks 2017) and applies the Multi Expression

Programming (MEP) technique (Oltean & Dumitrescu,

2002) to encode and evaluate the chromosomes. MEP was

based on the activation of programs or code with integers

and can efficiently encode or decode functions compared

to other techniques (Oltean & Dumitrescu, 2002). Table 3

Table 3. Settings for the Genetic Algorithm

Parameter

Parameter Setting

Number of generations

60

Population size

2000

Function set

power, exponential,

logarithmic, hyperbolic tangent

Chromosome length

20

Fitness function

Mean Squared Error (MSE)

Mutation rate (%)

10

Crossover rate (%)

90

Crossover type

Uniform with brood

recombination

Population size for brood

crossover

4

Brood crossover rate (%)

50

Population size for brood

constant refinement

50

Tournament selection size

2

Initial operator likelihood (%)

30

Initial variable likelihood (%)

40

Initial constant likelihood (%)

30

shows the settings of the GA.

3.4.2 Creating Chromosomes

For a given problem, a potential solution is represented by

a chromosome. In this investigation, the chromosomes with

MEP were linear entities, or arrays, and represented a

function for the unit side resistance of a pile. The genes, or

entries within the arrays, were divided into two

components. The first part indicated the activation of a

function component, such as a variable, constant, or

operator. The second part links the action of the operators.

Figure 3 shows an example to decode an MEP

chromosome. The first row of the chromosome in the figure

has negative integers to represent the operators. In this

example, -1 is for addition. Positive integers designated the

activation of variables and constants, which are

represented in general by and in the figure. A constant

or variable must be the first entry within the chromosome

to prevent illogical errors during evaluation (Oltean &

Dumitrescu, 2002). The last two rows indicate the

locations, or column numbers, for the operators to be

performed. During evaluation, the result of every gene is

stored, and the operators are applied to the results from

Figure 3. Example of Decoding the Chromosome

previous portions of the chromosome. Since variables and

constants are numerical values, their corresponding links

in the chromosome are meaningless.

The GA in this investigation was capable of simple

arithmetic, but it also included power, logarithmic, and

hyperbolic tangent operators because they represent

nonlinear relations. However, the possible combinations

for a GA to search can also increase exponentially if many

operators are added (Banzhaf et al. 1998).

The population of chromosomes were initially created

randomly, but a probability was assigned for the likelihood

of occurrence for the operators, constants, and variables.

The chromosomes were given a maximum length of 20

genes.

3.4.3 Evaluation of the Chromosomes

The goal of the GA in this study was to find the function

with the best fitness to represent the unit side resistance of

a pile. During evaluation, the changing shear strength from

the soil conditions were considered by dividing the pile into

several segments. The GA predicted the unit side

resistance for each layer, and the total side resistance of a

pile was found by the summation of the side resistances on

the pile segments. Load-displacement responses were

measured at the top of the piles during testing. Thus, the

fitness function compared the predicted total side

resistance () to the measured side resistance ()

with the mean squared error (MSE):

[3]

Where n is the number of analyzed piles. A lower MSE

indicates a better fit between the measured and predicted

values.

Generally, care is needed to ensure that illogical errors

do not occur during evaluation. Examples include dividing

by zero or taking the logarithm of a negative value. Division

operators may be protected by simply returning the

numerator if a denominator of zero is found (Banzhaf et al.

1998), but Oltean & Dumitrescu (2002) recommend

mutating division into a variable or constant. Other

operators were protected and transformed as suggested by

Brameier & Banzhaf (2007).

3.4.5 Selection of the Parents

A pair of parents were selected for mating using

tournament selection. For each parent, a number, or

tournament size, of chromosomes were randomly

sampled, and the chromosome from this group with the

highest fitness became a parent. Tournament selection

was repeated until the new population size matched the

original size.

3.4.6 Crossover and Mutation

The activation of crossover was assigned a probability. If

crossover was chosen to not occur, the parents were

copied and sent for mutation. Otherwise, uniform crossover

was applied with brood recombination (Figure 4). Uniform

crossover randomly distributes the genes from the parents

Figure 4. Example of Uniform Crossover with Brood

Recombination

to the offspring. Brood recombination was inspired by

organisms having a litter of offspring (Tackett 1994), and it

attempts to extract the best attributes from two parents.

Two parents performed crossover several times to create

a subpopulation () of new chromosomes. The two

offspring with the best fitness continued for mutation.

Ifevery pair of parents experienced brood recombination,

the total number of created offspring would be multiplied

by the population size, and the computational effort would

be significantly increased (Banzhaf et al. 1998). Thus, the

chance of brood recombination was assigned a probability.

For mutation, a selected gene would be transformed

randomly into a different component type. For example, an

addition operator could become a constant. The chance of

mutation was set to be low at 10 %. After mutation, the

resulting offspring replaced the worst chromosomes from

the original population if they developed a higher fitness.

3.4.7 Constant Refinement

For symbolic regression, the constants are either

evolutional or non-evolutional (Banzhaf et al. 1998). Non-

evolutional constants are kept the same throughout a

generation, but the GA can apply operations to manipulate

the value of a constant within a function. For evolutionary

constants, optimization techniques, such as the

Levenberg-Marquardt algorithm (Marquardt 1963) or

Nelder-Mead simplex method (Nelder and Mead 1965),

can be applied. These methods are mathematically

complex and usually iterative. They may take numerous

trials to terminate on a potential solution, especially with

several variables. Since the population of chromosomes

may be large, the computational effort should be

minimized. Brood recombination was applied in this GA as

a simple approach to refine the values of the constants. For

every chromosome, the values of the constants were

randomly changed for 50 attempts. The values that

provided the best fitness were kept as the new constants.

3.5 Results from the Genetic Algorithm

The GA analyzed both pipe piles and H piles separately

with 2000 chromosomes for 60 generations. The plots in

Figures 5 and 6 show the average and lowest MSE within

the population of chromosomes for pipe and H piles. For

Figure 5. Fitness Performance with Pipe Piles

Figure 6. Fitness Performance with H Piles

each of the 5 trials, the analysis usually terminated with a

similar MSE. As a better links were made, the brood

recombination during crossover and constant refinement

resulted in sudden drops in the best fitness throughout the

generations.

At the end of the 5 trials, the function with the best

fitness (BF) was collected for each pile type. The MSE by

itself may seem misleading since the pipe piles had lower

side resistances on average than the H piles. Yet, as

shown in Figures 7 and 8, the best-fit function for pipe and

H piles had a reasonably good R2, and results were also

mainly within ± 25 % of the 1:1 line. For pipe piles, the

function with the lowest MSE had a R2 of 0.73:

[4]

The function with the best fit for unplugged H piles had a

R2 of 0.82:

[5]

0

20000

40000

60000

80000

010 20 30 40 50 60

Fitness (Mean Squared Error)

Generation

Trial 1 Average

Trial 1 Best

Trial 2 Average

Trial 2 Best

Trial 3 Average

Trial 3 Best

Trial 4 Average

Trial 4 Best

Trial 5 Average

Trial 5 Best

30000

60000

90000

120000

150000

010 20 30 40 50 60

Fitness (Mean Squared Error)

Generation

Trial 1 Average

Trial 1 Best

Trial 2 Average

Trial 2 Best

Trial 3 Average

Trial 3 Best

Trial 4 Average

Trial 4 Best

Trial 5 Average

Trial 5 Best

For pipe piles, the developed function had a predicted

to measured resistance ratio ( ) of 1.09 on

average, and it overestimated the resistance of the piles

dominating in cohesive soils. The overestimation likely

resulted since a limited number of piles were fully

embedded in clay. In general, the GA rarely considered the

soil type for H piles because noncohesive soils dominated

the sites. While observing the applied variables in the final

generation, functions frequently contained the slenderness

ratio for H piles, and Equation 5 does not apply any other

variable. This result may indicate the unreliability of SPT or

the soil plugging and installation effects of H piles. Equation

5 typically underestimated the side resistance with an

average of 0.94. Equations 4 and 5 may also tend

to be more conservative for piles with higher resistances or

longer lengths.

The function with the lowest fitness, as demonstrated

Figure 7. Comparison of Measured and Predicted Side

Resistances by GA for Pipe Piles

Figure 8. Comparison of Measured and Predicted Side

Resistances by GA for H Piles

with Equation 5, is not always practical, beneficial, or

appropriate. Another function for each pile type was then

selected by Pareto optimization (PO). The results from the

final generations of the 5 trials were pooled together to

create a population of 10000 functions. These functions

were then graphically evaluated by their fitness and

complexity. The complexity is the number of components

in a function, and the Pareto front was created in Figures 9

and 10 by finding the best fitness for each complexity. In

general, a lower complexity, or a shorter function, results in

a higher MSE, but a longer function can have several

operations to create a better fitness. The orange square

markers are points on the Pareto front, and the blue circles

are the remaining results. Any point along the Pareto front

can be a potential solution; thus, the preferred solution

mainly relies on the tolerable error and judgement of the

investigator (Smits & Kotanchek 2005).

For pipe piles, the improvement of the MSE is low for a

complexity between 9 to 15. The function on the Pareto

front with 9 components was selected since shorter

functions had a significantly higher MSE. The

corresponding function is below (R2 = 0.69):

[6]

The Pareto front in Figure 10 was linear for H piles, and

the sudden increase in fitness at a complexity of 15 may be

due to the volatile nature of brood recombination. A

preference was given to a function containing several

variables. The selected function initially had a complexity

of 9 but was simplified to the following (R2 = 0.76):

[7]

The fitness of Equations 6 and 7 is displayed in Figures 7

and 8. The functions from the Pareto optimization have a

small difference in R2 compared to the functions with the

lowest MSE. Since Equation 6 included the soil type, it

bears more information on the soil conditions than

Equation 4, and it had a slightly better average of

1.06. Equations 7 and 5 did not include the soil type, and

Equation 7 tends to overestimate compared to Equation 5

with an average of 1.16. The effective stress was

Figure 9. Pareto Front from GA results for Pipe Piles

BF: y = 0.75x + 96

R² = 0.73

PO: y = 0.80x + 85

R² = 0.69

0

200

400

600

800

1000

0 200 400 600 800 1000

Predicted Total Side Resistance (kN)

Measured Total Side Resistance (kN)

Best Fit Function

Pareto Evaluated Function

BF: y = 0.85x + 62

R² = 0.82

PO: y = 0.72x + 231

R² = 0.76

0

500

1000

1500

2000

0 500 1000 1500 2000

Predicted Total Side Resistance (kN)

Measured Total Side Resistance (kN)

Best Fit Function

Pareto Evaluated Function

Pareto Front

1:1

-25%

+25%

1:1

-25%

+25%

Figure 10. Pareto Front from GA results for H Piles

not included in any of the functions from the GA.

3.6 Performance of Existing Design Methods

The side resistances of the piles were calculated with

design methods that were intended for both cohesive and

noncohesive soils: Shioi and Fukui (1982), Decourt (1982),

and Brown (2001). N-values were corrected and limited as

mentioned by the references, and H piles were assumed to

be fully plugged as suggested by Brown (2001). The results

of the predictions are provided in Figures 11 to 13.

The three existing design methods mainly

overestimated the side resistance and gave erratic results.

Especially for the pipe piles, a logical linear relationship

with a decent fitness could not be established between the

measured and predicted values. The approach by Brown

(2001) had the worst performance with an average

of 2.51 and 2.97 for pipe and H piles, respectively.

The method by Decourt (1982) overestimated the side

resistance by 2.40 times on average for both pile types,

Figure 11. Comparison of Measured and Predicted Side

Resistances by Shioi and Fukui (1982)

Figure 12. Comparison of Measured and Predicted Side

Resistances by Decourt (1982)

Figure 13. Comparison of Measured and Predicted Side

Resistances by Brown (2001)

and it gave the best results among the existing methods.

The greatest over predictions occurred with piles in clays

or very stiff soils.

4 CONCLUSIONS AND DISCUSSIONS

This preliminary investigation demonstrated the capability

of a simple GA to predict the side resistance of 23 piles with

SPT N-values. Although a small sample size was analyzed,

the GA was given more detail on the soil measurements by

dividing the piles into segments. This GA was then tailored

to consider heterogenous soil conditions, and the

correlated functions were refined with Pareto optimization.

For both pipe and H piles, a function was initially

selected from two different criteria: the best fitness and

Pareto optimization. Equations 6 and 7 were determined

HP: y = 1.14x + 538

R² = 0.48

0

1000

2000

3000

4000

0 1000 2000 3000 4000

Predicted Total Side Resistance (kN)

Total Measured Side Resistance (kN)

Pipe Pile

H Pile

HP: y = 1.23x + 604

R² = 0.44

0

1000

2000

3000

4000

0 1000 2000 3000 4000

Predicted Total Side Resistance (kN)

Total Measured Side Resistance (kN)

Pipe Pile

H Pile

PP: Trend?

HP: y = 1.50x + 759

R² = 0.44

0

1000

2000

3000

4000

0 1000 2000 3000 4000

Predicted Total Side Resistance (kN)

Total Measured Side Resistance (kN)

Pipe Pile

H Pile

Pareto Front

1:1

-25%

+25%

PP: Trend?

1:1

-25%

+25%

PP: Trend?

1:1

-25%

+25%

from the Pareto evaluation, and they are recommended

over the functions from the best fitness. Thus, the following

equation is proposed for pipe piles (R2 = 0.69):

[8]

The function below is suggested for unplugged H piles (R2

= 0.76):

[9]

For these two functions, it is suggested, like Meyerhof

(1976), to limit the unit side resistance to 100 kPa. From

the studied piles, the measured unit side resistance did not

surpass this value.

Both Equations 8 and 9 were directly proportionate to

the SPT N-values and indicate a higher unit side resistance

with stiffer soils. They also apply the inverse of the

slenderness ratio. This variable was commonly applied by

the GA, and it can indicate in the equations that the soil

disturbance is lower towards the pile base. The side

resistance could also be higher towards the pile base

during pull-out because every pile had an over-sized base

plate or reinforcement base plate. Since the sites

dominated in the noncohesive soils, the common use of the

slenderness ratio could also indicate the influence of the

effective stress, but it is difficult to evaluate without results

from fully instrumented piles.

The results from the GA were more accurate compared

to the existing design methods. Yet, the existing design

methods solely relied on the SPT N-values and were

intended for weaker soils. Cohesive soils were the main

cause of overestimation, but Equation 6 from the GA

assumes cohesive soils have a lower side resistance than

noncohesive soils. Shioi and Fukui (1982) received the

opposite result. This investigation did not have many piles

in stiff undrained clays; thus, Equations 6 and 7 may be

more appropriate for noncohesive soils and drained clays.

Although the findings heavily rely on the extent of the

site investigations and pile load tests, the performance of

the existing methods demonstrates a need in Ontario for

locally-developed design methods for the pile capacity. The

GA gained practical functions with multiple variables and

soil measurements along the piles. It can likely provide

more accurate results with advanced soil testing, such as

the cone penetration test, or data from fully instrumented

piles load tests. The GA was also efficient at considering

nonlinear relationships, which would be difficult to achieve

with traditional statistics. In all, machine learning

techniques can help address uncertainty in geotechnical

engineering and offer better design methods for future

infrastructure projects in Ontario.

ACKNOWLEDGEMENTS

The presented research was made possible with funding

and a master’s scholarship from the National Sciences and

Engineering Research Council of Canada and support and

resources provided by the Ministry of Transportation of

Ontario. The authors would like to thank Mr. David Staseff

from MTO for sharing the database of pile load tests. The

authors also appreciate the help from Mr. Andy Lai, Mr.

Filipe Batista, Ms. Chantel Yung, Ms. Maeeda Khan, and

Ms. Maribel Castro with the collection of data.

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