finite element modelling of laterally loaded piles in clay

8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay

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Proceedings of the Institution of

Civil EngineersGeotechnical Engineering 162 June 2009 Issue GE3

Pages 151–163doi: 10.1680/geng.2009.162.3.151

Paper 800013Received 15/02/2008

Accepted 23/12/2008

Keywords: foundations/mathematical modelling/piles &

piling

M. M. AhmadiAssistant Professor,

Department of Civil

Engineering, Sharif University

of Technology, Tehran, Iran

S. AhmariPhD student, the University

of Arizona, US

Finite-element modelling of laterally loaded piles in clay

M. M. Ahmadi PhD and S. Ahmari

A three-dimensional finite-element procedure is used to

analyse laterally loaded piles in clay. A strain-hardening

von Mises constitutive law is used in the analyses. Two

field-measured full-scale case studies, one in soft clay and

the other one in stiff clay, are investigated by the

constructed finite-element model. In order to study soilanisotropy and soil mass secondary structure, the real

shear strength and elastic modulus are back-calculated

by fitting the pile head load–deflection curve to the field

results. Comparing back-calculated shear strength values

with the measured ones indicates high anisotropy effect

in stiff clay. In order to verify the model validity, the

maximum occurred moment and moment distribution

are compared with the field results. The comparison

shows satisfactory correspondence. Finally, the p – y

curves are extracted from the finite-element model and

compared with the two p – y sets proposed by Matlock

and Wu et al. The comparison shows good agreement

with hyperbolic curves for the initial portion and with

those proposed by Matlock for the ultimate portion.

NOTATION

a ratio of the soil domain dimension to the pile diameter

B pile diameter

C a pile–soil adhesion

C u soil undrained shear strength

C uh horizontal soil shear strength

C uv vertical soil shear strength

D vane diameter

E i soil elastic modulus

EI pile rigidity E py max initial slope of p –y curve

H vane height

K 0 coefficient of soil pressure at rest

M moment along pile length

M max maximum moment along pile length

N number of elements in loading direction in front of pile

P t applied lateral load at pile head

p isotropic stress

p – y soil resistance and pile deflection at a depth

q deviator stress

Rf soil failure ratio

T total torque applied to vaneY t pile-head deflection

ratio of soil displacements at 100% and 50% of

ultimate resistance

soil strain

50 soil strain at half of ultimate stress

factor relating soil elastic modulus to initial slope of

p – y curve

1, 3 first and third principal stresses

1. INTRODUCTION

There are two general approaches to analyse laterally loaded

piles: simplified methods and continuum-based methods.

Simplified methods principally use the theory of a beam on an

elastic foundation. The so-called ‘p – y curve method’ is one

such conventional and semi-empirical method. The assumption

of soil non-linear behaviour may be an advantage for the p – y

curve method, but the simulation of three-dimensional (3D)

pile–soil interaction by a one-dimensional spring element is a

disadvantage of this method.

There are two main continuum-based approaches for analysinglaterally loaded piles. The first approach1–5 suggests that the

soil around the pile be treated as an elastic continuum. These

solutions are based on Mindlin’s solution for a point load in an

elastic half-space using superposition. In this approach the

appropriate elastic properties may be obtained by back-

analysing experimental results, and hence most continuum-

based methods need experimental information for calibration

of the required parameters. The major deficiency of these

elastic solutions is that they assume a constant elastic modulus

throughout the model, whereas in practice the soil close to the

pile shows a lower stiffness than the soil located further away.

This is because the soil close to the pile undergoes higher

strains, and so its stiffness decreases.

The second continuum-based approach applies non-linear

numerical methods to model the soil–pile interaction. Because

of the computational difficulties of 3D modelling, two-

dimensional models have been used in many studies. Some

researchers6–8 have demonstrated a 3D finite-element analysis

of laterally loaded piles in clay by using standard von Mises

constitutive law. Although they showed good trends in the

results of numerical analyses, they did not provide sufficient

field data for verification purposes. Comparison of soil ultimate

pressures predicted from finite-element analyses6 with

experimental observations shows that the finite-elementanalyses provide a stiffer response of the pile. It is argue d6 that

the lack of agreement between the predicted values of soil

ultimate pressure and field measurements is probably due to the

Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari 151

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limitations in the total stress approach and the constitutive

model used in the finite-element model. It is also argued that the

elastic-perfectly plastic von Mises constitutive law cannot

capture the stress path correctly.

Brown and Shie7 obtained finite-element analysis results that

were not in good agreement with the p – y curve results.

Compared with the results obtained from p – y curves, their

finite-element analyses predicted more resistance of the soil

near the ground surface. They attributed the discrepancy to the

following factors.

(a) The shear strength values measured by unconfined and

unconsolidated-undrained (UU) triaxial tests provide a

simple representation of the shear stress in the soil at

failure. The loading path near the ground level resembles a

triaxial extension test, and not a compression test.

(b) The simple von Mises constitutive model probably does not

represent the undrained loading in saturated clay in a

fundamental way; in reality the mobilised shear strength is

influenced by the loading path.

The total stress approach implies that the undrained shear

strength C u is independent of the stress path taken to induce

shear failure. This means that two stress paths, one for the

triaxial extension test and the other for the triaxial

compression test, will lead to the same shear strength values if

the von Mises model is used as the yield criterion. Near the

ground surface, the soil experiences a stress path similar to that

in the triaxial extension test. In this test the vertical stress is

kept constant while the horizontal stress gradually increases. In

contrast, in the triaxial compression test, the vertical stress

increases while the horizontal stress remains constant. In other

words, in the triaxial extension test the confining stress isincreased, whereas it is kept constant in the compression test.

Obviously, the difference of soil behaviour in these two tests is

due to the difference in the direction of application of stresses,

which induce different stress paths. The difference in soil

behaviour arising from applying stresses in different directions

and along accordingly different stress paths is attributed to its

anisotropy effect. The anisotropy effect in this study means

differing soil reactions depending on the direction of

application of stresses.

In addition to the anisotropy effect, the soil shear strength

values are influenced by the testing method. The measured

shear strength values do not reflect features of the soil massstructure, such as fissures and cracks. To compensate for this in

overconsolidated clays, Wu et al.9 proposed a reduction in the

shear strength depending on the soil overconsolidation ratio

and testing method.

The main objective of this study is to investigate the effect of

shear strength anisotropy on laterally loaded pile response in

clay by constructing a 3D finite-element soil–pile model. This

is done by back-calculating the shear strength and elastic

modulus and comparing this shear strength with the measured

value. No comparison is made for elastic modulus, since no

field measurement was made. The soil behaviour is assumed tobe governed by the strain-hardening von Mises model. The

study could be conducted by using an anisotropic constitutive

law, but because of the complication existing in the

constitutive laws (i.e. difficulties in determining the related

parameters) and the limitations imposed by the available

program, an isotropic von Mises constitutive law is selected to

represent the soil behaviour. Although such a model does not

consider the anisotropy effect directly, it is taken into account

indirectly by using back-calculated shear strength values.

In this paper, two case studies are considered in back-

calculating shear strength values. The associated pile-head

load–deflection curves are used in the back-calculation

procedure. The value of back-calculated shear strength is then

input to the model to predict the pile-head load–maximum

moment and moment distribution curves. Comparison is then

made between the predicted and measured curves. Finally, p – y

curves predicted numerically are also compared with

traditional ones. The computer program Ansys is used for all

the analyses performed in this study.

2. PHYSICS OF LATERALLY LOADED PILE AND SOIL

ANISOTROPY EFFECT

When a pile is loaded laterally, two principal phenomena occur

between the pile and the soil: a gap is opened behind the pile,and slip occurs between the pile and the soil in front and to the

side. The stress paths for the soil in front of the pile and behind

it are different. Similarly, they are different near the surface of

the ground and at depth. A soil element behind the pile

undergoes a stress path similar to that experienced in a triaxial

compression test. For this case, the stress state may be

simulated by a triaxial compression test in which the confined

stress decreases while the vertical stress is constant. Since a

small volume of the soil behind the pile experiences lateral

stress release, and does not contribute significantly to the

equilibrium, its effect is neglected in this study. The pile

response under lateral load is influenced by the soil at shallowdepths in front of the pile. The soil at this location behaves in

extension mode, and therefore the focus of this study is this

extension effect in changing the soil strength.

Figure 1 shows three different stress paths: for the soil behind

the pile, for the soil in front of the pile, and for a triaxial

compression test with constant confining pressure. This figure

shows that the von Mises line gives the same strength for all

stress paths, whereas a suitable constitutive law gives different

strength values for different stress paths in its formulation.

However, the von Mises model may be applicable in this case

provided different shear strength values are used, depending on

the stress path that the soil undergoes. Since the properties of the soil in front of a pile play a much larger role on dictating

the lateral behaviour of the pile, only the strength anisotropy

in this zone is considered in the finite-element modelling. Path

3 in Figure 1 schematically shows the stress path in this zone.

The corresponding strength value for this stress path is

obtained by a back-calculation procedure.

In addition to the soil anisotropy effect, the soil structure may

be another effective factor in the laterally loaded pile response.

Wu et al.9 proposed using a reduced shear strength in

overconsolidated clays, because the secondary structure

(including cracks, fissures etc.) significantly affects the pileresponse. Marsland10 proposed a reduction in shear strength to

account for the test scale effect. For instance, a 30% reduction

in shear strength value was proposed for triaxial UU tests in

152 Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari



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overconsolidated clays. To account for both anisotropy and

testing method, a reduction in shear strength of more than 30%

may be needed.

2.1. A brief literature survey on soil anisotropy

Duncan and Seed11 and Morgenstern and Tchalenk o12 showed,

by conducting tests on kaolin, that the drained strength is

independent of the shear stress orientation relative to the fabric

orientation. For the undrained case, different shear strengths

were reported.11,13 It is suggested that the differences in the

undrained shear strength values measured in different

directions are due to the generation of pore pressures

developed during shear .11,13

Duncan and Seed11 showed that the strength in the vertical

and horizontal directions might differ by as much as 40% as a

result of fabric anisotropy. Ladd14 suggested that the ratio of

shear strength measured by triaxial extension test to that

measured by triaxial compression test varies from 50% for

low-plasticity, normally consolidated clay to about 90% for

highly plastic, normally consolidated clay. For slightly

overconsolidated clay, Berre and Bjerrum 15 suggested the ratioof 20% for low-plasticity to about 80% for highly plastic clay.

From a survey of the literature, it may be concluded that soil

plasticity and over consolidation ratio (OCR) are generally the

two most influential factors governing the anisotropy effect on

soil strength. Lower plasticity and higher OCR (in the case of

structured clay) result in a more intense anisotropy effect.

3. CONSTITUTIVE MODEL

The analyses performed in this study are meant to model

laterally loaded piles in clay. The finite-element procedure

consists of modelling pile, soil, and pile–soil interaction(Figure 2); each is represented in the model by a different

constitutive law. An interface element is introduced to simulate

pile–soil interaction.

3.1. Soil domain

The von Mises constitutive law is usually used for undrained

loading condition in clay. Loading is assumed to be rapid, and

hence the undrained condition is applicable to this case.

The multilinear von Mises constitutive law, which uses the von

Mises criterion coupled with an isotropic strain-hardening

assumption, has been used for all analyses. The material

behaviour is described by a multilinear stress–strain curve

determined by the hyperbolic relationship16

1 3 ¼

1=E ið Þ þ 1=2C u Rf ð Þ1

where E i, C u and Rf are the soil elastic modulus, shear strength

and failure ratio respectively. The necessary input parameters

for the model include soil elasticity parameters (elastic modulus

and Poisson’s ratio) and the stress–strain curve. In addition to

the soil elastic modulus, the soil failure ratio and shear strength

are required to obtain the stress– strain relationship.

Wu et al.9 have reported a relationship between the and Rf .

They have reported lower and upper limits for . They suggest

a lower limit of 8 in soft clay and an upper limit of 11 in stiff

clay. Given this, the value for Rf is obtained as 0.857 for soft

clay and 0.9 for stiff clay.

The lateral elastic modulus is determined by a trial-and-error

procedure with the assumption of soil elastic behaviour. The

trial analyses are performed until the resulting numerical pile-

head load–deflection curve converges with the initial portion

of the field-measured curve. For the first trial, the elastic

modulus is calculated from Equation 2, which is the Duncan

and Chang16 hyperbolic relationship (Equation 1). Equation 2 is

derived by substituting 50 (the strain at half of the ultimate

stress) for strain, and C u for stress.

1

E i¼

50

C u1

1

2Rf

2

12

3

q

p

A suitable failure line

von Mises failure line

Figure 1. Stress paths for: 1, a soil element behind the pile;2, compression triaxial test with constant confined pressure;3, a soil element in front of the pile. Note: p and q denoteisotropic stress and deviator stress respectively

Soil

domain

Pile–soil

interface

Pile

Soil

domain

Figure 2. Components of the analytical model




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In this equation, the soil strain at half of the ultimate stress is

assumed to be 0.015 for soft clay and 0.005 for stiff clay.

Poisson’s ratio is assumed to be 0.3 for stiff clay and 0.495 for

saturated soft clay. The value of 0.495 is used instead of 0.5 to

avoid numerical divergence.

Owing to the limitations of the program used, and complexities

in those constitutive laws that consider the soil anisotropy

effect, this phenomenon is not directly applied to the analysis,

but indirectly to the isotropic von Mises constitutive law by

changing the measured shear strength and elastic modulus. The

changed value of shear strength obtained from the back-

calculation procedure will account for both the soil anisotropy

effect and its secondary structure.

Both the elastic and strength parameters used in the analyses

are assumed to be anisotropic, although they have been used in

the isotropic von Mises law. In fact, these parameters are

obtained by a back-calculation procedure through a series of

trial analyses. The comparison between the back-calculated

values and the initial values for the two case studies is made toshow the anisotropic nature of both the elastic and strength

parameters, and their different values in the vertical and

horizontal directions. However, this study focuses on the

strength anisotropy effect, because no measurements have been

reported for the elastic modulus.

The back-calculation procedure includes successive trial

analyses. First, the elastic modulus is obtained by fitting the

resulted pile-head deflection curve and the initial portion of

the field-measured curve. In these trial analyses, a linear elastic

model is employed for soil behaviour. Then another finite-

element model, in which the back-calculated elastic modulus is

the input parameter, is used in trial analyses to obtain the

shear strength. In this model, a strain-hardening von Mises law

is employed for the soil behaviour. In the first trial, the

measured strength value is used; then, after several trials, the

strength value is decreased until the predicted curve converges

with the field-measured curve.

3.2. Pile– soil interaction

Pile–soil contact is modelled for sliding beside and in front of

the pile and gapping behind. Pile–soil contact behaviour

depends on the drainage conditions. Since loading is rapid, and

undrained behaviour is assumed for the soil mass, it would be

reasonable to assume undrained behaviour for the pile–soilinterface. The interface behaviour is modelled by a Mohr–

Coulomb elastic-perfectly plastic model with zero friction angle.

The input parameters are the elastic modulus, Poisson’s ratio,

and pile–soil adhesion. Pile–soil adhesion is obtained by the

Æ-method. This method is a well-known method in evaluating

the axial bearing capacity of pile in clay, and is described by

Tomlinson.17 The contact elastic modulus and Poisson’s ratio

are assumed to be the same as that of the soil.

3.3. Pile domain

Two kinds of pile are modelled in this study, namely steel andconcrete, and for both materials elastic behaviour is assumed.

Two parameters—the elastic modulus and the Poisson’s ratio—

need to be specified for both materials. Elastic moduli of 2.4 3

108 kPa and 2 3 107 kPa are used for steel and concrete

respectively. The elastic modulus of steel will increase in the

case of pipe piles, since they are modelled as solid piles. An

average value of 0.25 is assumed for Poisson’s ratio for both

materials. The Poisson’s ratio for concrete and steel materials

can be accurately specified, based on recommended values in

various codes. However, an error of the order of 0.1 would not

affect the analysis results.

4. NUMERICAL ANALYSIS

The finite-element mesh used in the analyses is shown in

Figure 3. The mesh is cylindrical in shape. The pile is modelled

as a solid cylinder inside the mesh. In the case of the pipe pile,

the pile is modelled as a solid cylinder. Therefore the elastic

modulus of the pile is increased proportionally in such a way

that the pile bending stiffness (EI ) remains constant. Owing to

the symmetrical nature of the loading direction, only half of

the model is used in the analysis. The curved boundary is

restrained in both the tangential and radial directions. The

surface of symmetry is restrained in the normal direction, and

for the bottom horizontal surface the nodes are restrained inthe vertical direction. The constructed model properties are

summarised in Table 1 (case 1).

The loading condition is simulated in two load steps. Initial

stresses are induced in the first step by applying the

gravitational body force. In the second step, a lateral load of

120 kN is applied at the pile head. The pile-head load is applied

in 20 increments, meaning that the load is applied in 20 steps

to the pile head. Using the Broms method,18 the ultimate load

is calculated to be 195 kN. Thus the pile is loaded up to 61% of

its lateral capacity.

The at-rest condition is simulated by allowing the soil mass to

first settle under its own weight: thus the horizontal stresses

x

y

Figure 3. The mesh used in the analysis




5/13

are generated automatically. Values of K 0 (the coefficient of

soil pressure at rest) of around 1 and 0.7 are achieved for soft

clay (case 1 in Table 1) with an associated Poisson’s ratio of

0.495 and stiff clay (case 2 in Table 1) with a Poisson’s ratio of

0.3 respectively. As discussed later, study of case 2 shows that

the analysed model without any initial stresses will result in an

increase in deflection of as much as 36%, and an increase in

maximum bending moment of 6%, compared with the model

with initial stresses. This means that failure to model the initial

stresses exactly may not cause much loss of accuracy in the

results, particularly for the bending moment.

The model features 20-node cubic elements (known as solid95)

and eight-node contact elements for pile–soil interaction. It

can tolerate irregular shapes without much loss of accuracy.

solid95 elements implemented in Ansys have compatibledisplacement shapes, and are well suited to modelling curved

boundaries, so it is suitable for modelling pile–soil interaction.

Large-strain analysis is used, owing to the large displacements

experienced by the soil in front of the pile.

Ansys 6.1 has the option of smart mesh generation, which

automatically produces 3D elements based on the given degree

of fineness. This ranges from 1 to 10, indicating the greatest

degree and smallest degree of fineness respectively. A degree of

3 has been chosen in the analysis. As shown in Figure 3, the

meshing is congested in the vicinity of the pile body.

5. ANALYSIS DISCUSSION

Figure 4 shows the predicted pile-head load–deflection

curve obtained from the analysis. As can be seen, the non-

linear pile–soil system

response is captured well in

this finite-element analysis.

The figure shows that the

pile head displaces 76 mm

at a lateral load of 120 kN,

equal to 61% of its ultimate

load.

Figure 5 shows the

displacements at a load of

97 kN along the x and y

axes shown in Figure 3.

The horizontal axis of the

coordinate system in Figure

5 signifies depth for the

solid curve and distance

from the pile axis for the

dotted curve. This figure

shows that the displacements

decrease more rapidly in the

horizontal direction than inthe vertical direction. In

other words, the deformed

soil mass extends in depth

rather than horizontally. This

complies with the Yang and

Jeremic19 study on clay,

which showed that the

plastic zone propagates

fairly deeply but does not

extend far from the pile in clay.

The pile bending moment diagram for a lateral load of 97 kN

applied at the pile head is shown in Figure 6. The bending

moment at each depth is calculated by extracting the normal

strain along the pile length at each depth using the basic

mechanics of materials formulae, assuming elastic behaviour

for the pile. The moment distribution in Figure 6 suggests that

the moment has a sharp variation around the point of

maximum moment, at a depth of 2.5 m.

6. COMPARISON WITH CASE STUDIES

The results of the numerical analysis carried out in this study

are compared with two case studies, one for a pile in soft clay

Case no. 1 2

Pile properties Pile type Driven steel pipe Cast-in-place pile

Diameter: m 0.319 0.762Wall thickness: mm 12.7EI: kN-m2 31280 400,000Embedment depth: m 12.8 12.8Elastic modulus. 2e8 2.4e7

Poison ratio 0.25 0.25e*: m 0.0635 0.076

Soil properties Soil type Highly plastic clay Over-consolidated claywith secondary

structure

Cu: kPa 32 105Total unit weight: KN/m3 20 19.350 0.012 0.005Ei(i)†: kPa 6400 47250Ei(f)†: kPa 2000 395000 0.495 0.3K0 0.98 0.55-1

Rf 0.857 0.9Æ‡ 1 0.5

* e: denotes pile head distance to the ground level.† E i(i) , Ei(f): denote calculated elastic modulus from Equation 1 and back calculated elastic modulusfrom analysis, respectively.‡ Æ denotes pile-soil adhesion ratio.

Table 1. Summary of pile and soil properties for two case studies.

80604020

0

20

40

60

80

100

120

140

0

Y t: mm

P t :kN

Figure 4. Numerical prediction of pile-head load–deflectioncurve




6/13

and the other for a pile in stiff clay. The soil elastic modulus

and the soil shear strength parameters were back-calculated by

various trial analyses. Two separate models were constructed

for each case study in order to back-calculate the soil elastic

modulus and shear strength separately. The soil elastic modulus

is back-calculated with the assumption of soil elastic

behaviour. Equation 2 was used to estimate the soil elastic

modulus in the first trial. The elastic modulus was then

repeatedly changed so that the pile-head load–deflection curvehad a good match with the initial portion of the field-measured

curve. Having done this, in another model, with the assumption

of elastic-hardening plastic behaviour of soil, the soil shear

strength was also reduced to match the final portion of the

pile-head load-deflection curves. Measured shear strength

values reported for each case study were used in the analyses

for the first trial. It can be assumed that the soil elastic

modulus governs the initial portion of the pile-head load–

deflection curve, while the shear strength governs its ultimate

portion. In fact, the effect of a change in soil elastic modulus

on the final portion is so small that it can be neglected.

Therefore, the elastic modulus and shear strength can be

independently back-calculated in separate analyses by

matching the initial and ultimate portions of the curves. The

back-calculated shear strength value was compared with the

measured value to study its anisotropy effect. Finally, the pile-

head load–maximum moment curve and moment distribution

along the pile length were cross-compared with the field results

to verify the model’s validity.

The first case study is reported by Matlock ,20 for a steel pipe

driven in soft clay. The soil is described as slightly

overconsolidated by desiccation, slightly fissured, and

classified as CH according to the Unified Soil Classification.21

The average corrected vane strength is 32 kPa. However, a UUtriaxial test resulted in a shear strength value of 40 kPa.20

The second case study is reported by Reese and Welch.22 A

cast-in-place pile in overconsolidated clay is tested. The water

table is at 5.5 m below ground level. The soil shear strength is

measured by UU compression triaxial test. Table 1 summarises

the pile and soil properties for these two case studies. In

addition, the measured soil property profiles and the assumed

design line are shown in Figures 7a to 7e.

Measured and back-calculated shear strength profiles are

shown in Figures 7(a) and 7(b) for both cases. As the figure

shows, the undrained shear strength for case 1 is fairly

constant. Thus case 1 is modelled as one single layer, with a

constant undrained shear strength value. However, case 2 is

modelled in four layers, based on the strength profile. The ratio

of soil elastic modulus to shear strength (E /C u) is assumed to

be constant through depth, since it is dependent on soil

overconsolidation ratio as well as on the soil’s index

properties.21

The comparison between numerical predictions and field-

measured values is demonstrated in Figure 8 and later in

Figure 10 f or each case study separately. Pile-head load–

deflection, pile-head load–maximum bending moment, andbending moment diagram along the pile length are cross-

compared for the two cases, and are discussed below.

6.1. Comparison for case 1

The comparisons in Figure 8 show a satisfying correspondence

between the numerical predictions and field measurements for

case 1. Figure 8(a) shows a small gap at higher loads. Figure

8(c) shows that the predicted bending moment values along the

pile length agree reasonably well with the measured field data

down to a depth of 4.5 m. Below this depth, the two diagrams

deviate slightly from each other.

The numerical analysis carried out in this study gives an elastic

modulus of 2000 kPa. This value is around one third of the

elastic modulus estimated by Equation 2. The back-calculated

0·01

0·00

0·01

0·02

0·03

0·04

0·05

0·06

0

Distance: m

On -axisy

On -axis x

Displacement:m

654321

Figure 5. Soil displacement along x -axis and y -axis (shown inFigure 3) at load of 97 kN

0

2

4

6

8

10

12

14

0

M : kN m

Depth:m

15010050

Figure 6. Pile bending moment diagram for lateral load of 97 kN applied at pile head




7/13

lateral shear strength is 32 kPa, which is the same as the

corrected vane strength. This means that the shear strength

measured by vane shear test needs no reduction to match the

analysis results with field-measured data. On the other hand,

the soil shear strength reported by UU triaxial test gives a shear

strength of 40 kPa. This means that a 20% reduction in the

shear strength measured by UU triaxial test is needed to obtain

analytical results that are consistent with the field results.

The analysis shows that corrected values of shear strengthmeasured by field vane are more reliable for this case study,

since they do not need any reduction. This may be attributed to

the failure mechanism that occurs in soil during the vane test,

and the correction factor applied to the measured strength

value. In the vane shear test, both horizontal and vertical soil

resistance are mobilised against the rotating vanes. According

to analytical investigations23 on the determination of strength

anisotropy by vane test, it can be stated that the vane shear

test gives a shear strength that results from the weighted

average of horizontal and vertical shear strength. Equation 3,

originally presented by Aas,23 shows this concept clearly. In

addition to the failure mechanism, in this case study acorrection factor resulted in a vane strength value close to the

back-calculated strength value. The correction factor, proposed

by Bjerrum,24 is the outcome of a case study on embankment

failure, and was later developed by other researchers. This

factor accounts for rating effect and failure mode.

T 2

D2 H ¼ C uv þ C uh

D

3 H 3

where T is the total torque, D and H are vane diameter and

height, and C uv and C uh are the vertical and horizontal shear

strengths.

Marsland10 has suggested that the shear strength be reduced,

depending on the overconsolidation ratio and testing method.

For triaxial test results he suggested no reduction for OCR

between 1 and 2, and a 15% reduction for OCR between 2 and

8. In addition, for the field vane test, he suggested no reduction

for OCR between 1 and 2, and a 50% reduction for OCR

between 2 and 8. Although OCR is undetermined in this case

study, it is assumed to be between 1 and 2, since the clay is

categorised as slightly overconsolidated near ground level.

Therefore, according to Marsland’s suggestion,10 no reduction

is applied to shear strength as measured by vane or triaxial

compression test to account for testing method. Based on thisassumption, the whole 20% reduction in the case of the triaxial

compression test may account for soil anisotropy. However, it

would be reasonable to conclude that some percentage of the

0

2

4

6

8

10

12

14

0

Water content: %

Depth:m

Case 1

Case 2

604020

(a)

0

2

4

6

8

10

12

14

18·5

Total unit weight: kN/m3

D

epth:m

Case 1

Case 2

Case 2 usedin analysis

20·520·019·519·0

(b)

0

2

4

6

8

10

12

14

0Strain at half of ultimate stress

De

pth:m

Averaged for case 1

Measured for case 2

0·0150·0100·005

(c)

0

2

4

6

8

10

12

14

16

0

C u: kPa

Depth:m

Measuredstrength

Back-calculatedstrength

605040302010

200150100500

2

4

6

8

10

12

14

0

C u: kPa

Depth:m

Measuredstrength

Back-calculatedstrength

(d) (e)

Figure 7. Soil properties variation with depth for cases 1 and 2: (a) water content; (b) total unit weight profile and the assumedprofile in the analysis; (c) variation of 50 (strain at half of ultimate stress) for case 2; (d) measured vane strength and back-

calculated strength profile for case 1; (e) measured UU triaxial strength and back-calculated strength profile for case 2




8/13

20% reduction arises from soil secondary structure owing to its

fissured structure. It cannot be determined how much of this

percentage accounts for the soil secondary structure or testing

method effect. This percentage of reduction complies withother researches on soil anisotropy. For example, Berre and

Bjerrum15 suggested a 20% difference between vertical and

horizontal strengths for a slightly overconsolidated plastic clay.

In addition, Ladd14 suggested a 10% reduction for highly

plastic, normally consolidated clay.

6.2. Comparison for case 2

The back-calculation procedure results in an elastic modulus of

395 MPa for the first layer. This means that the ratio of soil

elastic modulus to shear strength is 5200. This is very far from

the value estimated using Equation 2. Simulation of the initial

stresses in the finite-element model results in K 0 varying by depth: it is 0.87 at ground level, and reaches 0.55 at depth of

0.5 m. For the lower elevations, K 0 remains constant. Figure 9

shows the resulting K 0 in the initial set-up of the model. As the

figure shows, K 0 has greater values near the ground surface

level, and it decreases with depth. Although Poisson’s ratio is

kept constant throughout the depth, it seems that the generated

K 0 value in the model set-up is dependent on other soil

properties, such as stiffness. The K 0 trend in Figure 9 seems

consistent with reality, as it has the largest value at ground

level and decreases with depth.

Figure 10 shows the results of the numerical analyses carried

out in this study and their comparison with the field

measurements for case 2. The pile-head load–deflection curve

is shown in Figure 10(a). Two trials, one with reduced shear

strength and one without, are shown in this figure. As can be

seen, reducing the shear strength results in better agreement.

The stiff clay in case 2 shows a much stiffer response without

strength reduction. Unlike the pile head load–deflection curve,

the other diagrams do not match sufficiently well. The

numerically derived maximum moment is more than that of

the field-measured data: at the highest load, the difference is

about 17%. Figure 10(c) shows that, at depths shallower than

the maximum moment depth, there is reasonable agreement

between the two diagrams.

In order to match the displacement curves, the soil shear

strength should be reduced by up to 80%. It has been show n24

that the reduction factor is dependent on the ratio of elastic

modulus to shear strength. Since this ratio is relatively

constant throughout the depth for a clayey soil, a constant

100 15050

0

20

40

60

80

100

120

140

0

Y t: mm

(a)

P t :kN

Field-measured

FEM

0

20

40

60

80

100

120

140

0

M max: kN m

(b)

P t :kN

Field-measured

FEM

0

2

4

6

8

10

12

14

0

M max: KN m

Depth:m

Field-measured

FEM

80604020

20015010050

(c)

Figure 8. Comparison between the numerical predictions inthis study and field-measured values for case 1: (a) pile-headload deflection; (b) pile-head load–maximum moment alongpile length; (c) moment diagram along pile length at load of 80.9 kN

0

0·5

1·0

1·5

2·0

2·5

3·0

3·5

4·0

4·5

0

K 0

Depth:m

1·00·80·60·40·2

Figure 9. Distribution of K 0 (coefficient of earth pressure atrest) with depth for case 2




9/13

factor is applied in this case study. The reduced shear strength

profile is shown in Figure 7(b).

For overconsolidated clay Marsland10 suggested a 30%

reduction in triaxial shear strength. Therefore a goodpercentage of the reduction (50% out of 80%) would be due to

the soil anisotropy effect. This means that a major part of the

reduction factor arises from the soil anisotropy effect.

6.3. Discussion

The difference between the numerically predicted and field-

measured bending moments, despite the good agreement for

displacements, may be attributed to inaccuracies in simulation

of the initial stresses in the model, to the constitutive law

applied for the soil behaviour, or to the assumed variation of

shear strength in the back-calculation procedure.

In order to investigate the effect of initial stresses on pile

response, the finite-element model constructed for case 2 is

reanalysed with the assumption of zero initial stresses. Figure

11 shows a comparison between the analyses assuming zero

initial stresses and non-zero initial stresses. Figure 11(a) shows

that the pile head deflects 36% more for the case with no

initial stresses, and Figure 11(b) shows that the corresponding

maximum moment is 6% more. This means that zero initial

stresses result in 36% less deflection in the pile head while the

maximum moment rises by 6%. Therefore it can be concluded

that the difference between the curves in Figure 10(b) is not

0

50

100

150

200

250

300

350

400

450500

0

Y t: mm

(a)

P t :kN

With initial stresses

Without initial stresses

0

2

4

6

8

10

12

14

50M : kN m

Depth

:m

With initialstresses

Without initialstresses

403530252015105

950750550350150

(b)

Figure 11. Comparison between numerical results withassumptions of zero and non-zero initial stresses: (a) pile-head deflections; (b) moment along pile length at load of 450 kN

0

50100

150

200

250

300

350

400

450

500

0

Y t: mm

(a)

P t :kN Field-measured

FEM with reduction

FEM without reduction

0

50

100

150

200

250

300

350

400

450

500

0

M max: kN m

(b)

P t :kN

Measured

FEM

0

2

4

6

8

10

12

14

50

M : kN m

Depth:m

Measured

FEM

3530252015105

1000800600400200

950450

(c)

Figure 10. Comparison between FEM results and field-measured results, case 2: (a) pile-head load–deflection curve;(b) pile-head load– maximum bending moment curve alongpile length; (c) bending moment distribution along pile lengthfor lateral load of 445 kN




10/13


11/13

8.2. Mesh fineness

As stated above, Ansys version 6.1 has the capability of generating meshes automatically, using a degree between 1

and 10. However, to represent an imaginary parameter

indicating mesh fineness, the element division ( N ) along the

loading direction in front of the pile is introduced. Figure 16

shows that the soil in front of the pile should be divided into at

least eight elements for an acceptable model; yet coarser

meshing may be used at low displacements.

8.3. Contact stiffness

As shown in Figure 17, the contact stiffness has no effect on

the pile response. In this figure, FKN is the ratio of contact and

0

5

10

15

20

25

30

35

40

0

y : m

(a)

p :kN/m

FEM

Matlock20

Wu .et al 9

0

510

15

20

25

30

35

40

45

p :kN/m

0

10

20

30

40

50

60

p :kN/m

0

10

20

30

40

50

60

70

80

90

0·200·150·100·05 0

y : m

(b)

FEM

Matlock20

Wu .et al 9

0·200·150·100·05

0

y : m

(c)

FEM

Matlock20

Wu .et al 9

p :kN/m

0·200·150·100·05 0

y : m

(d)

FEM

Matlock20

Wu .et al 9

0·200·150·100·05

Figure 13. Comparison of numerically predicted p – y curves in this study with curves suggested by Matlock 20 and Wu et al.9 atvarious depths (B ¼ diameter): (a) at ground level; (b) at depth of B; (c) at depth of 2B; (d) at depth of 4B

0

10

20

30

40

50

60

0

Depth/diameter

P u

l t :KN/m

FEM

Matlock20

Wu et al.9

4321

Figure 14. Numerically predicted soil ultimate resistanceagainst depth: comparison with Matlock 20 and Wu et al.9

methods

0

20

40

60

80

100

120

140

0

Y t: mm

P t :kN a 20

a 30

a 40

604020 80

Figure 15. Pile-head load–deflection curve for various meshdimensions (a ¼ ratio of mesh diameter to pile diameter)




12/13

soil stiffness. However, FKN is kept at 40 in the analyses in

order to avoid numerical error due to pile penetration into the

soil domain.

8.4. Pile– soil adhesion

Since undrained behaviour is assumed to be applicable to the

pile/soil interface, adhesion is the key factor that governs the

interface behaviour.

Figure 18 shows the pile-head load–deflection curve and its

variation with pile-soil adhesion C a for case 1. The gap

between the curves increases with the pile load, because the

friction between pile and soil is mobilised at an increased

number of points by loading the pile. An increase in adhesion

up to 30 kPa results in 12 mm less displacement of the pile

head at a load of 120 kN.

9. CONCLUSION

At 3D finite-element model is used to study laterally loaded

piles in clay. The strain-hardening von Mises model is assumed

for soil behaviour. The soil-hardening behaviour is defined by the Duncan and Chang hyperbolic stress–strain relationship.16

Since the von Mises model does not consider soil anisotropy,

modified shear strength is introduced in the analyses. The soil

elastic modulus and shear strength are back-calculated by

fitting the pile-head load–deflection curve with the field

results. The soil elastic modulus is back-calculated in a separateanalysis with the assumption of soil elastic behaviour.

Two field-measured case studies, one carried out in soft clay at

Lake Austin and reported by Matlock 20 and the other in stiff

clay and reported by Reese and Welch,22 are studied. Using the

back-calculated shear strength and elastic modulus leads to a

good correspondence between the results of finite-element

analysis and field measurements. Comparison of the back-

calculated shear strength value with that measured by UU

triaxial test for soft clay indicates that the measured shear

strength needs to be reduced by as much as 20% to account for

soil anisotropy effects and secondary structure. However, the

back-calculated shear strength is the same as the corrected

strength measured by field vane shear test. The difference

between soil vertical and horizontal (back-calculated) shear

strength is in the ranges presented in the literature.

The comparison of pile response in stiff clay with the results of

the analysis is not as satisfying as that for soft clay. However,

the back-calculated shear strength is 20% of the shear strength

measured by UU triaxial test. This suggests that the stiff clay is

more anisotropic than the soft clay, and that there are more

cracks and fissures in overconsolidated clay.

The comparison for elastic modulus does not lead us to areasonable conclusion, especially for case 2. This may be due

to inaccurate estimation of the elastic modulus values.

Nevertheless, this inaccuracy did not endanger the validity of

results, since this value was used in the first trial, but the

correct value was achieved by converging the analysis results

onto the field values.

The first case study, in soft clay, was considered for extracting

p – y curves and comparing them with the traditional curves

proposed by Matlock 20 and the hyperbolic p – y curves

suggested by Wu et al.9 The p – y curves are obtained by direct

integration of the stresses over the pile–soil interface and atfour depths: ground level, and at depths of one, two and four

times the pile diameter. The initial slope of the p – y curve

increases with depth, although the elastic modulus is constant

0

20

40

60

80

100

120

140

0

Y t: mm

P t :kN

C a 0 kPa

C a 10 kPa

C a 30 kPa

10080604020

Figure 18. Predicted pile-head load–deflection curve formodel with various values of pile–soil adhesion

0

20

40

60

80

100

120

140

0

Y t: mm

P t :kN N 4

N 5

N 8

N 9

80604020

Figure 16. Predicted pile-head load–deflection curve formodel with various values of mesh fineness (N ¼ number of soil elements in front of pile in loading direction)

0

20

40

60

80

100

120

140

0

Y t: mm

P t :kN

FKN 1

FKN 5

FKN 15

FKN 40

80604020

Figure 17. Predicted pile-head load–deflection curve formodel with various values of contact stiffness




13/13

throughout. Generally, there is satisfying correspondence

between the p – y curves predicted in this study and in other,

traditional ones. However, the correspondence between the

hyperbolic p – y curves proposed by Wu et al.9 and those

predicted in this numerical study is more satisfying. The

correspondence between the numerically derived curves and

those proposed by Matlock 20 is more significant for the final

portion. This may verify the validity of back-calculated shear

strength, since the p – y curves proposed by Matlock 20 are

based on the same case study as modelled in this paper.

A sensitivity analysis was carried out on the model dimensions,

mesh fineness, contact stiffness, and pile–soil adhesion. The

outcome of the analysis shows that the optimum soil domain

dimension is 40 times the pile diameter. Meshing as fine as

N ¼ 8 (number of soil domain divisions along loading

direction in front of the pile) is sufficient. Soil contact stiffness

has no effect on the pile response. The study of pile–soil

adhesion effect on pile-head deflection shows that the rate of

variation in pile-head deflection is much less than the rate of

variation in pile– soil adhesion.

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finite element modelling of laterally loaded piles in clay

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