8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
1/13
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
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
2/13
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
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
3/13
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
Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari 153
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
4/13
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
154 Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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 0.9Ƈ 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
Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari 155
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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
156 Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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
Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari 157
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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
158 Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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
Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari 159
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
10/13
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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)
Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari 161
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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
162 Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari
wnloaded by [ Universidade de Brasilia] on [10/12/15]. Copyright © ICE Publishing, all rights reserved.
8/18/2019 Finite Element Modelling of Laterally Loaded Piles in Clay
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.
REFERENCES
1. DOUGLAS D. J. and D AVIS T. G. The movement of buried
footing due to moment and horizontal load and the
movement of anchor plates. Ge ´ otechnique , 1964, 14, No. 2,
115–132.
2. SPILLER W. R. and STOLL R. D. Lateral response of piles.
Journal of the Soil Mechanics and Foundations Division,
ASCE , 1964, 90, No. 6, 1–9.
3. M AURICE J. and M ADIGNIER F. Pieu vertical sollicité
horizontalement. Annales des Ponts et Chausse ´ es, 1968,
No. 6, 337–383.
4. M ATHEWSON C. D. The Elastic Behavior of Laterally Loaded
Piles. PhD thesis, University of Canterbury, Christchurch,
New Zealand, 1969.
5. POULOS H. G. Behaviour of laterally loaded piles: II—Pile
groups. Journal of the Soil Mechanics and Foundations
Division, ASCE , 1971, 97, No. 5, 733–751.
6. BROWN D. A. and K UMAR M. p – y curves for laterally loaded
piles derived from three-dimensional finite element model.
Proceedings of the 3rd International Symposium on
Numerical Methods in Geomechanics, Niagara Falls, 1989,
683–690.
7. BROWN D. A. and SHIE C. F. Three-dimensional finite
element model of laterally loaded piles. Computers and
Geotechnics, 1990, 10 , No. 3, 59–79.8. A RISTONOUS M., TROCHANIS J. B. and P AUL C. H. Three-
dimensional non-linear study of piles. Journal of
Geotechnical Engineering, 1991, 117, No. 3, 429–447.
9. W U D., BROMS B. B. and CHOA V. Design of laterally loaded
piles in cohesive soils using p – y curves. Soils and
Foundations, 1998, 38 , No. 2, 17–26.
10. M ARSLAND A. Large in-situ test to measure the properties of
stiff fissured clay. Proceedings of the 1st Australia–New
Zealand Conference on Geotechnics, Melbourne , 1971, 1,
180–189.
11. DUNCAN J. M. and SEED H. B. Anisotropy and stress
reorientation in clay. Journal of the Soil Mechanics and
Foundations Division, ASCE , 1966, 92, No. 5, 21–52.
12. MORGENSTERN N. R. and TCHALENKO J. S. The optical
determination of preferred orientation in clays and its
application to the study of microstructure in consolidated
kaolin (I and II). Proceedings of the Royal Society of London,
Series A, 1967, 300, No. 1461, 218–234, 235– 250.
13. BISHOP A. W. The strength of soils as engineering materials.
Ge ´ otechnique , 1966, 16, No. 2, 89–130.
14. L ADD C. C. Stability evaluation during staged construction.
Journal of Geotechnical Engineering, 1991, 117, No. 4,
540–615.
15. BERRE T. and BJERRUM L. Shear strength of normally
consolidated clays. Proceedings of the 8th International
Conference on Soil Mechanics and Foundation Engineering,
Moscow, 1973, 1, 39–49.
16. DUNCAN J. M. and CHANG C. Y. Nonlinear analysis of stress
and strain in soils. Journal of the Soil Mechanics and
Foundations Division, ASCE , 1970, 96, No. 5, 1629–1653.17. TOMLINSON M. J. Some effects of pile driving on skin
friction. Proceedings of the ICE Conference on Behaviour of
Piles, London, 1971, pp. 107–114.
18. BROMS B. B. Lateral resistance of piles in cohesive soil.
Journal of the Soil Mechanics and Foundations Division,
ASCE , 1964, 90 , No. 2, 27–63.
19. Y ANG Z. and JEREMIC B. Numerical analysis of pile
behaviour under lateral loads in layered elastic plastic
soils. International Journal for Numerical and Analytical
Methods in Geomechanics, 2002, 26, No. 14, 1385–1406.
20. M ATLOCK H. Correlations for design of laterally loaded piles
in soft clay. Proceedings of the 2nd Annual Offshore
Technology Conference, Houston, Texas, 1970, 1 , 577–594.
21. REESE L. C. and IMPE V. Piles under Lateral Loading.
Balkema, Rotterdam, 2001.
22. REESE L. C. and W ELCH R. C. Lateral loading of deep
foundations in stiff clay. Journal of the Geotechnical
Engineering Division, ASCE , 1975, 101, No. 7, 633–649.
23. A AS G. Vane tests for investigation of anisotropy
of undrained shear strength of clays. Proceedings of
the Geotechnical Conference , Oslo, 1967, Vol. 1,
pp. 3–8.
24. BJERRUM L. Embankments on soft ground: state of the art
report. Proceedings of the ASCE Specialty Conference on
Performance of Earth and Earth-supported Structures,Lafayette, IN, 1972, Vol. 2, pp. 1–54.
25. A HMADI M. M. and A HMARI S. Numerical investigation of
soil anisotropy effect on laterally loaded piles in clay .
Proceedings of the 60th Canadian Geotechnical Conference,
Ottawa, 2007, pp. 1250–1257.
26. SKEMPTON A. W. The bearing capacity of clays. Proceedings
of the Building Research Congress, London, 1951, Vol. 1,
pp. 180–189.
What do you think?To comment on this paper, please email up to 500 words to the editor at [email protected]
Proceedings journals rely entirely on contributions sent in by civil engineers and related professionals, academics and students. Papersshould be 2000–5000 words long, with adequate illustrations and references. Please visit www.thomastelford.com/journals for authorguidelines and further details.
Geotechnical Engineering 162 Issue GE3 Finite-element modelling of laterally loaded piles in clay Ahmadi • Ahmari 163
Top Related