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Numerical modeling of lateral response of long flexible piles in sand

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 Geotechnical Engineering Journal of the SEAGS & AGSSEA Vol. 44 No.3 September 2013 ISSN 0046-5828

Numerical Modeling of Lateral Response of Long Flexible Piles in Sand

Md. Iftekharuzzaman1 and Bipul C Hawlader2*
1
Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5, Canada
2
Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5
*E-mail: bipul@mun.ca

ABSTRACT: The behavior of a steel pipe pile in sand subjected to lateral load is examined by finite element (FE) analysis. Three-
dimensional finite element analyses are performed for pure lateral load applied at 0.3m above the ground surface. The FE analyses are
performed using the commercially available software package ABAQUS/Standard. The sand around the pile is modeled using a modified
form of Mohr-Coulomb soil constitutive model. The modification involves the variation of mobilized angle of internal friction and dilation
angle with plastic shear strain. The nonlinear variation of elastic modulus with mean effective stress is also considered in the present FE
analyses. These important features of soil constitutive model have been implemented in ABAQUS/Standard using a user subroutine.
Numerical analyses are also performed by using the LPILE software, which is based on the p-y curve. The FE and LPILE results are
compared with the results of a full-scale test. It is shown that the FE analysis with modified Mohr-Coulomb soil model can successfully
simulate better the response of a pile under lateral load. Comparing the numerical results with the full-scale test results some limitations of
the p-y curve method are highlighted.

1. INTRODUCTION (Brown and Shie 1991, Kimura et al. 1995, Wakai et al. 1999, Yang
and Jeremic 2002). Brown and Shie (1991) performed three-
The lateral resistance of pile foundations is one of the key design dimensional finite element analysis modeling the soil using von
considerations in many civil engineering structures both in onshore Mises and extended Drucker-Prager constitutive model. Trochanis et
and offshore environment. Wind, wave, earthquake and ground al. (1991) examined the effects of nonlinearity in soil stress-strain
movement might create significant lateral load on pile foundations. behaviour and separation or slippage between the soil and the pile
If the deformation and bending moment induced by lateral load are surfaces. In addition, there are some full-scale test results (e.g. Cox
confined only to the upper part the pile is considered as flexible pile. et al. 1974, Long and Reese 1985, Brown 1985, Rollins et al. 2005,
The response of a pile under lateral load is governed by complex Ruesta and Townsend 1997) and centrifuge test results (e.g. Nunez
three-dimensional soil/pile interaction behaviour. Various et el. 1987, McVay et al. 1998, Grundhoff et at. 1997, Dyson and
approaches have been proposed in the past for analysis of a laterally Randolph 2001) are available in the literatures which were used in
loaded pile. As the main focus of the present study is to investigate the previous studies for model verification.
the response of a free-headed single steel pipe pile in sand under The purpose of this paper is to present a series of three-
lateral load, a review of previous studies related to this area are dimensional finite element analysis of a long steel pipe pile in sand
presented in the following sections. subjected to lateral load. The finite element results are compared
Hansen (1961) proposed a method for estimating the ultimate with LPILE analysis, and also with the results of a full-scale test.
lateral load resistance of vertical piles based on earth pressure The limitations of the p-y curve method are discussed based on
theory. Broms (1964 a, b) also proposed methods for calculating the lateral response of the pile.
ultimate lateral resistance based on earth pressure theory simplifying
the analyses for cohesionless and cohesive soils for short rigid and
2. FINITE ELEMENT MODELLING
long flexible piles. Meyerhof et al. (1981, 1988) also proposed
methods to estimate the ultimate lateral resistance and groundline The numerical analyses presented in this paper are carried out using
displacement at the working load for rigid and flexible piles. the finite element software ABAQUS/Standard 6.10-EF-1. The
The lateral deflection of pile head is one of the main finite element results are verified using the full-scale test results
requirements in the current design practice, especially in limit state reported by Cox et al. (1974). The full-scale test site was located at
design. Mainly two approaches are currently used for modeling the the Shell Oil Company tank battery on Mustang Island, near Port
lateral load deflection behaviour of piles. In the first approach, the Aransas, Texas. The test setup is shown in Figure 1.
response of soil under lateral load is modeled using nonlinear
independent springs in the form of p-y curves, where p is the soil-
pile reaction (i.e. the force per unit length of the pile) and y is the
lateral deflection of the pile. Then using the concept of beam-on-
elastic foundation the problem is solved numerically. The p-y curve
method is very similar to the subgrade reaction method except that
in the p-y curve method the soil resistance is nonlinear while in the
subgrade reaction method it is linear with displacement. Reese et al.
(1974) proposed a method to define the p-y curves for static and
cyclic loading. A modified version of Reese et al. (1974) is
employed by the American Petroleum Institute (API 2000) in its
manual for recommended practice. Both of these models have been
implemented in the commercially available software LPILE Plus 5.0
(2005). Ashour and Norris (2000) showed that the “Strain Wedge”
model is capable of evaluating some additional effects such as
bending stiffness of the pile, pile shape, pile head fixity and depth of
embedment on the p-y curves. The second approach of modeling
laterally loaded piles is based on continuum modeling. Poulos
(1971) presented finite element analysis of a single pile situated in
an ideal elastic soil mass. Finite element analyses of single piles Figure 1 Idealized soil and pile load test setup
under lateral load have also been conducted by other researchers (redrawn from Reese et al. 2001)

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 Geotechnical Engineering Journal of the SEAGS & AGSSEA Vol. 44 No.3 September 2013 ISSN 0046-5828

An excavation of 1.68m (5.5 ft) was carried out first to remove

the soil near the ground surface and to reach the groundwater table.
There was a clay layer of 0.76m (2.5 ft) near the groundwater table.
This clay layer was also removed and filled with clean sand similar
to in-situ condition. Pile load tests were conducted for static and
cyclic loading. In this paper comparison is performed only with the
test results of single pile under static load. Lateral load tests were
conducted for a steel pipe pile of 610mm diameter and 9.53mm wall
thickness. As shown in Figure 1, the top 9.75m length of the test pile
was instrumented to obtain the response of pile under lateral load. A
total of 40 strain gages were placed in the instrumented section of
the pile. Lateral load was applied at 0.3m above the ground surface
using a hydraulic jack and the load was measured using a universal
load cell. The lateral deflection under a given lateral load was
measured at two points above the load using two deflection gauges.
The data was analyzed and response was reported for lateral load
increments of 11.1kN up to 66.6kN and then in an increment of
5.56kN to the maximum lateral load of 266.9kN.
The finite element modeling in this study is carried out in
Lagrangian framework. Considering geometry of the problem and
loading conditions, the advantage of symmetry is used and only the
half of the model under lateral load is analyzed. A soil domain of
20m diameter and 30m height as shown in Figure 2 is modeled. The
Figure 2 Finite element model
pile is located at the center of the soil domain. The size of the soil
domain is sufficiently large and therefore boundary effects are not
expected on predicted lateral load, displacement and deformation 4. MODELING OF SOIL
mechanisms. The bottom of the soil domain is restrained from any Two boreholes were drilled at the Mustang Island pile load test site.
vertical movement, while the curved vertical face is restrained from Field tests and laboratory experiments on collected soil samples
any lateral movement using roller supports. The symmetric vertical from these boreholes were conducted for geotechnical
xz plane is restrained from any movement in the y-direction. No characterization (Cox et al. 1974). It was shown that the soil at the
displacement boundary condition is applied on the top, and therefore pile load test site is mainly sand with varying fine contents and
the soil can move freely. relative density. Approximately 3m thick soft to stiff clay with shell
Both soil and pile are modeled using the solid homogeneous fragments was encountered at 12.5m depth. As this clay layer has
C3D8R elements, which are 8-noded linear brick element with very small effect on lateral response it is ignored in the idealized soil
reduced integration and hourglass control. The size of the mesh has condition used in the present study as shown in Figure 1. In the
a significant effect on finite element modeling. Often finer mesh present study this clay layer is neglected as it does not have
yields more accurate results but computational time is higher. For significant effect on lateral behaviour of the pile. The top 0–6m is a
successful FE modeling, finer mesh is used in the critical sections. medium dense sand layer followed by a dense sand layer. Based on
The top five to ten pile diameters depth is critical for modeling piles borehole logs, the soil profile is idealized as two sand layers for
under lateral load. Therefore, finer mesh is used for the upper 6.0m numerical analyses as shown in Figure 1. The geotechnical
soil and medium mesh is used for 6.0 to 21.0m depth. For the soil parameters used in numerical analyses are shown in Table 1. These
layer below the pile (>21m depth) coarse mesh is used, as it does parameters are estimated from the information provided in borehole
not have significant effect on load-displacement behaviour of the logs and soil investigation.
pile. Based on mesh sensitivity analyses with different mesh size
and distribution, the optimum mesh consists of 18,027 C3D8R Table 1 Geometry and mechanical properties used in finite element
elements, shown in Figure 2 is selected for the present FE analysis. analysis

3. MODELING OF PILE AND SOIL/PILE INTERFACE Pile:

Length of the pile (L) 21.6 m
A free-head steel pipe pile of 610mm (24″) outer diameter with Diameter of the pile (D) 610 mm (24″)
9.53mm (3/8″) wall thickness is modeled in this study. The Thickness of the pile (t) 9.53 mm (3/8″)
embedded length of the pile is 21m. Lateral displacement is applied Modulus of elasticity of pile (Ep) 208x106 kN/m2
at 0.3m above the ground surface. Summing the nodal force Poisson’s ratio (νp) 0.3
component in the x-direction at at the point of loading, the lateral
force is calculated. The pile is modeled as linear elastic material Soil (sand)
with modulus of elasticity (Ep) of 208×106 kN/m2 and Poisson’s Poisson’s ratio, νs 0.3
ratio (νp) of 0.3. As shown later, the stress in the pile remains below Submerged unit weight of soil, γ′ 10.4 kN/m3
the elastic limit even at the maximum displacement applied and Upper medium sand (0 to 6m depth)
therefore the modeling of the pile as elastic material is valid. Reference modulus of elasticity, Eref 120,000 kN/m2
The Coulomb friction model is used for the frictional interface Angle of internal friction, φ′p 35°
between the outer surfaces of the pile and sand. In this method, the Maximum dilation angle, ψm 5°
friction coefficient (µ) is defined as µ=tan(φµ ), where φµ is the Initial modulus of subgrade reaction (k) 21,000 MPa/m
pile/soil interface friction angle. The value of φµ depends on surface Lower dense sand (6 to 30m depth)
roughness of the pile and effective angle of internal friction, φ′. Reference modulus of elasticity, Eref 140,000 kN/m2
Kulhawy (1991) recommended the value of φµ for steel pipe piles in Angle of internal friction, φ′p 39°
the range of 0.5φ′ to 0.9φ′, where the lower values are for smooth Maximum dilation angle, ψm 9°
steel piles. The value of µ=0.4 is used in this study. Initial modulus of subgrade reaction (k) 36,000 MPa/m

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When a dense sand specimen is sheared in drained condition the The built-in Mohr-Coulomb model in ABAQUS/Standard is
shear stress increases with shear displacement as shown in Figure 3. incapable of simulating the varying modulus of elasticity as a
The shear stress is reached to the peak at a relatively small strain function of means effective stress and the post-peak strain softening
and then strain softening is occurred. The strain at which the peak behaviour of sand. Therefore, in this study they are incorporated in
shear stress is developed depends upon mainly density of soil and ABAQUS/Standard using a user subroutine called USDFLD written
applied normal/confining stress. At large displacement the shear in FORTRAN. The mean effective stress and plastic shear strain is
stress remains constant which is considered as the critical state. The called at each time increment and two field variable is defined using
volume of a dense sand specimen is increased with shear these values. The model parameters E, φ′ and ψ are updated based
displacement, which is normally characterized by dilation angle (ψ). on these field variables.
At the critical state, shearing is occurred at constant volume. Most The top layer of soil (0–6m) is medium dense sand which is
of the numerical analyses conducted in the past for modeling modeled using the following soil parameters: angle of internal
laterally loaded piles used a constant value of φ′ and ψ. An friction at the peak, φp′=35°; maximum dilation angle, ψm = 5°;
appropriate value between the peak and ultimate condition is needed reference modulus of elasticity, E0 = 120,000 kPa; and Poisson’s
for this type of analyses. ratio, ν=0.3. The soil layer below 6m is dense sand. The soil
In the present FE analysis the strain softening behavior is properties used for this layer are: φp′=39°, ψm = 9°, E0 = 140,000
modeled by varying the mobilized friction angle (φ′) and dilation kPa, and ν=0.3. The location of the groundwater table is at the
angle (ψ) with plastic shear strain. The variation of φ′ and ψ for ground surface. Submerged unit weight of 10.4 kN/m3 is used for
medium and dense sand used in the analysis are shown in Fig. 3. both soil layers.
The critical state friction angle (φ′c) of 31° is used. Based on a large
number of experimental data, Bolton (1986) showed that the angle 5. LPILE ANALYSIS
of internal friction is related to the angle of dilation as φ′= φ′c +
0.8ψ, which is used to calculate the mobilized dilation angle shown Analysis of pile under lateral static load is also conducted using
in Figure 3. LPILE Plus 5.0 (2005) software. LPILE is a finite difference
software where the pile is modeled as a beam with lateral stiffness
based on elastic modulus and moment of inertia of the pile. The
nonlinear p-y curves are defined using the method proposed by
Reese et al. (1974). In this method the ultimate soil resistance per
unit length of the pile is calculated using the angle of internal
friction of the soil. The initial straight-line portion of the p-y curve is
defined using the initial modulus of subgrade reaction (k). The
variation of k with φ′ and relative density is shown in Figure 4 as
recommended by the American Petroleum Institute (API, 2000). The
selection of an appropriate value of φ′ is very important in LPILE
analysis as the effect of dilation angle and post-peak softening of
dense sand cannot not be directly used in this software. The angle of
internal friction φ′ in the horizontal axis at the top of Figure 4 is
related to relative density as φ ′ = 16 Dr2 + 0.17 Dr + 28.4 , where φ′ is
in degree, and Dr is the relative density (API 1987). Using the value
of φ′ calculated from this equation, Rollins et al. (2005) showed that
it underestimates the friction angle and predicts significantly higher
lateral displacement and bending moment compared to pile load test
results. Therefore, in the present LPILE analyses φ′=35° for medium
and φ′=39°for dense sand is used, which is consistent with Reese et
al. (1974).

Figure 3 Mobilized angle of internal friction and dilation angle with

plastic strain

The selection of appropriate values of elastic properties is

equally important as the response of a pile depends on these
parameters. In this study isotropic elastic properties are used.
Experimental studies (e.g. Janbu, 1963; Hardin and Black, 1966)
show that the elastic moduli of granular materials increase with the
increase in mean effective stress (p′). It has been also shown by
previous researchers that the elastic modulus depends on void ratio.
Various expressions have been proposed in the past in order to
account the effects of void ratio and mean effective stress on elastic
moduli. Yimsiri (2001) compiled the available expressions in the
literature. Based on these studies, the modulus of elasticity (E) is
varied with mean effective stress (p′) as

E = E 0 ( p ' / pa )
n
(1)

Where pa is the atmospheric pressure (100 kPa) and n is a constant.

The reference modulus of elasticity (E0) represents the value of E at
p′=100 kPa. Experimental results show that the value of n is Figure 4 Lateral modulus of subgrade reaction as function of relative
approximately equal to 0.5 for sands (Yimsiri 2001). density and friction angle (API 2000)

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 Geotechnical Engineering Journal of the SEAGS & AGSSEA Vol. 44 No.3 September 2013 ISSN 0046-5828

6. NUMERICAL RESULTS LPILE compute higher bending moment than measured in the full-
scale test.
The finite element analysis consists of mainly two major steps: The depth at which the maximum bending moment is occurred
gravity step and loading step. In gravity step the soil domain is in the finite element analysis is less than that of LPILE analysis. For
reached to the in-situ stress condition. In loading step the lateral example, the maximum bending moment for 266.9kN is obtained at
displacement in the x-direction is applied on the nodes of the pile at 2.5m if FE analysis while it is at 3.0m in LPILE analysis
0.3 m above the ground surface. (Figure 6d).
It is to be noted here that the pile is in elastic condition even at
6.1 Load-deflection curves the maximum lateral load applied. For the maximum lateral load of
Figure 5 shows the variation of lateral load with lateral displacement 266.9kN the computed maximum bending moment is 550kN-m.
of the pile at the ground surface obtained from finite element This gives the maximum tensile/compressive stress of 175MPa,
analysis and LPILE analysis. The results of full-scale test (Cox et al. which is less than yield strength of steel. That means, the analyses
1974) are also shown in this figure. conducted in this study using elastic behaviour of the pile is valid
In finite element analysis the lateral displacement is applied at even for the highest lateral load.
0.3m above the ground surface. The lateral load is calculated by
adding the horizontal (x) component of nodal force at this level. The
lateral displacement at the ground level is calculated by averaging
the lateral displacement of all the nodes of the pile at ground level.
In LPILE the lateral load is applied in 11 increments. The pile is
divided into 100 small divisions. The lateral displacement at the
ground surface is obtained from the displacement of the element at
this level.
Figure 5 shows a very good agreement between the full-scale
test results and present finite element analysis. LPILE computed
displacement for a given lateral load is higher than the measured
displacement.

Figure 6(a) Variation of bending moment with depth (Load cases:

33.4kN, 55.6kN and 77.8kN; solid lines: FE analysis, dashed line:
LPILE and data points: full-scale test)

Figure 5 Comparison of load displacement between numerical

predictions and full-scale test result

6.2 Bending moment with depth

Figures 6 (a-d) shows the variation of bending moment with depth
for the upper 6m length of the pile. In these figures the depth in the
vertical axis represents the distance from the point at which the
lateral load is applied on the pile. Although the pile is 21m length
the variation of bending moment only for upper 6m is shown
because the maximum bending moment and its variation mainly
occur in this zone. Comparison between computed and measured
values for 11 lateral load cases (33.4kN, 55.6kN, 77.8kN, 101.1kN,
122.3kN, 144.6kN, 166.8kN, 189kN, 211.3kN, 244.6kN, and
266.9kN) are presented in these figures. In finite element analyses
the bending moment is obtained from the axial stresses in the pile.
In LPILE it can be easily obtained as the pile is modeled as a beam. Figure 6(b) Variation of bending moment with depth (Load cases:
The computed bending moment in the present finite element 101.1kN, 122.3kN and 144.6kN; solid lines: FE analysis, dashed
analysis compares very well with the measured data. However, line: LPILE and data points: full-scale test)

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 Geotechnical Engineering Journal of the SEAGS & AGSSEA Vol. 44 No.3 September 2013 ISSN 0046-5828

Figure 6(c) Variation of bending moment with depth (Load cases:

166.8kN, 189kN and 211.3kN; solid lines: FE analysis, dashed line: Figure 7 Comparison of maximum bending moment and lateral load
LPILE and data points: full-scale test)
6.4 Lateral displacement
Figure 8 shows the computed lateral displacement of the pile with
depth for 11 load cases for FE and LPILE analyses. As shown in this
figure that LPILE predicts higher lateral displacement than the
present FE simulation. For comparison with field data the
displacement at the ground surface obtained in the full-scale test is
also shown in this figure by solid circles, which match very well
with the present FE analysis.

Figure 6(d) Variation of bending moment with depth (Load cases:

244.6kN and 266.9kN; solid lines: FE analysis, dashed line: LPILE
and data points: full-scale test)

6.3 Maximum bending moment

Figure 7 shows the variation of the maximum bending moment with
lateral load. The maximum bending moment increases with increase
in lateral load. At low values of lateral load, both finite element and
LPILE compare well with full-scale test data. However, at larger Figure 8 Lateral displacement of pile (solid lines: FE analysis;
loads the computed maximum bending moment using LPILE is dashed line: LPILE: solid circles: measured at ground line in pile
higher than the values obtained from the present finite element load test)
analysis and full-scale test.

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6.5 Soil reaction segment, which is mainly govern by k value, (ii) parabolic segment
between the initial linear segment and lateral displacement of D/60,
Lateral soil reaction (force per metre length of the pile) is plotted in (iii) linear segment between lateral displacements of D/60 and
Figure 9. For clarity the calculated results for 5 load cases are shown 3D/80, and (iv) constant soil resistance segment after lateral
in this figure. In finite element analysis, the x-component (lateral) of displacement of 3D/80. The p-y curves obtained from the finite
nodal force is calculated first for all the nodes at a given depth. element and LPILE analyses are also compared with full-scale test
Dividing the sum of the nodal force in the x-direction by the vertical data (Cox et al. 1974). As shown in Figure 11, the p-y curves
distance between two sets of nodes in the pile, the lateral soil obtained from the finite element analysis match better with the
reaction is obtained. In LPILE analysis the soil reaction can be measured values.
easily obtained from the output file as the pile is modeled as a beam
supported by discrete springs. As shown in this figure that
calculated soil reaction from both LPILE and FE is very similar up
to 1.2m depth. However, below 1.2m the soil reaction obtained from
the FE analysis is higher than the reaction obtained from LPILE.
Moreover, after reaching to the maximum value of soil reaction, it
decreases quickly with depth in the finite element analysis. The
maximum soil pressure is developed at greater depth for larger value
of lateral load.

Figure 10 Variation of shear force in pile with depth (solid lines: FE

analysis, dashed line: LPILE)

Figure 9 Soil reaction on pile (solid lines: FE analysis and dashed

line: LPILE)

6.6 Shear force in pile

Figure 10 shows the variation of shear force in the pile with depth
for five lateral loads. In the finite element analysis the shear force is
obtained by subtracting the sum of the x-component of nodal force
above the point of interest from the lateral load applied at pile head.
As shown in Figure 9 that the calculated soil reaction in the finite
element analysis is higher near the ground surface. Therefore, the
shear force is decreased quickly in the finite element analysis near
the ground surface as shown in Figure 10. The maximum negative
shear force from LPILE analysis is higher than that obtained from
the finite element analysis. Below the depth of 9m the shear force is
negligible.
Figure 11 Comparison of p-y curves at four depths (solid lines: FE
6.7 p-y curves analysis, dashed line: LPILE, and data points: full-scale test)

In the current engineering practice the modeling of a laterally loaded 7. DISCUSSION AND CONCLUSIONS
pile is generally performed as a beam on elastic foundation, where
soil is modeled by discrete springs. The load deformation behaviour The p-y curve based software packages, such as LPILE, are widely
of the soil spring is defined using nonlinear p-y curves. The p-y used in engineering practice to calculate the load-displacement
curves for four depths are shown in Figure 11. In LIPILE the p-y behavior of laterally loaded piles. Although this method is very
curve for a given depth can be easily obtained from the output file. simple, it has a number of limitations. The soil resistance is modeled
In the finite element analysis the soil is modeled as a continuum, not as discontinuous nonlinear springs defining the properties
as discrete springs. The values of p and lateral displacement are empirically. Moreover, the pile/soil interface behavior cannot be
calculated from nodal forces and displacement, respectively. In this modeled in the p-y curve method. In the present study three-
study the model proposed by Reese et al. (1974) for static lateral dimensional finite element analyses are performed for a laterally
loading is used in LPILE analysis. The p-y curve in Reese et al. loaded flexible pile in sand. Analyses are performed using a
(1974) consists of four segments (Figure 11): (i) initial linear modified form of Mohr-Coulomb soil constitutive model, where the

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variation of mobilized angle of internal friction and dilation angle Grundhoff, T., (1997). “Horizontal impact loads on large bored
with plastic shear strain is considered. The non-linear variation of single piles in sand”, Proceedings of the International
elastic modulus with mean effective stress is also considered in the Offshore and Polar Engineering Conference, v 1, pp. 753-
present FE analyses. Numerical analyses are also performed by 760, 1997
using the commercially available LPILE software. The geotechnical Hansen, Brinch J. (1961). “The ultimate resistance of rigid piles
parameters require in the FE analysis can be easily obtained from against transversal forces”, Danish Geotechnical Institute
the conventional laboratory shear strength tests. The variation of (Geoteknisk Institut) Bull. Copenhagen, 12:5-9.
mobilized friction angle and dilation angle with plastic shear strain Hardin, B.O. and Black, W.L. (1966). “Sand stiffness under various
can be obtained from triaxial test data. On the other hand, the post- triaxial stresses”, Journal of the Soil Mechanics and
peak softening behavior cannot be incorporated in the p-y curve Foundations Division, ASCE, Vol. 92, No. SM2, pp. 27-42.
method. Therefore, a constant representative value of φ′ between the Janbu, N. (1963). “Soil compressibility as determined by oedometer
peak and critical state is required to be selected. The initial modulus and triaxial tests”, Proc. Euro. Conf Oil Soil Mech. 111/1.1
of subgrade reaction (k) is also related to φ′ and relative density as FUUlld. Ic·llgrg., German Society for Soil Mechanics and
shown in Figure 4. Note that k is not a fundamental soil property. Foundation Enginec:ring, Wissbaden, Germany, Vol I, 1925.
Consider a pile foundation in dense sand having the peak and Kimura M, Adachi T, Kamei H, Zhang F. (1995). “3-D finite
critical state friction angles of 41° and 31°. For successful prediction element analyses of the ultimate behaviour of laterally loaded
of the response of a laterally loaded pile using the p-y curve method cast-in-place concrete piles”, In Proceedings of the Fifth
a representative value of φ′ between 41° and 31° is needed. API International Symposium on Numerical Models in
(1987) recommended an empirical equation for estimating the Geomechanics, NUMOG V, pp. 589–594.
representative value of φ′ as a function of relative density. However, Kulhawy, F. H. (1991). “Drilled shaft foundations, Chapter 14 in
the computation with this recommended value of φ′ over predicts the Foundation Engineering Handbook”, 2nd ed, Hsai-Yang Fang
maximum bending moment and lateral displacement (Rollins et al. Ed., Van Nostrand Reinhold, New York.
2005). The limitations of the p-y curve method could be overcome LPILE Plus 5.0 (2005). ENSOFT, INC., 3003 West, Howard Lane,
by using FE modeling as presented in this paper. The response of Austin, Texas 78728.
the pile is calculated using the fundamental soil properties such as Long, J. H., and Reese, L. C., (1985). “Methods for predicting the
friction angle, dilatancy and stiffness. It is also shown that the FE behaviour of piles subjected to repetitive lateral loads”, Proc.,
model can successfully simulate the full-scale test results. 2nd Shanghai Symp. On Marine Geotechnology and
Nearshorea Offshore Structures, Shanghai, Chaina.
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practice for planning, designing and constructing fixed Meyerhof. G, G., Mathurs, S. K., and Valsangkara, A. J. (1981).
offshore platforms”, API Recommended practice 2A (RP “Lateral resistance and deflection of rigid walls and piles in
2A), 17th Ed. layered soils”, Canadian Geotechnical Journal, 18, pp. 159-
American Petroleum Institute (API). (1993) Recommended Practice 170.
for Planning, Designing and Constructing Fixed Offshore McVay, M., Zhang, L., Molnit, T., and Lai, P. (1998). “Centrifuge
Platforms – Working Stress Design, API Recommended testing of large laterally loaded pile groups in sands”, J.
Practice 2AWSD (RP 2A-WSD), 20th edition, p191 Geotech. Geoenviron. Eng., 124(10), pp. 1016–1026.
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