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ORIGINAL PAPER
Parametric Study and Centrifuge-Test Verification
for Amplification and Bending Moment of Clay–Pile System
Subject to Earthquakes
Subhadeep Banerjee .Minu Joy .Debdeep Sarkar
Received: 5 June 2014 / Accepted: 29 February 2016
ÓSpringer International Publishing Switzerland 2016
Abstract This paper examines seismic effects on
fixed-head, end-bearing piles installed through soft
clay. The numerical analyses were conducted using
ABAQUS with a hypoelastic constitutive model for
the clay. The dimensionless parameters involving the
major parameters such as pile modulus, soil modulus,
slenderness ratio, natural frequencies of clay layer and
pile–raft, superstructure mass, density of the soil and
peak ground acceleration were obtained from the
parametric studies. The relationships for the amplifi-
cation of ground motions and the maximum bending
moment in the pile were developed based on regres-
sion of the numerical data. The computed results from
the proposed relationships were compared with the
results reported in the past studies.
Keywords Earthquake Piles Clays
Amplification Bending moment
1 Introduction
Many major cities such as, Shanghai, Bangkok,
Mumbai, Kuala Lumpur, Jakarta and Singapore are
built overlying soft clay. As a result many important
inland and offshore structures such as bridges, port and
harbours, tall structures like water tanks, chimney etc.
are supported on pile foundations to achieve the
required bearing capacity. In such situations, the
response of pile and surrounding soil subjected to
earthquake loading is an important factor affecting the
integrity of infrastructures.
In past, there are various analytical, experimental
and numerical studies reported on the response of piles
subjected to seismic loading. Nikolaou et al. (2001)
and Tabesh and Poulos (2007) presented design charts
and empirical forms of bending moments and shear
forces developed along the pile length during the
passage of seismic waves through soil. They have also
suggested that the response of soil-pile system is
generally affected by the soil and pile modulus, the
peak ground acceleration, the frequency of base
excitation and the superstructure loading (Kavvadas
and Gazetas 1993; Nikolaou et al. 2001; Tabesh and
Poulos 2007).
However it was noted that the majority of the
research in this field is concentrated to the seismic
S. Banerjee (&)
Department of Civil Engineering, Indian Institute of
Technology Madras, Chennai 600036, India
e-mail: subhadeep@iitm.ac.in
M. Joy
Geotechnical Engineering Division, Department of Civil
Engineering, Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: mail2sban@gmail.com
D. Sarkar
Department of Civil Engineering, Bengal Engineering and
Science University, Shibpur 711103, India
e-mail: sban345@gmail.com
123
Geotech Geol Eng
DOI 10.1007/s10706-016-9999-4
analysis of piles and pile groups embedded in sand.
Nevertheless Wilson (1998) noted that the piles in firm
cohesionless soils generally perform better during
earthquakes than those in soft clay. Hence, there is a
need to study the response of soil-pile system embed-
ded in clay subjected to earthquake loadings.
The present paper describes the details and results
of parametric study carried out for short piles embed-
ded in homogenous clay layer. The present research
comprises of four major components: (1) a parametric
study based on the numerical analyzes of a clay–pile
system, (2) identification of dimensionless groups
affecting the seismic clay–pile response, (3) develop-
ment of the predictive relations for the maximum
bending moment and amplification of seismic waves,
(4) comparison of the developed correlations with the
results published in the past literatures.
2 Numerical Simulation of Clay–Pile–Raft System
Three-dimensional finite element analysis of the clay–
pile–raft system was carried out using ABAQUS v6.8.
Figure 1shows the 2 92 pile–raft system embedded
in normally consolidated kaolin clay subjected to far-
field earthquake motion. The engineering properties of
the kaolin clay as reported by Goh (2003) were
adopted in the study and are shown in Table 1. Each
pile of diameter 0.9 m and length 13 m is rigidly
connected to a raft (12.5 m 97.5 m 90.5 m) on top.
Table 2shows the different types of piles used in the
study. The pile to pile spacing ‘s’ is chosen such that
s/d ratios in the direction of shaking were approxi-
mately 11.67 and 6.11 along the direction of the
seismic excitations. The piles are widely spaced to
minimize the group effect. By considering the geom-
etry and loading symmetry, half of the prototype was
modeled using the 20 noded quadratic brick elements
(Fig. 2). However it is widely accepted that the solid
brick elements, where strain energy derived from
displacement formulation of finite element analysis is
smaller than the exact strain energy of the mechanical
system, may exhibit extremely rigid behaviour due to
over-estimation of structural stiffness. To avoid such
transverse shear locking reduced integration was used
(Bathe 1996). The nodes on the vertical plane of
symmetry were restrained against any horizontal
displacements in the direction normal to this plane,
and as well as in other two rotational degrees of
freedom. The remaining three vertical faces, as well as
the base of the mesh, were restrained against vertical
motion. The effect of superstructure was considered as
additional masses (Table 3) lumped at the raft level.
Pile was modeled as linear elastic material. The input
ground motions were applied at the base of the
numerical model as prescribed acceleration time
histories. The vertical planes of symmetry were
restrained in horizontal direction. All the other three
vertical faces as well as the base of the model were
restrained in vertical direction.
2.1 Soil Model
It is well established that the stress–strain behavior of
natural soils during earthquake loading is highly
12.50 m
500 mm sand
layer for
drainage path
25 m
13.25 m
0.9 m
14.25 m
12.50 m
7.5 m
1.0 m
Pile in cross-
section
Kaolin clay
Fig. 1 Clay–pile–raft system used for numerical simulations
Table 1 Geotechnical properties of kaolin clay (After Goh
2003)
Properties Range
Bulk unit weight (kN/m
3
)16
Water content (%) 66
Liquid limit (%) 80
Plastic limit (%) 40
Compression index 0.55
Recompression index 0.14
Coefficient of permeability (m/s) 1.36 910
-8
Geotech Geol Eng
123
nonlinear and the shear modulus generally decreases
with increase in shear strain (Hardin and Drnevich
1972). Moreover it is also noted that the degradation of
shear modulus with shear strain, or shear stress,
significantly influences the performance of a founda-
tion system (Snyder 2004). This is particularly
important when a pile is subjected to lateral loading
in which the shear strain in the surrounding soil
progressively increases (Zhu and Chang 2002).
In the present study, ABAQUS in-built hypoelastic
stress–strain model is used to define the soils that
exhibits nonlinear, but reversible, stress strain behav-
ior even at small strains. The constitutive law for a
hypoelastic solid can be shown as,
drij ¼2Gdeij þm
12mdekkdij
ð1Þ
where Gand mare the shear modulus and Poisson ratio
respectively, corresponding to the stress (r
ij
) and
strain (e
ij
) tensors with d
ij
=1when i=j, and d
ij
=0
when i=j. Physically, Eq. 1indicates that the model
considers the shear modulus of soil degrades hyper-
bolically with respect to increasing shear strain within
the soil mass. Vucetic and Dobry (1991) presented sets
of design curves for variation of modulus reduction
with strain amplitudes for different plasticity index
(Fig. 3). These well-established data sets were used to
derive the values of shear modulus corresponding to a
specified strain and used as inputs to the constitutive
model. The plasticity index of 45 % was chosen for the
typical analysis.
2.2 Input Earthquakes
The earthquake motions considered were the typical
far-field events from previous Sumatran earthquakes
with long periods and long duration as measured at
bedrock level in Singapore (as in USGS database).
Three synthetic ground motions, which were gener-
ated using the response spectra of such earthquakes,
were used in the study (Yu and Lee 2002). The input
ground motions having identical frequency content
and duration were scaled to different peak ground
accelerations (PGA) of 0.022, 0.07 and 0.1 g respec-
tively (Fig. 4). In the present paper three ground
Table 2 Different types of piles used in the numerical simulations
Pile material Length of pile (m) Diameter of pile (m) Slenderness ratio (l/r) Flexural rigidity,
EI (kN m
2
)
Hollow stainless steel 13 0.9 28.89 3,545,002
Hollow stainless steel filled with PCC 13 0.9 28.89 4,285,785
Solid stainless steel 13 0.9 28.89 10,308,351
Flexible beam
Nodes/locations where accelerations are
computed
Fig. 2 ABAQUS half-model for clay–pile–raft system
Table 3 Different types of superstructural masses used in the
numerical simulations
Type Prototype mass (tonnes)
Mass-1 368
Mass-2 605
Mass-3 863
0
0.2
0.4
0.6
0.8
1
1E-06 1E-05 0.0001 0.001 0.01 0.1
G/G
max
Shear strain (%)
PI=200
.PI=100
.PI=50
.PI=30
.PI=15
PI=NP
Fig. 3 Modulus reduction curves proposed by Vucetic and
Dobry (1991)
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123
motions are referred as PGA-1, PGA-2 and PGA-3
respectively.
2.3 Results and Observations
Figure 5a, b shows the acceleration time histories
computed at the clay surface (5 m from the edge of the
raft) and top of the raft (5 m from the centre of the raft
at the raft surface). Figure 2shows the location at
which the accelerations time histories are obtained.
For this numerical simulation, solid stainless steel
piles with added mass (Mass-3) was used. The model
was subjected to the ground motion of PGA-3. By
comparing the computed histories at the clay surface
and top of the raft with those of the input ground
motion, it is evident that the amplification of ground
motion occurred in both the clay and the structure as
the seismic waves propagate upwards. However,
despite being at the same elevation, there are differ-
ences noted between the acceleration histories com-
puted at the clay and raft, which suggest that the raft
does not move in tandem with the ground. This will be
further examined below.
Figure 5c shows the response spectra for the
computed histories at the clay and raft along with
the response spectra of the input ground motion PGA-
3. At the clay surface, the response spectrum, which
computes accelerations in the clay adjacent to the raft,
shows a resonance period of about 2.28 s. The
response spectrum for raft, as shown on Fig. 5c,
indicates that the resonance period at the surface of the
embedded raft is about 1.68 s. This is about 0.6 s
lower than that measured in the adjacent soil. The
difference in the computed resonance period between
the soil and the structure provides another indicator,
besides the time history plots, that the soil motion may
not be representative of the raft motion. Figure 5cis
replotted in Fig. 5d with the amplification of the input
-0.1
-0.05
0
0.05
0.1
020406080
Acceleration (g)
Time (sec)
PGA-1 = 0.022g
PGA-2 = 0.07g
PGA-3 = 0.1g
Fig. 4 Input ground motions
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0 5 10 15 20 25
Accelerat ion (g)
Time (sec)
0
0.5
1
1.5
2
01234
Period (sec)
Cla
y
surfa ce
Top o f ra f t
Amplification
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 5 10 15 20 25
Acceleration (g)
Time (sec)
0
0.05
0.1
0.15
0.2
0.25
0.3
01234
Spectral accelerati on (g)
Period (sec)
Clay surface
Top o f r a ft
Input base motion (PGA-3)
(a) (b)
(c) (d)
Fig. 5 Acceleration time histories, response spectra and
amplification computed for solid stainless steel piles with added
mass (Mass-3) subjected to the ground motion of PGA-3.
aAcceleration time history at clay surface, bacceleration time
history at top of raft, cresponse spectra, damplification
Geotech Geol Eng
123
ground motion (PGA-3) obtained by normalizing the
spectral acceleration at the clay and raft with respect to
the base response. Figure shows that the amplifications
at the clay surface and top of raft are 1.85 and 1.62
respectively.
To measure the bending moment developed along
the pile length, 3-noded quadratic space beam ele-
ments (Timoshenko beam element, B32) were intro-
duced along the centerline of the pile (see Fig. 2). The
flexural rigidity of the beam was chosen as 10
6
times
less than that of the pile so that the beam deformed
freely without interfering with the structural response
of the pile. The actual bending moment was obtained
by multiplying computed beam moments by the
scaling factor of 10
6
. Figure 6shows the typical
maximum bending moment profile plotted along the
pile length. The profile shows that the maximum
moment occurs near the pile head, and reduces along
the pile length to very small value near the pile tip.
Further Fig. 7plots the computed maximum bend-
ing moment envelope for three pile types of different
flexural rigidities with added mass (Mass-1) subjected
to: (a) PGA-1 and (b) PGA-3. As shown in figure, the
maximum bending moment increases with flexural
0
2
4
6
8
10
12
14
-1000 0 1000 2000 3000
Depth below the bottom of pile-raft (m)
Bending moment (kNm)
Fig. 6 Maximum bending moment profile computed for solid
stainless steel piles with added mass (Mass-3) subjected to the
ground motion of PGA-3
0
2
4
6
8
10
12
14
-200 0 200 400 600 800
Depth below the bottom of pile-raft (m)
Bending moment (kNm)
0.9m hollow
steel piles
EI= 354 5002 kNm2
0.9m hollow
steel piles filled with PCC
EI= 428 5785 kNm2
0.9m solid
steel piles
EI=103 08351 kNm2
0
2
4
6
8
10
12
14
-1000 0 1000 2000 3000
Bending moment (kNm)
Depth below the bottom of pile-raft (m)
(a) (b)
Fig. 7 Computed
maximum bending moment
envelope for three pile types
of different flexural
rigidities with added mass
(Mass-1) subjected to:
aPGA-1 and bPGA-3
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123
rigidity of the pile. In addition it can also be noted that
the extent of the significant positive moment also
increases with pile stiffness. For the 0.9 m diameter
hollow steel pile, the positive moment terminated at a
depth of less than half a pile length, below which the
induced moments are generally insignificant. The
similar observations were also reported for flexible
piles by other researchers (Poulos and Davis 1980;
Nikolaou et al. 2001). It can also be concluded that the
simulations show that the flexible piles can derive
lateral support even from soft soil. It may therefore be
surmised that, depending upon the relative pile and
soil stiffness, the latter can either provide lateral
support or impose lateral loading on the pile. On the
other hand, in stiffer piles, such as the 0.9 m solid steel
piles shown in Fig. 7, the bending moment decreases
roughly linearly with depth. A small negative moment
is present near the pile toe, but this is much smaller
than the maximum moment at the pile top and is likely
to depend upon the rotational fixity at the pile toe.
3 Formulation of Dimensionless Parameters
Review of literature suggests that the response of clay
and piles subjected to seismic loading is affected by
various factors such as pile modulus, soil modulus,
slenderness ratio, natural frequencies of clay layer and
pile–raft, superstructure mass, density of the soil and
peak ground acceleration (Kavvadas and Gazetas 1993;
Nikolaou et al. 2001;TabeshandPoulos2007;Banerjee
2010). In the present study, five dimensionless groups
involving different parameters are identified as follows:
1. Stiffness ratio (T
p
/T
s
) is the ratio of the time period
of the superstructure without the soil around it to
that of the time period of the soil without any
superstructure.
The pile–raft structure can be considered as a
single degree of freedom system where, m is the
mass of the raft, mass of pile is negligible
compared to raft and EpIpis flexural rigidity of
the pile.
Now, stiffness of the system can be worked out
from simple structural analysis as,
K¼XEpIp
l3
a
ð2aÞ
where Xis a constant whose value depends on the
end condition. Hence predominant time period of
the pile–raft system without soil can be shown as,
Tp¼2pffiffiffiffiffiffiffiffiffiffiffi
mL3
p
3EpIp
sð2bÞ
where L
p
is the length of pile, E
p
is the modulus of
elasticity, I
p
is the moment of inertia and mis the
superstructure mass.
The time period of the soil layer is given by,
Ts¼4h
ffiffiffi
G
q
qð3Þ
where his the height of the soil layer, Gis the
shear modulus of the soil layer and qis the density
of the soil layer.
2. PGA is the peak ground acceleration of the base
excitation expressed in terms of acceleration due
to gravity (g).
3. Mass ratio (m/qr
p
3
) is the ratio of mass of the
superstructure to equivalent mass of soil. r
p
is the
radius of pile.
4. Frequency ratio (f
b
/f
0
)wheref
b
is the predominant
frequency of the input ground motions and f
0
(=1/T
s
)
is the natural frequency of the clay layer.
5. Slenderness ratio (L
p
/d) is the ratio of the length of
the pile to the diameter of the pile.
4 Parametric Study
A total of 27 numerical simulations involving three
different pile types, superstructural masses and ground
motions were carried out to establish semi-empirical
formulations for amplification at clay surface, top of
raft and maximum bending moment in pile.
4.1 Amplification at Clay Surface (A
s
)
A detail regression analysis shows that the amplifica-
tion at clay surface can be expressed as an exponential
function (Fig. 8) of above mentioned dimensionless
groups as shown in Eq. 4a and 4b.
As¼1:228 e57802xwhere;ð4aÞ
Geotech Geol Eng
123
x¼Tp
Ts
0:4
PGAðÞ
7m
qr3
p
!
0:05
fb
f0
0:6
ð4bÞ
By substituting, f
0
(=1/T
s
)
x¼Tp
0:4Ts
ðÞ
0:2PGAðÞ
7m
qr3
p
!
0:05
fb
ðÞ
0:6
ð4cÞ
It can be noted that the amplification at the clay
surface primarily depend on PGA. It is also observed
from Eq 4c, that the amplification at the clay surface
increase with the increase in time period of clay which
is inversely related to clay stiffness.
4.2 Amplification at Top of Raft (A
r
)
Amplification at the top of raft is expressed asa function
of the amplification at the clay surface. Figure 9shows
the results of the regression analysis as follows,
Ar=As¼1:991 As
ðÞ
0:93 ð5Þ
From Eq. 5it is noted that the amplification at the
top of raft increase with the increase in the amplifi-
cation at the clay surface.
4.3 Maximum Bending Moment Developed
Along the Length of the Pile
In addition to amplifications, the maximum bending
moment developed in a pile is also a key parameter for
the sustainable design. The maximum moment is
represented as a dimensionless formulation, Md/E
p
I
p
where Mis the maximum moment, dis the diameter of
the pile, E
p
I
p
is the flexural rigidity of the pile. The
semi-empirical formulation of the maximum bending
moment obtained by regression analysis (Fig. 10)isas
follows,
Md
EpIp
¼3106z
fg
2:545 ð6aÞ
z¼Tp
Ts
0:4
PGAðÞ
0:3m
qr3
p
!
0:02
fb
f0
0:05
Lp
d
0:2
ð6bÞ
Equation 6a,6b suggests that that the stiffness ratio is
the main factoraffecting the maximumbending moment
response of the pile. It also shows that the maximum
bending moment increases with the pile modulus, peak
ground acceleration and super-structural load. This is in
accordance with the findings of Nikolaou et al. (2001),
Tabesh and Poulos (2007) and Kang et al. (2012).
y = 1.228e
57802x
R² = 0.773
0
1
2
3
4
5
6
0 0.000005 0.00001 0.000015 0.00002 0.000025
y = Amplification at the surface, A
s
x = (T
p
/T
s
)
0.4
×(PGA)
7
×(m/ r
p3
)
0.05
×(f
b
/f
0
)
0.6
Fig. 8 Semi-empirical relationship for amplification at clay
surface
Fig. 9 Semi-empirical relationship for amplification at the top
of raft
Fig. 10 Semi-empirical relationship for maximum bending
moment developed along the length of pile
Geotech Geol Eng
123
5 Validation of the Predictive Relations
Preceding discussion shows that the clay and pile
response can be represented as semi-empirical func-
tions of dimensionless groups. The responses com-
puted from the proposed relationships are compared
with the results reported in previous studies.
5.1 Comparison with the Centrifuge Tests Results
by Banerjee (2010)
Banerjee et al. (2007) and Banerjee (2010) reported a
series of shaking table experiments conducted using
geotechnical centrifuge at National University of
Singapore. The shaking table tests were conducted
on the prototypes clay–pile raft model as shown in
Fig. 1. Input earthquake motions and the soil types are
used as the same as that considered in the numerical
simulations. The accelerometers and strain gauges
were used to measure acceleration time histories and
bending moments respectively.
The soil used in the study was Malaysian kaolin
clay of PI =40 %. The corresponding variation of
shear modulus and damping ratio with the shear strain,
as provided by Vucetic and Dobry (1991), were used
as the input to the hypoelastic model.
Figure 11 presents the comparison of the results
computed from the proposed semi-empirical relation-
ship with the results obtained from the centrifuge tests
for the amplification at the clay surface. The fig-
ure shows that, despite the uncertainties involved in
the centrifuge tests, the predicted results matched the
test results with reasonable accuracy. Figure 12 shows
the comparison between the computed and measured
amplifications at the top of raft. The figure shows that
the proposed correlations compares satisfactorily
PGA-2 (0.07 g) and PGA 3 (0.1 g) whereas the
centrifuge results obtained from test with ground
motion of PGA-1 (0.022 g) tends to deviate from the
prediction. However the ground motion with PGA of
0.022 g is too small to be a concern in the context of
amplifications. Figure 13 shows the comparison
Fig. 11 Comparison of amplification at the clay surface
computed from proposed relationship with that obtained from
centrifuge tests (Banerjee 2010)
Fig. 12 Comparison of amplification at the top of raft
computed from proposed relationship with that obtained from
centrifuge tests (Banerjee 2010)
Fig. 13 Comparison maximum bending moments computed
from proposed relationship with that obtained from centrifuge
tests (Banerjee 2010)
Geotech Geol Eng
123
between the bending moments predicted by the
proposed correlation and the measured values
obtained from the centrifuge tests. The figure shows
that the results computed from the proposed correla-
tions matched satisfactorily with the results obtained
from the centrifuge tests.
5.2 Comparison with the Semi-Empirical
Relationship Proposed by Nikolaou et al.
(2001)
Nikolaou et al. (2001) developed a semi-empirical
relationship for maximum bending moment in piles
embedded in layered soils (Eq. 7).
max M0:042asq1h1d3l
d
0:3Ep
E1
0:65 V1
V2
0:5
ð7Þ
where a
s
is the free field acceleration, q
1
is the density
of top soil (soil layer 1), h
1
is the height of the layer 1,
l/d is the slenderness ratio of the pile, E
p
is the modulus
of elasticity of pile, E
1
is the modulus of elasticity of
layer 1, V
1
and V
2
are the shear wave velocities of layer
1 and 2 respectively. In the present study, the soil layer
is homogenous. Hence, V
1
/V
2
=1 and h=13 m
(corresponding to the prototype pile length).
It can be observed from Fig. 14 that the agreement
between the proposed correlation and the formulation
by Nikolaou et al. (2001) is fairly good. The slight
deviations that is observed may be attributed to the
Fig. 14 Comparison between bending moments computed
using proposed relationship and Nikolaou et al. (2001)
Table 4 Different cases considered for the comparison with Poulos and Tabesh’s (1996) analysis
Sl. No. Pile length (m) Pile modulus (MPa) Soil modulus (MPa) Diameter (m) Earthquakes (All the earthquakes
are scaled to a PGA of 0.1 g)
1 12 30,000 50 0.6 Meckering (1968)
2 0.9
3 1.2
4 1.5
5 12 30,000 50 0.9 Whittier (1987)
6 1.2
7 1.5
8 12 30,000 30 0.6 Newcastle (1994)
Fig. 15 Comparison of the bending moments computed from
the proposed relationship with that obtained from Poulos and
Tabesh (1996) for different earthquakes
Geotech Geol Eng
123
effect of superstructure mass, which is not taken into
account in the formulation by Nikolaou et al. (2001).
5.3 Comparison with the Analysis Reported
by Poulos and Tabesh (1996)
Poulos and Tabesh (1996) presented an analysis for
the seismic response of single piles ignoring inertia of
piles. Table 4shows the different parameters consid-
ered for the study. Figure 15 plots the bending
moments computed from the proposed relationship
along with Poulos’ analysis. Figure shows that, in
general, good agreement is achieved between the two
analyses.
6 Conclusion
The foregoing discussion suggests that the response of
clay and piles subjected to seismic loading is affected
by various factors such as pile modulus, soil modulus,
slenderness ratio, natural frequencies of clay layer and
pile–raft, superstructure mass, density of the soil and
peak ground acceleration. Several major conclusions
can be inferred from the present study:
1. The amplification of the ground motion primarily
depends on the PGA. The amplification increases
with the increase in peak ground acceleration.
Additionally amplification of the ground motion
also increases with the predominant frequency of
the input motion.
2. An increased amplification at the adjacent clay
surface indicates an increased amplification at the
top of raft.
3. Flexural rigidity of the pile is the most important
factor affecting maximum bending moment.
Besides it is also concluded that the maximum
bending moment increase with the pile modulus,
peak ground acceleration and superstructural load.
4. The developed correlations are favorably vali-
dated with the previously published experimental
results (Banerjee 2010) as well as the numerical
analysis reported by Nikolaou et al. (2001) and
Poulos and Tabesh (1996).
5. However it should be noted that the developed
correlations are valid for fixed-head end-bearing
piles in homogenous clay.
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