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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

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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.

References

Banerjee S (2010) Centrifuge and numerical modelling of soft

clay–pile–raft foundations subjected to seismic shaking.

Ph.D. Thesis. National University of Singapore, Singapore

Banerjee S, Goh SH, Lee FH (2007) Response of soft clay strata

and clay–pile–raft systems to seismic shaking. J Earthq

Tsunami 1(3):233–255

Bathe KJ (1996) Finite element procedures. Prentice-Hall Inc.,

Upper Saddle River

Goh TL (2003) Stabilization of an excavation by an embedded

improved soil layer. Ph.D. Thesis. National University of

Singapore, Singapore

Hardin BO, Drnevich VP (1972) Shear modulus and damping in

soils: design equations and curves. J Geotech Eng Div

ASCE 98(7):667–692

Kang MA, Banerjee S, Lee FH, Xie HP (2012) Dynamic soil–

pile–raft interaction in normally consolidated soft clay

during earthquakes. J Earthq Tsunami 6(3):1250031–1–

1250031–31

Kavvadas M, Gazetas G (1993) Kinematic seismic response and

bending of free-head piles in layered soil. Geotechnique

43(2):207–222

Nikolaou S, Mylonakis G, Gazetas G, Tazoh T (2001) Kine-

matic pile bending during earthquakes: analysis and ﬁeld

measurements. Geotechnique 51(5):425–440

Poulos HG, Davis EH (1980) Pile foundation analysis and

design. Wiley Inc., New York

Poulos HG, Tabesh A (1996) Seismic response of pile founda-

tions: some important factors. In: Proceedings of the 11th

WCEE Paper No. 2085

Snyder JL (2004) Full scale test lateral load tests of a 3 95 pile

group in soft clays and silts. M.Sc. Thesis, Brigham Young

University, USA

Tabesh A, Poulos HG (2007) Design charts for seismic analysis

of single piles in clay. Proc ICE (UK) Geotech Eng

160(GE2):85–96

Vucetic M, Dobry R (1991) Effect of soil plasticity on cyclic

response. J Geotech Eng ASCE 117(1):89–107

Wilson DW (1998) Soil–pile–superstructure interaction in liq-

uefying sand and soft clay. Ph.D. Thesis. University of

California, Davis, California, USA

Yu Y, Lee FH (2002) Seismic response of soft ground. In:

Proceedings of the ICPMG’02, pp 519–524

Zhu H, Chang MF (2002) Load transfer curves along bored piles

considering modulus degradation. J Geotech Geoenviron

Eng ASCE 128(9):764–774

Geotech Geol Eng

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