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SEISMIC STRAIN WEDGE MODEL TO ANALYZE SINGLE PILES
UNDER LATERAL SEISMIC LOADING
Aslan SADEGHI HOKMABADI 1, Ali FAKHER
2, Behzad FATAHI
3
ABSTRACT
One of the most effective methods of analyzing a single pile and pile groups under lateral loading is Strain
Wedge Model (SWM). SWM has a number of advantages in comparison with traditional p-y curves, but
this method traditionally could be used to analyze piles under monotonic loads. In the present paper,
SWM has been modified to consider dynamic lateral loading. Based on this new method called Seismic
Strain Wedge Model (SSWM), a Lateral Analysis of Piles (LAP) computer code has been developed.
Using LAP, some case studies have been analyzed and the results show good agreement with test data.
This paper introduces SSWM as a simple and powerful solution to analyze piles under lateral seismic
loading.
Keywords: Strain Wedge Model, Seismic loading, lateral behavior, Single pile
INTRODUCTION
Lateral vibration of piles is an important consideration in the design of piled structures subjected to
dynamic excitations due to earthquake, wind, operation of machines and waves in offshore environment
(Das & Sargand, 1999). The seismic response of pile foundations is a complex process involving inertial
interaction between structure and pile foundation, kinematics interaction between piles and soil, and the
non-linear response of soil to strong earthquake motions (Finn, 2005). Several methods have been
developed for dynamic response analysis of pile foundations listed in Table 1. Depending on how piles
and soils are modeled, these methods may be broadly classified into Continuum-base approaches and
Winkler (or subgrade reaction) approaches.
In the Continuum-base approaches, soil has been modeled as continuum media several soil properties are
required as input for the analysis. Due to complexity and unavailability of soil properties, the application
of methods in the second category, subgrade reaction approaches, is more common. As an example, the
load-transfer method models the pile as an elastic member and the soil is viewed as distributed springs and
dashpots with constant or frequency dependent concentrated at a finite number of nodes. The spring
constants are obtained from analytical calculation or experimental data. The major advantage of this
approach lies in its ability to simulate nonlinearity, heterogeneity, and hysteretic degradation of the soil
surrounding the pile by simply changing the spring and dashpot constants (Das & Sargand, 1999). In
contrast, the main drawback of load-transfer approach is idealization of the soil continuum with discrete
soil reactions (Allotey & El Naggar, 2008). In other words, the shear transfer between the springs is one of
1 PhD Student, School of Civil and Environmental Engineering, University of Technology Sydney (UTS),
Sydney, Australia, e-mail: aslan.sadeghihokmabadi@student.uts.edu.au 2 Associate Professor, School of Civil Engineering, College of Engineering, University of Tehran, Iran. 3 Assistant Professor, School of Civil and Environmental Engineering, University of Technology Sydney
(UTS), Sydney, Australia.
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile the obviously missing fundamental mechanisms in Winkler models (Finn, 2005). Strain Wedge Model
(SWM) overcomes this drawback of Winkler methods by creating relationship between the three-
dimensional responses of soil-pile to the Beam on Elastic Foundation parameters (Ashour et al., 1998).
However, the current SWM analysis is limited to piles under monotonic loads. In the presented research
SWM is modified in order to include dynamic loads.
Table 1. Summary of the lateral seismic analysis of piles methods
Methods Reference Remarks
Equivalent Cantilever
Davisson & Robinson (1965);
Nair et al. (1969)
Pile is reduced to an equivalent cantilever; No information can be obtained on the moment, stresses, and displacements along the length of the pile; Only good for initial analysis.
Beam on Elastic Foundation
Briaud & Tucker (1984)
Presents the soil inertial force on the Winkler springs stiffness, and the pile inertial force and soil damping as an additional force at each node. A new governing equation of Beam on Elastic Foundation (Including inertial force and damping) is solved with the Finite Deference Method.
Novak’s Analysis Method
Novak (1974) This approach derives stiffness and damping constants for piles, and thus enables the use of the simple “lumped-parameter” approach.
Column of Soil Parmelee et al.(1964); Idress & Seed (1968)
Soil mass is lumped at discrete points along the depth of the each layer and these masses linked by springs and Dashpots connected in parallel; Earthquake effect is presented as a horizontal acceleration at the base; It is assumed that soil and pile have the same displacement in each node (the pile is moved essentially with the soil) which is not acceptable in layered soils.
P-y Curves Matlock (1970); Reese et al. (1974)
Pile is modelled as an elastic member and the soil is modelled as a series of nonlinear springs (p-y curves); This is a semi-empirical method that accounts for dynamic loads by modifying the static p-y curves based on empirical data. (different researchers suggests different curves)
Springs and Dashpots to model soil
El-Naggar & Bently (2000); Tavaraj(2001);
Gerolymos & Gazetas(2006)
Pile is modelled as an elastic member, and soil is modelled as a series of springs and dashpots (different models are suggested); These methods, based on the determination of the near- and far-field responses, can be grouped into coupled and uncoupled models.
Continuum-Base Approaches
Kuhlemeyer(1979); Banerjee et al.(1987); Brown & Shie(1990)
Soil is modelled as a continuum media and different numerical approaches such as the Finite Element Method or Boundary Element Method are used to solve the governing equations.
METHOD OF ANALYSIS
To develope general equations of SSWM, three methods including Horizontal Slice Method, Pseudo-
Dynamic Method, and Strain Wedge Model are used and combined. Horizontal Slice Method presents the
idea of dividing passive soil into horizontal slices; Pseudo-Dynamic Method is used to calculate the
additional earthquake force applied at each slice or each depth along the pile; and Strain Wedge Model is
employed to determine the soil resistance against the lateral loading by the three-dimensional passive
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile wedge of the soil in front of the pile. In this section, each of these three methods are described, and then
the formulation of SSWM is presented.
Horizontal Slice Method Horizontal Slice Method (HSM) was initially developed for seismic stability analysis of reinforced slopes
and walls (Shahgholi et al., 2001). HSM is a limit equilibrium method assuming a failure surface with a
failure wedge divided into a number of horizontal slices (Figure1). Because of horizontal slices, the failure
surface does not intersect reinforcements; accordingly the reinforcements have no direct influence on inter-
slice forces. According to Nouri et al. (2006), force and moment equilibrium equations for each slice of the
whole sliding wedge can be satisfied.
Figure 1. Horizontal Slice Method: (a) dividing soil in to horizontal slices, (b) Forces acting on a
single horizontal slice containing reinforcement (after Shahgholi et al., 2001)
Pseudo-Dynamic Method
Pseudo-static methods are commonly used for solving various design problems associated with pile
foundations subjected to earthquake motions (Finn, 2005). However, the pseudo-static methods consider
the dynamic nature of earthquake loading very approximately (Kramer, 1996), and do not consider the
effects of time and body waves travelling through the soil during the earthquake. The phase difference due
to finite shear wave propagation can be considered using a new method, called Pseudo-dynamic method
(Steedman & Zeng, 1990). In the Pseudo-dynamic method it is assumed that the shear modulus is constant
with depth along the pile. Therefore, the following equations can be written:
2/1)/( GVs ! (1)
2/1)]21(/)22([ " # $$! GVp (2)
sVLT /4/2 !! %& (3)
where, Vs is shear wave velocity (m/s), G is shear modulus of soil (N/m2), is density of soil (kg/m3), Vp
is the primary wave velocity (m/s), ! is Poisson’s ratio, T is period of lateral shaking (s), and " is angular
frequency of base shaking (rad/s). In Pseudo-dynamic method, only the phase and not the amplitude of the
acceleration is varying. In addition, in this method it is assumed that both the horizontal and vertical
vibrations, with accelerations ah and av, respectively, start at exactly the same time, and there is no phase
shift between these two vibrations resulting in the critical condition for design (Nimbalkar et al., 2006).
However, the seismic acceleration is considered as harmonic sinusoidal acceleration, which is one of the
limitations of the original pseudo-dynamic method proposed by Steedman & Zeng (1990).
Vi
Hi+1
x
y
Ti
Ni
Si
(1+Kv)WiKhWi
L
Li+1
(b)(a)
Reinforcement
elements
Failure surface
Vi+1
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile As shown in Figure 2, if the base is subjected to harmonic horizontal and vertical seismic accelerations
with amplitudes ah and av, the horizontal and vertical accelerations at depth x below the ground surface at
time t can be express as:
)(sin),(s
hhV
xLtatxa
$$! %
(4)
)(sin),(p
vvV
xLtatxa
$$! %
(5)
In the SSWM, the above accelerations are employed to calculate the additional earthquake force applied at
each depth along the pile.
Figure 2. Pseudo-dynamic method for slopes
Strain Wedge Model
Non-linear springs (p-y) are widely used to analyze single piles under static lateral loads. However, the p-
y curve employed does not consider soil continuity and pile properties such as pile stiffness, pile cross
section, and pile head conditions (Reese, 1983). SWM overcomes these limitations and allows the
assessment of the p-y response of laterally loaded piles based on the three-dimensional soil-pile
interaction and its dependence on both soil and pile properties (Norris & Abdollaholiae, 1985).
In the SWM, the soil resistance against the lateral loading is determined by the three-dimensional passive
wedge of soil that develops in front of the pile. As shown in Figure 3, geometry of the mobilized passive
wedge is characterized by base angle, m; the current passive wedge depth h; and the wedge fanning angle,
!m. All of these parameters are the functions of soil horizontal strain in each step of loading. Therefore,
the geometry of the soil wedge is a function of the strain level in soil (i.e level of loading). The complete
formulation of the SWM is addressed by Ashour et al. (1998 & 2004).
av
av
ah (x,t)
av (x,t)
x
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile
Figure 3. Passive wedge of soil as developed in front of the pile in the SWM (Ashour et al., 1998)
The SWM analysis maintains two types of stability, local stability of the soil sublayer (horizontal slice);
and global stability of the pile and the passive soil wedge. According to Hetenyi (1946) for the global
stability of the system, the governing equation of Beam on Elastic Foundation (Equation 6) should be
satisfied.
0)()()(
2
2
4
4
!'' yEdx
ydP
dx
ydEI sx
(6)
where, EI is pile stiffness (N. m2), y is pile deflection at depth x (m), x is vertical distance between any
point in soil mass and external borders of soil mass (m), Px is applied axial load at the pile head (N), and
Es is modulus of subgrade reaction (N/m2). On the other hand, local stability is performed by dividing the
soil layer into thin sublayers and the equilibrium of forces acting on each sublayer (slice) should be
satisfied. As shown in Figure 4, the existing loads are horizontal stresses in front of the wedge (#$h), pile
side shear stresses ((), soil-pile reaction forces (p), and the wedge side forces (F). It should be noted that
the wedge side forces are in equilibrium in the normal direction.
Figure 4. Geometry and equilibrium of each sublayer in SWM
B C
P
!"h
F F #m
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile
SEISMIC STRAIN WEDGE MODEL (SSWM)
The Seismic Strain Wedge Model (SSWM) is developed by considering the earthquake horizontal
acceleration (ah) and vertical acceleration (av) at the base of the soil-pile system (Figure 5). Using pseudo-
dynamic method, acceleration at each depth along the pile at particular time can be obtained from
Equations (4) and (5). It is assumed that all the assumptions of SWM are valid in SSWM. Therefore, the
soil medium in the passive wedge represents the soil response to the lateral loads. As shown in Figure 5b,
the soil mass of ith sublayer can be calculated as below:
))(tan(3 xhL m $! )
(7)
ii H
DBCLV )
2
)(3
'! (8)
iii Vm *! (9)
ii HDBC
Lm +,
-./
0 '!
23 (10)
where, L3 is Horizontal length of wedge (m), %m is passive wedge angle (rad), h is depth of passive wedge
(m), Vi is the volume of ith sublayer (m3), BC is front width of the soil wedge (m), D is the pile diameter
(m), Mi is the mass of ith sublayer (kg), and Hi is thickness of the soil sublayer.
Figure 5. Development of Seismic Strain Wedge Model (SSWM)
Using the concept of Horizontal Slice Method (HSM), the additional horizontal force that is generated by
the earthquake in ith layer (Pdhi) is,
ih
dhi Wg
txaP *!
),( (11)
ah (x,t)
av (x,t)
x
av
ah
1
1
3
i
n
H
L3
BC
D
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile
ihidhi WKP *! (12)
where, Khi is seismic acceleration coefficient in horizontal direction, g is acceleration due to gravity, and
Wi is the weight of soil in the wedge at each sublayer (N). As shown in Figure 6, for the equilibrium of the
ith layer, local stability should be satisfied by including the induced earthquake load (Pdhi).
Figure 6. Local equilibrium of a soil-pile sub layer in the presence of seismic loads
The critical condition occurs when Pdhi is in the same direction as the static lateral soil-pile interaction
load (Figure 5) Thus:
dhisii PPP '! (13)
21 2)( DSSBCPihsi (1 '2!
(14)
where, Psi is the static lateral soil-pile interaction load, Pi is the total lateral soil-pile reaction (static plus
seismic), S1 and S2 are pile shape factors, and $hi is the horizontal stress change in passive wedge in front
of pile. Similarly, the additional vertical force induced by the earthquake in the ith sublayer is obtained by:
i
vdvi W
g
txaP *!
),( (15)
ividvi WKP *! (16)
where, Pdv is the vertical seismic force in the ith sublayer (N) and kvi is seismic acceleration coefficient in
vertical directions. As shown in Figure 5, the upward vertical acceleration is the critical direction (this
assumption is explained further in the following section). The upward vertical acceleration, which is
critical, contributes to reduce the soil effective vertical stress as explained below,
3$
!
$!21
1
)(m
i i
dviiimvd
A
PH 41 (17)
3$
! '
'*
$!21
13
3
)2
(
)2
(
)(m
i
iivi
iimvd DBCL
HDBC
LK
H
441 (18)
iivi
m
i
mvd HK 41 )1()(1
1
$!2 3$
!
(19)
where, ($vd)m is the total (static and seismic) effective vertical stress (N/m2). Pseudo-static condition is
occurred when no phase change in the body waves travelling through the soil medium is considered.
Under this condition, accelerations ah(x,t) and av(x,t), in all of the sublayers are assumed to be constant,
thus:
B C
Pdhi
Psi
!"h
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile
ihih
ih
vdhi
vWKW
g
aW
g
txap
ss
!!!5656
)),(
(lim)(lim (20)
33 3$
!
$
!
$
!565656
$!$!$!21
1
1
1
1
1
)1()1(lim)),(
1(lim)(limm
i
iiv
m
i
m
i
iiv
vii
v
vmvd
vHKH
g
aH
g
txa
ppp
4441 (21)
To compare the results of earthquake modelling with pseudo-static and pseudo-dynamic method, a case
study is present. The algorithm of solution with the SSWM and the developed computer code (LAP) is
described in the following section.
LATERAL ANALYSIS OF PILES (LAP) CODE
Lateral Analysis of Piles (LAP) computer code was initially developed by the authors to analyse the
lateral behaviour of single piles and pile groups under static loading (Fakher et al., 2009). LAP allows the
use of different methods such as SWM to analyse piles under lateral static loading (Hokmabadi et al.,
2009). In this study, LAP has been modified to analyse piles under seismic lateral loading using SSWM.
A detailed flowchart of calculation method is presented in Figure 7. The flowchart is a modification of the
original development by Ashour et al. (2004) for SWM.
Figure 7. Flowchart of Seismic Strain Wedge Method for a single pile
Input DATA
Soil static properties (&, ', (50, Su and layer thickness)
Pile Properties (EI, D, L, Targeted deflection, Y0)
Soil dynamic properties (G, !)
Loading (M, L, Px, PT, ah, av)
Dividing soil layers into thin soil sublayers (i)
Assume lateral strain (() in soil in front of the pile,
#t=T/Nt, t= #t
Based on ah, av , and Eq. (4),(5) calculate ah(x,t),
av(x,t) and Pdhi and (#$dv)i at time t
Using the current profile of Es, the laterally loaded
pile is analyzed by Eq. 3 under an arbitrary pile-
head lateral static load (PT). The pile head
deflection (Y0) and h assumed using BEF analysis
are compared to those of the SWM analysis.
IF
(h)SWM = (h)BEF
(Y0)SWM = (Y0) BEF
Final (converged) geometry of the
passive wedge ('m, %m, BC in each soil
sublayer i and h) and the associated (E
and Es profile,Pxt, and Yot) of the pile
NO
STOP
Based on ( (assumed), (50, $vo(Ashour et al. 98)
calculate #$h, SL, 'm, h (assume h in the first trial),
BC, and Es in each sublayer i (i.e. Es profile along
the pile) at #$h = $d and (
IF
Tt 7
TtYY t 77! 0),max( 00
TtPP t 77! 0),max( 00
Yes
NO
Yes
t=t+ t
START
(h)new and (P0i)new
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile
VERIFICATION
In order to verify the SSWM, a centrifuge test results on a single pile carried out by Finn & Gohl (1987)
are used. In the prototype model, a single pile with a diameter of 0.57 meter and a length of 12.9 meter
was subjected to a base motion of the maximum horizontal acceleration of 0.158g, and the pile head
acceleration and the maximum moment along the pile were measured. The pile was embedded in sand
with '=30 degrees, 4 =14.7 kN/m3, and e0=0.78. Details of the test and the prototype model are explained
further by Tabesh (1997).
The above mentioned piles are analysed by LAP including SSWM. Figure 8 presents the results of these
analyses for four set of data including measurement data, Pseudo-Dynamic analysis, Pseudo-Static
analysis, and analysis using SAPAP program performed by Tabesh (1997). As shown in Figure 8, the
results of analysis by LAP using SSWM are in good agreement with the measured maximum moment
along the pile and the location of the maximum point. It should be mentioned that SSWM uses a simple
method to consider the seismic behaviour of the system by including the minimum number of parameters.
Parametric study is performed in order to investigate the affect of base acceleration on the pile head
displacement. Various weights on piles head and different input base acceleration are included in this
parametric study (Figure 9).
Figure 8 Measured and calculated values of maximum moment along the pile
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile
Figure 9. Effect of base acceleration on the pile head displacement using the SSWM
As shown in Figure 9, larger horizontal base acceleration (Kh) causes larger pile head displacement. Based
on Equation (4), when the horizontal base acceleration (Kh) increases, the horizontal seismic acceleration
at each depth at time t increases, resulting in increasing of additional earthquake horizontal force in each
layer (Pdhi) (Equations 11 & 12). Therefore, considering the local equilibrium at each sublayer (Figure 6)
and the governing equation of beam on elastic foundation (Equation 6), increasing of earthquake
horizontal force in each layer (Pdhi) causes larger pile head displacement.
Larger upward vertical base acceleration (Kv) increases the pile head displacement as well. According to
Equation (5), when the vertical base acceleration (Kv) increases, the vertical seismic acceleration at each
depth at the time t increases resulting in the increasing of the additional earthquake horizontal force in
each layer (Pdhi) (Equations 15 & 16). Therefore, according to Equation (19), the soil effective vertical
stresses decrease. Reduction in the soil effective vertical stresses results in decreasing of the springs’
stiffness (soil resistance) against the lateral loading in SWM and increasing of pile head displacement.
However, the influence of the vertical base acceleration on the pile head displacement is less than the
horizontal base acceleration.
CONCLUSION
In this study, a new method called Seismic Strain Wedge Model (SSWM) is proposed for analysing piles
under lateral seismic loads. The main formulation of this method is based on SWM and the additional
Earthquake force is calculated using Pseudo-Dynamic Method. Verification of the model with a case study
shows good agreement between the predictions and laboratory measurements of the maximum moment
along the pile. However, further verifications will be helpful to examine the model to predict the pile head
movement. In addition, according to the parametric study performed to investigate effects of input
earthquake base acceleration on the pile head displacement, larger horizontal base acceleration (Kh) causes
larger pile head displacement. Increasing in the upward vertical base acceleration (Kv) has the similar
influence on the pile head displacement; however, vertical base acceleration has less impact on the pile
head displacement compared to the horizontal base acceleration.
The SSWM approach presented here provides a simple and powerful method for solving the problem of
the seismic analysis of laterally loaded piles. The SSWM overcomes the main drawback of the traditional
p-y approach, which is not considering stress transfer between the springs. In addition, the SSWM can
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile consider the effect of phase difference in seismic travelling through the soil during the earthquake
excitation. It should be noted that input data, required in the SSWM, can be obtained from the basic soil
properties that are typically available to the designers.
REFERENCES
Allotey, N. and El-Naggar M.H. (2008). Generalized dynamic Winkler model for nonlinear soil-structure
interaction analysis, Canadian Geotechnical Journal, 45(4), 460-573.
Ashour, M., Norris, G. and Pilling, P. (1988). Lateral loading of a pile in layered soil using the strain
wedge model, Journal of Geotechnical and Geoenviromental Engineering, 124 (4), ASCE, 303-315.
Ashour, M., Pilling, P. and Norris, G. (2004). Lateral behavior of pile groups in layered soils, Journal of
Geotechnical and Geoenviromental Engineering, 130 (6), ASCE, 580-592.
Banerjee, P.K., Sen, R. and Davies. T.G. (1987). Static and dynamic analysis of axially and laterally
loaded piles and pile Groups. In: Sayed, S.M. (Ed.). Geotechnical Modeling and Applications, 211-
243.
Briaud, J.L. and Tucker, L.M. (1984). Piles in sand: a method including residual stresses, Journal of
Geotechnical Engineering, 110(11), 1666-1680.
Brown, D.A. and Shie, C. (1990). Three dimensional finite element model of laterally loaded piles,
Computers and Structures,10(1), 59-79.
Das, Y.C. and Sargand, S.M. (1999). Forced vibration of laterally loaded piles, International Journal of
Solids and Structures, 36(33), 4975-4989.
Davisson, M.T. and Robinson, K.E. (1965). Bending and Buckling of Partially Embedded Piles, Proc. of
6th International Conference on Soil Mechanics and Foundation Engineering, Canada, 3 (3-6), 243-
246.
El-Naggar, M.H. and Bentley, K.J. (2000). Dynamic analysis for laterally loaded piles and dynamic p-y
curves, Canadian Geotechnical Journal, 37(6), 1166-1183.
Fakher, A., Hokmabadi, A.S. and Saeedi-Azizkandi, A. (2009). Assessment of lateral load-transfer
methods of piles by full scale in-situ tests, Proc. of the 2nd International Conference on New
Developments in Soil Mechanics and Geotechnical Engineering, Nicosia, Cyprus, 230-238.
Finn, W.D. (2005) A study of piles during earthquakes: Issues of design and analysis, Bulletin of
Earthquake Engineering, 3, Springer, 141–234.
Finn, W.D. and Gohl, B. (1987). Centrifuge Model Studies of Piles under simulated earthquake Lateral
Loading, In Dynamic Response of Pile Foundations-Experiment, Analysis, and Observation,
Geotechnical Spec. Publications, 11, ASCE, 21-38.
Gerolymos, N. and Gazetas, G. (2006). Development of Winkler model for static and dynamic response of
caisson foundations with soil and interface nonlinearities, Journal of Soil Dynamic and Earthquake
Engineering, 26(5), ELSEVIER, 363-376.
Hokmabadi, A.S., Seyfi, H. and Fakher, A. (2009). Analysis of single piles under lateral loading using the
Strain Wedge Model, Proc. of the 8th International Congress of Civil Engineering (8ICCE), Shiraz,
Iran.
Idriss, I.M. and Seed, H.B. (1968). Seismic response of horizontal layers, Journal of Soil Mechanics and
Foundations, 94(4), ASCE, 1003-1031.
Kuhlemeyer, R.L. (1979). Static and dynamic laterally loaded floating piles, Journal of Geotechnical
Engineering, 105 (2), ASCE, 289-304.
Nair, K., Gray, H. and Donovanm, C. (1969). Analysis of pile group behaviour, In Performance of deep
foundations, American Society for Testing and Materials, Special Technical Pub. 444, 118-159.
Nimbalker, S.S., Choudhury, D. and Mandal, J.N. (2006). Seismic stability of reinforced-soil wall by
pseudo-dynamic method, Geosynthetics International, 13(3), Thomas Telfords Ltd, 111–119.
5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13
Santiago, Chile Norris, G. and Abdollaholiae, P. (1985). Laterally loaded pile response: studies with the strain wedge
model, State of California, Department of Transportation, Report No. CCEER-85-1.
Nouri, H., Fakher, A. and Jones. C,J.F.P. (2006). Development of horizontal slice method for seismic
stability analysis of reinforced slopes and walls, Geotextiles and Geomembranes, 24(3), ElSEVIER,
175–187.
Novak, M. (1974). Dynamic stiffness and damping of piles, Canadian Geotechnical Journal, 11(4), 574–
598.
Matlock, H. (1970). Correlations for design of laterally loaded piles in soft clay, Proc. of 2nd Annual
Offshore Technology Conference, Dallas, paper OTC-1204, 577–607.
Parmelee, R.A., Penzien, J., Scheffey, C.F., Seed, H.B. and Thiers, G.R. (1964). Seismic effects on
structures supported on piles extending through deep sensitive clays, Institute of Engineering
Research, University of California, Berkeley, Rep.SESM64-2.
Reese, L.C. (1983). Behavior of piles and pile groups under lateral load, Report prepared for the U.S.
department of transportation, Federal Highway Administration, Office of research, Development, and
Technology, Washington, D.C.
Reese, L.C., Cox, W.R. and Koop, F.D. (1974). Analysis of laterally loaded piles in sand, 6th Annual
Offshore Technology Conference, Austin Texas, 2(OTC2080), 473-485.
Shahgholi, M., Fakher, A. and JONES, C.J.F.P. (2001). Horizontal slice method of analysis, Technical
note. Geotechnique, 51 (10), 881-885.
Steedman, R.S. Zeng, X. (1990). The influence of phase on the calculation of pseudo-static earth pressure
on a retaining wall, Geotechnique, 40 (1), 103–112.
Tabesh, A. (1997). Lateral seismic analysis of piles, PhD. Thesis, supervisor: Poulos, G., University of
Sydney, Australia.
Thavaraj, T. (2001). Seismic analysis of pile foundations for bridges, Ph.D. Thesis, University of British
Columbia, Vancouver, B.C., Canada.
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