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DYNAMIC SOIL STRUCTURE INTERACTION ANALYSIS...
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DYNAMIC SOIL STRUCTURE INTERACTION ANALYSIS FOR
AYMMETRICAL BUILDING
by
Pallavi Ravishankar, Neelima Satyam
in
50th INDIAN GEOTECHNICAL CONFERENCE
College of Engineering (Estd. 1854), Pune, India
Report No: IIIT/TR/2015/-1
Centre for Earthquake EngineeringInternational Institute of Information Technology
Hyderabad - 500 032, INDIADecember 2015
50
th
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50th
INDIAN GEOTECHNICAL CONFERENCE
17th
– 19th
DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
DYNAMIC SOIL STRUCTURE INTERACTION ANALYSIS FOR AYMMETRICAL
BUILDING
Pallavi Badry1, Neelima Satyam D.
2
ABSTRACT
All of the civil engineering structures involve some type of structural element which is in direct contact
with soil. To estimate the accurate response of the superstructure it is necessary to consider the response
of the soil supporting the structure and is well explained in the soil structure interaction analysis. Many
attempts have been made to model the SSI problem numerically, but have been found that the soil
nonlinearity, and foundation interfaces, application of boundary element makes analysis more complex
and computationally costlier. To overcome this problem the attempt has been made to optimize the
computational efficiency by applying an equivalent pier method for the deep foundation system. In this
research paper the L-shape 11 storey building supported by a pile foundation with homogeneous local soil
condition is analyzed for dynamic loading including the SSI effect. A new approach has been proposed to
provide simplicity in SSI modeling and reduce the computational cost (memory wise). The approach
includes the applicability of the equivalent pier method for the asymmetrical pile group system, including
SSI effect of the pile foundation system. The approach is validated for group effect and study has been
found that the extended equivalent pile method can successfully be adopted and helps to reduce the
computational cost of SSI problem. The study has been extended to understand the effect of wave
propagation through soil mass. In this regards the SSI analysis has been carried out for different soil
type including cohesive, cohesionless and the combination of both with specific bearing capacity
consideration. It has been observed that the kinematic interaction is governed primarily by bearing
capacity that the soil stiffness.
Keywords: DSSI, Asymmetrical building, Soil pile interaction, Asymmetrical pile group, Equivalent pier
The seismic response of structure is influenced by the medium on which the structure is founded. The
dynamic response of the superstructure founded on the rock is different from soil and even varies with the
soil type and its state at that particular instant. When the interaction effect included in the analysis the
responses of the superstructure is found to more than the fixed base analysis [1,3]. As the asymmetrical
buildings are one of common and unavoidable construction the more attention must be given towards the
precise analysis which included the interaction effect. But once the interaction effect included in the
1PhD student, Geotechnical Engineering laboratory, International Institute of Information Technology, Hyderabad, INDIA,
[email protected] 2Assistant Professor , Geotechnical Engineering laboratory, International Institute of Information Technology, Hyderabad,
INDIA, [email protected]
Pallavi Badry & Neelima Satyam D.
numerical analysis the modeling becomes very complex and the time of analysis also increases
exponentially due to consideration of soil element and up to the infinite domain.
Thus, it is significantly needed to suggest the approach which simplifies the modeling of SSI system and
reduce the time of analysis. This study aimed to suggest the approach for reducing the complexity in SSI
modeling and reducing the analysis time by implementing the Equivalent Pier Method (EPM) for the
asymmetrical building supported by piles.
The finite element program developed for the DSSI analysis includes the two types of finite elements viz.
2 noded 3-D beam elements and 3-D 8 noded brick element. In the present study the soil structure
interaction analysis for asymmetrical building has been considered for a homogenous soil condition.
The DSSI model has been reduced by using the Equivalent Pier Methodology suggested by Paulos &
Davis (1980). In this method, the pile group is replaced by a pier of similar length to the piles in the group
and with an equivalent diameter (Deq), estimated as follows [13]. The responses of the superstructure
have been compared to the Equivalent Pier Model and General pile layout system for the applied Bhuj
(2001) Ground motion (Fig.2). The responses have been checked for the different soil type conditions
including cohesive and non cohesive soil with the various bearing capacity values.
Fig. 2 Floor wise response comparison for
EPM and General pile layout system under dynamic loading in X,Y and Z direction
The study concluded that the complexity in modeling the integrated soil structure problem has been
reduced with considerable extent. It has been observed that the time required to get the solution is reduced
to 68 % for all EPM configuration than the general pile layout, the EPM approach is satisfactory for the
SSI problems where the numerical cost and CPU memory is required very high.
The peak displacement varies w.r.t the soil type since the material properties of the soil, including
Young’s modulus, Poisson’s ratio contributes to the response. In the S1soil (Ø soil) the response is lesser
as Young’s modulus and bearing capacity are much more than the soil type S3 (C soil S3). Hence the soil
having more bearing capacity gives lesser displacement values. From this the study concludes that the
responses of the superstructure govern primarily by the bearing capacity of the supporting strata than its
young’s modulus.
50
th
IG
C
50th
INDIAN GEOTECHNICAL CONFERENCE
17th
– 19th
DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
DYNAMIC SOIL STRUCTURE INTERACTION ANALYSIS FOR
AYMMETRICAL BUILDING
Pallavi Badry1 , PhD Student, International Institute of Information Technology,
Neelima satyam D. 2, Assistant Professor, Institute of Information Technology, [email protected]
ABSTRACT: All of the civil engineering structures involve some type of structural element which is in direct
contact with soil. To estimate the accurate response of the superstructure it is necessary to consider the response of
the soil supporting the structure and is well explained in the soil structure interaction analysis. Many attempts have
been made to model the SSI problem numerically, but have been found that the soil nonlinearity, and foundation
interfaces, application of boundary element makes analysis more complex and computationally costlier. To
overcome this problem the attempt has been made to optimize the computational efficiency by applying an
equivalent pier method for the deep foundation system. In this research paper the L-shape 11 storey building
supported by a pile foundation with homogeneous local soil condition is analyzed for dynamic loading including
the SSI effect. A new approach has been proposed to provide simplicity in SSI modeling and reduce the
computational cost (memory wise). The approach includes the applicability of the equivalent pier method for the
asymmetrical pile group system, including SSI effect of the pile foundation system. The approach is validated for
group effect and study has been found that the extended equivalent pile method. The evaluated that EPM method
can successfully be adopted and helps to reduce the computational cost of SSI problem.
The study has been extended to understand the effect of wave propagation through soil mass. In this regards the
SSI analysis has been carried out for different soil type including cohesive, Cohisionless and the combination of
both with specific bearing capacity consideration. It has been observed that the kinematic interaction is governed
primarily by bearing capacity that the soil stiffness.
INTRODUCTION
The seismic response of structure is influenced
by the medium on which the structure is founded.
The dynamic response of the superstructure
founded on the rock is different from soil and
even varies with the soil type and its state at that
particular instant. When the interaction effect
included in the analysis the responses of the
superstructure is found to more than the fixed
base analysis [1].
Thus, it is highly recommended that, the effect of
soil structure interaction is needed to consider in
the analysis in order to get the more precise
response of the superstructure. In Soil structure
Interaction (SSI) analysis the structural response
is governed by the interplay between the
characteristics of the soil, the structure and the
input motion. It determines the actual loading
experienced by the soil–structure system
resulting from the free-field seismic ground
motions. According to Chandler et al. (2010),
Mid-rise buildings are aggregations of dwelling
buildings ranging from 5 to 15 stories [17]. With
respect to this definition, to cover this range the
G +10 pile supported L-shape R.C.C. building is
considered .The initial configuration of the pile is
decided depending upon the critical load case of
earthquake and frame gravity load. The selected
span width conforms to architectural norms and
construction practices of the conventional
buildings in mega cities.
BACKGROUND
Pallavi Badry & Neelima Satyam D.
Seismic damage surveys and analyses conducted
on modes of failure of building structures during
past, severe earthquakes concluded that most
vulnerable building structures are those, which
are asymmetric in nature. However, the
destruction of numerous asymmetric buildings in
the 1985 Mexico earthquake made researchers
focus on soil–structure interaction effects and on
the response behavior of such systems [1]. So
far, several researchers have attempted to
incorporate the flexibility of foundation in
asymmetric system models. Among them,
Balendra (1982) used simple springs to represent
frequency-independent values and to
approximate the frequency-dependent foundation
impedance functions in an asymmetric multistory
building [17]. Subsequently Tsicnias and
Hutchinson (1985) extensively investigated the
steady-state response of flexibility supported
torsionally coupled buildings subjected to
harmonic ground motions by using frequency-
independent springs and dashpots [5].
The response of the asymmetrical building has
been investigated by Lin (2009) and Olariu
(Olariu 2014) by analytical approaches like
arithmetic sum method and spectral acceleration
method to understand the behavior of shallow
foundation by incorporating the interaction effect
by spring and dashpot [20,2]. Mason (Mason
2013) and Bui (2014) carried out the
experimental study with scaled down model of
the asymmetrical dwarf building to study the soil
structure interaction effect on the structural
response under earthquake [6]. Still the
approaches not extended for the pile supported
asymmetrical buildings. Chopra and Gutierres
(1978) highlighted out that the numerical
methods are most appropriate and accurate
methods for soil structure interaction analysis
[1]. Followed by this several researchers,
including Wegner, Yao and Bhullar (2009),
Maridan and Tsai (2009), Sharma and Pandey,
(2011) carried out the study for SSI analysis of
the asymmetrical building supported by the
isolated, raft and shallow foundation system by
considering the 3-D and the 2-D nonlinear
analysis [14,11,17]. Venkatesh (2012), Yigit
(2013), Tehrani and Khoshnoudian (2014),
Isbiliroglu and Taborda ( 2014), Irfan (2014)
attempted to analyze the nonlinear dynamic SSI
system of an asymmetrical building supported by
shallow foundation and effect of interaction has
been modeled by the spring and dashpot
[17,12,16]. As the asymmetrical buildings are
one of common and unavoidable construction the
more attention must be given towards the precise
analysis which included the interaction effect.
But once the interaction effect included in the
numerical analysis the modeling becomes very
complex and the time of analysis also increases
exponentially due to consideration of soil
element and up to the infinite domain.
Thus, it is significantly needed to suggest the
approach which simplifies the modeling of SSI
system and reduce the time of analysis. This
study aimed to suggest the approach for reducing
the complexity in SSI modeling and reducing the
analysis time by implementing the Equivalent
Pier Method (EPM) for the asymmetrical
building supported by piles.
METHODS FOR ESTIMATION
SETTLEMENT OF PILE GROUP
Many methods have been presented in the
literature for estimating the settlement of pile
foundations, ranging from empirical methods,
through simple hand calculation methods, to
sophisticated numerical finite element and finite
difference analyses. The importance of
appropriate estimation of Geotechnical
parameters will be emphasized, and finally, it
will be demonstrated that misleading results can
arise from the imprudent application of group
settlement analysis. In this way, an attempt will
be made to narrow some of the gaps that have
developed between research and practice.
The soil pile interaction effect can be
implemented with more preciseness in equivalent
pier method than the other empirical methods
(Paulos, 1983). Thus, in the present study the
dynamic dipacement of pile group and
superstructure has been estimated by reducing
the pile group in to single pier of equivalent
stiffness.
50
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50th
INDIAN GEOTECHNICAL CONFERENCE
17th
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DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
DSSI MODEL OF T-SHAPE
ASYMETRICAL BUILDING
In the present study the finite element program
using C++ has been developed to analyze the SSI
system. The Program can perform nonlinear
static and dynamic analysis, including node to
node contacts. The input need to be provided
through the text files in the specified format. The
program takes the input, including geometry, i.e.
nodes and elements, contact information,
boundary conditions, material data, constraints
and Load data with respect to the DOFs.
The program produces nodal displacement,
element stresses at integration points as output.
All required output data has been created in the
text files. The program also produces binary files
in LS-PP format for creating the evectional and
sectional views.
The modeling of the DSSI system for G+10 L-
shape a symmetrical building with generalized
pile layout has been explained in detail. The
finite element program developed for the DSSI
analysis includes the two types of finite elements
viz. 2 noded 3-D beam elements and 3-D 8
noded brick element. In the present study the
soil structure interaction analysis for
asymmetrical building has been considered for a
homogenous soil condition. Table 1 explains the
engineering properties of the various modeling
parameters of superstructure, soil and the piles
and interface/contact considered.
Table 1 Engineering properties of soil and
structure considered
Soil
type
Uni
t
Wt.
(kN
/m3)
Fric
tion
ang
le,
(0)
Pois
son’
s
Rati
o
E
(kN/m2
)
Vs
(m/s)
sand 18 35 0.35 445,87
2
300
Super
structu
24 0 0.15 2.0x
107
120
0
re
Pile 24 0 0.15 2.0x
107
120
0
Raft 24 0 0.15 2.0x
107
120
0
Materi
al
model
parame
ters
Poisson’s
ratio =
0.35
Friction angle = 35°
Interfa
ce data
Friction angle (δ)= 1/3 ɸ' = 11.4°
The G+10 superstructure components, including
beams and column have been modeled with 2
noded 3-D beam elements. The joints between
beam and column are considered to be rigid. The
connection between the raft and first storey
column is modeled as the rigid connections. Half
space of size 20 x 20 x 20 m is modeled using as
sandy silt and the engineering properties of the
soil domain has been explained in detail in Table
1. The nonlinear behavior of the supporting soil
is captured using Drucker –Prager material
model.
The 0.5 m thick L-shape raft with the 1.0 m
offset from all the sides of the base of the
superstructure have been modeled with the 3-D
brick elements. The circular piles with 0.45 m
and 9.0 m length have been modeled with the 3-
D brick elements. The L-shape layout of piles
accommodates the 21 piles spaced at 1.5 m c/c.
The joints between the raft and pile have been
modeled with the rigid contacts. The meshing of
the finite element model has been created by
using GSA 2-D mesher.
The SSI effect has been incorporated in the
analysis by modeling the interfaces between soil
and pile and viscous boundary soil mass
considered. The finite element model of L-shape
SSI system developed to understand the coupled
response of the soil and structure is shown in
figure 1.
Pallavi Badry & Neelima Satyam D.
a. Plan b. Isometric view c. Meshed
model
Fig. 1 General finite element model for G + 10
building for DSSI
The interface between the pile and soil has been
modeled as a node to the node friction contact
using Lagrange multiplier method. These
interface elements replicated the penetration and
sliding effect under loading. All four sides of the
sole domain has been modeled with the viscous
boundary where the nodes of the extreme
elements provided with the extra force which is
equal to the force estimated at the of each time
step to nullify the forces at the node. The bottom
element of the soil domain is considered with the
earthquake boundaries which provide the
displacement in the same direction of earthquake
given in the analysis and the rest of the DOF of
the elements will be assigned as zero. In present
study E-W (x-direction) component of Bhuj
earthquake (2001, 0.31g) has been given to study
the response of SSI system. The finite element
model of the SSI system is given
SEISMIC ANALYSIS OF SSI SYSTEM
The model is analyzed for both static and
dynamic loading conditions. Initially the SSI
system is analyzed for static load in order to get
the initial stress condition which includes the self
weight of the superstructure and the foundation
system. The static analysis has been carried out
by applying the fixed boundary condition in
normal direction i.e. constraining the
displacements only in the normal direction to
surface to the nodes of the extreme element of
the soil volume considered.
The stresses and displacement so obtained at the
end of static analysis has been considered as the
initial response for the dynamic analysis. The
2001 Bhuj ground motion (PGA= 0.31G, E-W)
has been applied at the bottom nodes of the soil
domain and the analysis has been carried out for
the peak response which lies in the 15 Sec (Fig.
2).
Fig. 2 Bhuj ground motion and Part of
ground motion considered for study
FE MODEL OF SSI SYSTEM USING
EQUIVALENT PIER METHOD
The dynamic soil structure interaction problem is
a very huge size problem as includes the
structure elements, foundation elements and
supporting soil domain which need to extend in
all 3 directions depending upon the base size of
the structure and the depth of deep foundation
system to avoid the effect of wave reflection.
Thus, there is tremendous need to reduce the
interaction problem to optimize the
computational cost, efforts, accuracy in results
and reality in the model simulation.
In the present study, an attempt has been made to
reduce the computational cost by applying an
equivalent pier method for the existing pile group
of the structure and interfaces has been applied to
the equivalent pile which gives the ease in the
modeling of the huge domain problem.
THEORY OF EQUIVALENT PIER
METHOD
Paulos & Davis (1980) proposed an Equivalent
Pier method for heavy and large superstructures
where a large pile group needs to analyze.
Horikoshi & Randolf (1999) adopted this method
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17th
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to find out the settlement analysis for the huge
pile group [13]. In this method the pile groups as
a whole pier to simplify the procedure for
estimating the settlement of pile groups which
equals that of single pile by means of load-
transfer functions. In this method, the pile group
is replaced by a pier of similar length to the piles
in the group (Fig. 3), and with an equivalent
diameter (Deq), estimated as follows (Poulos,
1993).
Fig. 3 Concept of equivalent pier method
The diameter of the equivalent pier is given by
the following equation
or (1)
Where, Ag plan area of pile group, including the
soil between the piles.
The lower value in Eq.1 is more relevant to
predominantly end bearing piles, while the
largest value is more applicable to predominantly
friction or floating piles.
As in equivalent pier includes the soil entrapped
in the pile spacing it is needed to modify the
Young’s modulus in the analysis. The Young’s
modulus of the equivalent pier is given by the
following formula
(2)
Where, Ep is the Young’s modulus of the pile,
Es is the Young’s modulus of the soil
penetrated by the piles
Anp is the total cross sectional area of the
piles in a group
Ag is the plan area of pile group,
including the soil between the piles.
Poulos (1993) and Randolph (1994) have
examined the accuracy of the equivalent pier
method for predicting group settlements, and
have concluded that it gives good results [13].
Poulos (1993) has examined group settlement as
a function of the number of piles, for a group of
end bearing piles. Solutions from the computer
program DEFPIG, the equivalent raft method and
the equivalent pier methods were compared, and
for more than about 9 piles, the settlements given
by all three methods agreed reasonably well.
Thus the applicability of EPM has been validated
for the symmetric pile group, but there is no
attempt has been made for the asymmetrical pile
group.
In the present study the entire pile group is
replaced by the single equivalent pier of with
equivalent diameter and stiffness (Table 2).
Table 2 Details of an equivalent pier (EPM)
configurations considered in the study
Deq
(m)
Es
(kN/m2
)
Eeq
(kN/m2)
Location
(x,y) (m,m)
5.8 445872 3.67 x 106 (2.5,2.5)
The finite element model has been developed by
taking the engineering properties associated with
the equivalent pier for the same configuration of
superstructure and soil type (Fig.4).
Fig. 4 Finite element model for different EPM
configuration.
RESULTS
Lp
Eeq , Aeq
Eeq, Deq
Pallavi Badry & Neelima Satyam D.
The G+10 R.C.C. L-shape asymmetrical building
supported by the pile foundation system in a
homogenous soil strata analyzed for Bhuj ground
motion (2001, PGA =0.31g). The results are
estimated with the view of the applicability of
the Equivalent Pier Method to reduce the
computational efforts and the complexity in
modeling, effect of the supporting soil type on
the superstructure response. The preceding
sections explain the analysis results with
considering each issue independently.
Response of building, including SSI for
general pile layout
The response of the system, including
superstructure and foundation system has been
estimated for a general pile layout at the different
corners of the building. The figure shows the X,
Y and Z direction response obtained at the
leftmost corner of the L layout for the general
pile system (Fig. 5).
Fig. 5 Superstructure response for general pile
system.
The effect of EPM on building response
In the present study the existing pile group is
replaced by the equivalent pier with modified
diameter and the modulus of elasticity (Table 2).
The method is good enough for the symmetric
pile group but need to extend its applicability in
an asymmetrical pile group. The displacements
obtained at each storey level and at different pile
locations are compared with the response
obtained from the general pile configuration. In
finite element model the interaction effect is
included by introducing the interfaces at pile soil
nodes and structure raft location.
The CPU time required to obtain the converged
nonlinear dynamic solution has been noted for
each EPM and general pile system to check the
numerical expense lies with each model. The
Figure 6 shows the comparative storey wise
response obtained responses of superstructure
obtained for the general pile layout and EPM
system in X, Y and Z direction.
Fig. 6 Floor wise response comparison for
EPM and General pile layout system under
dynamic loading in X,Y and Z direction
The numerical adaptability of the proposed
approach for soil structure interaction of the pile
supported building has been checked by
measuring the CPU running time to get the
converged solution. The table 3 and 4 shows the
quantitative metric for each configuration to
understand the numerical expense lies with each
model in details.
Table 3 Peak response at the top of
superstructure for different EPM configuration
Configuration
Gen
EPM
Percentage
deviation
(%)
X-Disp. (cm) 6.29 6.16 2.09
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Y-Disp. (cm) 4.91 3.72 19.58
Z -Disp. (cm) 8.87 9.13 -2.89
Table 4: Expense comparison
Numerical attributes General EPM
Dof s 73,927 30,653
Element 22515 8872
No. of Nodes 24665 10227
No. of Nodes in
Contact 1505 328
Least element size in
FE model (m) 0.11 0.15
Critical time step
taken (Sec.) 5 x 10
-5 8 x 10
-5
CPU time to get the
response (Hrs) 51.17 15.35
The study has been further extended to
understand wave propagation in the soil mass
which shows the kinematic interaction in the
system. In this regards in the present study the
effect of different soil, including Sandy soil (S1),
Sandy clay (S2) and clay (S3) on the G+10
building response to L shape supported by the
pile group has been estimated.
the bearing capacity has been assumed with the
recommendations given by the IS IS 1904-1978
for the type of soils which has been used in the
analysis of the parametric study (Table 5).
Table 5 Engineering properties of the soil
considered for parametric study.
Soil
Type
Young’s
Modulus
(kN/m2)
,
Density
(kN/m3)
Shear
wave
velocity
(m/s)
Angle of
friction
(°),Cohesion
(kN/m2)
Bearing
capacity
(kN/m2)
S1 645,872
; 20
300 42, 0 240
S2 545,872
;20
200 30, 20 350
S3 445,872
; 18
100 0, 30 150
The displacements in X directions for top floor
of the superstructure have been compared for
each type of soil type for T shape structure in
order to study the influence of soil type on the
behavior of the superstructure (Fig.7).
Fig. 7: Displacement time history of various soil
types in X direction of T- Shape building at the
top storey
CONCLUSIONS AND DISUSSIONS
The soil structure analysis is complex research
problem and need much computational capability
and time. Especially in direct method it is
essential to model superstructure and foundation
along with the soil half space, in such case the
analysis become very numerically expensive and
sometimes the solution goes out of the bond of
the computer memory. Another challenge lies
with the complexity in SSI modeling. To
overcome this complication present research
work, an attempt has been made to reduce the
size of the problem numerically by applying the
Equivalent Pier Method for the existing pile
group. With this the no. of piles get reduced and
the time of computation and the complexity in
modeling has been reduced.
Pallavi Badry & Neelima Satyam D.
The Dynamic soil structure analysis has been
carried out and following are the conclusions
drawn from the present study.
Applicability of EPM for asymmetrical pile
group
The pile group has been reduced to 4 different
configurations by dividing the asymmetrical area
into multiple symmetrical areas. For each EPM
configuration the response of the superstructure
including interaction effect has been estimated at
each floor level. The displacement in X, Y and Z
directions have been estimated for all EPM
models.
It has been found than superstructure responses
in X and Z directions are found to have good
agreement with the responses of the
superstructure with general pile configuration
with the deviation of +-2%.
Coming to the Y direction response the deviation
in responses for EPM and general pile layout is
observed at 20%. Thus, this EPM configuration
is found to be more conservative as compared to
the general pile layout system configuration and
thus promises the more safety of the structure
during earthquakes.
Effect of Complexity and Numerical Expense
It has been observed that the no. of contact nodes
has been greatly reduced from 1505 to 328 which
gives the measure of reducing the complexity
and time reduction in iterating the contact
displacements. This is found to be the countable
advantage to EPM approach.
The no. of elements and DOFs are the key
parameters which impacts the numerical cost. In
EPM approach the no. of elements reduces to
8872 from 22,515 and DOF s reduces 30,653
from 73,000 which prove the numerical
efficiency of the approach.
In this study the solution has been obtained by
the explicit solver where the time step is needed
to be taken very small and depends upon the least
element size in the finite element model. In EPM
approach the equivalent piers gives the larger
diameter, which gives the bigger size elements
after mashing. This facilitates to take the larger
time step which is one of the prime factors which
reduces the solution time.
In general pile layout the critical time step is
needed to be taken as 5 x 10 -5
sec. For the 0.11 m
element size of the pile (with pile dia 0.45 m)
which is average least element size in models.
When the dynamic load (duration 15 Sec.)
applied to the system the solution obtained is in
51 hours for the general pile configuration. But
when the EPM configuration facilitates to take
critical time step 8 x 10 -5
sec as the minimum
element size is found to 1.5 m (where the
equivalent diameter is 5.0 m), thus gives the
results in average 15 hours for the same dynamic
loading duration. Thus, all EPM configurations
give the solution in quicker than the original pile
layout which proves the EPM is one of the
reliable approaches which reduces the analysis
time of the huge size problem like SSI.
It has been observed that the time required to get
the solution is reduced to 68 % for all EPM
configuration than the general pile layout, the
EPM approach is satisfactory for the SSI
problems where the numerical cost and CPU
memory is required very high.
Effect of supporting soil type
In dynamic analysis the propagation of the wave
and the attenuation effect of the wave amplitude
when it travels through the solid media plays
important role in transferring the vibration to the
structure.
In the present study among the three types of soil
considered as the supporting stratum the soil type
S3 (C soil) shows more transfer of vibration to
the superstructure than the S2 (C- Ø) and S1 (Ø)
respectively. Thus the floor wise peak
displacement values are found to be more in case
of soil type S3 as a supporting strata than the
other two types of soil S1 and S2. It has been
observed that the % difference in the peak
displacement values lies in the range of 12 to 15
%.
The peak displacement varies w.r.t the soil type
since the material properties of the soil, including
Young’s modulus, Poisson’s ratio contributes to
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INDIAN GEOTECHNICAL CONFERENCE
17th
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DECEMBER 2015, Pune, Maharashtra, India
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the response. The Young’s modulus which
governs the strength of soil also contribution has
more effect on the superstructure response. In the
S1soil (Ø soil) the response is lesser as Young’s
modulus and bearing capacity are much more
than the soil type S3 (C soil S3). But it has been
observed that though Young’s modulus of soil
type S2 (C-Ø soil) is lesser than S1 (Ø soil ), the
responses of the superstructure with supporting
soil condition than that of the soil type S2 (Ø) is
lesser than S1. The reason for this is the bearing
capacity of the strata. Thus the soil type S2 has
more bearing capacity than soil type S1 and S3.
Hence the soil having more bearing capacity
gives lesser displacement values. From this the
study concludes that the responses of the
superstructure govern primarily by the bearing
capacity of the supporting strata than its young’s
modulus.
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