Response of low-rise buildings under seismic ground excitation
incorporating soil–structure interaction
Sekhar Chandra Duttaa,*, Koushik Bhattacharyaa, Rana Royb
aDepartment of Civil Engineering, Bengal Engineering College (D. U.), Howrah 711 103, West Bengal, IndiabDepartment of Applied Mechanics, Bengal Engineering College (D. U.), Howrah 711 103, West Bengal, India
Accepted 2 July 2004
Abstract
In the conventional design, buildings are generally considered to be fixed at their bases. In reality, flexibility of the supporting soil medium
allows some movement of the foundation. This decreases the overall stiffness of the building frames resulting in a subsequent increase in the
natural periods of the system and the overall response is altered. The present study considers low-rise building frames resting on shallow
foundations, viz. isolated and grid foundation. Influence of soil–structure interaction on elastic and inelastic range responses of such building
frames due to seismic excitations has been examined in details. Representative acceleration–time histories such as artificially generated
earthquake history compatible with design spectrum, ground motion recorded during real earthquake and idealized near-fault ground motion,
have been used to analyze the response. Variation in response due to different influential parameters regulating the effect of soil-flexibility is
presented and interpreted physically. The study shows that the effect of soil–structure interaction may considerably increase such response at
least for low-rise stiff structural system.
q 2004 Elsevier Ltd. All rights reserved.
Keywords: Seismic response; Ground motion; Low-rise buildings; Soil–structure interaction; Isolated footing; Grid foundation
1. Introduction
The common design practice for dynamic loading
assumes the building frames to be fixed at their bases. In
reality, supporting soil medium allows movement to some
extent due to its natural ability to deform. This may decrease
the overall stiffness of the structural system and hence, may
increase the natural periods of the system. Such influence of
partial fixity of structures at the foundation level due to soil-
flexibility in turn alters the response. On the other hand, the
extent of fixity offered by soil at the base of the structure
depends on the load transferred from the structure to the soil
as the same decides the type and size of foundation to be
provided. Such an interdependent behaviour between soil
and structure regulating the overall response is referred to as
0267-7261/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.soildyn.2004.07.001
* Corresponding author. Address: Department of Civil Engineering,
Bengal Engineering College, Deemed University, Howrah 711 103, West
Bengal, India. Tel.: C91-33-668-4561; fax: C91-33-668-2916.
E-mail address: [email protected] (S.C. Dutta).
soil structure interaction in the present study. In this context,
a critical examination of the response spectrum curve
reveals that the spectral acceleration may change consider-
ably with change in natural period. So, such increase in
lateral natural period may considerably alter the response of
the building frames under seismic excitation. Such possi-
bility is highlighted through a very limited number of case
studies in a few earlier research works [1,2]. In case of high-
rise structures, i.e. for flexible systems, lateral natural period
is expected to lie in the long period region of the response
spectrum curve. Hence, the response is generally expected
to get reduced due to an increase in lateral natural period for
such systems. Thus, it is believed that the conventional
practice of ignoring the effect of soil-flexibility in the
process of design may lead to a conservative one. However,
for low-rise buildings, generally, the lateral natural period is
very small and may lie within the sharply increasing zone of
response spectrum. Hence, an increase in lateral natural
period due to the effect of soil–structure interaction may
cause an increase in the spectral acceleration ordinate.
Soil Dynamics and Earthquake Engineering 24 (2004) 893–914
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S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914894
Moreover, due to the effect of soil-flexibility, various
natural frequencies may space closer leading to an increase
in cross-modal coupling terms contributing to the overall
seismic response. Thus, the effect of soil–structure inter-
action on the dynamic characteristics, at least for low-rise
buildings, may be of major concern. The aim of the present
study is to observe the effect of the same on seismic
response of buildings under three typical kinds of ground
motions viz. (a) two uncorrelated artificially generated
earthquake time histories consistent with the design
spectrum of Indian earthquake code [3], (b) one recorded
earthquake history and (c) idealized near-fault-ground
motion. Efforts have earlier been directed to study the
seismic behaviour of multistoried building frames. For
instance, a recent revealing investigation [4] has focused on
the behaviour of a six storey and a 20-storey building with
steel moment resisting frame. An exhaustive list of the same
is available in NEHRP Recommended Provisions for the
Development of Seismic Regulations for New Buildings
[5]. However, the present effort has its significance in
incorporating the effect of soil–structure interaction par-
ticularly on low-rise building frames in its real three-
dimensional form. Furthermore, a wide variety of such
buildings are included in the scope of the study through a
systematic and detailed parametric variation to comprehend
the influence of soil–structure interaction and evaluate
seismic base shear realistically.
It is customary to design the structures so that they
behave inelastically during strong ground shaking. Thus, it
is also interesting and necessary to examine the behaviour of
the structural system in the inelastic range of loading
accounting for the effect of soil–structure interaction.
Ductility demand and hysteretic energy demand are two
crucial parameters to measure the inelastic range response
of the load-resisting structural elements. Hence, an attempt
has been made in the present paper to see the influence of
soil–structure interaction on such demands. Idealized single
storey systems with elasto-plastic material characteristics
has been analyzed under the ground motions mentioned
earlier. Such systems have been considered to rest on
different representative soil medium. Outcome of such
endeavour points out the need of accounting for the effect of
soil-flexibility for realistic assessment of the inelastic range
behaviour of the structural system.
1.1. Idealization of the system
1.1.1. Structural idealization
Two nodded frame elements along with four nodded
plate elements with appropriate dimensions obtained using
standard design are used to model three-dimensional space
frames. During seismic excitations, owing to the lateral
loading at floor levels, building frames experience in-plane
lateral sway deformation parallel to the direction of the
force. The brick in-fill within the panel tends to resist this
deformation offering enough stiffness against the shortening
along one of the diagonals and thus, effectively behaves like
a compressive strut. This attributes significant additional
lateral stiffness to the buildings [6,7] and changes the shear
distribution [8]. To incorporate this additional stiffening
effect in the building frames, ‘equivalent strut approach’
[6,7] has been used in the present study. The dimensions and
properties of these diagonally placed equivalent compres-
sive struts have been chosen from the literatures [6,7,9] to
simulate the effect of the brick walls. However, at the
locations of openings, the stiffness due to brick in-fill is not
expected. But, at the same time, the frame and panel of
windows/doors may provide a substantial amount of
stiffness, which may compensate for the stiffness contri-
bution of the brick in-fill if it were at the openings. It is
difficult to assert, without case specific detailed investi-
gation, as regard to the extent of such complimentary
contribution in real situations as the same may depend on
many factors such as size of panel, orientation of grillage,
material used etc. Hence, the equivalent struts to represent
the action of brick in-fill walls have been considered even at
the locations of openings as a fair compromise between
rigor and simplicity. Such idealization has been presented
schematically in Fig. 1a and b for a typical low-rise building
frame. All the building frames are analyzed with and
without tie beams. In reality, tie beams, placed in the form
of grids connecting the columns at the plinth level
strengthen the column members by reducing the effective
length of the same and the lateral stiffness of the structure is
increased. This also helps to transfer the wall load of the
ground storey to the column. The same has been modeled by
two-nodded frame elements. Further details of structural
idealization are available elsewhere [10,11].
To analyze the inelastic range behaviour, structure has
been idealized as rigid diaphragm model with three degrees
of freedom at each floor level, two translations in two
mutually perpendicular directions and one in-plane rotation
as shown in Fig. 1c. Mass is assumed to be concentrated at
the floor level and the load-resisting elements connecting
the floors contribute to the stiffness only. In domestic
regular buildings, load-resisting structural members are
often distributed over its plan uniformly. Thus, in the
present study, six element system [12] has been adopted to
represent such stiffness distribution (Fig. 1d). Fifty percent
of the total lateral stiffness has been distributed equally
between the two edge elements, whilst the rest is assigned to
the middle element. Similar systems have been adopted in
many other previous studies perhaps because of its
capability to represent realistic stiffness distribution
[13,14]. A bilinear elasto-plastic hysteresis model has
been utilized to analyze the inelastic behaviour of the
structural system. Single storey systems with various
periods representative of one, two and three storey building
frames have been considered. Strength has been attributed,
in all cases, in proportion to the stiffness considering a
feasible range of variation of response reduction factor.
Fig. 1. Idealization of structure. (a) Typical low-rise building with brick in-fill, (b) Idealized representation of low-rise building used to analyze elastic range
behaviour. (c) Idealized representation of low-rise building used to analyze inelastic range behaviour. (d) Plan view showing stiffness distribution.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 895
1.1.2. Idealization of Soil
Impedance functions associated with rigid massless
foundations are utilized to incorporate the effect of soil–
structure interaction in the analysis. Sizes of the footings are
first determined on the basis of allowable bearing capacity
obtained with various soil properties mentioned in Table 1
[10,11]. The dimension of grid foundation has been arrived
at on the basis of the guidelines prescribed in the literatures
[15,16]. Mass of the foundation so designed has also been
properly incorporated in the analysis through consideration
of consistent mass matrix. Three translational springs, two
in principal horizontal directions and one in vertical,
together with the rotational springs about these mutually
perpendicular axes have been attached below the footings
for buildings with isolated footings. Likewise, the entire
grid foundation is conceived as a combination of a series of
parallel foundation strips oriented in two mutually orthog-
onal directions resting in the same plane. Hence, springs in
all six degrees of freedom have been attached to the
foundation strips at centre of gravity of the same. For better
understanding, such idealization has been schematically
presented in Fig. 2a and b.
Table 1
Details of soil parameters considered as used in [10,11]
Type of clay N value C (kN/m2) f (degree) gsat (kN/m3) Cc e0
Very soft 1 9.8 0.0 13.5 0.279 1.2
Soft 3 18.5 0.0 17.0 0.189 0.90
Medium 6 36.8 0.0 18.5 0.135 0.72
Stiff 12 73.5 0.0 19.4 0.12 0.67
Very stiff 22 147.0 0.0 19.8 0.099 0.60
Hard 30 220.0 0.0 21.0 0.093 0.58
N, C, f, gsat, Cc and e0 denote N value obtained from SPT test, cohesion value, internal friction angle, density in the saturated condition, compression index and
initial void ratio of soil, respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914896
Comprehensive research [17,18,19] has been carried
out to evaluate the stiffness of such springs. Closed form
expressions for such spring stiffnesses as depicted in the
literature [19] have been furnished in Table 2 of the
present paper for the sake of convenience. The same has
been adopted in the present investigation as made in the
earlier studies [10,11]. Values of shear modulus (G) for
different types of soils have been evaluated using
the empirical relationship GZ120N0.8 t/ft2 [20] i.e.
GZ12916692.48N0.8 MPa. Here, N is the number of
blows to be applied in standard penetration test (SPT) of
the soil; and Poisson’s ratio (n) of soil has been assumed
to be equal to 0.5 for all types of clay [21] to evaluate the
stiffness of the equivalent soil springs.
Variation of inertia force with the frequency of the
excitation force may conveniently be accounted through
considering a frequency dependent behaviour of equival-
ent soil springs [19,22]. However, such influence is very
difficult to incorporate in the analysis under real earth-
quake due to the participation of the pulses with wide
frequency range in the same. Hence, such effect is not
generally incorporated in the study. However, the present
study, in the elastic range, examines the influence of such
frequency dependent soil properties for some critical cases
with a view to achieving upper and lower bound
responses. Frequency dependent behaviour of equivalent
soil springs is conveniently accounted by multiplying the
stiffness of the soil springs with a suitable factor expressed
in terms of a0ZuB=Vs [19,22], where u is the frequency
of the forcing function, B is the half of the width of the
footing and Vs is the shear wave velocity in soil medium.
a0 could be determined based on the dominant eigen
frequencies of the structure or based on the dominant
frequency of the earthquake excitation. Consequently, the
present study includes the frequency dependent soil-
flexibility at a0Z0.0 and 1.5 for building frames with
isolated footing. For buildings resting on grid foundation,
three critical cases at a0Z0.0, 0.3 and 1.5 are considered.
These cover the combinations of the highest and the
lowest possible range of variation in stiffnesses of
equivalent soil springs in different degrees of freedom
and hence are expected to yield lower and upper
boundaries of response.
With this idealization of the structure and subgrade
medium, effect of soil–structure interaction on low-rise
building frames has been analyzed in details.
2. Ground motions considered
The effect of soil–structure interaction on elastic and
inelastic range responses of the building frames is studied
under three different types of ground motions. Two
uncorrelated artificially generated earthquake acceleration
histories of PGA 0.1 g are used in the analysis. An average
of the responses obtained from the same is utilized to
understand the general trend in variation. These ground
motions are consistent with design spectrum of an older
version of Indian earthquake code [3]. The simulated
ground motions used in the present study are generated by a
procedure outlined in the literature [23]. This set of ground
motions is referred to as spectrum consistent ground
motions. The target design spectrum and the spectrum
regenerated from one of the ground motions along with the
corresponding acceleration–time history as presented in
some other studies (e.g. Ref. [14]) are reproduced as Fig. 3a.
A close match between two spectra proves that these
spectrum consistent ground motions retain the character-
istics intended through design spectrum. Seismic response
of the structures is also studied under north–south
component of El-Centro earthquake (Peknold version,
1940) having PGA 0.31 g available in the literature [24].
This earthquake data is referred to as El-Centro ground
motion in the rest of the study. The response spectrum
generated from El-Centro ground motion and the corre-
sponding acceleration–time history are shown in Fig. 3b.
The comparison between Fig. 3a and b shows that the
spectrum generated from the El-Centro ground motion has a
flatter peak which continues to about 0.7 s, while for the
spectrum consistent one, the narrower peak region continues
only up to 0.4 s. Moreover, for the El-Centro ground
motion, spectral ordinate decreases slowly to about 70% of
its peak value at a period of 1 s, while rate of decrease is so
sharp for the spectrum consistent artificial ground motion
that the spectral ordinate decreases to even less than 50% of
its peak value at a period of 1 s. This clearly points out that
Fig. 2. Idealization of foundation system. (a) Typical layout of idealized grid foundation system in plan showing spring locations. (b) Arrangement at a typical
column-grid and equivalent soil spring junction idealized in the study.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 897
El-Centro ground motion has stronger domination of short
period pulses of less than 1 s as compared to the spectrum
consistent ground motions considered. In addition to these
two types of ground motions, the effect of soil–structure
interaction on the building frames is also studied under
idealized near-fault ground motions. This is because a few
recent investigations [25–27] point out that the near-fault
ground motions consisting of large duration pulses may
often result in crucial response. These near-fault motions
may be considered to have behaviour like a large single
pulse having very less number of zero crossings. For this
type of ground motions, the ratio of the lateral natural period
(Tx) of the building frames to the duration (T1) of these
pulses is found to be the most crucial parameter to influence
Table 2
Expressions for stiffnesses of equivalent springs along various degrees of freedom as presented elsewhere [19] and used in [10,11]
Degrees of freedom Stiffness of equivalent soil spring
Vertical [2GL/(1Kn)](0.73C1.54c0.75) with cZAb/4L2
Horizontal (lateral direction) [2GL/(2Kn)](2C2.50c0.85) with cZAb/4L2
Horizontal (longitudinal direction) [2GL/(2Kn)](2C2.50c0.85)K[0.2/(0.75Kn)]GL[1K(B/L)]
Rocking (about the longitudinal) [G/(1Kn)] Ibx0.75 (L/B)0.25 [2.4C0.5(B/L)]
Rocking (about the lateral) [3G/(1Kn)] Iby0.75 (L/B)0.15
Torsion 3.5G Ibz0.75 (B/L)0.4(Ibz/B
4)0.2
Ab, area of the foundation considered; B and L, half-width and half-length of a rectangular foundation, respectively; Ibx, Iby, and Ibz, moment of inertia of the
foundation area with respect to longitudinal, lateral and vertical axes, respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914898
the responses. Large duration pulse having Tx/T1 ratio 0.05
is only considered in the present study as the same is
observed to be the most critical in other relevant studies [26,
28,29]. This type of ground motion consists of two distinctly
different nature of pulses, viz. fault-normal and fault-
parallel motion. While fault-parallel ground motion has a
net residual slip; the fault-normal motion has no residual
slip but there is a half-cycle displacement pulse, indicating
momentary opening and closing of the earth in slip region.
Accordingly, the idealized form of the near-fault pulses
considered in the study is chosen following other studies
[26,28,29] and presented in Fig. 3c. This set of ground
motions is referred to as near-fault motion in the rest of the
study. Response under the two sets of near-fault motion is
averaged likewise the cases corresponding to the spectrum
consistent ground motions to recognize the general trend.
3. Method of analysis
Finite element method is adopted to formulate the mass
and stiffness matrices for the building frames. Consistent
mass matrix is used to make the formulation as accurate as
possible. Response under ground motions is obtained from
step by step integration [24]. It is reasonable to consider 5%
of the critical damping for a reinforced concrete buildings at
fixed base condition. Soil damping is calculated following
the guideline prescribed in the literatures [17,22] consider-
ing the contribution of radiation and material damping for
an isolated footing-soil spring vibrating system due to a
feasible range of footing size. This shows that for such an
isolated footing-soil spring system, the overall soil damping
is not more than about 5% of the critical damping for such
system, if the frequency of exciting pulses is not very small.
This is in line with the experimental damping ratio for
coupled sway-rocking of such isolated shallow/surface
foundation (with embedment about half of its least lateral
dimension) and equivalent soil spring system for a number
of cases reported in the literature [30]. Even the compu-
tational value of damping ratio as per Gazetas [19] does not
considerably exceed about 5% for the corresponding cases
[30]. However, it may substantially be increased due to
embedment [19]. Again, the effect of soil-damping will be
further reduced if the effect is considered with respect to
the entire structure foundation-soil spring system instead of
an isolated foundation-equivalent soil spring system as
considered in the previous literatures [18,19,22]. Hence, 5%
of critical damping in each mode of vibration is considered
for all the cases in the present study. To analyze the inelastic
range behaviour, the nonlinear equations of motions for the
structures have been solved in the time domain by
Newmark’s b-g method with modified Newton–Raphson
technique that ensures accuracy at each step and eliminates
cumulative error. Newmark’s parameters are chosen as
bZ0.25 and gZ0.5 to achieve unconditional stability.
Sufficiently small time-step obtained through sample case
studies (not presented) has been used to ensure convergence
for each of the systems considered. Response, in each case,
has been studied with and without considering the effect of
soil-flexibility. The variation in percentage change in base
shear and various inelastic range demands reflecting
damage of load-resisting structural elements are expressed
due to the variation of different influential parameters.
4. Results and discussions
4.1. Elastic range response
Seismic base shear may reflect the seismic lateral
vulnerability in the elastic range and this is considered as
one of the fundamental inputs for seismic design. Hence, this
section presents the variations in base shear due to the effect
of soil–structure interaction under three types of ground
motions considered for the class of building frames specified
incorporating the effect of brick infill. The additional
stiffness due to brick infill makes the structure stiffer. Thus
the overall stiffness of the structural system considerably gets
lessened for the inclusion of soil flexibility through the
introduction of equivalent soil springs in series. This leads to
the appreciable change in response and the same has been
presented graphically as a function of various influential
parameters over a feasible range of their variations. Such
change in response due to the effect of soil-flexibility
compared to the same at fixed-base condition by some
fraction expressed as percentage of the response at fixed-base
condition indicates an increase for positive value of such
quantity and decrease for negative one. The curves
Fig. 3. Ground motions used. (a) Spectrum of simulated ground motion, design spectrum of IS: 1893–1984 corresponding to 5% damping and acceleration–
time history as used elsewhere [12,13]. (b) Response spectrum corresponding to 5% damping and acceleration–time history of El-Centro earthquake, 1940
[24]. (c) Simulated near-fault ground motions in directions (i) parallel and (ii) normal to a strike-slip fault [26].
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 899
corresponding to the frames with tie beams at plinth level are
marked by the word ‘tie’, while those corresponding to the
frames without tie beams are not marked. Similarly, the
variation curves for building frames resting on different soil
types, viz. very soft, soft, medium, stiff and very stiff etc. are
marked with the corresponding soil type. The ratio of column
to beam stiffness is assumed as unity if not stated otherwise.
4.1.1. Effect of variation of clay
The change in base shear due to the effect of soil–
structure interaction is studied on 1, 2 and 4 storied building
frames with isolated footing each having 2 bays in two
mutually perpendicular directions and also for a 4!4 bay 1
storey building frame. These building frames resting on
isolated footing have been analyzed both with and without
Fig. 4. Variation of percentage changes in base shear for building frames with isolated footing under spectrum consistent ground motion.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914900
considering the effect of tie beam. The outcomes of these
analyses have been plotted as percentage change in base
shear versus ‘N’ value of different types of clay. Figs. 4
and 5 present the variation of base shear due to spectrum
consistent, El-Centro and near-fault ground motion,
respectively. Fig. 4 shows that the maximum increase in
base shear due to spectrum consistent ground motions is
around 63% for 4!4 bay 1 storey building frame without tie
beams, while for frames with tie beams, the maximum
increase is merely in the order of 20% for the same building
frame. Correspondingly, from Fig. 5a, it is observed that the
maximum increase in base shear due to El-Centro ground
motion is about 70% for 2!2 bay 1 storey building frame
without tie beams and around 30% for the same building
frame with tie beams. The percentage increase in base shear
due to near fault motion is on the order of 15 and 27 for 2!2
bay 1 storey building frame without and with tie beams,
respectively (Fig. 5b). Out of the exhaustive case studies,
the response of 2!2 bay 1 storey building frame is only
presented as this seems to exhibit the representative trend
and maximum effect due to soil–structure interaction under
El-Centro and near-fault ground motion.
For buildings with grid foundation, 3 storey, 4 storey
and 6 storey building frames each having 4 bays in two
mutually perpendicular directions together with another
6!6 bay 3 storey building frame have been analyzed both
under spectrum consistent and El-Centro ground motions.
To obtain the changes in base shear under near fault
motion due to the changes in ‘N’ values, only the 4!4 bay
3 storey building frame is presented as this exhibits the
maximum effect of soil–structure interaction. These
building frames are considered to be resting on soft,
medium and stiff clay to perceive the trend in behaviour.
This type of foundation is little bit unrealistic for very soft
clay and consequently uneconomic for very stiff clay and
hence not considered in the analysis. Detailed results of
such analysis have been plotted in Figs. 6 and 7a,b to
obtain the changes in base shear due to spectrum
consistent, El-Centro and near fault ground motions,
respectively. Response results corresponding to 4!4 bay
4 storey, 4!4 bay 6 storey and 6!6 bay 3 storey systems
under El-Centro ground motion, though computed, are not
presented for the sake of brevity. The maximum increase in
base shear due to spectrum consistent ground motion is
Fig. 5. Variation of percentage changes in base shear for building frames with isolated footing under (a) El-Centro and (b) near-fault ground motion,
respectively.
Fig. 6. Variation of percentage changes in base shear for building frames with grid foundation under spectrum consistent ground motion.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 901
Fig. 7. Variation of percentage changes in base shear for building frames with grid foundation under (a) El-Centro and (b) near-fault ground motion,
respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914902
around 20% for 4!4 bay 3 storey building frame without
tie beams, while for frames with tie beams, the maximum
change is merely in the order of 12% (Fig. 6). For
El-Centro ground motion, the corresponding maximum
percentage increases are 38 and 3 for building frames
without and with tie beam, respectively (Fig. 7a). The
corresponding changes in base shear due to near fault
motion are very small (Fig. 7b). The frequency of the
pulses in this type of ground motion is too small as
compared to the frequency of the low-rise buildings. Thus,
the tuning between excitation pulse and the natural
frequency is very less. This explains the marginal effect
exhibited by the building frames resting on both isolated as
well as grid foundation due to soil-flexibility. Hence, while
studying the effect of other influential parameters on the
change in response due to the effect of soil–structure
interaction, this ground motion is not used further, in
general.
The results presented in the graphical form clearly point
out the significance of considering the effect of soil-
flexibility while calculating the base shear for particular
building frames under particular ground motions irrespec-
tive of the foundation type. Figs. 4–5 and 6–7 exhibit the
gradually diminishing effect of soil–structure interaction
with increasing hardness of soil for the building frames
resting on isolated and grid foundation, respectively in
maximum number of cases. Both the buildings with isolated
as well as grid foundations exhibit larger increase in base
shear under El-Centro ground motion than that under
spectrum consistent artificial ground motion. This may be,
perhaps, due to the larger content of short period pulses with
periods up to 1 s. The fundamental period of most of the
low-rise buildings remains within this limit even after
lengthening due to soil–structure interaction effect and thus
the fundamental modes are more severely excited under
El-Centro ground motion. Introduction of tie beam gener-
ally reduces the change in seismic base shear.
4.1.2. Effect of variation of number of stories
Out of a large number of cases studied, results for 2!2
bay building frame with isolated footing are presented here
to show the trend of variation with change in the number of
stories. For building frames with isolated footings, the
variation of percentage change in base shear due to
spectrum consistent ground motion is presented in Fig. 8a,
while Fig. 8b exhibits the same under El-Centro ground
motion. It is observed that a maximum of 23% increase in
base shear may occur due to the variation of number of
stories under spectrum consistent ground motion while for
El-Centro ground motion, the similar increase is around
70%. Fig. 9a and b exhibit variation of percentage changes
in base shear due to spectrum consistent and El-Centro
ground motions, respectively as a function of number of
stories for buildings with grid foundations. It is observed
that the increase in base shear for spectrum consistent
ground motion may vary from 18% to 2% for frames
without ties and from 10% to even less than 0% for frames
with ties due to variation of number of stories in building
frames with grid foundation. On the other hand, such
quantity, under El-Centro ground motion, may experience
an increase of about 40% and a decrease of around 20% for
building frames with tie beams.
Figures clearly indicate that the effect of soil–structure
interaction on the change in base shear generally decreases
with increase in number of stories in the building frame.
With the increase in number of storey, the building frame
itself becomes relatively flexible having a lesser stiffness
compared to a similar building frame with lesser number of
stories. If the equivalent soil springs of comparatively less
stiffness is conceived to act in series with less stiffness of
building having large number of stories, the resulting
fractional decrease in overall stiffness is lesser. Further, the
buildings with larger number of stories have a greater
foundation size leading to a larger stiffness of the equivalent
springs representing the soil behaviour. Thus, this factor
Fig. 8. Variation of percentage changes in base shear for building frames with isolated footing under (a) spectrum consistent and (b) El-Centro ground motions,
respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 903
additionally makes the effect of soil–structure interaction in
overall stiffness lesser in buildings with large number of
stories. Hence, change in base shear due to the effect of soil–
structure interaction, is relatively lesser for buildings with
greater number of stories. Building frames with tie beams
exhibit the marginal effect of soil–structure interaction due
to the similar reason. Consideration of tie beam at plinth
level enhances the flexibility of the structure and effectively
transfers the wall load to the footing. This causes an increase
in the size of the foundation and hence effective soil
stiffness. This renders the change in overall response
subdued. The maximum increase in base shear is found to
be higher under El-Centro ground motion keeping harmony
with the earlier observation.
4.1.3. Effect of variation of number of bays
Exhaustive research effort has been made to see the effect
of variation of number of bays on the overall seismic
Fig. 9. Variation of percentage changes in base shear for building frames with grid
respectively.
response of building frames incorporating soil-flexibility.
The change in base shear due to the effect of soil–structure
interaction is found to be the most amplified for buildings
with lesser number of stories. Hence, in the limited scope of
the paper, results corresponding to 1 storey building frame
with isolated footing and 3 storey frame with grid
foundation have been presented to exhibit the maximum
possible effect of soil–structure interaction. For buildings
with isolated footings, number of bay has been shown to be
varied as 1, 2 and 4. The percentage change in base shear as
a function of number of bay due to spectrum consistent
and El-Centro ground motions is presented in Fig. 10a and b
for building frames with isolated footings, while Fig. 11a
and b present the same for frames with grid foundations,
respectively. Fig. 10a and b show that the increase in base
shear due to soil-flexibility compared to the fixed-base
counterparts for frames with isolated footing may vary to
the extent of about 40% and 30%, for the two ground
foundation under (a) spectrum consistent and (b) El-Centro ground motions,
Fig. 10. Variation of percentage changes in base shear for building frames with isolated footing under (a) spectrum consistent and (b) El-Centro ground
motions, respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914904
motions, respectively, due to the change in number of bays
over a range of 1–4. From Fig. 11a and b, it is observed that
for building frames with grid foundation, similar increases
in base shear for spectrum consistent and El-Centro ground
motions are around 15% and 20%, respectively.
4.1.4. Effect of ratio of column to beam stiffness
Ratio of column to beam stiffness is considered to vary
over a practically feasible range of 0.25–4.0 maintaining the
same beam stiffness in two mutually perpendicular direc-
tions. Out of exhaustive case studies, results corresponding
to 2!2 bay 2 storey building frame resting on isolated
footing have been presented to show the trend in behaviour
in Fig. 12a and b for the changes in base shear under
spectrum consistent and El-Centro ground motions, respect-
ively. The figures show that the maximum variation in
Fig. 11. Variation of percentage changes in base shear for building frames with
motions, respectively.
percentage increase in base shear under spectrum consistent
ground motion is around 15% (for frames without tie beam),
while, under El-Centro ground motion, this is around 40%
due to the variation in the ratio of flexural stiffness of the
columns to that of beams for the building frame resting on
isolated footing. In the maximum cases, the effect is
relatively lesser for frames with tie beams. Similar variation
is not more than around 30% for both spectrum consistent
and El-Centro ground motions, respectively, for the
building frame resting on grid foundation (Fig. 13a and b,
respectively).
4.1.5. Effect of frequency on soil-flexibility
To study the influence of the frequency of the excita-
tion force on the overall behaviour of the soil–struc-
ture-foundation system, the present study incorporates
grid foundation under (a) spectrum consistent and (b) El-Centro ground
Fig. 12. Variation of percentage changes in base shear for building frames with isolated footing under (a) spectrum consistent and (b) El-Centro ground motion,
respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 905
the frequency dependent multiplier in the stiffnesses of the
equivalent soil springs for the two critical cases, i.e. a0Z0.0
and 1.5 for buildings with isolated footings as mentioned
earlier. The results of such study have been presented in
Fig. 14a–c for building frames with isolated footings under
spectrum consistent, El-Centro and near-fault motions,
respectively. The results corresponding to the frequency
independent behaviour of soil i.e. a0Z0.0 have also been
included for the sake of comparison. Maximum increase in
base shear for spectrum consistent ground motion is found
to be in the order of about 17% and 12% for a0Z1.5 and 0.0,
respectively, while the same is observed to be around 53%
and 60% for El-Centro, and around 20% and about 8%
under near-fault motions, (Fig. 14a–c).
Fig. 13. Variation of percentage changes in base shear for building frames with grid
respectively.
For buildings resting on grid foundations, the results
presented in Fig. 15a show that the maximum increase in
base shear under the spectrum consistent ground motion for
a0Z0.3 is around 7% (frame with tie beam). For a0Z1.5,
this increase is around 15% (frame with tie beam) as against
a peak increase of about 18% corresponding to a0Z0.0
(frame without tie beam). But, from Fig. 15b, it is seen that
the maximum change in base shear under El-Centro ground
motion is in the order of about 2% corresponding to a0Z0.3,
and about 33% for a0Z1.5; while such increase is found to
be in the order of 38% at a0Z0.0. Fig. 15c shows that no
such appreciable change occurs in case of near fault motion
due to the incorporation of this effect of frequency for this
type of building frame.
foundation under (a) spectrum consistent and (b) El-Centro ground motion,
Fig. 14. Variation of percentage changes in base shear for 2!2 bay 2 storey
building frames with isolated footing under (a) spectrum consistent,
(b) El-Centro and (c) near fault ground motions, respectively.Fig. 15. Variation of percentage changes in base shear for 4!4 bay 3 storey
building frames with grid foundation under (a) spectrum consistent,
(b) El-Centro and (c) near fault ground motions, respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914906
This shows that the effect of frequency of the forcing
function may influence the seismic behaviour of the system,
moderately. Such influence seems sensitive to the proximity
of the dominant frequency content of the ground motion to
the natural frequency of the system. Thus, such effect of
frequency is needed to be considered at least for important
structures.
Earlier investigation [31] reveals that the effect of
differential settlement due to gravity loading can be
Fig. 16. Variation of percentage changes in base shear for building frames with braces resting on isolated footing under spectrum consistent ground motion.
Fig. 17. Variation of percentage changes in base shear for building frames
with braces resting on isolated footing under spectrum consistent ground
motion.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 907
minimized in the building frames with isolated footings by
the addition of diagonal braces in all the peripheral panels of
the building frame [31]. However, the influence of the same
on the dynamic behaviour of the structure is needed to be
explored to adopt it in practice. The diameter of the steel
braces was adjusted in such a way that the axial rigidity i.e.
cross sectional area!modulus of elasticity is same as that of
the reinforced concrete columns. Change in base shear due
to the variation of soil (i.e. variation of N values) has been
studied for the building frames with diagonal braces in the
outer peripheral panels under all three ground motions.
However, in the limited scope of the paper, results
corresponding to 2!2 bay building frame under spectrum
consistent ground motion have been presented. Fig. 16
shows that the maximum percentage increase in base shear
due to various soil properties under spectrum consistent
ground motion is around 50% for 2!2 bay 1 storey building
frame without tie beam, while for the frame with tie beam,
this value comes down to about 13%. Fig. 17 shows that the
maximum percentage increase in base shear due to variation
Fig. 18. Variation of percentage changes in base shear for building frames
with braces resting on isolated footing under spectrum consistent ground
motion.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914908
of number of stories is around 45%, while such increase is
found to be on the order of around 60% with the variation of
number of bays as observed from Fig. 18. A comparison of
these results to the corresponding cases without diagonal
braces in the peripherial panels presented in Figs. 4, 8a
and 10a shows that the influence of such braces to alter the
seismic response is marginal. This is perhaps due to the fact
that the contribution of these braces to the lateral stiffness of
the frames is marginal as compared to that of the original
building frames with brick infill walls represented by
compression only diagonal braces.
4.2. Inelastic range response
Low-rise buildings may often experience inelastic range
vibration under moderately strong earthquakes. Thus
inelastic range behaviour of such structure is also of
paramount importance from practical viewpoint. Thus
attempts have been made to offer useful insight to such
behaviour through limited, yet representative, case studies.
Elastic range analysis primarily deals with the deformation
quantities, whereas; in the inelastic range analysis, damage is
the key concern. Such damage is generally measured in terms
of ductility demand and more precisely through hysteretic
energy demand of load-resisting structural elements. Endea-
vour has been made in the present section to see the influence
of soil–structure interaction on such quantities using simple
idealized single storey system. Three such single storey
systems have been considered having fundamental lateral
natural periods (Tx) of 0.18, 0.31 and 0.42 s at fixed-base
condition representative of typical one, two and three storey
structures, respectively. These characteristic lateral periods
are arrived at on the basis of the expression for lateral period
provided in the recent version of the Indian Standard Code
for earthquake resistant structures [32]. Structures are
considered to rest on soft, medium and stiff soils, in general.
For structure with TxZ0.42 s, representative of three storey
system, cases corresponding to soft soil have been excluded
from practical consideration. Variation in inelastic demand
quantities has been observed over a feasible range of
response reduction factor Rm (ratio of elastic force demand
of a structural element to the strength provided) that
measures the extent of inelastic range excursion that a
structural element is expected to experience under a specified
seismic acceleration–time history. The study primarily
attempts to judge the adequacy of the assumption made in
conventional design to consider the structures fixed at base.
Hence, in the present analysis, strength design for the
structural members has generally been made assuming the
structures to be fixed at base. Then, inelastic demands
are computed with both fixed base as well as flexible base
assumption. The demands estimated with fixed base
assumptions are traditionally estimated ones that are
normally used in capacity design. On the other hand,
the demands estimated from the consideration of flexible
base assumption are the ones expected to be exhibited by the
structures in reality. Comparison of the demands obtained in
these two ways helps to understand the consequence of
neglecting soil–structure interaction in estimating inelastic
demands for capacity design. Further, limited investigation
has also been made to see the influence of soil–structure
interaction on such damage quantities if the element
strengths are provided on the basis of elastic response
obtained incorporating the effect of soil flexibility. Variation
curves for such demands are plotted using lines with different
symbols annotated below the plots and the results are
attempted to be interpreted physically.
4.2.1. Ductility demand
Ductility demand expressed as the maximum strain
(including plastic) that a structural member undergoes
normalized by the yield strain of the same reflects
the demand for damage accommodating potential of
structural component for survival without collapse but with
plastic deformation or damage. Fig. 19a and b present the
variation of such demand with the variation of response
reduction factor Rm for structures resting on different types of
soils under spectrum consistent and El-Centro ground
motions, respectively. It is observed that such demand, as
expected, generally increases with increasing Rm Fig. 19a
shows, due to spectrum consistent ground motion, a
maximum increase of about 125% in ductility demand
(excluding a sporadic increase of more than 700% at RmZ4
for structure with TxZ0.31 s on medium soil) is observed for
system with TxZ0.18 s resting on medium soil compared to
its fixed base counterpart. A maximum demand of about
103% is exhibited by the same structure resting on stiff soil
under El-Centro ground motion (Fig. 19b). Such quantity is
observed to vary in the range of about 1–20 and 1–12 under
spectrum consistent and El-Centro ground motions, respect-
ively due to the variation of response reduction factor. From
close observation of the overall behaviour, it is evident that
Fig. 19. Variation of ductility demand for building frames under (a) spectrum consistent and (b) El-Centro ground motions, respectively for various lateral
natural period Tx (strength design made without SSI effect).
Table 3
Ductility demand of idealized single storey structure with TxZ0.31 s under
idealized near-fault ground motion at Tx/T1Z0.05
Rm Fixed base Soft Medium Stiff
1 1.0 1.0 0.9 0.8
2 103.5 106.8 102.6 101.2
4 1676.3 1682.5 1677.4 1684.9
8 5179.3 5196.8 5190.8 5187.1
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 909
the influence of soil flexibility considerably increases the
demand. For low-rise buildings with lateral natural period in
the short period ascending region of the response spectrum,
lengthening in period due to soil flexibility enhances the
elastic force response resulting in an increase in the strength
demand of the system. Thus effectively response reduction
factor increases due to the effect of soil-flexibility than what
is actually provided in the design on the basis of fixed-base
consideration. This expectedly allows additional inelastic
excursion of the load-resisting structural members and hence
increases the inelastic demand. A limited effort has also been
made to see such changes under idealized large duration
near-fault ground motion. The idealized near-fault ground
motion used in analyzing elastic range behaviour has again
been used for the same. Results of the same corresponding to
TxZ0.31 s system is only presented in the sample form in
Table 3. This shows that the demand quantity peaks
considerably even at fixed-base condition and the influence
of soil–structure interaction in further altering the response is
insignificant. Such increase is perhaps due to the large
duration of the pulse compared to the natural period of the
system. Structures, under this kind of loading, experience
sufficient plastic range deformation with very few load
reversals. Lengthening of lateral natural period due to soil-
flexibility is not appreciable compared to the pulse duration
and hence the influence of soil–structure interaction hardly
alters such response. However, such an immense amplifica-
tion in response is of remote possibility in practice as the
same may only be expected if the origin of the seismic
excitation is very close to the foundation of a low-rise
building frame.
4.2.2. Hysteretic energy demand
It is conventional to index the damage of the structures in
terms of ductility demand. However, such quantity
considers only the maximum displacement that the load-
resisting members undergo in its entire history. Obviously,
Fig. 20. Variation of normalized hysteresis energy ductility demand (NHEDD) for building frames under (a) spectrum consistent and (b) El-Centro ground
motions, respectively for various lateral natural period Tx (strength design made without SSI effect).
Table 4
NHEDD for idealized single storey structure with TxZ0.31 s under
idealized near-fault ground motion at Tx/T1Z0.05
Rm Fixed base Soft Medium Stiff
1 1.0 1.0 1.0 1.0
2 188.1 195.9 194.0 194.4
4 2560.9 2590.2 2575.6 2586.9
8 7101.0 7158.3 7138.1 7143.0
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914910
under reversible type loading in the inelastic range, this
parameter cannot account for the accumulated plastic strain
in all cycles of loading. In this context, a parameter termed
as normalized hysteretic energy ductility demand
(NHEDD), similar to ductility demand, has been proposed
[33] to be considered as a more meaningful parameter. This
is expressed as the energy dissipated by the element during
all inelastic cycles normalized to twice the energy absorbed
at the first yield plus one. Physically, this implies the ratio
between the equivalent displacement needed to dissipate the
same amount of energy as that in the original under a
monotonically increasing load and the yield displacement
equal to that of the original. This parameter has been used in
a few recent studies [28,34,35] perhaps because of its more
meaningful implications.
Variation in NHEDD for the load-resisting structural
elements has been presented as a function of response
reduction factor due to spectrum consistent and El-Centro
ground motions in Fig. 20a and b, respectively. Results show
a consistently increasing trend in response with increasing
Rm and enhanced demand due to the incorporation of the
effect of soil–structure interaction. This observation
conforms to the same made in terms of ductility demand.
A maximum increase of about 160% is observed for systems
with TxZ0.31 s resting on medium soil due to spectrum
consistent ground motion when compared to the response of
the same system with fixed base. Similar increase in
response in the order of around 138% is exhibited by the
same system under El-Centro ground motion when it is
considered to rest on soft soil. Similar quantity has
experienced a variation ranging from around 1 to 100 and
1 to 90 due to the variation of Rm over the domain considered
under spectrum consistent and El-Centro ground motions,
respectively. Considerable increase in such demand is
exhibited under near fault motion as furnished in Table 4
for the system with TxZ0.31 s. Likewise the earlier
observation, the influence of soil–structure interaction to
alter such demand under near-fault motion is observed to be
negligible.
Fig. 21. Variation of ductility demand for building frames under simulated spectrum consistent ground motion for various lateral natural period Tx (strength
design made with SSI effect).
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 911
Thus the present investigation crystallizes the fact that
the effect of soil–structure interaction may considerably
enhance the possibility of damage for low-rise building
frames designed as per usual practice, i.e. assuming building
frames fixed at the bases. However, it is interesting to
quantify such demands indicating the extent of damage at
various levels of Rm for structures designed incorporating the
influence of soil–structure interaction in the strength design
itself. Variation of ductility demand and NHEDD for the
idealized single storey systems so designed are presented in
Figs. 21 and 22, respectively. Such variation is presented
due to spectrum consistent ground motion only to represent
the trend indicating results. Results depict that a maximum
variation in the range of 1–12 and 1–60 may be expected in
ductility and energy demand as against a variation of 1–20
and 1–100 in the same for systems designed without soil-
flexibility due to variation of Rm over the same domain. A
comparison of these results with those obtained for the
corresponding systems designed without accounting for
Fig. 22. Variation of normalized hysteresis energy ductility demand (NHEDD) fo
various lateral natural period Tx (strength design made with SSI effect).
the effect of soil-flexibility (Figs. 19a, 20a), in general,
exhibits a lesser demand for the former and the demands are
virtually magnified in the latter. This may be attributed to
under estimation of the strength quantities in the process of
design ignoring soil-flexibility. For low-rise buildings, since
soil–structure interaction increases the design force, higher
response reduction factor is allowed in reality for the
structures designed from fixed-base assumption through an
underestimation of elastic force demand. Thus consideration
of soil–structure interaction effect in design seems impera-
tive in order to avoid an unsafe design at least for low-rise
buildings. This observation is also in keeping with the
response obtained in the elastic range.
5. Implication of the results
Thus the present investigation reveals that the effect of
soil–structure interaction may increase the seismic response
r building frames under simulated spectrum consistent ground motion for
Fig. 23. Variation in base shear for single storey plane frame with various
lateral natural periods due to (a) spectrum consistent and (b) El-Centro
ground motions, respectively.
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914912
of structures at least for low-rise buildings. However, this
observation may appear to lack conformity with the general
recommendation of ATC03 [36] and the conventional belief
regarding the influence of the same. Thus, to have a better
insight into the physics of the problem, a simple single
storey plane frame (SDOF system) having various lateral
natural periods has been analyzed over a feasible range of
variation of subgrade condition [10,11]. Spectrum compa-
tible synthetic ground motion and El-Centro ground motion
have been used in the analysis. Variation of change in base
shear due to the incorporation of soil-flexibility as compared
to the same obtained at fixed-base condition expressed as
a percentage of such response for systems at fixed-base
condition has been plotted. A set of such curves are drawn
for various lateral natural periods of the systems at fixed-
base condition (Tfix) considering ratio of the lateral natural
period at flexible base condition (Tssi) and the same at fixed-
base condition (Tfix) as the independent variable. Fig. 23a
presents such variation due to spectrum consistent ground
motion, while similar variation under El-Centro ground
motion is shown in Fig. 23b. Curves corresponding to the
fixed base lateral period in the short period range (up to
0.3 s), those corresponding to medium period range (more
than 0.3 s but less than 0.6 s) and those corresponding to
long period range (greater than 0.6 s) are drawn by firm and
two different types of dotted lines, respectively, for easy
identification. Results show that percentage change in base
shear is generally positive indicating an increase in response
for structures having Tfix up to 0.3 s such changes are
generally negative implying a decrease in response for all
other cases except some marginal increase for systems
having Tfix equal to 0.4, 0.5 and 0.6 s. Thus, seismic
response is generally expected to experience an increase for
systems having short period (0.1–0.3 s) while for systems
with large period (above 0.6 s), response due to soil–
structure interaction may decrease. Influence of soil–
structure interaction for systems with medium period
(0.3 s!Tfix!0.6 s) may undergo occasional change
(increase or decrease) or no change at all. Such response
scenario may be explained in the light of the change in
spectral acceleration ordinate of the response spectra with
change in lateral natural period. In the short period range,
such ordinate generally increases; while the same exhibits a
decrease in the long period region and very little or no
change in the medium period range. Such observation
regarding the nature of such interaction is in concurrence
with the comment made in the commentary on soil–
structure interaction of ATC03 under the heading ‘nature of
interaction effects’ in page 383 [36]. The same asserts that
‘depending on the characteristics of the structure and the
ground motion under consideration, soil–structure inter-
action may increase, decrease, or have no effect on the
magnitudes of the maximum forces induced in the structure
itself’. In this context, the present effort raises a serious
concern for low-rise building systems as the influence of
soil–structure interaction may increase seismic response of
such structures.
6. Conclusions
The present study attempts to assess the impact of soil–
structure interaction on regulating the design force
S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914 913
quantities under seismic loading both in elastic and inelastic
range of vibration for low-rise buildings. The results of the
study may lead to the following broad conclusions:
1.
The study shows that the effect of soil–structureinteraction may play a significant role to increase the
seismic base shear of low-rise building frames. However,
seismic response generally decreases due to the influence
of soil–structure interaction for medium to high rise
buildings.
2.
The study also shows that this effect may strongly beinfluenced by the frequency content of the earthquake
ground motion. The ground motions dominated by short
period pulses (period less than 1 s) are found to cause a
larger increase in response due to the effect of soil–
structure interaction. On the other hand, the near-fault
motion of large duration causes a small increase in
response as the frequency content of the ground motion
is, in general, largely apart from the system frequency
with or without considering the effect of soil–structure
interaction.
3.
Increase in seismic base shear due to soil flexibilitygenerally decreases with increasing hardness of soil and
increasing number of stories. Introduction of tie beam
also lessens the possibility of increasing base shear due
to soil–structure interaction.
4.
The effect of soil–structure interaction on the change inbase shear appreciably alters due to the change in column
to beam stiffness ratio, irrespective of the type of ground
motions, building frames and types of foundations.
Certain increases in base shear have been observed
with change in number of bays in the building frames. On
the other hand, excitation frequency of the forcing
function may moderately influence the seismic charac-
teristics of the buildings.
5.
Inelastic range demands of lateral load resistingstructural elements may experience considerable
increase due to the effect of soil–structure interaction.
If the strength design of a system is carried out on the
basis of fixed base assumption, then relatively lower
strength is provided as it demands due to its interaction
with soil. The inelastic demands of such systems may be
considerably more due to the effect of soil flexibility than
what is computed with fixed base assumption. However,
these inelastic demands are only marginally influenced
due to the effect of soil–structure interaction, under near-
fault motion.
6.
If the effect of soil flexibility is incorporated in thestrength design, then the increased strength provided
through the interaction effect in short period systems
may help to reduce the inelastic range demands of the
interactive systems considerably.
The study, as a whole, identifies the influential
parameters, which can regulate the effect of soil–structure
interaction on the change in base shear of building frames.
Such a study also helps to identify the category of worstly
influenced building frames. These may help to formulate
improved design guideline for low-rise building frames
accounting for the effect of soil–structure interaction.
Similar increase in elastic range response (computed by
CQC method) of low-rise structures on raft footings is
observed elsewhere [11]. Further, the limited effort to
analyze the inelastic behaviour of low-rise building frame
with soil–structure interaction indicating a possibility of
increasing inelastic demands prepares the background and
indicates the immediate need for a rigorous analysis on the
same. Demand quantities are expected to be further
aggravated for R/C structures that undergo sufficient
strength and stiffness degradation in the inelastic range. A
detailed investigation on the same to frame improved design
guidelines may be of ample interest in future course of
work. Such a course of study is planned to be undertaken up
by authors and may be reported as and when completed.
Acknowledgements
The authors gratefully acknowledge the support rendered
by a Major Research Project sanctioned by University Grants
Commission, Government of India [No. F. 14-13/2000
(SR-I)] towards thesuccessful completionof the present work.
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