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: scdind@netscape.net (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

www.elsevier.com/locate/soildyn

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–structure

interaction 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 be

influenced 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 flexibility

generally 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 in

base 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 resisting

structural 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 the

strength 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.

References

[1] Roy R, Dutta SC. Effect of soil-structure interaction on dynamic

behaviour of building frames on grid foundations. Structural

Engineering Convention (SEC 2001) Proceedings, Roorkee, India

2001;694–703.

[2] Roy R, Dutta SC, Moitra D. Effect of soil-structure interaction on

dynamic behaviour of building frames on isolated footings. National

Symposium on Advances in Structural Dynamics and Design

(ASDD), Proceedings, Chennai, India 2001;579–86.

[3] Indian standard criteria for earthquake resistant design of structures.

New Delhi, India: Bureau of Indian Standards; IS 1893–1984.

[4] Hall JF. Parameter study of the response of moment-resisting steel

frame buildings to near-source ground motions. EERL 95-08,

California, Institute of Technology, Pasadena, December, 1995.

[5] Federal Emergency Management Agency (FEMA). NEHRP rec-

ommended provisions for the development of seismic regulations for

new buildings. Part II: Commentary. Report No. FEMA-222,

Washington DC, USA.

[6] Smith BS. Lateral stiffness of infilled frames. J Struct Eng, ASCE

1962;88(ST6):183–99.

[7] Smith BS, Carter C. A method of analysis of infilled frames.

Institution of Civil Engineers, Proceedings 1969;44:31–48.

[8] Dowrick DJ. Earthquake resistant design: a manual for engineers and

architects. New York: Wiley; 1977.

[9] Curtin WG, Shaw G, Beck JK. Design of reinforced and prestressed

masonry. Thomas Telford House, 1 Heron Quay, London E14 9XF:

Thomas Telford Ltd; 1988.

[10] Bhattacharya K, Dutta SC. Assessing lateral period of building frames

incorporating soil-flexibility. J Sound Vib 2004;269(3–5):795–821.

[11] Bhattacharya K, Dutta SC, Dasgupta S. Effect of soil-flexibility on

dynamic behaviour of building frames on raft foundation. J Sound Vib

2004;274:111–35.

S.C. Dutta et al. / Soil Dynamics and Earthquake Engineering 24 (2004) 893–914914

[12] Dutta SC. Effect of strength deterioration on inelastic seismic

torsional behaviour of asymmetric RC buildings. Build Environ

2001;36(10):1109–18.

[13] Dutta SC, Das PK. Inelastic seismic response of code-designed

reinforced concrete asymmetric buildings with strength degradation.

Eng Struct 2002;24:1295–314.

[14] Das PK. Effect of coupled lateral torsional vibration on inelastic

seismic behaviour of R/c buildings with uni-directional and bi-direc-

tional asymmetry. PhD Thesis 2004. Department of Applied

Mechanics, Bengal Engineering College, Howrah, India 2004.

[15] ACI Committee 436 (De Simone SV. (Ch)). Suggested design

procedures for combined footings and mats. J Am Concr Inst 1966;

63(10):1041–57.

[16] ACI Committee 336 (Ulrich J. (Ch)). Suggested analysis and design

procedures for combined footings and mats. J Am Concr Inst 1988;

86(1):304–24.

[17] Dobry R, Gazetas G. Dynamic response of arbitrarily shaped

foundations. J Geotech Eng, ASCE 1986;112(2):109–35.

[18] Dobry R, Gazetas G, Stokoe II KH. namic response of arbitrarily

shaped foundations: experimental verifications. J Geotech Eng, ASCE

1986;112(2):136–54.

[19] Gazetas G. Formulas and charts for impedances of surface and

embedded foundations. J Geotech Eng, ASCE 1991;117(9):1363–81.

[20] Ohsaki Y, Iwasaki R. On dynamic shear moduli and Poisson’s ratio of

soil deposits. Soils Found 1973;13(4).

[21] Determination of dynamic properties of soil-method of test. New

Delhi, India: Bureau of Indian Standards; IS: 5249-1992.

[22] Bowles JE. Foundation analysis and design Civil engineering series:

McGraw-Hill International Editions, 5th ed.

[23] Khan MR. Improved method of generation of artificial time histories,

rich in all frequencies. Earthquake Eng Struct Dyn 1987;15(8):985–92.

[24] Chopra AK. Dynamics of structure. New Delhi, India: Prentice Hall;

1998.

[25] Goel R, Chopra AK. Inelastic seismic response of one-storey,

asymmetric plan systems: effect of stiffness and strength distribution.

Earthquake Eng Struct Dyn 1990;19(7):949–70.

[26] Murty CVR, Hall JF. Earthquake collapse analysis of steel frames.

Earthquake Eng Struct Dyn 1994;23(11):1199–218.

[27] Naeim F. On seismic design implications of 1994 Northridge

earthquake records. Earthquake Spectra 1995;11(1):91–109.

[28] Dutta SC, Das PK. Validity and applicability of two simple hysteresis

model to assess progressive seismic damage in RC asymmetric

buildings. J Sound Vib 2002;257(4):753–77.

[29] Das PK, Dutta SC. Effect of strength and stiffness deterioration on

seismic behaviour of asymmetric RC buildings. Int J Appl Mech Eng

2002;7(2):527–64.

[30] Gazetas G, Stokoe II KH. Free vibration of embedded foundations:

theory versus experiment. J Geotech Eng, ASCE 1991;117(9):

1382–401.

[31] Roy R, Dutta SC. Differential settlement among isolated footings of

building frames: the problem, its estimation and possible measures.

Int J Appl Mech Eng 2001;6(1):165–286.

[32] Indian standard criteria for earthquake resistant design of structures,

New Delhi, India: Bureau of Indian Standards; IS 1893-2002.

[33] Mahin SA, Bertero VV. An evaluation of inelastic seismic design

spectra. J Struct Eng, ASCE 1981;107:1777–95.

[34] Chandler AM, Correnza JC, Hutchinson GL. Seismic torsional

provisions: influence on element energy dissipation. J Struct Eng,

ASCE 1996;122(5):494–500.

[35] Goel RK. Seismic response of asymmetric systems: energy based

approach. J Struct Eng, ASCE 1997;107:1444–53.

[36] Tentative provisions for the development of seismic regulations for

buildings, Applied Technology Council, NSF and NBS; 1982.