Structure soil-structure interaction literature review

Structure–soil–structure interaction: Literature review
Lou Menglina
, Wang Huaifenga,n
, Chen Xib
, Zhai Yongmeic
a
State Key Laboratory for Disaster Reduction in Civil Engineering, TongJi University, Shanghai 200092, China
b
Department of Civil Engineering, TongJi University, Shanghai 200092, China
c
Shanghai Institute of Disaster Prevention and Relief, TongJi University, Shanghai 200092, China
a r t i c l e i n f o
Article history:
Received 27 February 2011
Received in revised form
26 April 2011
Accepted 24 July 2011
Available online 11 August 2011
a b s t r a c t
The concept of structure–soil–structure dynamic interaction was introduced, and the research methods
were discussed. Based on several documents, a systematic summary of the history and status of the
structure–soil–structure dynamic interaction research that considers adjacent structures was proposed
as a reference for researchers. This study is in the initial stage, given its complexity and excessive
simplification of the model for soil and structures, and should be carried forward for its significance.
An attempt was made to summarize the common major computer programs in this area of study.
Furthermore, the advantages, disadvantages, and applicability of such programs were discussed. The
existing problems and the future research trend in this field were also examined.
& 2011 Elsevier Ltd. All rights reserved.
1. Introduction
With the rapid development of society and economy and the
global explosion of population, the construction of the cluster of
high buildings is on the rise gradually due to the lack of space in
cities. Thus, numerous high-rise buildings are emerging in cities,
as shown in Fig. 1.
As in the metropolitans, such as Kobe in Japan, the building
structures are built closely to each other over the soft soil deposit.
Under such circumstances, the dynamic interaction among build-
ing structures must occur through the radiation energy emitted
from a vibrating structure to other structures. Hence, the dyna-
mical characteristics as well as the earthquake response char-
acteristics of a structure are unable to be independent of those of
the adjacent structures. In accordance with the parameterized
study of Jiang and Yan [1] in 1998, those two buildings with
distance less than 2.5 times of width of foundation are interacting
with each other. And when the distance was less than one time of
width of foundation, the response of structures may increase or
decrease tens of percent. Thus, the interactions between neigh-
boring buildings have to be investigated.
Soil–structure interaction, one of the most major subjects in
the domain of earthquake engineering, has been paid compre-
hensive attention by international in recent decades. Soil–
structure interaction phenomena concern the wave propagation
in a coupled system: buildings erected on the soil surface. Its
origins trace back to the late 19th century, evolved and matured
gradually in the ensuing decades and during the first half of the
20th century, and progressed rapidly in the second half stimu-
lated mainly by the needs of the nuclear power and offshore
industries, by the debut of powerful computers and simulation
tools such as finite elements, and by the needs for improvements
in seismic safety.
Investigations of soil–structure interaction have shown that
the dynamic response of a structure supported on flexible soil
may differ significantly from the response of the same structure
when supported on a rigid base [2–4]. One of the important
reasons for this difference is that part of the vibrational energy of
the flexibly mounted structure is dissipated by radiation of stress
waves in the supporting medium and by hysteretic action in the
medium itself. Analytical methods to calculate the dynamic soil–
structure interaction effects are well established [5]. When there
is more than one structure in the medium, because of interference
of the structural responses through the soil, the soil–structure
problem evolves to a cross-interaction problem between multiple
structures.
Structure–soil–structure interaction (SSSI), put forward in
recent decades, means the dynamic interaction problem among
the multi-structure system through soil-ground. To the writer’s
knowledge, it is Luco and Contesse [6] in 1973 to come up first
with the Structure–soil–structure interaction designation for this
area of study. Its additional name is dynamic cross interaction
(DCI), derived from several publications about nuclear power
plant (NPP). And owing to those previous studies were just
confined to consider foundations placed on soil without super-
structures, SSSI was also call foundation–soil–foundation interac-
tion (FSFI). SSSI studies the influence of the presence of adjacent
structures to the others further through the interaction effect of
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/soildyn
Soil Dynamics and Earthquake Engineering
0267-7261/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.soildyn.2011.07.008
n
Corresponding author.
E-mail address: forgotten.wang@yahoo.com.cn (Wang).
Soil Dynamics and Earthquake Engineering 31 (2011) 1724–1731

the sub-soil under dynamic disturbances. The dynamic distur-
bances can be either externally applied loads or seismic waves. In
the case of external loads one evaluates the foundation response
by first determining the dynamic stiffness (impedance) of the
soil–foundations system, while in the case of seismic waves by
first determining the input motion matrix. In such a situation,
each foundation which diffracts the incident wave field can be
regarded as a disturbance producing a secondary wave field
affecting the adjacent ones.
SSSI is an interdisciplinary field of endeavor, which lies at the
intersection of soil and structural mechanics, soil and structural
dynamics, earthquake engineering, geophysics and geomechanics,
material science, computational and numerical methods, and
diverse other technical disciplines. With the successful outcome
about SSI, various kinds of theory methods and experimental
installations are used to promote the study of SSSI.
2. History and status
In accordance with technical development, the methods for
the study of SSSI come down to analytical method, analytical–
numerical method, numerical method, experiment and prototype
observation. Several publications have featured the research
status of SSI, and thus there is no need to discuss it here in detail.
Since the methods used for the study of SSSI are almost the same
as that of SSI, the relevant theories will not be discussed here. The
following is just an overview of SSSI according to the above-
mentioned methods.
2.1. Analysis method and analytical–numerical method
In 1969, Whitman [7] first introduced the through-the-soil cou-
pling of foundations as an important problem that requires further
study. The 1970s was the initial phase of SSSI study. This soil–
structure system model can be a multi-mass or multi-spring-mass
system, or several geometries on an elastic or viscoelastic stratum over
rigid bed rock. The dynamical characteristics are usually discussed in
the form of transfer functions.
The theory proposed by Reissner [8] in 1936 about vibrational
foundation marked the beginning of the SSI study, whereas the
study of Warburton et al. [9–11] between 1969 and 1972 initiated
the start of the SSSI study. Taking advantage of the soil–structure
model proposed by Parmelee, the authors derived some equations
for the response of two geometrically identical cylindrical bodies,
attached to the surface of an elastic half-space. The result shows
that when one of the bodies is excited by an external harmonic
force, the presence of the second mass modifies the vertical
component of displacement of the excited mass by relatively
small perturbations. The perturbations occur at resonant frequen-
cies of the second mass, and introduce relatively small rocking
and horizontal translational displacements of the first mass. This
is the first publication that expounded the significance of SSSI.
Soon after, MacCalden and Matthiesen [12] in 1973 extended the
work of Bycroft [13] in 1956, which determined an analytical
model for the motion of a single rigid circular foundation on an
elastic half-space, and developed a matrix formulation for the
solution of the induced dynamic displacement of a foundation
near a harmonically loaded foundation attached to an elastic half-
space. However, comparison studies presented in the latter
publication reveal that theoretical and experimental results
showed significant discrepancies.
The rapid progress of SSSI studies in recent decades has been
stimulated by the needs of nuclear power, which always consists
of a reactor building adjacent to a turbine building and control
building. The SSSI effect should be considered as one of the
dynamic characteristics of NPP reactor buildings if the effect is
too large to ignore. The difference in the dynamic characteristics
of reactor buildings affects not only the aseismic performance of
the reactor building itself but also the equipment related to NPP
safety. In 1973, Lee and Wesley [14,15], in their pioneering work,
investigated primarily the influence of SSSI effect on the seismic
response of several adjacent nuclear reactors using a 3D scheme.
An approximate analytical–numerical approach was proposed to
solve the interaction problem that involved three rigid circular
foundations on the surface of the half-space, which are subjected
to vertically propagating S-waves along two orthogonal directions
and spring-mass models for the superstructures attached to the
foundations.
An earthquake is a widely known stochastic process. In nature,
two completely identical earthquakes do not exist. Thus, more
and more scientists resort to the random method to study seismic
motion. In 1973 and 1974, Kobori et al. [16,17] studied the cases
of identical two and seven-mass systems and those of identical
and different two-spring-mass system, which are along a line on
the surface of the Voigt type viscoelastic stratum over rigid bed
rock. There are two types of excitation: the force excitation in one
of the multi-mass systems or one of the basement masses of the
multi-spring-mass system and the uniform displacement excita-
tion on the surface or at the soil–rock interface of the stratum. The
stochastic nonstationary process of these systems was theoreti-
cally developed by discussing the formulation and power flow
expressed in the matrix forms of such interaction configuration
systems. Overall, this is just the first study on SSSI associated with
the stochastic process.
Luco and Contesse [6] in 1973, followed by Wong and Trifunac
[18] in 1975, and Murakarni and Luco [19] in 1977, addressed the
two-dimensional (2D) antiplane problem of the interaction
between two or more infinite shear walls placed on rigid circular
foundations and subjected to obliquely or vertically incident
harmonic SH-waves. They actually solved a 2D wave diffraction
problem and, through parametric studies, showed that groups of
Fig. 1. Numerous cluster of high-rise buildings in tiny space.
L. Menglin et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 1724–1731 1725

closely spaced buildings could result in interaction effects near
the fundamental frequencies of the buildings and at very low
frequencies. Assuming that each structure consists of the lumped
mass and cylindrical embedded foundation and that a three-
dimensional (3D) space model of the soil ground is subdivided by
several horizontal planes, Kobori and Kusakabe [20,21] investi-
gated a cross-interaction system between two structures from
1978 to 1980.
A special mention should also be made to the mathematically
rigorous solutions presented by Triantafyllidis and his co-worker
[22–26] between 1986 and 1989 which, however, are unavoid-
ably restricted to specific geometries. The authors investigated a
finite number of rigid rectangular and circular foundations
bonded to the surface of a linear-elastic, isotropic, and homo-
geneous half-space, subjected to harmonic excitation. Further-
more, using an analytical–numerical approach, Triantafyllidis and
Neidhart [27] in 1989 analyzed the dynamic cross-interaction of
two rigid circular surface foundations on the surface of a linear-
elastic, isotropic, and homogeneous half-space subjected to Ray-
leigh waves impinging at an arbitrary angle, showing that, in
addition to loads along the direction of incidence of the incoming
wave, additional loads perpendicular to the direction of propaga-
tion act on the foundations due to scattered waves.
Soil is a multi-phase porous medium with high variability and
strong randomness of material properties and space distributions.
The random heterogeneities in the soil medium seem to have a
tremendous effect on the dynamic soil–structure interaction,
which explains why utilizing the deterministic parameters for
the properties of soil is not reasonable. In this field, Hryniewicz
[28] in 1993 considered the randomness in the soil medium for
the first time. The author investigated two 2D strip foundations,
based on a semi-infinite medium, which consists of a layer with
random, depth dependent, shear modulus and density resting
on a homogeneous half-space, excited by indented seismic
SH-waves.
The lumped parameter method is a common method used for
the analysis of SSI and SSSI, where soil is simulated by spring,
mass, and damper, or an equivalent impedance function [29].
Between 1994 and 1998, Mulliken and Karabalis [30–32]
presented efficient discrete models with frequency-independent
masses, springs, and dampers. Each model has modes of vibration
considered independent degree of freedom (DOF) for predicting
the dynamic interaction between adjacent rigid surface founda-
tions, which are supported by a homogeneous, isotropic, and
linear elastic half-space. This finding is achieved using a proposed
modification of the Wilson-y method; thus, the time-lagging
effects due to wave propagation are also considered. The basic
foundation interaction model is also extended to the evaluation of
coupled building–foundation systems.
Spatial variability of ground motion includes deterministic and
stochastic components. Known as the wave passage effect, the
deterministic component is actually the solution of the wave
equation in a medium consisting of homogeneous layers. In this
case, the wave front is a plane and if it does not impinge on the
foundation vertically, then it leads to motions at the neighboring
points which are just delayed repetitions of each other. The
consequences of such an action have been the subject of many
previous studies. However, the study of the random component,
which arises from the spatial incoherence of seismic ground
motion, started relatively recently. The term spatial incoherence
refers to a phenomenon where motions at two different points of
the ground surface tend not to vary together, i.e., if one is large
the other is small.
Several factors contribute to the spatial incoherence of the
free-field ground motion. In particular, the individual wave trains
may impinge the foundation at different instants and with
different angles of incidence or may propagate through paths of
different physical properties; they may also be affected differently
in both amplitude and phase. Spatial incoherence calls for a
stochastic description, whereas the wave passage effect can be
specified deterministically.
In 1999, considering primarily the spatial variability of ground
motion, Behnamfar and Sugimura [33] investigated an idealized
2D system made up of two structural systems, each consisting of
a rigid roof at the top held by massless and elastic columns. The
columns are connected to the rigid foundations which are bonded
to the surface of a medium consisting of a homogeneous,
viscoelastic layer resting over a half-space, and considering
P-, SV- and Rayleigh-waves through deterministic and random
approaches.
All those discussions have laid a solid theoretical and practical
foundation for the subsequent research on SSSI. However, most of
those studies are based on the elastic half-space theory, which
make analyzing the structure with a shallow foundation attached
to a homogeneous and thick soil layer simple and practicable for
engineers. Seed [34] in 1975, deemed it was not suitable for the
analysis of the dynamic interaction of structure with a deep
foundation for the exclusion of material damping and radiation
damping. Due to the difficulty of the solution for the analysis
method and the excessive simplification of the model for soil and
structures, it was far from the real solution for problems of SSSI.
When superstructures, foundations, and topographic and geolo-
gical conditions become complicated, producing a mathematical
solution can be difficult.
2.2. Numerical method
The numerical method greatly developed because of the rapid
progress of computers. This method of calculation is considered
one of the most effective tools for the study of SSSI. Thus, some
seismologists have used it, and a great deal of publications based
on it have spring up from 1980 up to the present.
2.2.1. Finite element method
Finite element method (FEM), an efficient common computing
method widely used in civil engineering, discretizes a continuum
into a series of elements with limited sizes to compute for the
mechanics of the continuum. FEM can simulate the mechanics of
soil and structures better than other methods, deal with compli-
cated geometry and applied loaded, and determine non-linear
phenomena. To date, there are many general-purpose programs
developed by commercial corporations for research in the engi-
neering field. Specifically, FEM is used frequently in the study of
SSI, and has produced some notable achievements in the field
of SSSI.
In considering the radiation damping of semi-infinite space,
the scale of the soil should be large enough. This requirement
demands a serious consumption of time and the internal memory
of a computer to have full FEM. Many studies have proposed
various boundaries to reduce the scale: viscous boundary by
Lysmer and Kuhlemeyer [35] in 1969, consistent boundary by
Lysmer and Wass [36] in 1972, superposing boundary by Smith
[37] in 1974, unified boundary by White et al. [38] in 1977,
paraxial boundary by Engquist and his co-workers [39,40] in
1977, transmitting boundary by Liao and Wong [41] in 1982, and
viscous-spring boundary by Deeks in 1994.
Laing [42] in 1974, Lysmer et al. [43] in 1975, and Aydinoglu
and Cakiroglu [44] in 1977 employed the FEM under plane
strain conditions to study the cross-interaction of two or more
foundations or structures subjected to vertically propagating
harmonic SV-waves. To model the half-plane properly, Laing used
L. Menglin et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 1724–17311726

consistent boundaries, Lysmer et al. employed viscous bound-
aries, and Aydinoglu and Cakiroglu relied on the discrete soil
stiffness matrix procedure.
A number of previous works have been based on circular or
semi-cylindrical foundations and superstructures simulated by
lumped mass with a single degree of freedom or cylindrical mass
blocks. Thus, Roesset and Gonzalez [45,46] in 1977 and 1978, and
Solari et al. [47] in 1980 employed the FEM in conjunction with
consistent boundaries to study the 3D problem of two squares,
their rigid foundations resting on a linear-elastic layer under
vertically propagating S-waves. Roesset and Gonzalez considered
embedded foundations, whereas Solari et al. focused on surface
foundations.
In most of devastating earthquakes, soil and structures appear
as large deformations, which get into the non-linear phase.
Through seismological observation of a reinforced concrete struc-
ture founded on piles in Los Angeles, Sivanovic [48] considered
the non-linear property of soil to be one of the most significant
factors influencing the seismic response of a structure. In 1980,
Roesset [49] indicated that the second element that controls the
veracity and rationality of the analysis of SSI is the non-linearity
of the soil. However, because of the complexity and time-
consuming calculation of non-linear phenomena, there has been
little work associated with non-linear property in this subject. In
1982, Matthees and Magiera [50] conducted a sensitivity study on
the interaction effects of adjacent structures of nuclear power
plants caused by horizontal seismic excitation. They primarily
considered the nonlinear behavior of soil and structure in this
subject.
In 1987, Lin et al. [51] conducted a parametric study on the
relative significance of various factors affecting the dynamic
interaction between adjacent embedded foundations by making
use of a 3D finite model in conjunction with consistent
boundaries.
In most practical engineering applications, depending on the
soil conditions and the structural type, the foundations are
partially or totally embedded in the ground and the effects of
the surrounding soil greatly alter their static and dynamic
response. As with the single foundation case, when the effect of
the embedment is included in the multiple foundations case,
analytical difficulties and enormous numerical calculations limit
the analysis of foundations of relatively simple geometry. In 2008,
Yahyai et al. [52] used the ANSYS5.4 program to simulate two
steel moment frames with concrete shear walls on three types of
soil, such as soft clay, sandy gravel, and compacted sandy gravel.
Yahyai et al.’s study is one of the works in the study of SSSI that
subtly models superstructures.
FEM requires the use of special transmitting boundaries or
infinite elements, which may lead to inaccuracy. In addition, FEM
also necessitates a rigid bedrock at a relatively shallow depth. The
model of soil and structures via FEM is still very large, and
although it introduces transmitting boundaries, it still requires
relatively much internal computer memory and time. The devel-
opment level of hardware and software has restricted the appli-
cation of FEM in the study of SSSI.
2.2.2. Boundary element method
The boundary element method (BEM), a new numeral method
developed after FEM, only discretizes the boundary of the defini-
tion domain. It is different from the discretization of total
continuum and uses functions satisfying the governing equation
to approximate boundary conditions. The BEM is more advanta-
geous than the FEM because it requires only a surface discretiza-
tion and satisfies automatically the radiation condition without
any need for using special complicated non-reflecting boundaries
as required by FEM [53,54]. This explains why the BEM is
frequently used by engineers to analyze SSI and why the some
publications on SSSI use BEM or its variations as their computa-
tional tool.
In their pioneering work from 1977 to 1986, Wong and Luco
[55–57] extended the boundary integral question approach,
which they had presented previously for isolated foundations to
the case of multiple rigid foundations of different shapes resting
on an elastic or viscoelastic half-space and subjected to external
forces and seismic waves. They found that the choice of discre-
tization of the foundations has a significant effect on the calcu-
lated impedance functions for extremely small separations. They
also determined that the extensive numerical results presented
by Sato et al. [58] and Yoshida et al. [59] in the case of vanishing
small separation between the foundations are erroneous.
Huang [60] in 1993 and Karabalis and Huang [61] in 1994
reported on a time-domain solution of a 3D system, consisting of
massive square rigid foundations resting on a homogeneous,
isotropic, linear elastic half-space using the time domain BEM in
conjunction with the Stokes fundamental solutions.
Moreover, the interaction between adjacent rigid surface
foundations resting on a viscoelastic layered soil medium was
studied by Karabalis and Mohammadi [62–66] between 1991 and
1998. A 3D frequency domain BEM formulation in conjunction
with the infinite space fundamental solutions and the so called
’’successive stiffness method’’ were used for the simulation of a
layered soil medium. During the same period, Qian and Beskos
[67,68] in 1995 and 1996 employed the direct BEM in the
frequency domain in conjunction with quadratic quadrilateral
elements and the half-space surface Green’s function to study in
detail the cross-interaction between two square rigid massless or
massive surface foundations subjected to obliquely incident
harmonic P-, SV-, SH-, and Rayleigh-waves. The accuracy of the
method Qian and Beskos used may be lower than that used by
Bielak and Coronato [69] in 1981, who investigated the dynamic
behavior of the two square foundations resting on the surface of
an elastic half-space due to a harmonic seismic excitation by the
BEM. However, this method can be used for arbitrary foundation
shapes.
Later, a boundary element formulation of the substructure
deletion method is presented by Romanini et al. [70] and Betti
et al. [71,72] in 1996 to 1997 for the seismic analysis of the
dynamic cross interaction between multiple embedded founda-
tions. The surrounding soil was represented by a homogeneous
viscoelastic half-space whereas the foundations were assumed to
be rigid and subjected to incoming SH-, P-, and SV-waves
arbitrarily inclined in both the horizontal and the vertical planes.
One disadvantage of BEM is its difficulty of application in the
case of a heterogeneous medium. Likewise, the advantage will not
occur if BEM is utilized for non-linear problem due to the
appearance of integral component in the total domain.
2.2.3. Finite element method-boundary element method
Owing to the respective disadvantages of FEM and BEM, the
coupling method of FEM and BEM (FEM–BEM) was developed in
the field of SSSI in the 1990s. This method shows the advantages
of both FEM and BEM. Generally in a general way, FEM is used for
simulation of superstructures, foundations and near-field soil,
whereas BEM is applied for far-field soil.
Applying 3D BEM and 2D FEM, Imamura et al. [73] in 1992
studied the seismic response characteristics of an embedded
nuclear system, consisting of a reactor building, a turbine building
and a control building, excited by an artificially generated motion.
Despite the fact that it was not a real FEM–BEM, it revealed to
some extent the advantages of the coupling method. In the same

year, Wang and Schmid [74] used a real finite elements–boundary
elements coupling models to investigate the dynamic interaction
between 3D structures founded on square embedded foundations
for a harmonic force applied on both mass-lumped structures and
mass-distributed structures.
In most of the abovementioned previous studies, foundations are
considered rigid bodies. This assumption is based on the fact that
actual foundations usually have material moduli much higher than
the underlying soil. However, significant out-of-plane deformations of
foundations have also been observed in dynamic tests of actual
buildings. Moreover, with increasing frequency, even a stiff founda-
tion exhibits a relatively flexural response. Although the assumption
of a rigid footing has been noted to be not always valid, only a few
studies have addressed the problem of the effects of footing flexibility
on dynamic behavior. Considering the lack of study in the field, Qian
et al. [75] and Tham et al. [76] in 1996 and 1998 extended the
frequency domain of BEM in association with the half-space Green’s
function. They also extended eight-node finite elements to study the
interaction effects between systems of two or more flexible footings
of arbitrary shape that bears on an elastic half-space.
Later, in 2001, a numerical hybrid model was developed by
Lehmann and Antes [77] to investigate the dynamic interaction
systems submitted to time-harmonic loads. The soil was approxi-
mated using the 3D symmetric Galerkin boundary element method
(SGBEM) for viscoelastic domains. The multi-storey buildings were
represented by a finite element model, which considers the complex
geometry of the cross-section as well as the warping and secondary
torsion. One of the most notable recent works is the one conducted
by Padron et al. [78] in 2009. The author utilized FEM-BEM in the
frequency domain to analyze the influence of SSSI on lateral spectral
deformation, vertical and rotational response, and shear forces at pile
heads for several configurations of shear one-storey buildings under
incident S- and Rayleigh-waves.
2.3. Experiment
Experiment is an important mean for scientists and engineers to
improve humans’ knowledge about the nature law. Field forced-
vibration tests for two foundations were carried out by Maccalden
[79] in 1969, which are the earliest experiment about SSSI, and
followed by Kobori et al. [80] in 1977. Afterwards, a series of
experiments about SSSI occurred in Fuchinobe district, Kanagawa
Prefecture in the west of Tokyo, Japan. In 1980, Mizuno [81] firstly
clarified actual phenomena of SSSI by a series of experiments such as
forced vibration tests, microtrem or measurements and earthquake
observations for a full-scale building and a model structure as shown
in Fig. 2.
In order to evaluate this effect, the Nuclear Power Engineering
Corporation (NUPEC) has been planning and implementing field
and laboratory tests, with the name of ’’Model Test on Dynamic
Cross Interaction Effect of Adjacent Structures’’ under a commis-
sion from the Ministry of International Trade and Industry
Japan(MITI) taking advantage of models of reactor buildings and
adjacent structures from 1994 to 2002. The program provides
field data for the study of the methodologies commonly asso-
ciated with seismic analyses concerning the SSSI effect. In the
field tests, three kinds of model conditions are introduced,
namely, a single reactor building model, two identical reactor
models, and two buildings of different types (a reactor and a
turbine). Forced vibration tests and earthquake observations are
executed in the field test. The laboratory test is planned to
evaluate basic characteristics of the SSSI effect by employing
simple soil model made of silicon rubber and structure models
made of aluminum. In this test, forced vibration tests and shaking
table tests are conducted [82,83]. As part of a collaborative
program jointly conducted by the United States and Japan on
seismic issues related to NPP applications, the U.S. Nuclear
Regulatory Commission sponsored a program at Brookhaven
National Laboratory (BNL) to perform independent seismic ana-
lyzing which applied common analysis procedures to predict the
building response to recorded earthquake events for the test
models with SSSI effect. The SSSI methodology put into applica-
tion in the nuclear industry was evaluated respectively by
comparing the analysis results computed though utilizing the
SASSI program [84] and FEM–BEM method [85] to record data.
2.4. Prototype observation
Studies of recorded responses of instrumented structures
constitute an integral part of earthquake hazard-reduction pro-
grams, leading to the improved designing or analyzing proce-
dures. Strong-motion instrumentation programs are carried out in
lots of seismically active regions such as Los Angeles, where, in
addition to several smaller active faults, the two major faults, the
San Andreas and San Jacinto faults, generate earthquakes with
magnitudes of 7.0–8.0 and recurrence intervals of approximately
150 years [86,87]. Therefore, studies into the responses of
instrumented structures will facilitate better prediction of the
performance of structures in future earthquakes. Data about SSI is
so abundant [48,88,89]. However, according to the writer’s
knowledge, there are no strong-motion records from two, adja-
cent, instrumented buildings, other than that reported by Celebi
[90,91] in 1993. He studied the Oct. 1, 1987 Whittier–Narrows
earthquake (Ms¼5.6) response data set from a cluster of strong-
motion instrumentation (triaxial accelerograph) deployed at
three free-field locations within two adjacent seven-story build-
ings and at a downhole below the foundation of one of these two
buildings.
3. SCI
More recently, some work [92–99] has been done to analyze
the influence of large groups of buildings as well as site effects
due to subsoil configuration, on the seismic response of the
overall system by means of several experimental and numerical
models.
Seismologists have known for a long time that it is not a good
idea to install seismological stations close to trees. During the
past decades, it has also become clear how large the effects of
surface heterogeneities, which are commonly called ’’site effects’’
(SE, concerning soft soils as well as topographic features), can be.
On this basis, it is legitimate to wonder whether a large buildingFig. 2. Experiment model.

on a soft soil can contaminate the ground motion in its immediate
vicinity (phenomenon hereafter abbreviated as ’’CGMB’’, Contam-
ination of Ground Motion by Buildings). To go one step further
from CGMB, we may ask about the overall effect of such
contamination in a densely urbanized area. It evolves to the
plausibility of this kind of ’’global’’ interaction between all the
buildings of a city and its subsoil, which we call ’’site-city
interaction’’ (SCI). For the reason that Bard et al. [100] have had
an overview about it, studies on SCI will not be discussed here.
4. Computer programs
The development of computer technology has provided
powerful support for SSI analysis and thus computing has become
an indispensable tool. The common analysis programs include
CLASSI, FLUSH, ALUSH, SASSI and HASSI and so on. Moreover,
general finite element programs are also often used to analyze SSI.
4.1. CLASSI
CLASSI, developed by Wong and Luco, is a frequency domain
computing method that applies fast Fourier transform (FFT) based
on the multiple-step substructure analysis method. Uniform
continuous or horizontal-layer elastic or viscoelastic half space
is adopted in the soil model whereas the lumped mass-bar model
or the finite element model based on rigid foundation is applied
in the structure model. Earth shakes functioning on the surface of
the foundation produce seismic body waves in various directions
and Rayleigh-wave as well as Love-wave in horizontal transmis-
sion. However, programs such SHAKE are still required to produce
soil parameter data compatible with the strain of the soil model.
CLASSI can be used to analyze the dynamic response of
multiple foundations whose forms need to be surface. The
response of buried foundation needs to be modified and that of
deep foundation may be unclear.
4.2. FLUSH and ALUSH
FLUSH and ALUSH are the 2D finite element programs devel-
oped in 1970s by professor Lysmer, who worked in Earthquake
Engineering Research Center of Berkeley campus of University of
California, for analyzing SSI. FLUSH program is one of the inter-
national common programs used for seismic resistance analysis of
NPP and is also one of the programs recommended by American
Nuclear Regulatory Commission. FLUSH and ALUSH are also the
frequency domain computing methods based on FFT. Seismic
waves enter through rigid bottom and spread upwards perpendi-
cular to the soil layer.
FLUSH and ALUSH are specially designed for seismic response
analysis considering SSI. However, when analyzing SSSI, they are
unable to apply external dynamic loading. Meanwhile, seismic
waves can only enter vertically. More importantly, the rationality
and accuracy of the adopted 2D model approximating a 3D
system need to be further proven through additional research.
4.3. SASSI
SASSI program is also the frequency domain computing
method developed by professor Lysmer with FFT. The 3D finite
element substructure method of discrete half-space model is
adopted. Uniform continuous or horizontal-layer elastic or vis-
coelastic half-space is applied in the soil model. Discrete depth of
the half space changes with frequency variation (in inverse
proportion to frequency), and the bottom of the half space is laid
with a viscous boundary. Earth shakes functioning on the surface
of the foundation produce seismic body waves in various direc-
tions and Rayleigh-wave as well as Love-wave in horizontal
transmission. Besides, programs such SHAKE are still required to
produce soil parameter data compatible with the strain of the
soil model.
SASSI can be applied to structures with flexible, buried, or
multiple foundations. The author believes that currently it is the
suitable software for SSSI analysis.
4.4. General finite element programs
However, the abovementioned programs have conspicuous
disadvantages in that they only analyzes in frequency domain
and are incapable of nonlinear analysis. At present there are a
large number of available commercial finite element programs
(such as ANSYS, ABAQUS, MSC.MARC), which have friendly inter-
face and powerful nonlinear solver. They process well and are
easy to master for users with great generality and therefore are
very popular among SSI studies. When applying them to study
SSSI, the biggest problem lies in how to solve the huge calculation
amount brought by the large range of soil.
5. Future research tendency
SSSI effects turn out to be significant, and one immediate
consequence is that erecting or dismantling a building or a group
of buildings could change the seismic hazard for the neighbor-
hood. This leads to significant conceptual changes, especially
concerning seismic microzonation studies, land-use planning,
and insurance policies.
As one of the branches of SSI, the development of SSSI is based
upon the research results of SSI and the progress of the dynamics
analysis of soil and structure. Through the about four decades of
study, some relevant theories have made extraordinary progress.
However, there is still plenty of work to be done in the coming
years.
1. Deep foundations (including pile foundation). For simplifica-
tion and calculability, most of those works to date are
restricted to shallow foundations and surface foundations.
With the continual increase of superstructure height, deep
foundations are widely used and the depth is augmenting. The
study of dynamic interaction of deep foundations is of essen-
tial importance.
2. Non-linear analysis. As mentioned above, the effect of soil and
structures usually exceeds the linear elastic phase and requires
elastoplastic analysis. And to solve the problem of SSSI
successfully, nonlinear analysis of both soil and structure must
be considered. Nowadays, there is scarcely any research
considering this.
3. Spatial analysis of full model in 3D. To reduce the amount of
calculation, many existing publications simplify extremely the
superstructure to spring-mass-damper model or geometries
and some studies in the past were limited to the interaction
between two or more foundations. The steric effect, which is
very important to complicated and massive structures, is
neglected and must be considered carefully in future studies.
4. Experiment. Many SSSI researches are just theoretical deriva-
tion and numerical calculation. There are few SSSI experiment.
As the technique of shaking table and centrifuge is getting
increasingly mature, plenty of field tests and laboratory tests
are yet to be done.
5. Seismic damage investigation and seismological observation.
Seismic damage provides a large amount of the realistic,
effective, and rich data. Currently there are abundant data

about SSI, but there is only one seismic damage investigation.
By launching seismic damage investigation, more data can be
acquired to validate the existing work and promote the study
of SSSI.
6. Residential buildings interaction. Many works are focus on
the NPP on account of its great significant and huge quality.
However, the difference of structure types of residential building
and NPP restricts the application of research achievement. So
more work must be done on the complex residential buildings.
7. Practical simplified calculation method. The purpose of study
is to provide guidance for real projects, so simplification
and practical applicability are the key criteria. The existing
FEM-based and BEM-based model is far too complicated and
time-consuming for engineer and designer. Simpler method is
imperative for application.
8. Existing important buildings. That the importance and urgency
of further studies about SSSI phenomena and their influence
on structural seismic risk are obvious. According to existing
studies, nearby buildings can significantly increase the seismic
response of a structure. Therefore, studies of the magnitude of
this coupling phenomena on the dynamic behavior of existing
important buildings in presence of other close structures, or of
existing groups of special buildings, should be carried out.
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