an overview of structure-soil-structure dynamic

Journal of Chongqing University (English Edition) [ISSN 1671-8224]

Vol. 10 No. 3 September 2011

101

Article ID: 1671-8224(2011)03-0101-12

To cite this article: WANG Huai-feng, LOU Meng-lin, CHEN Xi, ZHAI Yong-mei. An overview of structure-soil-structure dynamic interaction research [J]. J Chongqing Univ: Eng Ed [ISSN 1671-8224], 2011, 10(3): 101-112.

An overview of structure-soil-structure dynamic interaction research

WANG Huai-feng 1,†, LOU Meng-lin 1, CHEN Xi 2, ZHAI Yong-mei 3 1 Institute of Structural Engineering and Disaster Reduction, Tongji University, Shanghai 200092, P. R. China

2 Department of Civil Engineering, Tongji University, Shanghai 200092, P. R. China 3 Shanghai Institute of Disaster Prevention and Relief, Tongji University, Shanghai 200092, P. R. China

Received 28 February 2011; received in revised form 8 May 2011

Abstract: The concept of structure-soil-structure dynamic interaction was introduced and the research methods were summarized. Based on lots of documents, a systematic summary of the history and current situation of structure-soil-structure dynamic interaction research considering adjacent structures was proposed as reference for researchers. The existing matter and the prospect of future research trend in this field was also examined. Keywords: soil-structure interaction (SSI); structure-soil-structure interaction (SSSI); dynamic cross interaction (DCI); foundation-soil-foundation interaction (FSFI); adjacent structure

CLC number: TU435 Document code: A

1 Introduction a

With rapid social and economic development and global population explosion, buildings are built taller and closer to each other for accommodating constantly increasing urbanized populations due to the lack of available land in cities. Crowded quarters as shown in Fig. 1 are very common.

As in a metropolis, like Kobe in Japan, building structures are built close to each other soft soil deposit. In such circumstances, dynamic interactions among building structures exist via radiation energy emitted from a vibrating structure to other structures. Hence the dynamical characteristics as well as the earthquake response characteristics of a structure are unable to be isolated from those of adjacent structures. Thus, the interactions between neighboring buildings have to be investigated.

† Corresponding author, WANG Huai-feng (王淮峰): [email protected].

Fig. 1 Numerous high and close buildings in tiny space

H. F. Wang, et al. Structure-soil-structure dynamic interaction

J. Chongqing Univ. Eng. Ed. [ISSN 1671-8224], 2011, 10(3): 101-112 102

Soil-structure interaction (SSI), one of the major subjects in the domain of earthquake engineering, has been actively researched in recent decades. Soil-structure interaction phenomena involve wave propagation in a coupled system: buildings erected on the soil surface. Its understanding traced 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 with a vigorous drive mainly by the needs of 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 that when supported on a rigid base. [1-3] One of the important reasons for this difference is that part of the vibrational energy of a flexibly mounted structure is dissipated by radiation of stress waves in the supporting medium and by hysteresis of the medium itself. Analytical methods to calculate the dynamic soil-structure interaction effects are well established. [4] When there is more than one structure in the medium, because of interference of the structural responses through soil, the soil-structure problem evolves to a cross-interaction problem between multiple structures.

Structure-soil-structure interaction (SSSI), put forward in recent decades, refers to the dynamic interaction problem in a multi-structure system through soil horizon. It is also called dynamic cross interaction (DCI), in literature about nuclear power plant (NPP). Research efforts so far have been confined to dealing with foundations placed on soil without superstructures, SSSI is hereby also called foundation-soil-foundation interaction (FSFI). SSSI studies the influence of adjacent structures to each other through interacting with sub-soil under dynamic disturbances. The dynamic disturbances can be either externally applied loads or seismic waves. In the case of external loads, the foundation response is evaluated by in the first step the determination of dynamic stiffness (impedance) of the soil-foundation system; whereas in the case of seismic waves by the determination of the input motion matrix. In such a situation, a foundation which diffracts the incident wave field can be regarded as a disturbance producing a secondary wave field affecting adjacent foundations.

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 theoretical methods and experimental installations are used to promote the study of SSSI.

There are so many publications about the research status of SSI, so there is no need here to go into the detail. The following is an overview on SSSI.

2 History and status of SSSI

The through-the-soil coupling of foundations was first introduced by Whitman [5] in 1969 as an important problem requiring study. The ensuing period of 1970s is the initial phase of study of SSSI. The model of such a soil-structure system is supposed to be a multi-mass or multi-spring-mass system or several geometries on a elastic or visco-elastic stratum over rigid bed rock and the dynamical characteristics are usually discussed in the form of transfer functions.

The mark of the beginning of SSI study is the theory about vibrational foundation proposed by Reissner [6] in 1936; whereas the start of SSSI study should be the work of Richardson and his co-workers [7-9] between 1969 and 1972. Taking advantage of the soil-structure model proposed by Parmelee, [10] Richardson and his co-workers derived equations for the response of two geometrically identical cylindrical bodies attached to the surface of an elastic half-space, with one of the two bodies excited by an external harmonic force. The result indicated that the presence of the second mass modified the vertical component of displacement of the excited mass by relatively small perturbations, occurring at resonant frequencies of the second mass, and induced relatively small rocking and horizontal translational displacements of the first mass. This was the first publication expounding the significance of SSSI. Soon after, MacCalden and Matthiesen [11] in 1973 extended the work of Bycroft [12] 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 last section, between theoretical and experimental results showed significant discrepancies.

Rapid progress of SSSI research in recent decades



was just stimulated by the needs of the nuclear power, which was generated from NPP where a reactor building was always adjacent to a turbine building and a control building. The SSSI effect should be considered as one of the dynamic characteristics of NPP buildings if the effect is too large to ignore. Meanwhile, the difference in dynamic characteristics of NPP buildings affects not only the aseismic performance of the buildings themselves but also the equipment associated with NPP safety. In 1973, Lee and Wesley, [13-14] in their pioneering work, investigated firstly the influence of SSSI effect on the seismic response of several adjacent nuclear reactors using a 3-D scheme. An approximate analytical-numerical approach was proposed for the solution of interaction problem involving three rigid circular foundations on the surface of the half-space subjected to vertically propagating S-waves along two orthogonal directions, and spring-mass models were proposed for the superstructures attached to the foundations.

The fact that an earthquake is a stochastic process is admitted widely. In nature there are no two completely identical earthquakes. So more and more scientists have recourse to the random method to study seismic motion. In 1973 and 1974, Kobori et al [15-16] studied the cases of identical two- and seven-mass systems and of identical and different two-spring-mass systems, which are along a line on the surface of the Voigt type visco-elastic stratum over rigid bed rock, under two types of excitation, one of which was the force excitation at one of the multi-mass system or one of the basement masses of the multi-spring-mass system and the other was the uniform displacement excitation at the surface or soil-rock interface of the stratum. The stochastic nonstationary processes of those systems were theoretically developed by discussing formulation and power flow expressed in the matrix forms of such an interaction configuration system. This was the commencement of study on SSSI associated with a stochastic process.

Luco and Contesse [17] in 1973, followed by Wong and Trifunac [18] in 1975, and Murakarni and Luco [19]

in 1977, addressed the 2-D 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 2-D wave diffraction problem and through parametric studies showed that groups of closely spaced buildings can result in interaction effects near the fundamental frequencies of the

buildings and at very low frequencies. Assuming that each structure consist of the lumped mass and cylindrical embedded foundation and that a 3-D space model of the soil ground be subdivided by several horizontal planed, Kobori and Kusakabe [20-21] investigated a cross-interaction system between two structures between 1978 and 1980.

A special mention should also be made of the mathematically rigorous solutions presented by Triantafyllidis and his co-worker [22-26] between 1986 and 1989 which, however, are unavoidably restricted to specific geometries. They investigated a finite number of rigid, rectangular and circular foundations bonded to the surface of a linear-elastic, isotropic and homogeneous half-space, and subjected to harmonic excitation. Furthermore, by using an analytical-numerical approach, Triantafyllidis and Neidhart [27] 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 Rayleigh 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 propagation act on the foundations due to scattered waves.

As known to all, soil is a multi-phase porous medium with high variability and strong randomness of material properties and space distribution. The random heterogeneity of soil imposes a tremendous effect on the dynamic soil-structure interaction. This is the reason why it is not reasonable to utilize deterministic parameters for properties of soil. In this field, Hryniewicz [28] considered the randomness in the soil medium in investigating two 2-D strip foundations, based on a semi-infinite medium of a single layer with randomness, depth dependent, shear modulus and density resting on a homogeneous half-space, excited by indent seismic SH-waves.

All those studies laid a solid theoretical and practical foundation for subsequent research. However, most of them are on basis of elastic half-space theory, which is simple and practicable for engineers to do analysis of a structure on a shallow foundation attached to homogeneous and thick soil layer. Seed [29] in 1975, deemed that the theory was not suitable for the analysis of dynamic interaction of structures on a deep foundation due to the exclusion of material damping and radiation damping. Meanwhile, because the existing analytical methods by then were not enough adequate for obtaining an acceptable solution to such



problems and the model was oversimple for soil and structures, the real solution of SSSI problems was still far away. When superstructures, foundations and topographic and geological conditions become complicated, the demand of mathematical computation is huge. Numerical methods, which are greatly developed as a result of the rapid progress of computer technology, are one of the most effective tool for SSSI study. Thus, some seismologists begin to study by numerical method and a great number of publications, based on it, have sprung up after 1980.

The finite element method (FEM), a common efficient computing method widely used in civil engineering, discretizes a continuum to a serial of elements with limited sizes for explaining the mechanics of continuum. It can simulate the mechanics of soil and structures better, more competent in dealing with complicated geometry and non-linear phenomena. Meanwhile, there are many general-purpose programs developed by commercial corporations for researchers. So FEM is used frequently in studies of SSI, and produces some achievement in the field of SSSI.

For considering the radiation damping of a semi-infinite space, the scale of soil should be large enough, which leads to the serious consumption of time and internal memory of computer with full FEM. Many researchers have proposed various boundaries, such as viscous boundary by Lysmer and Kuhlemeyer [30] in 1969, consistent boundary by Lysmer and Wass [31] in 1972, superposing boundary by Smith [32] in 1974, unified boundary by White [33] in 1977, paraxial boundary by Engquist and his co-workers [34-35] in 1977, transmitting boundary by Liao [36] in 1982, and viscous-spring boundary by Deeks in 1994, to reduce the scale.

Laing, [37] Lysmer et al, [38] and Aydinoglu and Cakiroglu [39] 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. In order to properly model the half-plane, Laing used consistent boundaries, Lysmer et al. employed viscous boundaries, and Aydinoglu and Cakiroglu relied on the discrete soil stiffness matrix procedure.

A lot of previous works were based on circular or semi-cylindrical foundations and superstructures simulated by lumped mass of single degree of freedom or cylindrical mass blocks. Thus, Roesset and Gonzalez [40-41] in 1977 and 1978 and Solari et al [42] in 1980 employed the FEM in conjunction with consistent

boundaries to study the 3-D problem of two square, rigid foundations resting on a linear-elastic layer under vertically propagating S-waves. Roesset & Gonzalez were considering embedded foundations, while Solari et al. surface foundations.

In the majority of devastating earthquakes, soil and structures all undergo be large deformation and get into a non-linear phase . By seismological observation of a reinforced concrete structure founded on piles in Los Angeles, Sivanovic [43] believed that the non-linear property of soil is one of the most significant factors that influence the seismic responses of a structure. And Roesset [44] reported that the second element controlling the veracity and rationality of analysis of SSI is the non-linearity of soil. But because of the complexity and time-consuming calculation of non-linear phenomena, there is little work associated with non-linear property on this subject. In 1982, a sensitivity study for the interaction effects of adjacent structures of nuclear power plants caused by horizontal seismic excitation was reported by Matthees and Magiera. [45]They firstly considered the nonlinear behavior of structures and soil on this subject.

Lin et al. [46] conducted a parametric study on the relative significance of various factors affecting the dynamic interaction between adjacent embedded foundations, making use of a 3-D finite model in conjunction with consistent boundaries.

In most practical engineering applications, depending upon soil conditions and the structural type, foundations are partially or totally embedded in the ground and the effects of the surrounding soil greatly alter their static and dynamic responses. 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 have limited the analysis of foundations of relatively simple geometry. In 2008, Yahyai et al. [47] used ANSYS5.4 program to simulate two steel moment frames with concrete shear walls on three types of soil including soft clay, sandy gravel and compacted sandy gravel. It is one of the works about SSSI that subtly model the superstructures.

FEM requires the use of special transmitting boundaries or infinite elements, which may lead to inaccuracy, as well as the presence of a rigid bedrock at a relatively shallow depth. A model of soil and structures via FEM is still so large, though introducing transmitting boundaries, that it needs much internal memory of computer and consumes plenty of time. The



development level of hardware and software of computer has restricted the application of FEM in SSSI.

Boundary element method, a new numeral method developed after FEM, only discretizes the boundary of domain of definition, different to the discretization of total continuum, and uses functions satisfying the governing equation to approximate boundary conditions. The BEM is more advantageous than the FEM, for it requires only a surface discretization and satisfies automatically the radiation condition at infinity without any need of using special complicated nonreflecting boundaries as the FEM. [48-49] This explains why the BEM is frequently used to analyze SSI by engineers and why the following publications about SSSI use the BEM or its variations as their computational tool.

In their pioneering work between 1977 and 1986, Wong and Luco [50-52] extended the boundary integral question approach presented by themselves before 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 discretization of the foundations has a marked effect on the calculated impedance functions for extremely small separations and the extensive numerical results presented by Yoshida et al [53-54] for the case of vanishingly small separation between the foundations are in error.

Huang [55] in 1993 and Karabalis and Huang [56] in 1994 reported on a time-domain solution of a 3-D system 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.

The interaction between adjacent rigid, surface foundations resting on a viscoelastic layered soil medium was studied by Karabalis and Mohammadi [57-60]

between 1991 and 1998. A 3-D frequency domain BEM formulation in conjunction with 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 [61-62] 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 used by them maybe lower than the one used by Bielak & Coronato [63] in 1981, who investigated the dynamic behaviors of the two square foundations resting on the surface of an elastic half-space due to a harmonic seismic excitation by the BEM too. However, this method can be used for arbitrary foundation shapes.

Later, a boundary element formulation of the substructure deletion method was presented by Betti and his co-workers [64-66] between 1996 and 1997 for the seismic analysis of the dynamic cross interaction between multiple embedded foundations. The surrounding soil was represented by a homogeneous viscoelastic half-space while the foundations were assumed to be rigid and subjected to incoming SH-, P-, and SV-waves arbitrarily inclined in both the horizontal and vertical planes.

The disadvantage of BEM is the difficulty of application in the field of heterogeneous medium. And the advantage will dissipate if it is utilized for non-linear problem due to the appearance of integral component in the total domain.

Owing to those respective disadvantages of FEM and BEM, the coupling method of FEM and BEM (FEM-BEM) emerged in the field of SSSI in 1990s. It enjoys the advantages of both FEM and BEM. In a general way, FEM is used for simulation of superstructures, foundations and near-field soil and BEM for far-field soil.

With 3-D BEM and 2-D FEM, Imamura et al. [67] 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. Though this was not a real FEM-BEM attempt, to some extent, it revealed the advantages of the coupling method. In the same year, a finite elements–boundary elements coupling model was used by Wang and Schmid [68] to investigate the dynamic interaction between 3-D structures founded on square embedded foundations, with a harmonic force applied on both mass-lumped structures and mass-distributed structures.

In many of the above-mentioned studies, foundations were considered as rigid bodies. This was 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 been observed in dynamic tests of actual buildings. Moreover, with increasing frequency, even a stiff foundation exhibits more or less a flexural



response. Although it has been noted that the assumption of a rigid footing may not always be valid, only a few papers have addressed the problem of the effects of footing flexibility on their dynamic behaviors. Considering that, Qian and his co-workers [69-70] in 1996 and 1998 extended the frequency domain boundary element method in association with the half-space Green’s function and 8-noded finite elements was extended to study the interaction effects between a system of two or more flexible footings of arbitrary shape bearing on an elastic half-space.

Later, a numerical, hybrid model was developed by Lehmann and Antes [71] in 2001 to investigate the dynamic interaction systems submitted to time-harmonic loads. The soil was approximated by means of a 3-D symmetric Galerkin boundary element method (SGBEM) for viscoelastic domains and the multi-storey buildings were represented by a finite element model taking the complex geometry of the cross-section into account as well as warping and secondary torsion. Recently, one of the most mentionable works is that delivered by Padron et al [72] in 2009. They utilized FEM-BEM in the frequency domain to analyze the influence of SSSI on lateral spectral deformation, vertical and rotational responses, and shear forces at pile heads, for several configurations of shear one-storey buildings under incident S- and Rayleigh-waves.

Lumped parameter method is another method for the analysis of SSI and also for SSSI, in which soil is simulated by spring, mass and damper or equivalent impedance function. [73]

Between 1994 and 1998, efficient discrete models, with frequency-independent masses, springs and dampers where each mode of vibration is considered as an independent DOF (degree of freedom), for predicting the dynamic interaction between adjacent rigid surface foundations supported by a homogeneous, isotropic and linear elastic half-space were presented by Mulliken et al, [74-76] and employing a proposed modification of the Wilson-θ method so that time-lagging effects due to wave propagation were also taken into consideration. The basic foundation interaction model was also extended to the evaluation of coupled building-foundation systems.

Experimentation is an important mean for scientists and engineers to improve humans' knowledge about the nature law. The first experiment about SSSI occurred in Fuchinobe district, Kanagawa Prefecture on the west of Tokyo, in Japan. In 1980, Mizuno [77] firstly clarify 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.

Fig. 2 Experiment model [77]

To evaluate this effect, the Nuclear Power Engineering Corporation (NUPEC) planned and carried out field and laboratory tests, named “Model Test on Dynamic Cross Interaction Effect of Adjacent Structures”, under a commission from the Ministry of International Trade and Industry Japan (MITI) using models of reactor buildings and adjacent structures from 1994 to 2002. The program provided field data to study the methodologies commonly associated with seismic analyses considering the SSSI effect. In the field tests, three kinds of model conditions were introduced, a single reactor building model, two identical reactor models, and two different type buildings (a reactor and a turbine). Forced vibration tests and earthquake observations were executed in the field test. The laboratory test was planned to evaluate basic characteristics of SSSI effect using simple soil model made of silicon rubber and structure models made of aluminum. For this purpose, forced vibration tests and shaking table tests were executed. [78-79] As part of a collaborative program between 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 analyses which applied common analysis procedures to predicting the building responses to recorded earthquake events for the test models with SSSI effect. The SSSI methodology applied in the nuclear industry was evaluated by respectively comparing the analysis results computed using the SASSI program [80] and FEM-BEM method [81] with recorded data.



Studies of recorded responses of instrumented structures constitute an integral part of earthquake hazard-reduction programs leading to improved design or analysis procedures. 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 to 8.0 and recurrence intervals of approximately 150 years. [82-83] 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. [43, 84-85] However, to our knowledge, there are no strong-motion records for two adjacent instrumented buildings, other than those reported by Celebi [86-87] in 1993. He studied the Oct. 1, 1987 Whittier-Narrows earthquake (surface wave magnitude Ms=5.6) response data set from a cluster of strong-motion instrumentation (triaxial accelerograph) deployed at three free-field locations in two adjacent seven-story buildings and at a downhole location below the foundation of one of these two buildings.

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 of homogeneous layers. In this case, the wave front is plane and if it does not impinge on the foundation vertically, it leads to motions at neighboring points which are just delayed repetitions of each other. The consequences of such an action have been the subject of numerous studies. However, the study of the random component arising from spatial incoherence of seismic ground motion, started relatively recently. The term spatial incoherence refers to a phenomenon in which 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, individual wave trains may impinge the foundation at different instants and with different angles of incidence, or they may propagate through paths of different physical properties and may be affected differently in both amplitude and phase. While the wave passage effect can be specified deterministically, spatial incoherence calls for stochastic description.

In 1999, considering spatial variability of ground motion, Behnamfar and Sugimura [88] investigated an

idealized 2-D system, two structural systems each consisting of a rigid roof at their top held by massless and elastic columns that are connected to the rigid foundations bonded to the surface of a medium of a homogeneous, viscoelastic layer resting over a half-space, considering P-, SV- and Rayleigh-wave by deterministic and random approaches.

More recently, some work [89-96] has been done on analyzing the influence of large groups of buildings, as well as that of 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, 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 building on a soft soil can contaminate the ground motion in its immediate vicinity (phenomenon hereafter abbreviated as “CGMB”, Contamination of Ground Motion by Buildings). Going 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 buildings of a city and its subsoil, which we call “site-city interaction” (SCI). An overview of SCI can be referred to Bard et al. [97]

3 Future research tendency

SSSI effects turn out to be significant, and one immediate consequence is that erecting or destroying a building, or a group of buildings, could modify seismic hazard for the neighborhood, which in turn could lead to significant conceptual changes, especially concerning microzoning studies, land-use planning, and insurance policies.

As a branch of SSI, the development of SSSI is on the basis of SSI research results and is dependent on the progress in dynamic analysis of soil and structure. Through the about 40 years of study, extraordinary progresses have been achieved in some relative theories. However, there are still plenty of work should be done in the future.

1) Deep foundations (including pile foundations). For simplification and calculability, those works to date mostly are restricted to shallow foundations so much as surface foundations. With the continual



increase of height of superstructures, deep foundations are widely used and the depth is augmenting. The study on dynamic cross interaction of deep foundations is obviously necessary.

2) Non-linear analysis. As mentioned above, soil and structures almost always exceed the linear elastic phase and get into non-linear plastic state. And to solve the problem of SSSI successfully, the consideration of non-linearity of both soil and structures are of the essence. Nowadays, there is scarcely any research considering this.

3) Spatial analysis of full model in 3-D. For the reduction of amount of calculation, many of the existing publications simplify extremely the superstructure to a spring-mass-damper model and some are limited to the interaction between two or more foundations. The steric effect, which is important to a complicated massive structure, is omitted and should be considered carefully hereafter.

4) Experimentation. Many reported SSSI studies are only theoretical derivation and numerical calculation. There is very little experimental verification of SSSI calculation to examine the theoretical outcomes. The technique of shaking table and centrifuge is getting maturer. Plenty of field tests and laboratory tests should be done.

5) Seismic damage investigation and seismological observation. Seismic damage is the most real test and provides abundant precious data. There are so abundant data about SSI, but there is only one seismic damage investigation until now. By launching seismic damage investigation, more data will be obtained to check the existing work and promote the study of SSSI.

6) Residential buildings interaction. Many works are focused on the NPP on account of its great significant and huge quality. However, the differences in structural types of residential building and NPP restricts the application of research achievement. So more work on residential buildings should be done by virtue of the advance of building complexity.

7) Practical simple calculation method. The purpose of study is to provide guidance for actual projects; so simplification and practical applicability are the key criteria. Existing models based on FEM and BEM are too complicated and time-consuming for engineers and designers. Simpler methods are imperative for application.

8) Existing important buildings. It is apparent that further studies of SSSI phenomena and their influence on structural seismic risk are mandatory, as it has been

shown that nearby buildings can significantly increase the seismic responses of a structure. Therefore, studies of the magnitude of this coupling phenomenon 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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