Structure-Soil-Structure Interaction Literature Review [PDF]

Zitiervorschau

Soil Dynamics and Earthquake Engineering 31 (2011) 1724–1731

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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn

Structure–soil–structure interaction: Literature review Lou Menglina, Wang Huaifenga,n, Chen Xib, Zhai Yongmeic a b c

State Key Laboratory for Disaster Reduction in Civil Engineering, TongJi University, Shanghai 200092, China Department of Civil Engineering, TongJi University, Shanghai 200092, China Shanghai Institute of Disaster Prevention and Relief, TongJi University, Shanghai 200092, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 February 2011 Received in revised form 26 April 2011 Accepted 24 July 2011 Available online 11 August 2011

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 building structures must occur through the 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 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 neighboring buildings have to be investigated. Soil–structure interaction, one of the most major subjects in the domain of earthquake engineering, has been paid comprehensive 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

n

Corresponding author. E-mail address: [email protected] (Wang).

0267-7261/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2011.07.008

gradually in the ensuing decades and during the first half of the 20th century, and progressed rapidly in the second half stimulated 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 superstructures, SSSI was also call foundation–soil–foundation interaction (FSFI). SSSI studies the influence of the presence of adjacent structures to the others further through the interaction effect of

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Fig. 1. Numerous cluster of high-rise buildings in tiny space.

the sub-soil under dynamic disturbances. The dynamic disturbances 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 abovementioned methods. 2.1. Analysis method and analytical–numerical method In 1969, Whitman [7] first introduced the through-the-soil coupling 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

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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 frequencies 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 halfspace. 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 excitation on the surface or at the soil–rock interface of the stratum. The stochastic nonstationary process of these systems was theoretically 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

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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 threedimensional (3D) space model of the soil ground is subdivided by several horizontal planes, Kobori and Kusakabe [20,21] investigated 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 unavoidably 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 homogeneous half-space, subjected to harmonic excitation. Furthermore, 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 linearelastic, 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. 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 foundations, 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 geological 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 complicated 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 engineering 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

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consistent boundaries, Lysmer et al. employed viscous boundaries, 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 structure 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 timeconsuming 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 development level of hardware and software has restricted the application 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 definition 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 advantageous than the FEM because it requires only a surface discretization and satisfies automatically the radiation condition without any need for using special complicated non-reflecting boundaries

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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 computational 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 discretization of the foundations has a significant effect on the calculated 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 foundations. 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

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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 foundation 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 approximated 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 forcedvibration 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 commission 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 associated 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 analyzing 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 application 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 programs, leading to the improved designing or analyzing 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 7.0–8.0 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, adjacent, 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 strongmotion instrumentation (triaxial accelerograph) deployed at three free-field locations within two adjacent seven-story buildings and at a downhole below the foundation of one of these two buildings.

3. SCI

Fig. 2. Experiment model.

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 building

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on a soft soil can contaminate the ground motion in its immediate vicinity (phenomenon hereafter abbreviated as ’’CGMB’’, Contamination 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.

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of the foundation produce seismic body waves in various directions 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

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 transmission. 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.

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 interface 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 neighborhood. 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.

4.2. FLUSH and ALUSH FLUSH and ALUSH are the 2D finite element programs developed 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 international 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 perpendicular 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 viscoelastic 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

1. Deep foundations (including pile foundation). For simplification 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 essential 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 derivation 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

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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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