Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

Abstract In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.

[1]  Frank J. Rizzo,et al.  An advanced boundary integral equation method for three‐dimensional thermoelasticity , 1977 .

[2]  D. Beskos,et al.  Boundary Element Methods in Elastodynamics , 1988 .

[3]  O. von Estorff,et al.  Dynamic response of elastic blocks by time domain BEM and FEM , 1991 .

[4]  J. Lysmer,et al.  Finite Dynamic Model for Infinite Media , 1969 .

[5]  O. von Estorff,et al.  Dynamic response in the time domain by coupled boundary and finite elements , 1990 .

[6]  P. K. Banerjee,et al.  Developments in boundary element methods , 1979 .

[7]  Dimitri E. Beskos,et al.  Dynamic response of flexible strip-foundations by boundary and finite elements , 1986 .

[8]  O. A. Pekau,et al.  Time domain procedure of FE‐BE‐IBE coupling for seismic interaction of arch dams and canyons , 1995 .

[9]  I. Lee,et al.  UNIFIED BOUNDARY FOR FINITE DYNAMIC MODELS , 1976 .

[10]  Dimitri E. Beskos,et al.  Dynamic stress concentration studies by boundary integrals and Laplace transform , 1981 .

[11]  Tatsuo Ohmachi,et al.  A FE–BE method for dynamic analysis of dam–foundation–reservoir systems in the time domain , 1993 .

[12]  John P. Wolf,et al.  Dynamic‐stiffness matrix of unbounded soil by finite‐element multi‐cell cloning , 1994 .

[13]  J. Watson,et al.  Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics , 1976 .

[14]  Nasser Khalili,et al.  1D infinite element for dynamic problems in saturated porous media , 1997 .

[15]  Joseph Penzien,et al.  Infinite elements for elastodynamics , 1982 .

[16]  Y. C. Wang,et al.  A numerical model for wave scattering problems in infinite media due to p‐ and sv‐wave incidences , 1992 .

[17]  O. Estorff,et al.  On FEM-BEM coupling for fluid-structure interaction analyses in the time domain , 1991 .

[18]  G. Dasgupta A Finite Element Formulation for Unbounded Homogeneous Continua , 1982 .

[19]  Prasanta K. Banerjee,et al.  Two-dimensional transient wave-propagation problems by time-domain BEM , 1990 .

[20]  Chongbin Zhao,et al.  Dynamic response of concrete gravity dams including dam–water–foundation interaction , 1992 .

[21]  J. Bernard Minster,et al.  A numerical boundary integral equation method for elastodynamics. I , 1978 .

[22]  T. Cruse,et al.  A direct formulation and numerical solution of the general transient elastodynamic problem. II , 1968 .