Seismic soil-structure interaction analysis by direct boundary element methods

Abstract Upon establishing the mathematical framework necessary for a proper understanding of the analytical theory, a regularized form of the conventional direct boundary integral equation formulation for three-dimensional elastodynamics is presented for a general anisotropic medium. Founded on the basis of a full decomposition of the Greens functions into regular and singular parts, the alternative boundary integral equation format is compact and without demand ingmathematical and numerical complexities such as Cauchy principal values. Extended to deal with general seismic soil-structure interaction problems in semi-infinite media, the formulation is implemented computationally together with a rigorous treatment of singular dynamic multi-layered viscoelastic half-space Greens functions and interfacial boundary tractions arising in typical soil-structure-foundation configurations. A set of new benchmark numerical results are included.

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

[2]  Ramón Abascal,et al.  Dynamics of Foundations , 1987 .

[3]  Akira Mita,et al.  IMPEDANCE FUNCTIONS AND INPUT MOTIONS FOR EMBEDDED SQUARE FOUNDATIONS , 1989 .

[4]  Ted Belytschko,et al.  A variationally coupled FE–BE method for transient problems , 1994 .

[5]  Meng H. Lean,et al.  Accurate numerical integration of singular boundary element kernels over boundaries with curvature , 1985 .

[6]  Carlos Alberto Brebbia,et al.  Topics in Boundary Element Research , 1985 .

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

[8]  Dimitri E. Beskos,et al.  Dynamic analysis of large 3‐D underground structures by the bem , 1995 .

[9]  N. A. Haskell The Dispersion of Surface Waves on Multilayered Media , 1953 .

[10]  R. Christensen,et al.  Theory of Viscoelasticity , 1971 .

[11]  W. Thomson,et al.  Transmission of Elastic Waves through a Stratified Solid Medium , 1950 .

[12]  T. Triantafyllidis,et al.  Dynamic stiffness of rigid rectangular foundations on the half-space , 1986 .

[13]  R. J. Apsel,et al.  On the Green's functions for a layered half-space. Part II , 1983 .

[14]  Eduardo Kausel,et al.  Elements for the numerical analysis of wave motion in layered strata , 1983 .

[15]  Dimitris L. Karabalis,et al.  Three-Dimensional Soil-Structure Interaction by Boundary Element Methods , 1987 .

[16]  R. Pak,et al.  Mathematical boundary integral equation analysis of an embedded shell under dynamic excitations , 1994 .

[17]  B. Guzina,et al.  Static fundamental solutions for a bi-material full-space , 1999 .

[18]  L. Wheeler,et al.  Some theorems in classical elastodynamics , 1968 .

[19]  F. Hartmann Elastic potentials on piecewise smooth surfaces , 1982 .

[20]  Regularized integral representation of thermoelastic stresses , 1991 .

[21]  J. E. Luco,et al.  Dynamic Response of a Rigid Footing Bonded to an Elastic Half Space , 1972 .

[22]  Unified Symmetric BEM‐FEM for Site Effects on Ground Motion—SH Waves , 1991 .

[24]  John L. Tassoulas Dynamic Soil-Structure Interaction , 1989 .

[25]  Frank J. Rizzo,et al.  A boundary integral equation method for radiation and scattering of elastic waves in three dimensions , 1985 .

[26]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis: Part II (1986-1996) , 1997 .

[27]  Dimitri E. Beskos Boundary Element Methods in Structural Analysis , 1989 .

[28]  J. E. Luco,et al.  Tables of impedance functions for square foundations on layered media , 1985 .

[29]  Michihiro Kitahara,et al.  Application of the boundary integral equation (BIE) method to transient response analysis of inclusions in a half space , 1986 .

[30]  C. Brebbia,et al.  Advances in boundary element methods for fracture mechanics , 1993 .

[31]  Ronald Y. S. Pak,et al.  Forced vertical vibration of rigid discs with arbitrary embedment , 1991 .