Applications of an Advanced Time Domain BEM to 3-D Problems in Geomechanics

Abstract

A class of challenging problems encountered in geomechanics pertains to the prediction of the transient response of elastic systems of infinite or semi-infinite extent subjected to time dependent loading and boundary conditions. The nature and complexity of such problems restrict the range of available closed form solutions to the ones of linear problems of highly simplified geometries and boundary conditions. Among the numerical techniques, the most popular and well established one is the Finite Element Method (FEM) which can routinely handle complex geometries, medium inhomogeneities, and material non-linearities, and is well suited for both frequency and time domain analysis. However, the FEM by nature encompasses the major disadvantage of modeling infinite, and semi-infinite domains by finite size meshes violating, thus, the radiation damping condition. The problem is confronted, to some extend, by the development of hybrid techniques, and transmitting boundaries, for frequency domain analysis. Yet, time domain FEM solutions involving unbounded 3-D solid media, if available at all, may increase the size of the problem to computationally prohibitive levels. An alternative to the FEM is the Boundary Element Method (BEM), which is based on integral equation formulations, developed in the beginning of the century. The first 3-D time domain BEM formulation, associated with soil-structure interaction problems, has been reported by Karabalis and Beskos [1]. In this formulation the Stokes fundamental solutions are developed on the basis of a step impulse forcing function.