Boundary Integral Techniques for Stochastic Problems in Geomechanics

Abstract

A review of Boundary Element Methods (BEM) in the field of geomechanics over the last fifteen years clearly shows the substantial contributions that these methods have made in analysing geotechnical problems. There is, however, a need to expand these integral equation-based techniques to the case where the ground is represented as a stochastic medium. This is especially true in the case of time-dependent problems where, depending on the characteristics of the propagating disturbance, it is quite possible for the wavelength to be of comparable dimension as the spacing of the randomly distributed inhomogeneities in the ground. As a result of this, the propagating disturbance can be noticeably altered, primarily through reduction of its mean amplitude due to scattering from the random irregularities. In addition, the analysis of stochastic problems serves as a stepping stone for other important topics such as sensitivity and reliability of geotechnical designs to basic soil and rock material parameters. This work outlines the general formulation and solution in terms of random integral equations for problems involving a random medium and subsequently discusses approximate, perturbation-based techniques. The methodology is applied to shear wave propagation in stochastic soil.