On the application of finite-element techniques to problems concerning potential distribution and stress analysis in the earth sciences

Abstract

The elastic response (i.e., displacement fields, strain and stress distributions) has been determined by structural matrix analysis for a homogeneous rock layer subjected to two-dimensional distributions of vertical displacement applied along a basal boundary. The results obtained compare favorably with biharmonic function solutions obtained bySanford [42]2) and the authors. The analysis was then extended: the effects of different magnitudes of superposed gravitationally-induced stresses, release of a constrained side boundary, and introduction of pronounced heterogeneity were each quantitatively evaluated. Each of these changed conditions effected important alterations in response characteristics, e.g., in configuration of stress trajectories, predicted locations and configurations of initial fracture surfaces, shear stress distributions, and displacement fields.