Three-dimensional elastic analysis by the displacement discontinuity method with boundary division into triangular leaf elements

Abstract

The authors have developed a computing system for 3-D elastic analysis by the distribution of constant displacement discontinuities over a boundary divided into triangular leaf elements. Use of the triangular element allows the extension of the Displacement Discontinuity Method (DDM) to include the boundary value problems with any structural boundary in three dimensions, although the method is not very useful unless the boundaries include faults/cracks. The DDM for the 3-D solution of the various “expressions of influence coefficients”, which are theoretically derived through integration over a triangular element and its partial differentiations, is described. The solution procedure is also briefly presented. The accuracy of the results, which are numerically calculated by the procedure, is demonstrated by comparison with the strict solutions of excavation-induced displacements and stresses around both a spherical cavity and a penny-shaped crack in two kinds of stress fields, respectively.