Technical Notes - Clarification of Three-Dimensional Plane of Weakness Concepts

The author recently proposed a technique for handling the effect of planes of weakness on failure in geologic material.1 The technique employed an "extended" Mohr's rupture envelope, on which was superimposed a generalized three dimensional stress representation. Subsequently, the method was applied to so-called two-dimensional stress states" which were in reality degenerate three-dimensional ones. Since a two-dimensional stress solution usually refers to a plane stress condition, the terminology was confusing. The distinction between a plane stress state and a degenerate three-dimensional one is shown in Fig. 1. The solution of problems involving a generalized three-dimensional stress state is greatly aided by continual reference to the basic principle that no stress components can act on a plane, oriented as is the weakness plane, which lies outside of the weakness plane's rupture enVelope.2 This is shown in Fig. 2; and if it is also remembered that the radii of the Mohr's Circles give the orientation of such a plane, solutions are easier to follow, and perform. Sample Problem 1: Site Location (generalized three-dimensional case).' Given: 1) Both rupture envelope for the solid and plane of weakness. 2) Existing principal stresses and orientations in space (?12, ?13) obtained from a stress analysis of the proposed structure. Find: Permissible orientations of the weakness plane in order to select a suitable site.