The generalized plane strain problem and its application in three-dimensional stress measurement

Abstract

This paper proposes a complete definition of the plane strain problem. It consists of five subtypes: the classical one and four subtypes of the generalized plane strain problem. Among them the axial strain is a compatible condition. Following that definition, for problems which are not more complex than that, the axial load as well as axial strain are linear functions of x, y, and the problems can be solved as a plane strain problem. Their solutions are found by simply superposing the solutions of three of the fundamental equations. According to the fourth subtype of the generalized plane strain problem mentioned, the solutions of a hollow inclusion adhered inside a round hole in an infinite object are given, by which the six stress components of virgin stresses in a rock mass stress measurement using CSIR or CSIRO triaxial probes can be fixed. Comparing the calculated results by the method proposed in this paper with the existing methods, utilizing the data of some authors, it is noticed that the axial stress component calculated by the former method is reduced and that the principal stresses and their directions are altered, which may directly explain the discovery by some authors that the axial stress analyzed by the existing methods tends to a higher value.