Stresses in anisotropic media with particular reference to problems of rock mechanics

Abstract

The recently developed finite element method of numerical stress analysis has been previously applied to the analysis of the stress distribution in isotropically elastic materials and is here extended to deal with a particular form of anisotropy. The case of anisotropy considered is that generally referred to as transverse isotropy, i.e. where the material is isotropic in the yz plane but non-isotropic with respect to directions normal to this plane. The analysis is restricted to the consideration of two-dimensional plane strain problems in the xy plane. The individual element axis orientation may be varied at will with respect to the overall co-ordinate system so that problems may be treated where the direction of isotropy varies from point to point within the material. It is suggested that this system of anisotropy is particularly relevant to the analysis of stress distributions in stratified rock masses. Previous approaches to this problem are outlined in Appendix 1. A series of illustrative examples are shown, first, to compare the numerical solution to a problem with a known analytical solution to that analytical solution and, second, to show the application to more complex situations with no known analytical solutions. It is concluded from the first comparison that the method is capable of giving good accuracy.