Gravitational stresses in anisotropic rock masses

Abstract

This paper presents closed-form solutions for the stress field induced by gravity in anisotropic rock masses. These rocks are assumed to be laterally restrained and are modelled as a homogeneous, orthotropic or transversely isotropic, linearly elastic material. The analysis, constrained by the thermodynamic requirement that strain energy be positive definite, gives the following important result: inclusion of anisotropy broadens the range of permissible values of gravity-induced horizontal stresses. In fact, for some ranges of anisotropic rock properties, it is thermodynamically admissible for gravity-induced horizontal stresses to exceed the vertical stress component; this is not possible for the classical isotropic solution. Specific examples are presented to explore the nature of the gravity-induced stress field in anisotropic rocks and its dependence on the type, degree and orientation of anisotropy with respect to the horizontal ground surface.