Gravitational stresses in anisotropic rock masses with inclined strata

Abstract

Abstract This paper presents closed-form solutions for the stress field induced by gravity in generally anisotropic, orthotropic and transversely isotropic rock masses. These rocks are assumed to be homogeneous and linearly elastic continua with strata inclined with respect to a horizontal ground surface. It is found that the stress field is multiaxial. The vertical stress is always a principal stress and is equal to the weight of the overlying material. The horizontal stresses are strongly correlated to the rock mass fabric. The expressions for the gravity-induced horizontal stresses are different for rock masses deforming under conditions of no lateral strain and no lateral displacement (uniaxial strain). The gravity-induced horizontal stresses depend on several parameters such as the type, degree and orientation of the rock anisotropy with respect to the ground surface. It is found that depending on the value of those parameters, and constrained by the thermodynamic requirement that the strain energy of the rock must always be positive-definite, the gravity induced horizontal stresses can be larger, equal or less than the vertical stress. Furthermore, for a certain range of elastic properties of a transversely isotropic rock mass with inclined strata only, it is thermodynamically admissible for the horizontal stress parallel to the dip direction of the strata to be tensile.