Gravitational stresses in long symmetric ridges and valleys in anisotropic rock

Abstract

The effect of topography and rock mass anisotropy on gravitational stresses in long isolated symmetric ridges and valleys is modeled using an analytical method proposed earlier by the first two authors. The rock mass deforms under a condition of plane strain. A parametric study is presented on the effect of (1) topography, (2) orientation of anisotropy and (3) degree of anisotropy on the magnitude and distribution of gravitational stresses in transversely isotropic rock masses with planes of anisotropy striking parallel to the ridge or valley axis. It is found that compressive stresses develop near ridge crests and that tensile stresses develop in valley bottoms and valley walls. The magnitude of the gravitational stresses is of the order of the characteristics stress ϱgβbβ where ϱ is the rock density, g is the gravitational acceleration and βbβ is the height of the ridge or depth of the valley.