Gravitational and tectonic stresses in anisotropic rock with irregular topography

Abstract

An analytical method is presented to predict stresses in rock masses with smooth and irregular topographies formed by the superposition of multiple long and symmetric ridges and valleys. The rock masses are subject to gravity, uniaxial tectonic horizontal compression or tension acting normal to the ridge and valley axis, or to combined gravitational and tectonic loadings. The method can be applied to ridges and valleys of realistic shape, in generally anisotropic, orthotropic, transversely isotropic, or nearly isotropic rock masses. Numerical examples are presented to show the nature of the in situ stress field in transversely isotropic rock masses with different symmetric and asymmetric topographies under gravitational loading, uniaxial tectonic horizontal loading, or combined gravitational and tectonic loading. Under gravity alone, it is shown that non-zero horizontal compressive stresses exceeding the vertical stress develop at and near ridge crests, and that horizontal tensile stresses develop under isolated valleys. Addition of a horizontal uniaxial compression to gravity increases slightly the horizontal compression at the crest of ridges and diminishes the horizontal tension in valley bottoms. Addition of the horizontal tectonic stress has little effect on the magnitude of the vertical stress.