Stresses in Anisotropic Rock Mass with Irregular Topography

Abstract

This paper presents a new analytical method for determining the state of stress in a homogeneous, general anisotropic, and elastic half‐space limited by an irregular and smooth outer boundary. The half‐space represents a rock mass with an irregular and continuous topography. The rock mass is subject to gravity and surface tractions. The stresses are determined assuming a condition of generalized plane strain, and are expressed in terms of three analytical functions following Lekhnitskii's complex function method. These analytical functions are determined using a numerical conformal mapping method and an integral equation method. As an illustrative example, it is shown how the proposed method can be used to determine the state of stress in long isolated and symmetric ridges and valleys in orthotropic or transversely isotropic rock masses. It is found that the magnitude of the stresses is of the order of the characteristic stress ρg|b|, where ρ is the rock density, g is the gravitational acceleration, and |...