Analytic Method of Stress Analysis for an Orthotropic Rock Mass with an Arbitrary-Shaped Tunnel

Abstract

Rock mass often exhibits anisotropic properties. Even isotropic rocks will behave anisotropically if cut by regular joint sets. Many rock masses can be regarded as orthogonal anisotropic linear elastic bodies. To date, there is no analytic method available to determine the stresses in an arbitrary-shaped tunnel (except for elliptic holes and circles) in an orthogonal anisotropic rock mass under the action of in situ stresses. To obtain analytical solutions, the conformal transformation method is used, in which with three polar coordinates are introduced. By introducing the power series method, a new analytic method used to determine stresses in an orthogonal anisotropic rock mass with an arbitrary-shaped tunnel is proposed. The analytic solutions are verified by numerical analyses using computer simulation software.