Influence of axial stress and dilatancy on rock tunnel stability

In many existing elastoplastic plane-strain solutions for a circular tunnel excavated in a homogeneous, isotropic rock mass under a hydrostatic stress field, the longitudinal axial stress (or the out-of-plane stress) sigma(z) is not correctly evaluated. This paper describes the concepts and a numerical method to calculate this stress component and proposes analytical solutions for practical applications. The computed numerical solutions are compared with theoretical solutions where possible. The relations between rock-mass dilatancy, tunnel displacements, and the in-situ stress field are investigated. Mohr-Coulomb and Hoek-Brown yield criteria with appropriate plastic potential functions and nonassociated flow rules are used in the brittle plastic calculations. The effects of various boundary conditions on the numerical analyses are discussed and several important practical conclusions are drawn from the investigations.