Analytical solution for determining the plastic zones around twin circular tunnels excavated at great depth

Abstract

Many existing planar elastoplastic analyses have been limited to the case of only one tunnel excavated in rock mass. The Mohr-Coulomb failure criterion, which is widely used in rock engineering, is considered in this paper to propose an analytical method for determining the plastic zones around twin circular tunnels of equal size excavated at great depth. The premise is that the plastic zone around each tunnel can completely enclose the tunnel edge and the two plastic zones are not connected. The unknown elastic zone on the physical plane is mapped onto an annular region on the image plane using the conformal transformation in the complex variable method, which transforms the problem of determining the elastoplastic interfaces into solving the mapping function coefficients. On the basis of the stress continuity conditions along the two elastoplastic interfaces, the nonlinear equations about the mapping function coefficients are established, and then solved effectively by the differential-evolution algorithm, in which the coefficients are considered as design variables. The presented solution is verified by numerical solution. The influence of tunnel spacing, cohesion, internal friction angle and in-situ stresses on plastic zones are analyzed.