Elastic-viscoplastic solution of a circular tunnel in Hoek-Brown rock mass

Abstract

A closed-form analytical solution to rheological phenomena is obtained based on Hoek-Brown (HB) yield criterion and the generalized Bingham model. Once the circular tunnel is excavated, an initial plastic region is formed. When the total stresses fulfil the yield condition, the initial plastic region steps into the viscoplastic region, in which the displacement develops with time. The one-dimensional constitutive equation of the generalized Bingham model is transformed into a three-dimensional expression in polar coordinates by combining the plane strain condition. With the help of equilibrium differential equation, geometric equation and boundary condition, the stress and displacement in the initial plastic region can be expressed. At the moment of t, the stresses and displacements are described similar to the solutions of the elasto-plastic state. The stresses, strains and displacements after transformation can be expressed in the viscoplastic region. The proposed solution was verified by the closed-form solution of circular tunnels in elastic-brittle-plastic rock mass.