Circular tunnel in a gradient elastoplastic rock mass

Abstract

This paper attempts to study the mechanical behavior of an elastoplastic rock mass around an underground circular excavation by using gradient theory. The problem (in plane conditions) is reduced to that of a circular hole within an elastoplastic geomaterial which is subjected to a far-field uniform compression. At the perimeter of the hole an all-around uniform pressure is applied. The constitutive law adopted for the elastic region is a special form of gradient elasticity while for the plastic region around the tunnel; the Tresca failure criterion is used. Appropriate boundary conditions (classic and extra) are taken in order to solve the corresponding boundary value problem, and the analytical expressions of stresses, strains and displacements in the elastic and plastic regions are presented. The solution for the elastoplastic boundary is achieved numerically and the observed size effect, i.e. the dependence of the elastoplastic boundary on the tunnel radius, is described. © 2020 ISRM.