The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek–Brown failure criterion

Abstract

Abstract This paper is intended to illustrate the relationship between the Hoek–Brown parameters describing the strength of rock masses and the mechanical response of underground openings. A formulation of the elasto-plastic behavior of rock in terms of the Hoek–Brown criterion is presented. The analysis assumes that the joint system present in the rock mass has no preferred orientation so that the medium can be considered to behave as an isotropic continuum. It is shown that appropriate scaling of the Hoek–Brown parameters leads to considerable simplification in defining the elasto-plastic response of the rock mass. The classical case in which the excavation process is treated as a uniform reduction of internal pressure in symmetrically loaded cylindrical and spherical cavities is considered. Closed-form expressions are given for the extent of plastic behavior and the related stress and displacement fields. A dimensionless graphical representation of these solutions is provided that allows accurate estimates of the response of excavations in Hoek–Brown materials to be made quickly and easily. Examples are given to illustrate the use of the graphs. Illustrative applications of the derived closed-form solutions are also described. The construction of ground reaction curves for the design of cylindrical tunnels according to the convergence–confinement method and a case study of stability analysis of spherical cavities produced by underground nuclear explosions in French Polynesian atolls are discussed.