Rock Wedge Stability

INTRODUCTION A study has been made of the stability of blocks and wedges of rock subjected to gravity forces in the roofs of underground excavations. Rock wedges may become wholly or partly self supporting with the mobilization of shear resistance of discontinuities bounding such wedges. The influence of in-situ stresses and the relative stiffnesses of the intact rock, and shear and normal stiffnesses of the discontinuities has been investigated. A two dimensional, plane strain model of symmetric rock wegdes in a horizontal stress field has been utilized. A comparison between the results of an extension of a closed form solution proposed by Bray(1981), and numerical analyses with Displacement Discontinuity elements (Crouch, 1976), are presented. These analyses indicate that the stability of the wedge and the stress redistribution around the wedge upon excavation of an opening is markedly influenced by the ratio of intact rock stiffness to seam normal and shear stiffness. It is shown that the analytical solution provides a reasonable measure of the lower and upper bounds of the loads necessary to cause failure of the wedge. MODELS The problem considered (Fig. 1) is a two dimensional plane strain model containing two discontinuities. The discontinuities are symmetrically disposed with respect to a horizontal excavation which forms a wedge of rock bounded by these discontinuities. The angle of the intersecting discontinuities at the apex of the wedge is 2[a]. Mechanical properties of the two discontinuities are identical, being represented by linear normal and shear joint stiffnesses Kn and Ks and angle of friction [o]. The rock wedge is loaded by an in-situ horizontal stress field [ah]