A general analytical solution for the required anchor force in rock slopes with toppling failure

A general analytical solution is presented for the limit equilibrium of block toppling failure in rock slopes. The method follows the well-known solution of Goodman and Bray, but with infinitesimal thickness of blocks. This leads to a set of ordinary differential equations that can be integrated ill cases of simple geometry. The case of a uniform slope is analysed in detail. Two main failure modes have been identified: sliding toe (ST), and tension toe (TT), depending on the relative values of the dip, cut slope and friction angle. The solution can be considered as accurate enough for slopes higher than 20 30 times the average block thickness. For thicker blocks, a linear reduction of the force is proposed. The method has been applied to a number of actual cases and a particular example is presented in detail. (C) 2001 Elsevier Science Ltd. All rights reserved.