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 in 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.