Stability analysis of multi-directional anchored rock slope subjected to surcharge and seismic loads

More than one set of anchors with different orientations can be an economical solution to completely stabilize the rock slope. In this note, a general analytical expression for the factor of safety of a multi-directional anchored rock slope (MDARS) against plane failure is derived, incorporating most of the practically occurring destabilizing forces under surcharge and seismic loading conditions. Several special cases of this expression are found to be similar to those reported in the literature. A graphical presentation shows that for any specific inclination of one set of anchors to the normal at failure plane, the variation in the inclination of the second set of anchors to the normal at failure plane, when greater than approximately 60°, does not cause a significant change in the factor of safety of the MDARS.