An issue in the current definition of the factor of safety for rock slopes and suggestions for improvement

Abstract

To evaluate the stability of a rock slope a common practice is to calculate the factor of safety by dividing the driving forces on the resisting. Hoek and Bray [1] proposed a formula for the calculation of the factor of safety FS for rock slopes reinforced by pre-tensioned bolts and anchors, so-called active support devices. The formulas have been used worldwide for active support of rock slopes in the past 40 years and are also incorporated in different rock slope stability software. The reinforcement force of the active support is in the formula considered a negative driving force. On the other hand, for passive support, referring to reinforcement by non-tensioned bolts and anchors, the reinforcement force is counted as an additional resisting force in the calculations. In this paper, the two definitions to the factor of safety are examined with the help of an example of simple block equilibrium, which demonstrates issues regarding the formula for active support. It is concluded that the reinforcement force should always be counted as a resisting force in the calculation of the factor of safety regardless it is active or passive support. Concepts of factors of safety for shear failure and collapse are proposed and verified with a calculation example.