Flexural toppling failure is one of the most probable instability of rock slopes. If rock slope is composed of a set of parallel discontinuities dipping steeply against the face slope, the rock mass will have potential of flexural toppling failure. As such, the rock mass behaves like inclined cantilever rock columns which are placed on top of each other, and bended by their own weights. If the bending stress exceeds the rock columns tensile strength, flexural toppling failure will be initiated. Since the rock columns are "statically indeterminate" hence, their factors of safety may not be determined solely by equilibrium equations. In this paper, rock columns with a potential of flexural toppling are modeled with a series of inclined and inter-bedded cantilever beams. The model is based on principle of compatibility equations and leads to a new method by which the magnitudes and points of application of intercolumn forces are determined. As a result, factor of safety for each rock column can be computed independently. Therefore, on this basis, every rock column will have a unique factor of safety. The least factor of safety exists in any rock column is selected as rock mass representative safety factor based on which a simple equation is proposed for a conservative rock slope stability analysis and design. The result of such an equation is compared with the results of existing experimental flexural toppling failure models for further verification.
Toppling failure is a serious instability of rock slopes [1, 2, 3, 4, 5, 6]. This failure has been classified into four principal types: flexural, blocky, blocky-flexural and secondary . Flexural toppling failure occurs due to bending stresses. In order to describe the mechanism of such a failure, it is presumed that rock slope is composed of a set of parallel discontinuities dipping steeply against the face slope. As such, the rock mass behaves like a series of inclined cantilever rock columns which are placed on top of each other (Figs. 1 and 2). The body force of each rock column is analyzed into two components; normal to and parallel with the rock column longitudinal axis. The normal component will cause the rock column to bend and transfer the load to the underlying one. The bending moment produces tensile and compressive stresses in every cross-sectional area of each rock column. If the tensile stress exceeds the rock column tensile strength, failure of rock slope will be initiated. Hence, to compute the factor of safety of the rock slope against flexural toppling failure, the magnitude of maximum tensile stress in rock columns must be determined. Theoretically, the rock columns are "statically indeterminate" and the maximum tensile stress can not be determined only by equilibrium equations. Therefore, in order to compute the factor of safety of rock slope against flexural toppling failure, boundary conditions and/or principle of compatibility equations must be satisfied. A brief review of these approaches is given hereunder.
Fig. 1. Schematic diagram of flexural toppling failure in rock slopes. (available in full paper)