Kinematics of Overhanging Slopes in Discontinuous Rock

The kinematics of overhanging rock slopes and the mechanical constraints associated with this specific slope geometry were studied. Investigation of the problem began with a generalized rigid body analysis and was followed by a numerical discontinuous deformation analysis, both of which were performed in two dimensions. It was found that eccentric loading and hence the development of tensile stresses at the base of overhanging rock slopes control their stability. Global slope instability, which is typically manifested in a forward rotation failure mode, may ensue if a through-going vertical discontinuity, typically referred to as “tension crack,” transects the slope at the back. The transition from stable to unstable configurations depends on the distance between the tension crack and the toe of the slope. On the basis of the analysis, a simple threefold stability classification—stable, conditionally stable, and unstable—is proposed. In addition, geometrical guidelines, based on standard field mapping data, for the above stability classification are provided. Finally, the optimal reinforcement strategy for overhanging slopes is explored. The stability of overhanging slopes is determined by their eccentricity ratio, defined by the ratio between the base $\left(B\right)$ and top $\left(L\right)$ lengths: $e_r=B∕L$ . It was found that an overhanging slope with eccentricity ratio of $e_r<0.38$ is unstable and requires reinforcement. With an eccentricity ratio between $0.38<e_r<0.62$ , the slope is considered conditionally stable against toppling failure, and reinforcement should be considered if the geometry approaches the lower bound eccentricity of 0.38. A comparison of full and partial face reinforcement schemes showed that full face reinforcement is preferable. The findings of this study were demonstrated by using an illustrative case study in which the stability of a $34\mathrm{m}$ high overhanging slope in a highly discontinuous rock mass was studied and an optimal rock bolt reinforcement scheme was designed.