The Influence of Curvature on the Stability of Rock Slopes

"Slope stability analysis is performed most commonly using limit equilibrium calculations or numerical models assuming a two-dimensional slice through an infinitely long slope surface. In areas such as open pit mining, where most slope surfaces are not planar, the importance of curvature becomes important due to the economic gains associated with creating a steeper slope. With advances in computing capabilities within the last decade, three-dimensional slope analysis can be performed within reasonable time frames. Some work has been done on the potential importance of curvature on slope stability, mainly assuming homogenous materials with a circular shear-failure mechanism. However, many open pit mines are excavated in jointed rock mass where a completely different set of failure mechanisms can be seen. Depending on the geometry and radius of the pit, the curved geometry may influence the factor of safety and failure behaviour compared to a two-dimensional slice.A series of numerical analyses were performed to investigate the effect of curvature on jointed rock slope stability compared to an equivalent two-dimensional slope analysis. By using discrete element method models, the influence of joint planes and interaction between distinct blocks can be seen. With a three-dimensional model, the effect of curvature can be combined with multiple joint sets at any orientation, which cannot be seen in a single slice. Numerous three-dimensional models are created, along with an equivalent unit-thick slice. The effect of curvature on a variety of different types of failure mechanisms is observed, and graphical relationships are created to quantify the difference between the three-dimensional factor of safety and the two-dimensional factor of safety based on the degree of curvature."