A generalized solution for tetrahedral rock wedge stability analysis

Abstract It has been found that the limit equilibrium approach commonly used for tetrahedral rock wedge stability analysis is statically indeterminate and the conventional method proposed in textbooks actually involves an assumption that the shear forces applied on the failure planes are parallel to the line of intersection. A new method that allows an input of various shear force directions is presented in this paper. This method starts from an assumed wedge displacement vector that can be related to the shear force directions. By applying the limit equilibrium conditions a governing equation calculating the factor of safety has been obtained. This equation also permits a formal demonstration to confirm that a maximum factor of safety exists when the rock wedge dilates at values of friction angles to the left and right failure planes respectively, the direction required Mohr–Coulomb's associative flow law. The generalized method therefore provides a theoretical support to some fundamental postulates in Plasticity. The factors of safety obtained by the conventional method and the generalized approach are not substantially different if the shear strength of the failure planes involves a reasonable value of cohesion. However the deviations between the two approaches can be remarkable if the material is purely frictional. Further study by physical model testing and field investigation is recommended.