Limiting equilibrium versus BS3D analysis of a tetrahedral rock block

In order to analyze the stability of a 3D rock block using a limiting equilibrium method, some simplifications must be introduced, such as neglecting the effects of deformability of the rock block, fractures, and the surrounding rock mass, the progressive failure and the mobilization of shear strength of fractures, and changes in in situ stresses with block displacement. These limitations may cause some errors when calculating the factor of safety of the block. This paper quantifies the error caused by these simplifications comparing the results against those obtained with a numerical method (BS3D). In addition, the effects of the normal stiffness of the fractures, dilatancy, the tunnel radius, and the block size on stability of the tetrahedron are investigated using the numerical tool to demonstrate the importance of the effects eliminated by the limiting equilibrium approach. © 2010 John Wiley & Sons, Ltd.