A cone surface in three-dimensional analyses of slopes with tension cut-off

A three-dimensional limit analysis of slopes is presented in this paper, based on a right circular cone failure surface. The associated translational mechanism appears to yield better assessment of the safety in isotropic rock than the traditional wedge-type mechanism. The strength of a bonded geomaterial was described using a linear strength envelope truncated in the tensile regime. The tensile strength cut-off so introduced constitutes a non-linear portion of the strength envelope, and it allows constructing failure mechanisms that include rupture modes, in addition to the shear deformation mode. Consequently, the mechanisms in materials with tension cut-off are more critical than those in materials with a traditional linear strength envelope. It is also demonstrated that the failure mechanism based on the right circular cone failure surface in vertical slopes yields results as good as or better than the more complex rotational mechanisms, although the difference is not very significant.