Three-Dimensional Limit Analysis of Slopes with Pore Pressure

Three-dimensional (3D) slope stability analyses are not performed routinely because they involve increased effort compared with two-dimensional analyses, and because the latter yield more conservative results. However, in cases of distinct limitations of the width of the failure region (e.g., in the case of excavations), an assessment of safety using 3D stability analyses may be more appropriate. The kinematic approach of limit analysis for the assessment of stability of slopes is presented, based on a recently conceived rigid-rotation 3D mechanism modified to include below-toe failures, which are common for gentle slopes. The presence of pore-water pressure in the slope is included approximately using the scalar parameter $r_u$. The results are presented in terms of the critical height (or dimensionless coefficient $\gamma H/c$), and also in the form of charts and a closed-form approximation formula that allow for direct assessment of the safety factor for slopes with constrained width. Not surprisingly, the safety factor decreases with an increase in the pore-water pressure and with an increased width of the slope (increased failure zone).