Stability assessment of three-dimensional slopes with cracks

The stability of three-dimensional (3D) slopes with cracks is presented based on the kinematic approach of limit analysis. The sequence quadratic program optimization procedure is applied to obtain the least upper bound results. The most critical crack, including the crack depth and crack location in the 3D slope, is discussed. To provide a quick reference of the slope safety factor, stability charts are presented. The geometry of the critical failure surfaces, including the most unfavorable cracks for slopes with different width constraints and inclinations, are analyzed as well. Conclusions can be drawn that the critical height of the slope reduces due to the presence of cracks. A larger reduction in the critical height of slopes is found under plane strain conditions, compared to that under three-dimensional conditions. This reduction drops, however, with decreasing slope inclination angle. In addition, when compared with plane-strain conditions (slope width approaches infinity), the 3D slopes (with limited width) exhibit shallow sliding characteristics.