Limit Analysis and Stability Charts for 3D Slope Failures

The kinematic approach of limit analysis is explored in three-dimensional (3D) stability analysis of slopes. A formal derivation is first shown indicating that, in a general case, the approach yields an upper bound to the critical height of the slope or an upper bound on the safety factor. A 3D failure mechanism is used to produce stability charts for slopes. The slope safety factor can be read from the charts without the need for iterations. While two-dimensional (2D) analyses of uniform slopes lead to lower safety factors than 3D analyses do, a 3D calculation is justified in cases where the width of the collapse mechanism has physical limitations, for instance, in the case of excavation slopes, or when the analysis is carried out to back-calculate the properties of the soil from 3D failure case histories. Also, a 3D failure can be triggered by a load on a portion of the surface area of the slope. Calculations indicate that for the 3D safety factor of the loaded slope to become lower than the 2D factor for the same slope (but with a load-free surface), the load has to be very significant and equal to the weight of a soil column of the order 10−1 of the slope height.