A generalized upper-bound limit analysis approach for stability analysis of complex multistep and multilayer slopes

Although the upper bound approach of limit analysis has attracted extensive attention in the slope stability analysis, its derived analytical solutions have not been directly applied to the stability analysis of the slopes with arbitrary complicated multistep and multilayer. Adopting the rigid body assumption and the combined log-spiral rotational failure mechanism, we derive a unified integral expression for the external work rate and the related virtual work equation for slopes with arbitrary surface geometry and multiple soil layers. A generalized upper bound approach of limit analysis is proposed, by which the overall stability of complex multistep and multilayer slopes can be achieved. To overcome the difficulty in calculating integral formulations, the numerical integration technique is introduced. Based on this, the global factors of safety (FSs) and the corresponding CSSs of complex layered slopes are obtained by using the strength reduction technique combined with an optimization method. Several representative examples are employed to validate the analytical solutions and comparisons of the FSs and the corresponding CSSs obtained by various methods are also conducted. The results show that the proposed approach can yield the high-accuracy solutions and is widely applicable to the stability analysis of complex layered slopes. The new approach is applied to a typical multistep and multilayer slope case.