Unified solution of safety factors for three-dimensional compound slopes considering local and global instability

Abstract

Local instability of a compound slope is commonplace in practice. Extant analytical solutions only considered the single global failure pattern, which results in an inaccurate assessment of slope stability. This paper develops a unified analytical framework to account for the local and global instability of a compound slope. A failure pattern coefficient is proposed for the determination of instability behaviors. On this basis, the kinematically admissible three-dimensional (3D) failure mechanism is modified to describe the collapse of slopes. Under the framework of the upper-bound theorem of limit analysis, the external work rates and the internal dissipation rates can be calculated from the unified failure mechanism. The strength reduction technique is introduced into the work rate balance equation, and then the explicit solution of the safety factor is derived. The critical safety factor and slip surface are obtained through a hybrid optimization of the objective function. By way of example, the present solutions are compared with previous solutions and the results of the finite element method. Good agreements of the safety factor and slip surface show the good capability of this study to implement the stability analysis of compound slopes. A detailed parametric study is carried out to reveal the influence of slope geometry, soil strength, and external excitation on slope stability and failure pattern. The method presented in this paper provides a more rigorous solution for the stability assessment of compound slopes.