Factor of Safety of Three-Dimensional Stepped Slopes

Abstract

Stepped slopes have been widely used in slope and excavation engineering to improve slope stability. On the basis of the three-dimensional (3D) horn failure mechanism, this article proposes a new method to estimate the factor of safety (FS) of 3D stepped slopes. The method incorporates the force-increase technique and the upper-bound theorem. The FS is determined as the ratio of the internal energy dissipation rate to the external work rate. Seismic effects are included in the analysis by introducing a horizontal seismic coefficient. According to the calculations of external work rate and internal energy dissipation rate, an explicit expression for the FS of 3D stepped slopes is derived, which is of great use in geotechnical engineering applications. The lowest upper-bound solution is obtained from an optimization scheme in which the minimum of the FS is sought. Comparisons between the present results and the previously published solutions are presented to assess the validity of the proposed method, and a sensitivity analysis is presented to discuss the effects of different parameters on the FS of 3D stepped slopes. An example illustrates how to obtain the suitable shape of the stepped slope when the relative positions of the toe and the crest are fixed. Finally, tables giving the FS values for slopes with different parameters are listed for simplicity of practical use in stepped excavation.