Discussion on the Multi-Solution of Three-Dimensional Slope Safety Factor

Abstract

The limit equilibrium method cannot yield a unique value of safety factor in three-dimensional (3D) analysis of slope. However, the calculated value of safety factor according to limit equilibrium method directly determines the design of slope engineering. So, the study of multi-solution of three-dimensional slope safety factor may help people to judge further the reasonableness of the computation results and select the range of safety factor’s possible values. In this paper, the initial distribution of normal stresses over the sliding surface is assumed, which is then modified by a function involving four parameters to satisfy force and moment equilibrium conditions of the sliding body. Then, according to a series of assumed safety factors, the corresponding minimum value of the normal stress of sliding surface is calculated by force and moment equilibrium conditions of the sliding body. Then the reasonable range of slope safety factor is justified according to the reasonableness of the normal stress distribution over the sliding surface. The calculation results of engineering examples show that the reasonable range of safety factor for symmetric slopes is between 8 and 12% and that the reasonable range of safety factor for asymmetric slope is over 30%. Therefore, it is necessary to further verify the rationality of normal stress for the safety factor of three-dimensional asymmetric slope in order to further apply it to engineering.