Stability coefficient analysis of soil slopes with non-linear topography based on the ratio of internal to external power

Abstract

The limit analysis of slope stability has a relatively higher calculation efficiency and accuracy because it ignores the constitutive relation of materials. Compared to the limit equilibrium method, its assumptions are strict and realistic. In the classical upper bound limit analysis, the slope surfaces are required to be a regular straight line. However, the surfaces of natural or cutting slopes are normally nonlinear. In addition, the stability number Ns=c/γH is used to calculate the critical height of slopes without considering the external power caused by pore pressure. Different from the static equilibrium conditions adopted by the traditional limit equilibrium method, this paper aimed to evaluate the stability of slopes with nonlinear surfaces based on kinetic analysis. First, a method for determining the rotation center of landslides with nonlinear surfaces based on upper bound limit analysis and the principle of virtual work was proposed. Second, it was assumed that the sliding surface was a logarithmic helix, and the virtual work under gravity and energy equilibrium equation of slopes were established. Third, the stability coefficient K defined by the ratio of internal power to external power was proposed to evaluate the stability of the slope, and the results were compared with the Bishop method to verify its effectiveness. The influences of slope degree (β), internal friction angle (φ), cohesion (c) and pore pressure coefficient (ru) on the stability coefficient K of different natural and cutting slopes were analyzed. The results confirmed that the stability of steep slopes would be improved by cutting. The stability coefficient K increased with increasing cohesion and decreased with increasing pore water pressure coefficient. When the impact of cohesion on the stability coefficient K was more significant than that on the pore water pressure coefficient, K increased with increasing internal friction angle (φ). In contrast, the stability coefficient K decreases with increasing internal friction angle (φ). The above results followed the general understanding of slope stability analysis, and the rationality of the model was verified. By comparing the calculation results with the Bishop method, it was found that the intension of the critical state represented by safety factor FS=1 was the same as the stability coefficient K=0 defined in this paper. The stability coefficient K increased nonlinearly with increasing cohesion, which was in line with the progressive failure mode of the soil slopes.

Keywords

• soil slope
• non-linear topography slope
• upper bound limit analysis
• virtual work
• stability coefficient