Determining the Critical Slip Surface of Slope by Vector Sum Method Based on Strength Reduction Definition

Abstract

Slope-stability assessment involves the location of the critical slip surface and the corresponding factor of safety (FOS). Considering force-vector characteristics, the vector sum method was further studied based on the strength reduction definition of the FOS and stress field of slope, and the FOS can be calculated directly by the force limit equilibrium equation on the global sliding direction of the slope. For the sliding direction, it is rigidly proved to be determined only by the sliding shear stress along the slip surface based on the principle of minimum potential energy. Then, two examples with fixed slip surfaces were analyzed and the results were compared with the rigorous Morgenstern–Price method. Finally, two examples from the literature are investigated for searching the critical slip surface using the proposed method and a real-coded genetic algorithm. The calculated results revealed the rationality of the proposed method for both fixed slip surfaces and critical slip surfaces from the literatures in slope stability assessment. This proposed method provides a new path to assess the slope stability, which is worth to be further studied in practical engineering.