关键词: 安全系数, 矢量和, 滑动趋势, 极限抗滑剪应力矢量方向, 稳定性分析

Abstract: The vector sum method (VSM) based on real stress state has been applied recently for analysing the slope stability, considering its clear physical meaning. However, the factor of safety (FoS) defined by VSM could be negative in the case where total normal force vector projection is negative, and its absolute value is larger than total shear force vector projection. Moreover, deduced by Pan’s Principle, the direction of shear resistance stress vector of every point on potential slip surface is currently defined to be opposite to that of the projection of the potential slip direction of the possible slip mass on the tangential surface through this point. However, according to the definition of VSM safety factor and Pan’s Principle, the direction of the projection of the potential slip direction on the tangential surface through this point is opposite to that of the total resistance stresses including shear and normal ones. In this study, a vector-sum-based slip surface stress method for analysing slip mass stability was proposed to overcome these two disadvantages above of VSM. The slip surface was treated as a thin slip band, and forces undertaken by an arbitrary element of the slip band was analysed. The direction of the limit resisting shear stress of an arbitrary element was defined as the opposite direction of the real shear stress, and the possible slip direction was defined as the opposite direction of the resultant limit resisting shear force. Finally, FoS was defined as the ratio of the projection of the limit resisting shear force vector sum in the opposite possible slip direction to that of real dynamic shear force vector sum in the possible slip direction. Compared with the limit equilibrium method, the proposed method satisfied the force and moment equilibrium equations and compatibility conditions without any assumption. Compared with the shear strength reduction method, the proposed method defined that the FoS was explicit form avoiding iteration. The classic two-dimension static slope case was used to verify the proposed method with comparisons among main methods for slope stability analysis, which indicated that the proposed method was feasible. Additionally, the proposed method was applied to a three-dimensional engineering case to study its stability during the excavation process, which showed the proposed method could be used for practical application.

Key words: safety factor, vector sum, potential slip direction, limiting shear resistance stress vector, stability analysis