关键词: 边坡稳定性, 矢量和安全系数, 条分法, 条间力函数, 非线性规划, 广义简约梯度, 电子表格

Abstract:

The definition of vector sum factor of safety (VFOS) is clear in physics and mechanics. Generally VFOS is solved through the stress field computed by finite element method. A simple method for solving VFOS is proposed. Based on the general limit equilibrium method (GLE), the total force and moments equilibrium is satisfied. The VFOS formulation is deduced on the basis of method of slices. Nonlinear programming technique general reduced gradient method (GRG) is employed to search for the critical slip surface. Then the VFOS is solved on the slope of total shear strength of the slip surface. The computation is implemented in the spreadsheet software Excel, which makes the proposed method be easily spread in practice. The results of circle slip surface slopes show that: First, VFOS and the traditional FOS match well and their critical slip surfaces are close too. Second, the slope of shear strength resultant is less the slope angle and quite close to the slope of interslice force when interslice function is constant, thus under equilibrium framework the proposed method can be further simplified: assumes interslice forces is parallel and computes VFOS on the slope of interslice force. Third, The VFOS does not appear to be very sensitive to the interslice force functions (constant and half-sine function). The results of noncircular slip surface slopes show that: First, VFOS and the traditional FOS match well and their critical slip surfaces are close for homogeneous slopes, but there are some differences for slope with weak layers. Second, The VFOS does not appear to be very sensitive to the interslice force functions.

Key words: slope stability, vector sum factor of safety (VFOS), method of slices, interslice force function, nonlinear programming, general reduced gradient(GRG), spreadsheet