求解边坡矢量和安全系数的条分法

矢量和安全系数物理、力学意义明确,通常采用有限元计算得到的应力场来求解.提出一种简便的求解方法,在通用条分法(GLE)的基础上,满足力和力矩平衡的严格条件,推导了基于条分法的矢量和安全系数.采用广义简约梯度法(GRG)搜索临界滑面,在极限抗滑合力矢方向上求解矢量和安全系数.整个计算过程都在电子表格软件Excel内实现,易于在工程实践中推广.对于圆弧滑面边坡,其计算结果表明:①矢量和安全系数与代数和安全系数非常接近,对应的滑面位置也相近.②不同的条间力函数假设(常数和半正弦函数)对边坡的矢量和安全系数影响很小.③极限抗滑合力矢方向θ小于边坡坡角,其值与假定条间力平行时的条间力方向非常一致.在极限平衡分析框架内,计算方法可进一步简化为:假设条间力平行,将条间力方向作为矢量和安全系数的计算方向.对于非圆弧滑面边坡,其计算结果表明:①均质边坡的矢量和安全系数与代数和安全系数相对误差小于3 %,滑面位置接近,而软弱层边坡两种方法的计算结果有一定差别.②不同的条间力函数假设对边坡的矢量和安全系数影响很小.

Solving vector sum factor of safety of slope by method of slices

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.