多阶边坡滑移面搜索模型及稳定性分析

基于极限平衡理论,根据边坡尺寸及几何关系,建立辅助坐标系与基本坐标系。借助于基本坐标系,首先推导出滑移面几何控制参数与滑移面圆心坐标之间的函数关系,再推导出安全系数计算式中各变量与圆心坐标之间的函数关系,从而得出滑移面的控制参数与安全系数之间的函数关系。辅助坐标系可沿多阶边坡表面移动,控制搜索过程中滑移面的位置及几何参数,实现边坡内任意潜在的滑移面的搜索,从而计算边坡内任意潜在滑移面对应的安全系数,并进一步确定边坡最小安全系数及最危险滑移面。该方法适用于多阶土体边坡最危险滑移面的确定,可避免由经验公式确定滑移面圆心搜索区域造成的不准确性,较好地解决多阶边坡最危险滑移面难确定的问题,是一种由计算机搜索法求解多阶边坡稳定性的新模型。最后,编制多阶边坡稳定性计算程序,并进行实例分析与计算。

SEARCH MODEL OF SLIP SURFACE AND STABILITY ANALYSIS OF MULTI-STEP SLOPE

Based on limit equilibrium theory,a basic coordinate system and an auxiliary coordinate system are set up according to the size and geometrical relationship of slope.By virtue of the basic coordinate system,firstly,the function relations are deduced between the geometrical control parameter of slip surface and the center coordinate of circular slip surface.Then,the function relations are deduced between each variable in the safety factor expression and the center coordinate of circular slip surface.Thereby,the function relations are derived between the geometrical control parameter of slip surface and the safety factor of slope.By moving the auxiliary coordinate system along the slope surface,and controlling the position and geometrical parameter of slip surfacet,he arbitrary potential slip surface is generated to calculate the safety factor,and further the minimum safety factor and the most dangerous slip surface are determined.This method is suitable for the determination of the critical surface in multi-step slope,and it can avoid inaccuracy caused by using empirical formula to determine the search region of slip surface center,and solve the difficult problem to determine the critical slip surface in multi-step slope.It is a new computer search model to solve the stability of multi-step slope.Finally,a program is compiled,and a practical example is calculated and analyzed.