基于水平条分与斜条分相结合的边坡稳定性解析计算

Analytical Calculation of Slope Stability Based on the Combination of Horizontal and Oblique Slice Method

由于传统水平条分法并不能考虑边坡滑动面经过坡角这一情况,在边坡稳定性分析时,所计算的安全系数常常偏小。考虑一般的边坡潜在圆弧滑动面,采用拟静力法对地震作用下的边坡稳定性进行分析,将水平条分与斜条分结合起来分析了地震作用下土条的受力情况,考虑水平和竖向地震效应的影响,引入竖向中心角,建立了边坡安全系数关于竖向中心角的解析表达式。采用MATLAB中Fmincon函数(序列二次优化方法)对安全系数目标函数进行优化求解,通过算例验证了其方法和优化程序的正确性。分析了水平地震效应影响系数k_h、竖向地震效应影响系数k_v及比例系数ξ对边坡稳定性影响,结果表明:安全系数F_s随着k_h的增大而减小;随着比例系数ξ的减小、水平地震效应系数k_h的增大,边坡潜在滑动面逐渐变深,边坡失稳的范围越来越大,且分别随着k_h的增大、ξ的减小,这种趋势越明显。

As the traditional horizontal slice method cannot consider the situation that the critical slip surface does not pass below the toe of the slope,therefore the calculated safety factor is often smaller.Based on the horizontal slice method,considering the general slope sliding surface,the quasi-static method is used to analyze the seismic stability of the slopes.A combination of horizontal slice and oblique slice is adopted when the critical slip surface pass below the toe of slope.The horizontal and vertical seismic coefficient is both taken into account and the analytical expression related to vertical center angles is derived to calculate the factor of safety.The fmincon function（Sequence quadratic optimization method）of MAT-LAB is used to optimize the objective function of safety factor,and the correctness of the method and optimization program is verified by examples.The effects of horizontal seismic coefficient kh,vertical seismic coefficient kvand proportion coefficientξon slope stability are analyzed.The results show that the safety factor Fsdecreases with the increase of horizontal seismic coefficient kh.With the decrease of the proportion coefficientξand the horizontal seismic coefficient kh,the potential sliding surface of the slope gradually becomes deeper and the failure mass becomes bigger,and this trend is more obvious with the increase of the horizontal seismic coefficient khand the decrease of the proportion coefficientξrespectively.