非线性破坏准则下边坡稳定性极限分析斜条分法

Inclined slices method for limit analysis of slope stability with nonlinear failure criterion

考虑坡顶均布荷载和地震效应典型情况下,将边坡滑体进行任意斜条块划分,建立了具有倾斜界面的多块体破坏模型。基于极限分析上限法和非线性摩尔-库仑破坏准则,考虑岩体内正应力的不均匀性,引入多点切线法和强度折减法推导得出边坡临界破坏状态下的安全系数Fs通用计算公式。采用序列二次规划法对安全系数Fs的目标函数进行最优化计算,并与既有研究成果进行对比分析,其结果具有较好的一致性,相对误差不超过3.565%,表明了该方法的正确性。同时对比传统单点切线法计算结果,多点切线法较单点切线法获得的边坡安全系数值偏小,表明了多点切线斜条分法偏于保守,是安全的。参数分析表明坡顶均布荷载、地震效应和非线性参数均对边坡安全系数及潜在临界滑裂面有重要影响。多点切线法引入非线性摩尔-库仑破坏准则对边坡进行稳定性极限分析,为相关研究人员提供了一种新的思路与方法。

A slope stability limit analysis based on the translational failure mechanism is presented under typical uniformly-distributed loading and seismic loading conditions. The sliding body of slope is divided into arbitrary discrete blocks with inclined interfaces. Based on the upper-bound limit analysis method and nonlinear Mohr-Coulomb failure criterion, a general expression for safety factor Fs in state of critical failure is developed based on the multipoint tangent method and strength reduction method. In this expression, the inhomogeneity of normal stress in rock mass is considered. The upper bound solutions of the slope safety factor are obtained by applying a nonlinear sequential quadratic programming（SQP）. The contrastive analysis shows that agreement with the previous results can be achieved by a relative error less than 3.565%, demonstrating the rationality and reliability of the proposed method. Meanwhile, the slope stability safety factors Fs calculated by multipoint tangent inclined slices method are smaller than those obtained by traditional single tangent inclined slices method, showing that multipoint tangent inclined slices method is a conservative and effective method for slope stability analysis. Parametric analysis indicates that the uniformly distributed loading, seismic loading and nonlinear parameters have significant effects on safety factor and the potential critical slip surface of the slopes. This paper provides a new approach to analyzing the slope stability by introducing the multipoint tangent method into the nonlinear Mohr-Coulomb failure criterion.