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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。
Considering the uniform load on the top of a slope and the seismic effect, a typical slope block is divided into arbitrary slant blocks, and a multi-block failure model with inclined interface is established. Based on the upper bound method of limit analysis and the non-linear Mohr-Coulomb failure criterion, considering the inhomogeneity of the normal stress in the rock mass, the multi-point tangent method and the strength reduction method are introduced to derive the general safety formula Fs for the critical failure of the slope . The sequence quadratic programming method was used to optimize the objective function of the safety factor Fs, and compared with the existing research results. The results showed good agreement and the relative error was less than 3.565%, indicating the correctness of the method Sex. Compared with the traditional single-point tangent method, the multi-point tangent method is smaller than the single point tangent method, indicating that the multi-point tangent ramp method is conservative and safe. The parametric analysis shows that the load on the top of the slope, the seismic effect and the nonlinear parameters all have an important influence on the slope safety factor and the potential critical slip plane. The multi-point tangent method introduces the nonlinear Mohr-Coulomb failure criterion to analyze the stability of the slope, which provides a new idea and method for the related researchers.