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针对非均质边坡,尤其是内摩擦角非均匀边坡的上限分析问题,提出一种新的上限机构。该机构基于滑动面离散的基本思想,采用点到点的方式生成速度间断面,并满足相关联流动法则要求以及几何均匀性条件。推导该机构内外功率的计算方程,并采用序列二次规划(SQP)算法和二分法联合求解边坡的临界高度。利用Matlab编制程序进行求解。将该机构结果与已有文献以及数值模拟结果进行对比,证明该机构在均质、各向异性、非均质等多种工况下均有良好的适用性。最后利用该机构分析内摩擦角随深度线性变化边坡的临界高度变化规律,结果表明内摩擦角非均匀系数对临界高度有显著影响。
Aimed at the upper limit analysis of heterogeneous slopes, especially the non-uniform internal friction angle, a new upper limit mechanism is proposed. Based on the basic idea of sliding surface discretization, the agency uses a point-to-point approach to generate the velocity discontinuities and satisfies the requirements of the associated flow laws and geometric uniformity conditions. The calculation equations of internal and external power of the mechanism are deduced, and the critical height of the slope is solved jointly by the sequence quadratic programming (SQP) algorithm and dichotomy. Using Matlab programming to solve. Comparing the result of this mechanism with the existing literatures and the numerical simulation results, it is proved that this institution has good applicability under various working conditions such as homogenization, anisotropy and heterogeneity. Finally, the mechanism was used to analyze the variation of critical height of internal friction angle with depth, and the results show that the non-uniform coefficient of internal friction angle has a significant impact on the critical height.