非均质边坡上限分析的离散机构及应用

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。

Discrete mechanism for upper bound analysis of nonhomogeneous slopes

A new mechanism of two-dimensional failure was proposed for the upper bound analysis of nonhomogeneous slopes with the friction angle varying spatially. This failure mechanism obeys the associated flow rule and geometry uniform condition and was established based on the idea of discretized slip surface. The velocity discontinuity surface was generated point by point. The rate of external work and the internal energy dissipation were derived. The critical height of the slope was derived through the methods of sequential quadratic programming(SQP) and bisection searching. The effectiveness of the presented method was verified in homogeneous，anisotropic and nonhomogeneous conditions respectively. Finally，the critical height of the nonhomogeneous slope was analyzed using the failure mechanism with the friction angle increases linearly with the depth. The results show that the nonhomogeneous coefficient of friction angle has the significant effect on the critical height.