边坡稳定极限分析的单元集成法

Upper bound limit analysis of slope stability by element integration method

提出的单元集成法为采用塑性力学上限定理分析边坡的稳定性提供了一种通用性较强的手段。它采用类似于有限元网格划分的方式离散边坡计算区域,并设定一个机动许可的滑动机构(包括滑裂面位置和速度场,它与网格划分方式无关),在此滑动机构下可以很方便地计算每个单元贡献的外力功率和内能耗散率。把所有单元的能量相加就是滑坡体的总能量。然后,根据上限定理求得安全系数,并通过非线性数学规划方法找到最小值。对于直线滑裂面或对数螺旋滑裂面的单滑块机制,几个典型算例说明了该方法的有效性。

Element integration method provides a general approach for slope stability analysis based on the upper bound limit theorem in plasticity. Small triangle elements are used to discretize the slope media. A kinematically admissiable velocity field is supposed independed with the element meshing. Work done by the body forces, surface loads, as well as internal energy dissipations within an element are convenient to obtain under such a failure mechanism. The whole energy can be calculated from the energy integration among all the elements. The safety factor can therefore be solved from the upper bound limit theorem, and its minimum value can be obtained from optimization method. For single block mechanism, such as plane slip surface, or log-spiral slip surface, the validity of this method has been verified from three typical examples.