边坡下限求解的突变分析方法

Catastrophe Analysis Method of Slope Lower Bound Solution

以极限分析下限法为理论基础,利用理想铰接桁架假设构建边坡完整应力场分布,获得相应平衡方程;针对下限解析求解比较困难的问题,基于边坡结构破坏的非线性突变特征,引入突变理论,建立边坡破坏的基本突变模型,通过对突变模型特性及边坡破坏机理进行分析,获得边坡极限荷载下限解。针对已有边坡算例,将所述方法得到的下限解与经典塑性力学解及有限元解比较,验证了方法的可行性。研究利用突变分析理论解决了边坡下限分析中的关键难题,其执行思路可为边坡下限求解提供一种可供选择的新路径。

Based on the theoretical foundation of lower bound limit analysis method,corresponding equilibrium equation is derived by using complete stress field of slope which has been built based on perfectly pin connected truss assumption.Catastrophe model of slope failure is constructed based on mutation feature of slope failure.System model property and slope failure mechanism are analyzed,and the lower bound solution of slope failure is achieved.Ultimate load of a slope example is analyzed,and comparison between the solution acquired by the proposed method and the classical plastic theory and comparison between the solution acquired by the proposed method and the finite element method are adopted to illustrate the feasibility of the proposed method.The key difficult problem of slope lower limit analysis is solved by using the catastrophe theory.The executive idea of this research may provide a new optional approach to solve lower bound theoretical solution of ultimate bearing capacity of slope.