基坑稳定性的塑性极限分析上限法研究

Research on upper bound method of plastic limit analysis for excavation stability

基坑稳定性验算是基坑支护设计中的一项重要内容,将极限分析上限理论、有限元离散思想和数学规划方法结合起来研究基坑的稳定性。首先将基坑土体用三角形有限单元离散,然后根据上限定理构建同时满足公共边速度不连续条件、单元塑性流动约束条件和单元速度边界条件的机动许可速度场,并由内、外功率相等条件建立目标函数,构建基坑稳定性分析的上限法数学规划模型,通过对模型的优化求解,得到基坑整体稳定性分析的极限荷载(或安全系数)上限解及相应的破坏机构,最后分析了土体抗剪参数、支护结构嵌固深度及基坑开挖深度等因素对基坑整体稳定性的影响规律。

Evaluating the excavation stability is important in excavation support design.In this paper, the stability of excavations is studied by combining the upper bound theorem, finite element discretization and mathematical programming method. First, the triangular finite element is used to disperse the soil of excavations. Then according to the upper bound theorem, kinematically admissible velocity fields are established to satisfy the plastic flow constraint conditions of velocity discontinuities for common side, the plastic flow constraint conditions of triangular finite elements and the velocity boundary conditions. The objective function is established based on the internal and external energy balance equation, then the upper bound method mathematical programming model for excavations analysis are established. By solving the mathematical programming model with the help of optimization algorithm, the upper bound solution of the ultimate load and safety factor can be obtained. Finally, the effects of soil shear parameters, the depth of retaining structure and excavation depth on the overall stability of excavations are analyzed.