下限原理在岩土工程中的应用

Application of Lower Bound Theorem in Geomechnical Engineering

采用极限分析下限原理求解了岩土工程中基础的极限载力和边坡的安全系数。求解过程中把有限元法和非线性规划相结合,把整个结构离散化,设定每个结点的应力,把原问题变成一个以边坡的稳定安全系数或基础的极限承载力为目标函数,以结点应力为优化变量,以对可静应力场的各种制约为约束条件的非线性规划问题。采用序列二次规划法求解该非线性规划问题,得到了人为构造的严格满足应力边界条件、平衡微分方程、不违反Mohr-Coulomb或Drucker-Prager屈服准则的应力场,解决了三维可静应力场的构造问题。算例分析表明,本文的方法是正确、可行的。

Safety factors of slope stability analysis and limit bearing capacities of footings were solved by adopting lower bound theorem of limit analysis. Strict statically admissible stress field was constructed by combining finite element method with nonlinear programming. The whole structure was discretized and the nodal stresses were assumed, which can transfer the initial problem into a nonlinear programming problem with objective function of slope safty factor or bearing capacity of footing, nodal stresses of programming variables, and constrains of restrictions to the statically admissible stress field. The stress field satisfies boundary conditions, equilibrium differential equations and nowhere violates Mohr-Coulomb or Drucker-Prager yield rule. Examples indicate that the method of this article is correct and practicable.