基于非线性规划的边坡稳定性分析条分法研究

Research on Slice Method for Stability of Slope Based on Nonlinear Programming

针对边坡稳定问题,将边坡滑体划分为竖直条块或斜条块,将条块底面的作用力(包括法向力、剪切力)以及条块间的作用力(包括法向力、剪切力)作为未知变量,以边坡的稳定安全系数作为目标函数,结合条块的平衡方程、条块底滑面的屈服条件、条间接触面的屈服条件等约束条件,建立边坡稳定性分析的非线性数学规划模型,并使用优化算法求解全局最优的最大稳定安全系数。使用所提出的方法计算得到边坡安全系数具有下限解的性质。

Aiming at the slope stability,the slope slide was divided into vertical slices or oblique slices,the force at the slice bottom（ including the normal force and shear force） and the force between the slices（ including normal force and shear force） are taken as unknown variables,the safety factor of slope stability is taken as the objective function,the equilibrium equation of slice,the yield condition of bottom slip surface of slice,and the yield condition between contact surfaces of slices and other constraint conditions are combined,the nonlinear mathematical programming model for slope stability analysis is established and the optimization algorithm is used for solving the maximum stability safety coefficient. The safety factor of slope calculated with the method in this paper has the lower bound solution properties.