基于潘氏极大值原理的边坡稳定性的整体分析法

Global method for stability analysis of slopes based on Pan's maximum principle

基于整体分析法和潘家铮最大值原理,建立了求解给定滑面安全系数的非线性优化模型。该模型将安全系数和滑面法向应力视为独立变量,目标函数就是安全系数本身,约束条件包括平衡方程、滑面法向应力和条间推力不负,以及推力线位于滑体之内。由于目标函数又仅是线性函数,且约束函数至多是二次多项式函数,所以该模型的非线性程度较低,具有良好的收敛性,可利用经典的优化算法进行求解。

On the basis of global analysis procedure and PAN Jia-zheng＇s maximum principle for the stability analysis of slopes,a nonlinear optimum model is set up for calculating the factor of safety,which takes as independent variables the factor of safety as well as the normal stress on the slip surface.The objective function is just the factor of safety.The constraint conditions include that （1） the equilibrium equations are satisfied;（2） the normal stress and the interslice thrust are not negative;and （3） the thrust line is within the slip body.Since the objective function is linear and the constraint functions are polynomials of at most degree two,the model has weaker nonlinearity,enjoys a large scope of convergence,and can be solved by means of the conventional optimization algorithms.