基于最小二乘法的边坡稳定性分析

利用经典土压力理论设定合理土条推力线范围，根据静力平衡及力矩平衡条件建立以条块界面安全系数 为变量的线性超定方程组，应用MATLAB软件基于最小二乘方法对此方程组求解，依据极大值原理及合理性条件： ，最终获得边坡整体安全系数 。经算例验证得出如下结论：当条块界面与条块整体安全系数相等时，边坡抗剪能力发挥最大；安全系数随推力线位置的升高而减小，但影响并不大；由于考虑了极大值原理，该法求得的安全系数略微偏大于其他方法。

Slope stability analysis based on least square method

Utilizing the classical earth pressure theory for setting the reasonable thrust line position of soil slice,the linear equations including Fv as variable are established by the condition of static equilibrium and torque equilibrium,where Fv is safety factor of slice side.Least square method is applied to solving the above linear equations by means of MATLAB program based on the maximum principle and reasonable conditions: v s F ≥ F.Case studies show that the capacity for resisting shear deformation of slope is brought into play when v s F F The slope safety factor decreases with thrust line position increasing;but the impact of thrust on slope safety factor is negligible.The safety factor obtained by the above method is little larger than those by other methods.