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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Fv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:Fv≥Fs,最终获得边坡整体安全系数Fs。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。
Based on the classical theory of earth pressure, the range of reasonable thrust line of soil mass is set. Based on the static equilibrium and moment equilibrium conditions, a linear overdetermined system with variable Fv as the interface safety coefficient is established. Based on the least squares method, According to the maximum principle and the reasonable conditions: Fv≥Fs, the overall safety factor Fs of the slope is finally obtained. The numerical results show that the shear capacity of the slope is maximized when the overall safety coefficient of the block interface is the same as that of the block. The safety factor decreases with the increase of the thrust line, but the impact is not significant. Taking into account the principle of maximum, the safety factor obtained by this method is slightly larger than other methods.