边坡安全系数的多解性讨论

Discussion on multiple solution of safety factor of a slope

边坡安全系数计算结果直接影响边坡工程设计,而极限平衡法不能给出唯一的安全系数值,研究边坡安全系数的多解性,有助于对边坡稳定性计算结果有一个合理地判断与取舍。先假定滑面正应力的初始分布,然后采用含有3个待定参数的拉格朗日函数对其修正,保证滑体满足所有的力与力矩平衡条件;设定一系列安全系数分别求解平衡方程组,得到对应的待定参数值;最后根据滑面正应力分布的合理性判断边坡安全系数的合理范围。算例表明,圆弧滑面合理安全系数范围在5%以内,而任意形状滑面安全系数最大取值范围可达15%。

The calculated value of safety factor of a slope directly determines the design of slope engineering. However, the limit equilibrium method can not yield a single value of safety factor; thus the study of multiple solution of safety factor helps in justifying the reasonableness of the computation results and selecting the range of possible values of safety factor. The initial distribution of normal stresses over the slip surface is assumed, which is then modified by a Lagrangian function involving three parameters to satisfy the complete equilibrium conditions of the sliding body. Solving the equilibrium equations yields values of the three parameters associated with a series of prescribed safety factors, and the reasonable range of safety factor of a slope is justified according the reasonableness of the normal stress distribution over the slip surface. Example studies show that the reasonable range of safety factor for a circular slip surface is within 5 %; however, for non-circular slip surfaces, this range would be as large as 15 %.