对称边坡三维稳定性计算方法

METHOD OF THREE-DIMENSIONAL STABILITY ANALYSIS OF A SYMMETRICAL SLOPE

提出一种适合对称或近似对称边坡的三维稳定性计算方法。首先,根据简单的平衡条件,假设三维滑面正应力的初始分布;然后,用含有2个待定参数的修正函数对其进行修正,根据三维对称滑体的3个平衡条件,导出含安全系数及待定参数的平衡方程组,进而化简为关于安全系数的3次代数方程;最后,得到三维安全系数的显式计算公式。该方法的优点是不需考虑条柱间具体的作用力、严格满足三维平衡条件、计算过程简单。算例分析表明,初始正应力的假设与修正函数的选择对最终安全系数结果的影响不大,从而可保证该方法的合理性与有效性。

A new method is proposed for three-dimensional stability analysis of symmetrical or approximately symmetrical slopes.By using a simple equilibrium condition,the normal stress distribution over the three-dimensional slip surface is assumed,which is then multiplied by a modification function involving two unknown parameters.According to three equilibrium conditions of three-dimensional symmetrical slope,three equilibrium equations in terms of the factor of safety and two parameters are derived that are then reduced to a cubical equation in terms of the factor of safety and finally yield the explicit solution to the three-dimensional factor of safety.The presented method does not need consideration of the inter-column forces,rigorously satisfies the equilibrium conditions,and costs fewer computation efforts than the conventional methods of columns.Example studies show that the assumption regarding the initial normal stress distribution over the slip surface and the selection of modification functions has relatively insignificant effect on the value of factor of safety,thus ensures the reasonableness and effectiveness of the proposed method.