边坡稳定分析最大原理的理论分析和试验验证

Theoretical study and physical modeling on ‘Principle of Maximum’in slope stability analysis

载于教科书的边坡楔体稳定分析方法,假定作用于两个滑面上的剪力平行与交棱线。潘家铮曾对这一假定提出质疑。他认为边坡在破坏时剪力应调整到发挥最大抗力为止。本文提出了一个边坡稳定楔体分析的广义解,可以允许输入剪力与交棱线的任意夹角,并证明在楔体按摩尔–库仑相关联法则变位,即剪胀角为摩擦角时安全系数获得极大,从而使楔体稳定最大原理得证。本文还介绍了使用离心模型试验对最大原理的验证成果。

The conventional rock wedge stability analysis method proposed in textbooks actually involves an assumption that the shear forces applied on the failure planes are parallel to the line of intersection. Pan argued that the shear force does not necessarily act in such a way but would readjust to mobilize the maximum factor of safety. A new method that allows an input of various shear force directions is presented in this paper. By applying the limit equilibrium conditions a governing equation to calculate the factor of safety has been obtained, which permits a formal demonstration to confirm that a maximum factor of safety exists when the rock wedge dilates at values of friction angles to the left and right failure planes respectively along the direction required by Mohr–Coulomb’s associative flow law. Pan’s principle is therefore demonstrated. This paper also presents the results of centrifuge model tests that show reasonable evidence to support Pan’s principle of maximum.