边坡稳定性分析及滑移面快速确定

针对边坡稳定性分析及滑移面确定这一工程问题，提出一种解析法。首先根据基本假设及边坡的几何关系，建立边坡滑移面确定模型，推导出滑移面控制方程；然后基于极限平衡理论，采用解析的方法推导出与滑移面控制方程相关联的安全系数解析表达式；最后通过求解目标函数（一元函数）在定义域上的最小值，求出边坡最小安全系数及对应的临界滑移面。通过算例验证表明：本文方法的边坡稳定性分析结果与传统极限平衡条分法分析结果基本一致，最小安全系数偏差不超过±5%；本文方法所确定的临界滑移面与基于传统极限平衡条分法所广泛搜索的临界滑移面比较接近。本文方法对于高效、精准地进行边坡稳定性分析及滑移面确定具有借鉴意义。

Stability analysis of slope and quick determination of slip surface

To solve the problem of slope stability analysis and slip surface determination in projects,an analytical method was proposed in this paper.First,based on the basic assumption and the geometric relationship of slope,a model for determining the critical slip surface of slope was established,and the governing equation of slip surface was derived.Then,based on the limit equilibrium theory,the analytical expression of safety factor associated with the governing equation of slip surface was derived.Finally,the minimum safety factor and the corresponding critical slip surface could be obtained by solving the minimum value of objective function (unary function) in the definition domain.The calculation results showed that the analysis results of slope stability with the proposed method are basically consistent with those with the traditional limit equilibrium method,and the deviation of the minimum safety factor calculated by the two methods is less than ±5%;The critical slip surface determined by the proposed method is close to that widely searched by the traditional limit equilibrium method.The method in this paper can be used as a reference for efficient and accurate slope stability analysis and slip surface determination.