基于最小势能法的二维边坡整体滑动方向研究

Study on whole sliding direction of two-dimensional slope based on minimum potential energy method

最小势能法是一种计算边坡稳定系数的方法,其关键在于确定势能计算模型以及整体滑动方向。通过引入弹性地基梁模型确定了滑面上的弹性势能,并基于滑体在虚位移方向的整体平衡方程构建了剪切势能计算模型。当边坡的边界条件、受力形式确定之后,便可应用最小势能原理确定虚位移,并通过构建不同滑动方向的模型计算相应的稳定系数。通过分析计算,给出了3种整体运动方向表达式。最后,应用最小势能方法对固定滑面、非固定滑面边坡的下滑方向以及稳定系数进行比较。结果表明:以滑面各点滑动方向的矢量合成作为整体运动方向的方法物理意义明确,结果也较为合理。

The minimum potential energy method is an analysis method used to figure out the stability coefficient of slopes,whose core is to determine the potential energy model and the sliding direction.In this paper,the elastic energy on sliding plane was determined by introducing the elastic foundation beam model,and the shear potential energy calculation model was established based on the whole equilibrium equation of the sliding mass on the virtual displacement direction.After determining the boundary condition of the slope,the virtual displacement could be confirmed according to the principle of minimum potential energy,and by defining different sliding directions,different stability coefficients could be obtained.Three formulas were given out to determine the whole sliding direction of sliding mass.At last,we applied the proposed method to discuss the sliding direction and stability coefficient of engineering cases of fixed sliding surface and the non-fixed sliding surface.The results showed that using the vector synthesis of the sliding directions of different sliding points on the sliding surface as the whole sliding direction had good physical meanings,and the result was reasonable too.