基于变分法对边坡最不利滑裂面的分析

Analysis of slope's most dangerous sliding surface based on variational method

为了合理地确定边坡的最不利滑裂面、探讨坡顶开裂原因及出现滑坡险情时的应急措施,将变分方法用于边坡稳定性分析。通过建立一个与边坡稳定相关的泛函,根据边界条件选取适当的基函数,获得了边坡最不利滑裂面。基于所得最不利滑裂面,得到垂直边坡和普通边坡最不利滑裂面的分布随土体内摩擦角和内聚力的变化趋势,为垂直边坡和普通边坡采取正确的应急措施、提高边坡的稳定性提供了理论依据;根据泛函T沿最不利滑裂面的变化将边坡划分为主动滑动区和被动滑动区。比较分析得出:变分方法和Bishop条分法所获得的安全系数比较接近,且变分方法获得的安全系数略小。

To search out most dangerous sliding surface and explore the reason why the crack appears on the slope top and the emergency measures which should be are taken when slope is unstable,variational methods was applied to the analysis of slope stability.Setting up a functional in relation to slope stability,choosing the proper basis functional on the basis of boundary condition,then most dangerous sliding surface would be obtained.Then the influence of soil＇s internal friction angel and cohesion on the distribution of most dangerous sliding surface of vertical and general slopes was obtained.Distribution of most dangerous sliding surface was studied and theoretical basis was got which let people know what emergency measures should be adapted to reinforce the slope.According to functional T′s variation along most dangerous sliding surface,the slope was divided into two zone：active sliding zone and positive sliding zone.Comparative study shows that the safety factors obtained with variational methods and Bishop methods are close to each other,and the former safety factor is bigger than the later a little.