基于变分法的均质土坡稳定性分析

在平面应变条件下,从考虑强度折减的滑动土体极限平衡方程出发,推导出一般情况下均质土坡稳定分析的泛函极值等周模型。依据泛函取极值时必须满足的欧拉方程,通过坐标变换对变分问题求解,得到滑裂面函数及其上分布的法向应力函数。对于给定的边界条件及横截条件,土坡稳定问题转化为求解以两个拉格朗日乘子、安全系数和滑裂面一个端点的x坐标为4个未知量的函数极值问题,可以通过数值计算得到最小安全系数及所对应的最危险滑裂面。考虑坡顶拉裂缝,通过算例分析了不同的滑裂面位置及对应的安全系数。通过对ACADS边坡考题算例分析,在不考虑坡顶开裂的条件下,采用该方法的分析结果与依据极限平衡法得到的各裁判答案非常接近,在考虑坡顶开裂时,安全系数略有减小。

Homogeneous soil slope stability analysis based on variational method

Based on the condition of plane strain and the static equilibrium equations for sliding mass considering strength reduction, the functional extreme-value isoperimetric model of homogeneous soil slope stability in the general case is derived. Based on that the Euler’s equations which must be satisfied when extreme value are obtained by functional analysis, the critical slip surface and the normal stress along the sliding surface are obtained by coordinates transform. Combined with the pre-defined boundary conditions and transversal conditions, the stability analysis for the soil slop is transformed to solving the minimum of a function with four unknown variables including two Lagrange multipliers, safety factor and x-coordinate of the slip end. The minimum of safety factor and the corresponding critical surface can be obtained by analytical computation. By taking the tensile cracks at the top of slope into consideration, the positions of different sliding surfaces and the corresponding safety factors are analyzed through a case study. In addtion, the proposed method is verified by ACADS slope test and the test results indicate that the predicted results consistent with the answer obtained by the judging procedure when the influence of the tensile crack is not considered, while the safety factor is slightly smaller than the answer obtained by the judging procedure when the tensile crack is considered.