圆形凸坡的稳定性分析

通过三维数值分析表明圆形凸坡的破坏模式接近于轴对称破坏，采用一般的三维破坏模式会使计算结果偏于不安全，揭示了目前三维分析方法中滑裂面形状的假设并非总是合理。构建了轴对称条件下的容许速度场，得到了内摩擦角(=0时圆形凸坡临界坡高的上限解。同时提出了轴对称破坏模式下，计算圆形凸坡安全系数的极限平衡方法。比较了圆形凸坡和长直坡的稳定性差异，圆形凸坡的相对半径越小、土体越接近于纯黏性土时两者的差异越大，坡度较小时前者较稳定，坡度较大时则相反，进而纠正了以往认为平面应变模型计算圆形凸坡偏于不安全的错误认识。

Stability analysis of circular convex slopes

The failure mode of circular convex slopes is analyzed through three-dimensional numerical analysis, which indicates that this type of slope is prone to an axisymmetric failure and the results based on a non-axisymmetric failure mode will over-estimate the stability factor. Through this analysis, a question is put forward if it’s always reasonable when a general failure mode in the 3D slope stability analysis is applied. For the axisymmetric failure mode, an upper-bound solution for the case with (=0 is presented through the limit analysis, and a limit equilibrium method for general type of soil is also proposed. Compared with the results from the plane-strain analysis, the stability of circular convex slopes is notably different. If the relative radius becomes smaller or the soil is nearly purely cohesive, the difference will become larger. When the slope angle is small, a circular convex slope will be more stable than estimated from the plane-strain analysis, and it will be reversed when the slope angle is large enough, which corrects a misunderstanding that the circular slopes are always more unstable.