基于流形方法和图论算法的岩/土质边坡稳定性分析

目前边坡稳定性分析常用的极限平衡法存在着不能考虑实际岩土体的应力应变关系,假设过多等缺点,强度折减法也存在着需要重复计算工作量大,计算容易不收敛,难以考虑边坡应力路径影响及较难直接得到滑裂面等不足。从边坡的应力状态出发,借助基于物理覆盖系统、能较好统一连续和不连续分析的数值流形方法,得到土质边坡或存在着较多不连续面的岩质边坡的应力场分布,并将边坡稳定性分析转化为图论问题,利用Bellman-Ford搜索算法快速稳定地寻找出边坡的安全系数和最危险滑裂面。该方法无需做过多假设及迭代计算,可以反映边坡的应力路径影响,较好地统一岩质/土质边坡稳定性分析。

Graph theory for stability analysis of rock/soil slopes based on numerical manifold method

The widely-used analysis methods for slope stability based on the limit equilibrium conditions have limitations. In the limit equilibrium method, the constitutive model for soils or rocks cannot be considered, and assumptions are needed between slices of soils/rocks. The strength reduction method, another dominant method for slope stability analysis, requires iterative calculations and cannot represent the effect of stress paths. Besides, it does not give the slip surface directly. Based on the current stress state of slopes, the numerical manifold method, which can unify the continuum analysis and discontinuum analysis with its dual covers, is adopted to calculate the stress distributions of soil slopes or rock slopes with joints. Then the slope stability analysis is converted to a graph problem, and the Bellman-Ford algorithm is used to obtain the slip surface and the safety factor which is defined as the ratio of the resistant force and the slip force along the slip surface. The proposed method removes the difficulties in iterative calculations and unifies the stability analysis of rock/soil slopes, and is capable of including the effects of stress paths.