基于刚性块体系统的岩质边坡稳定性下限法研究

Lower bound method for stability of rock slopes based on rigid block assemblages

块状岩质边坡由岩块和结构面两部分组成,而且结构面的存在以及结构面的强度控制着岩体的强度和稳定性;将塑性极限分析下限法理论、块体离散技术以及数学规划手段结合起来,研究块状岩质边坡的稳定性。首先将边坡离散成为刚性块体系统+结构面的组合体,考虑岩块体与结构面的综合作用,然后基于塑性极限分析的下限定理,建立以边坡稳定安全系数为目标函数且同时满足平衡条件、屈服条件和边界条件的塑性极限分析下限法数学规划模型,进而提出了相应的求解策略并编制了计算程序。最后对4个经典算例进行了分析,得到了严格的下限解,并将计算结果与其他方法的结果进行了比较,验证了方法和程序的正确性。

The block rock slope is made up of blocks and structural surfaces, and the stability of the rock mass is controlled by the existence and the strength of structural surface. Researches on the stability of block rock slope are carried out by using the lower bound theorem of plastic limit analysis, block discretization technique and mathematical programming method. Firstly, the slope is discretized into block assemblages that consist of rigid blocks and structural surface, considering the integral interaction of each other. And then, regarding the safety factor of slope stability as the objective fimction, the nonlinear mathematical programming models are established based on the lower bound theorem, which satisfy the equilibrium equations, yield conditions and static boundary conditions. The solution strategies of models are put forward, and the calculation programs are compiled. Finally, four classic examples are analyzed by means of the proposed method, and the rigorous lower limit values of the strength safety coefficient of slope, and the corresponding statically admissible stress fields are obtained. The results are compared with those produced by other classical approaches, and the validity of the proposed method is indicated.