基于刚性块体系统的岩质边坡稳定性上限法研究

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摘要以块状岩质边坡为研究对象，将其离散为块体+结构面的几何系统。基于塑性极限分析上限定理并结合非线性数学规划方法，提出基于块体系统的岩质边坡稳定性分析上限法。该方法以块体、结构面的位移速率、转角速率为未知量，基于块体与结构面的变形协调方程，推导出满足关联流动法则的结构面塑性流动约束条件，结合结构面的屈服条件、块体平衡方程、边界条件以及附加约束条件，得到岩质边坡稳定性分析上限法求解超载系数、强度储备系数的非线性数学规划模型，并提出上限法非线性数学规划模型的求解策略。最后对3个经典算例进行分析，得到安全系数严格的上限解，并将计算结果与其他方法的结果进行比较，验证所提上限法的正确性。

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关键词 ：边坡工程, 岩质边坡, 塑性极限分析, 块体系统, 安全系数

Abstract：The block rock slope is investigated in this paper，and the rock slope is discretized into three- dimensional geometries which contain rigid blocks and interfaces. Then based on the upper bound theorem of plastic limit analysis and nonlinear mathematical programming，the three-dimensional upper bound method of rigid blocks assemblages interacting through interfaces is presented. The translation displacement rate and angular displacement rate of blocks and interfaces are taken as unknown parameters in the proposed method. Based on the deformation compatibility conditions of rigid blocks and interfaces，plastic flow conditions that take into account associated flow rules，yield conditions，equilibrium equations，boundary conditions and additional constraints conditions，the nonlinear programming models of upper bound limit analysis are established，which could solve the strength safety factors and overload safety factors of rock slopes. And then，the optimization strategy of nonlinear mathematical programming problem is provided. Finally，three cases of rock slopes are used to study stability，and the rigorous upper limit values of the safety factor of slope are obtained. The results are compared with those produced by other classical approaches，and the validity of the proposed method is indicated.

Key words： slope engineering rock slope plastic limit analysis block assemblages safety factor

收稿日期: 2013-05-20

引用本文:

李泽1，王均星2，张小艳3. 基于刚性块体系统的岩质边坡稳定性上限法研究[J]. 岩石力学与工程学报, 2014, 33(sl): 2844-2852.
LI Ze1，WANG Junxing2，ZHANG Xiaoyan3. RESEARCH ON UPPER BOUND METHOD FOR STABILITY OF ROCK SLOPE BASED ON RIGID BLOCKS ASSEMBLAGES. , 2014, 33(sl): 2844-2852.

链接本文:

http://www.rockmech.org/CN/Y2014/V33/Isl/2844

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