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基于块体元离散思想,将三维边坡离散为块体-结构面组成的块体系统,假定块体为刚体,以结构面上的应力为未知量;从下限定理出发,构造满足平衡条件、边界条件和屈服条件的静力许可场,平衡方程严格满足3方向力平衡及绕3个主轴方向的力矩平衡条件,为避免非线性规划,对屈服条件进行线性化处理;最后,建立了下限法数学规划模型,通过线性及非线性规划获得边坡稳定严格的下限解。用几个典型算例验证了文中方法的正确性及可行性。
Based on the idea of block element discretization, the three-dimensional slope is discretized into a block system consisting of block-structure plane. Assuming that the block is rigid body and the stress on the structure plane is unknown, starting from the lower bound theorem, Boundary conditions and yielding conditions, the equilibrium equation strictly satisfies the force balance in three directions and the moment equilibrium conditions around the three principal axes. In order to avoid the nonlinear programming, the yield conditions are linearized. Finally, the lower bound method Mathematical programming model, through the linear and nonlinear programming to obtain the slope of the stability of the lower limit solution. With several typical examples, the correctness and feasibility of the method in this paper are verified.