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自然界边坡破坏存在两种不同的模式:普通边坡模式和长边坡模式。针对长边坡的破坏模式,基于塑性力学极限分析原理,构建了符合实际的机动许可的三维速度相容场。推导该破坏机构的外力功率与内部能量耗散,根据功能互等原理,将长边坡的三维稳定性问题转变为多约束条件下的非线性规划数学问题。该规划问题的最优解计算结果表明:长边坡的三维稳定性随着边坡宽度的增大而减小,当边坡宽度达到一定值后,边坡的三维稳定系数与二维情况较为接近(误差在5%之内),此时二维分析即可满足工程需求。
There are two different modes of natural slope failure: normal slope mode and long slope mode. According to the failure mode of long slope, based on the principle of limit analysis of plasticity mechanics, a three-dimensional velocity-compatible field that is in line with the actual motorized permission is constructed. The external force and internal energy dissipation of the failure mechanism are deduced. According to the principle of reciprocal function, the three-dimensional stability problem of long slope is transformed into the nonlinear programming problem under multiple constraints. The optimal solution of the planning problem shows that the three-dimensional stability of the long slope decreases with the increase of the slope width. When the width of the slope reaches a certain value, the three-dimensional stability coefficient of the slope is more Close to (error within 5%), then two-dimensional analysis to meet the engineering needs.