边坡稳定分析的非连续面拓扑优化技术

Slope stability using discontinuity topology optimization technique

土工结构稳定性的极限分析方法研究一直是热点问题。提出的非连续面拓扑优化技术（DTO）的主要特征之处在于稳定性问题的极限分析根据节点及其连线而不是单元或实体来进行构造。替代的近似过程主要采用适量的栅格节点来离散问题几何域,临界破坏机构则由节点间的连线集构造而成。基于Mohr–Coulomb屈服准则构造目标函数,并通过优化来确定极限荷载系数。结合离散构造特征,引入孔隙水压力和安全系数,DTO可拓展处理涉及地下水的边坡稳定问题。DTO是建立临界破坏模式和确定相应安全系数的有效工具,而无需考虑滑移面的入口/出口限界或点的约束与假设。本研究以复杂条件下的边坡稳定性为例,深入分析DTO和其他各种方法所得结果的一致性和差异性。相关比较表明,对于材料特性要求高、几何边界和荷载作用条件复杂的边坡稳定分析而言,DTO技术是一种可靠的替代分析手段。

Many efforts have been focused on the stability problems of geotechnical structures with the limit analysis methods. A key advance of the proposed method is that the problem is described only in terms of nodes and discontinuities connecting those nodes rather than elements or bodies. The alternative approximation procedure might involve discretization of a given body under consideration using a suitably large number of nodes laid out on a grid, with the failure mechanism comprising the most critical subset of potential discontinuities interconnecting these nodes. The discontinuity topology optimization（DTO） technique using the Mohr-Coulomb failure criterion to formulate the objective function is developed and the collapse load multiplier is determined from optimization. Incorporating the pore-water pressure and factor of safety is consistent with the formulation of nodal grid and inter-node connections, and the ability of the DTO procedure extended to handle the slope problems involving ground water pressures is demonstrated. The use of DTO can be an effective tool for establishing a critical failure mechanism and its corresponding safety factor without the constraints or assumptions regarding entrance/exit limits or points of the slip surface. The uses of various methods and DTO for several examples that focus on complex geotechnical scenarios are compared to illustrate the agreement and difference between the analyses. The developed techniques are shown to provide a viable alternative to analyze the stability of slopes with demanding material behavior, complex geometry and loading conditions.