考虑土体-结构相互作用的数值极限分析上限法

Numerical upper bound limit analysis based on topology optimization considering soil-structure interaction

非连续面拓扑优化技术（discontinuity topology optimization,DTO）是考虑涉及土体-结构相互作用的岩土稳定性问题的极限分析数值上限法。稳定性问题的几何范围采用规则的栅格点阵进行离散,且点阵之间潜在连接线即滑移线或非连续面构造形成允许速度场或破坏模式。诸如土钉、支撑挡墙等结构体与土体建模时同时考虑,不用区别对待,而且非连续面可以穿过结构体是本文DTO技术的独特之处。DTO技术可以涵盖平动和指定边界区域结构体的转动。最终优化问题呈线性特征,并借助线性优化问题的内点法进行求解。刚性块体平动和转动以及刚塑性结构的塑性铰屈服破坏模式均可模拟。以拱桥结构、锚定板桩墙以及内支撑挡墙基坑稳定性问题为例证,检验程序的有效性。DTO的计算结果以图示的形式清晰且细致地表述了非连续面布局构造的临界破坏模式。

The discontinuity topology optimization （DTO） is an upper bound limit analysis technique for modeling the stability of geotechnical problems involving soil-structure interaction. The slip-lines or discontinuities used for DTO are typically generated by interconnecting a set of nodes located at regular grid points within a domain under consideration. A key feature of this implementation is that the soil reinforcement is simulated by the soil model such that allows the soil to flow past the reinforcement as might occur for soil nailing and propped wall. And also the procedure is extended to enable rotations at the boundaries of prescribed regions to be considered as well as translation failure mechanisms to be modelled. The resulting procedure is solved by the interior point method with linear programming formulation, which allows identification of a wide variety of failure modes, including translation and/or rigid body rotation, and rigid-plastic bending of the structure due to the formation of plastic hinge. The effectiveness of this procedure is demonstrated by analyzing the stability of masonry arch bridge, anchored sheet pile wall and propped wall. The DTO output is provided, which clearly illustrates the clarity and detail of the discontinuity collapse mechanism solutions.