基于有限元-时域分段自适应算法的围岩衬砌耦合渐进分析

以开挖时间、一衬时间、二衬时间划分时间区段，考虑围岩与衬砌为弹性/粘弹性介质，将围岩的“位移/应力释放不完全”、开挖等影响模拟为载荷的渐进释放，提出一个有限元-时域分段自适应算法，求解围岩衬砌耦合问题，并通过数值算例对算法进行了验证。所提方法给出了各时间区段的关联条件；可更准确描述各变量随时间的变化；同时将原时空耦合问题转化为一系列空间问题，并利用有限元方法递推求解；当步长变化时可通过自适应计算保证稳定的计算精度。此外，还建立了一个载荷渐进参数的反问题数值求解模型，并给出了相关算例。

A Finite Element-Temporally Adaptive Algorithm for Asymptotic Coupling Analysis of Rock Linings

A Finite Element-temporally adaptive algorithm is presented for the coupling analysis of rock linings. A coupled spatial and temporal problem is decoupled into a series of spatial problems which are recursively solved by FEM, and a steady computing accuracy can be maintained via an adaptive process with different step sizes. Insufficient release of stress/displacement of rock/linings, and impact of excavation are analogized as a kind of asymptotic load. The whole process is divided into three stages by excavation time, implement time of primary and secondary linings, and compatible conditions at the joints of different stages are proposed. Parameters related with asymptotic load can be determined by solving an inverse problem. Numerical examples are provided to verify the proposed approach.