双渐近透射边界下的隧洞-层状地基时域分析

高阶双渐近透射边界发展于改进比例边界有限单元法和连分式解，实现了时域局部化，获得在全频域范围内快速收敛的动力刚度准确解，兼具高精度和效率。本文将该边界推广应用到复杂层状地基弹性波传播问题，并与有限元耦合构建出一种隧洞-层状地基动力响应的时域耦合模型。耦合模型划分为近场与远场，其中，近场采用有限元单元离散，远场采用高阶双渐近透射边界模拟。通过数值算例分析上述耦合模型，结果表明：耦合模型计算结果稳定，与扩展网格解具有良好的一致性，同时兼顾精度与效率，适用于长时间的地震响应时域研究。该模型为研究地震动下隧洞-层状地基相互作用提供新的思路，可进一步用于实际工程中。

Time-domain analysis of tunnel-layered soil system based on doubly asymptotic transmitting boundary

Developed from the modified scale boundary finite element method and continued fraction solution, the high-order doubly asymptotic transmitting boundary can realize time localization and generate a stiffness matrix that converges rapidly to the exact solution over the whole frequency range, thereby achieving a high accuracy and good efficiency. This paper applies such a transmitting boundary to the propagation of elastic waves across complicated layered soil, and develops a time-domain coupled model by combining with FEM to study the dynamic responses of a tunnel-layered soil system. This coupled model divides the domain into a near field and a far field by a transmitting boundary, and calculates both separately using a FEM model and a high-order doubly asymptotic transmitting boundary method. Results of numerical examples demonstrate that the solutions are stable and agree well with those of the extended mesh method, achieving a good balance between accuracy and efficiency. And it is also applicable to long-time seismic response analysis of tunnel-layered soil interaction. Thus, the coupled model would provide a new approach for seismic analysis of tunnel-layered soil interaction and should be developed further for engineering application.