Multiscale method for long tunnels subjected to seismic loading

A multiscale method for the dynamic analysis of underground structures is proposed, which involves the concurrent discretization of the entire domain with both coarse-scale and fine-scale finite element meshes. The coarse-scale mesh is employed to capture seismic response characteristics of the integral system, whereas the fine-scale mesh describes in detail the dynamic response in positions of potential damage or interest. For both the coarse-scale and fine-scale meshes to overlap, a bridging scale term is introduced so that compatibility of dynamic behavior between the coarse- and fine-scale models is enforced. Both material and contact nonlinearities are considered in the multiscale model. As an application, the model is used for large-scale seismic response of a newly built long-distance shield tunnel. Results show that this multiscale method does not have spurious wave reflections at the fine/coarse interface and does not need filtering procedures, which is an advantage compared with the displacement coupling method. Stress and deformation response in lining segments and their connecting bolts are investigated and analyzed within the fine-scale model, and the capacity of critical structural components, such as bolts and joints is evaluated.