Transient SH-wave scattering by the lined tunnels embedded in an elastic half-plane

A direct half-plane time-domain boundary element method (BEM) was developed and successfully applied to analyze the transient response of ground surface in the presence of arbitrarily shaped lined tunnels, embedded in a linear elastic half-space, subjected to propagating obliquely incident plane SH-waves. To prepare the model, only the interface and inner boundary of the lining need to be discretized. The problem was decomposed into a pitted half-plane and a closed ring-shaped domain, corresponding to the substructure procedure. After computing the matrices and satisfying the compatibility as well as boundary conditions, the coupled equations were solved to obtain the boundary values. To validate the responses, a practical example was analyzed and compared with those of the published works. The results showed that the model was very simple and the accuracy was favorable. Advanced numerical results were also illustrated for single/twin circular lined tunnels as synthetic seismograms and three-dimensional frequency-domain responses. The method used in this paper is recommended to obtain the transient response of underground structures in combination with other numerical methods.