Anti-plane seismic ground motion above twin horseshoe-shaped lined tunnels

The ground surface response was obtained in the presence of twin horseshoe-shaped lined tunnels embedded in a linear elastic half-space, subjected to obliquely propagating incident plane SH-waves. A numerical approach known as direct half-plane time-domain boundary element method was used to prepare the model. First, the heterogeneous problem was decomposed into three parts, two closed linings and a double-hole half-plane. Then, the method was applied to each part to compute the required matrices. Finally, the problem was solved by satisfying the continuity conditions at the interfaces. After solving a verification example, an advanced parametric study was carried out for obtaining the surface response with shallow twin horseshoe-shaped lined tunnels as synthetic seismograms and 3-D amplification patterns. Some intended parameters were also considered to illustrate the ground response including the horizontal/vertical overlapping of the tunnels, depth and distance between them and incident wave angle. To summarize the results, some graphs were presented to obtain the maximum amplification ratio of the surface. Numerical results showed that the existence of twin horseshoe-shaped tunnels could amplify the ground surface response up to three and half times the free-field movement at dimensionless frequencies greater than one. Also, achievements indicated that the greater role of vertically overlapped tunnels in creating safe areas on the surface compared to the horizontally placed tunnels. The results can be practically used in clarifying seismic codes in the field of urban transportation geotechnics.