Seismic motions in a non-homogeneous soil deposit with tunnels by a hybrid computational technique

We study seismically induced, anti-plane strain wave motion in a non-homogeneous geological region containing tunnels. Two different scenarios are considered: (a) The first models two tunnels in a finite geological region embedded within a laterally inhomogeneous, layered geological profile containing a seismic source. For this case, labelled as the first boundary-value problem (BVP 1), an efficient hybrid technique comprising the finite difference method (FDM) and the boundary element method (BEM) is developed and applied. Since the later method is based on the frequency-dependent fundamental solution of elastodynamics, the hybrid technique is defined in the frequency domain. Then, an inverse fast Fourier transformation (FFT) is used to recover time histories; (b) The second models a finite region with two tunnels, is embedded in a homogeneous half-plane, and is subjected to incident, time-harmonic SH-waves. This case, labelled as the second boundary-value problem (BVP 2), considers complex soil properties such as anisotropy, continuous inhomogeneity and poroelasticity. The computational approach is now the BEM alone, since solution of the surrounding half plane by the FDM is unnecessary. In sum, the hybrid FDM-BEM technique is able to quantify dependence of the signals that develop at the free surface to the following key parameters: seismic source properties and heterogeneous structure of the wave path (the FDM component) and near-surface geological deposits containing discontinuities in the form of tunnels (the BEM component). Finally, the hybrid technique is used for evaluating the seismic wave field that develops within a key geological cross-section of the Metro construction project in Thessaloniki, Greece, which includes the important Roman-era historical monument of Rotunda dating from the 3rd century A.D.