## Fundamental solutions in modeling of vibrations radiated from tunnels with 2.5D - BEM

* Presenting author

Abstract:
In this talk, we present a boundary element method used to model vibrations within horizontally layered orthotropic soil containing a horizontal straight tunnel.We assume that the tunnel extends infinitely along the x direction. After taking the Fourier transform, the three dimensional problem reduces to several two dimensional problems in the wave-number k_x-domain.Taking the Fourier transform with respect to both horizontal variables x and y, the fundamental solution of the wave propagation has a simple structure in the wave-number (k_x, k_y)-domain. Inside a single layer, the fundamental solution can be represented by a superposition of six waves with complex wave numbers. Their corresponding coefficients are computed by solving a linear system, obtained by a boundary condition at the surface, continuity conditions at the interfaces between the layers, and a radiation condition at infinity. We study stabilizing strategies for the evaluation of the fundamental solution.We use linear elements, and approximate the solution by linear functions. Exploiting the explicit structure of the fundamental solution in the (k_x, k_y)-domain, we can evaluate one part of the derivation of the BEM-matrix analytically.