A note on response of tunnels to incident SH-waves near hillsides

In this study, diffraction of plane SH waves by a cylindrical tunnel embedded in homogeneous, isotropic and linear elastic quarter-space is investigated. Analytical solution techniques are used to solve the two dimensional wave propagation problem. When the excitation is assumed to be harmonic, the governing equation would be the Helmholtz equation. By applying separation of variables method to Helmholtz equation for cylindrical coordinates, general solutions are obtained in terms of Fourier-Bessel series. Unknown complex constants of the Fourier-Bessel series are to be determined from boundary conditions. Boundary conditions at inner and outer side of the tunnel are satisfied directly since they are defined in cylindrical coordinates. Stress-free boundary conditions at the ground and the hillside surfaces are satisfied in closed form via imaging method and addition theorems. Numerical examples are compared with earlier studies and the effect of the tunnel is discussed.