Analytical and numerical calculation of stresses and displacements around rectangular tunnel under SV waves in half space

摘要

The purpose of this research is the calculation of the stress field as well as the displacements occurring around tunnels of unlined rectangular shape, in a linear elastic ground due to SV seismic excitation. The numerical analyses are carried out with the finite-differences Code FLAC3D. Then, the results are compared to those obtained from an analytical method. The analytical model is based on infinite series expansion of Bessel & Hankel type for the estimation of the wave potentials of incident, reflected and scattered waves, in combination with conformal mapping. This mapping transforms the area between the free surface and a tunnel of depth H in plane w onto two unit circles in the plane ζ, the centers of which are at vertical distance b the one from the other. The analytical calculation of the stress field as well as the deformations of the sections of underground structures, subjected to seismic excitation of shear SV waves, is achieved with the use of MATLAB. A series of dynamic analyses are performed the thickness of the soil layer above the structure in a half space. The model is subjected to seismic excitation simulated by a harmonic vertically propagating shear wave in terms of stress history. SV waves cause racking motion of the cross section of the tunnel. The results of the analyses showed that the sectional stresses and deformations depend on the structure depth, i.e. the deeper the structure the smaller the effect. To sum up, the comparison between the analytical and the numerical method in the elasticity range provided satisfactory results.