Scattering Of Earthquake Waves By A Shallow Circular Tunnel And Its Dynamic Response

To release the city transportation pressure, it’s necessary to increase construction ofunderground structures such as highway and railway projects. Most areas in our coun-try are in seismic area, some of the underground structures have to be built in seismicareas inevitably. Severe damages in experienced earthquakes indicate that undergroundstructures will sufer severe damage to earthquake loads. The safety of undergroundstructures during earthquake has been remarked signifcantly by many researchers. Thefailure modes and dynamic mechanism of underground structure is completely diferentfrom that of ground structure under seismic loads. At present, the previous calculationmethods also cannot explain the seismic mechanism of underground structures very well.Therefore, it is signifcant to focus on the the seismic analysis of underground structuresboth in theory and in engineering application.The essential issue of the earthquake dynamic response of underground tunnel is thescattering of the seismic waves by underground tunnel and the half space. The localtopography conditions of seismic waves have signifcant efects on the propagation ofseismic waves as the reflection and scattering of seismic waves by local topography. Itshows the amplifcation and reduction function of the ground motion by local topography,which leads to the regional characteristics of the distribution of earthquake damage. Itis hard to study the scattering of seismic waves due to the interaction between the wavefeld disturbance. Few close-form solution of the scattering of seismic waves by a shallowcircular tunnel are available since it is difcult to deal with the orthogonality of boundaryconditions.Based on the plane complex variable theory and the image technique, an analyticalsolution is presented for scattering of plane waves by a shallow circular tunnel in an elastichalf space. The major contribution of this study is the treatment of the orthogonalityof the boundary conditions along the half surface and the cavity wall. The Holmholtzequation was established by introducing the displacement potential function. And itwas solved by using the separation of variables. Using conformal mapping functions, weobtained the complex-valued stresses and displacements of the elastic medium and theliner in the image domain, respectively. The boundary value problem results in a set ofinfnite algebraic equations. The convergence of solutions is proposed by truncation ofinfnite series. The accuracy of the present approach is verifed by comparing the presentboundary element solution results with the available published data. On the basis of the numerical results of the scattering of plane P, SV or Rayleighwaves by a shallow unlined tunnel, parametric study has been performed to investigatethe efect of incident angle and frequency on dynamic stress concentration factors anddisplacements. Furthermore, the efect of the embedment depth, the shear modulus,the thickness of the liner, incident angle and frequency on dynamic stress concentrationfactors, the radial stress and displacements are investigated base on the scattering of planeP, SV or Rayleigh waves by a shallow lined tunnel in an elastic half space. Parametricstudy indicates that the embedment depth, the shear modulus, the thickness of the liner,incident angle and frequency have signifcant influences on the dynamic response of theliner and the medium.