IBEM Simulation of Seismic Wave Scattering by a 3D Tunnel Mountain

The seismic wave scattering by a 3D tunnel mountain is investigated by the indirect boundary element method (IBEM). Without loss of generality, the 3D physical model of hemispherical tunnel mountain in an elastic half-space is established, and the influence of the incidence frequency and angle of P or SV wave on the mountain surface displacements is mainly examined. It is shown that there exists quite a difference between the spatial distribution of displacement amplitude under the incident P wave and the one under SV wave and that the incidence frequency and angle of wave, especially the existence of tunnel excavated in the mountain, have a great effect on the surface displacements of mountain; the presence of the tunnel in the mountain may cause the greater amplification of surface displacement, which is unfavorable to the mountain projects. In addition, it should be noted that the tunnel may suffer the more severe damage under the incident SV wave.

Characterizing Seismic Scattering in 3D Heterogeneous Earth by a Single Parameter

ABSTRACT We derive a theoretical parameter for three seismic scattering regimes where seismic wavelengths are either much shorter, similar, or much longer than the correlation length of small-scale Earth heterogeneities. We focus our analysis on the power spectral density (PSD) of the von Karman autocorrelation function (ACF), used to characterize the spatial heterogeneity of small-scale variations of elastic rock parameters that cause elastic seismic-wave scattering. Our analysis is based on the assumption that the PSD of the medium heterogeneities at the corresponding wavenumber is related to the wavefield scattering. Our theoretical findings are verified by numerical simulations. The seismic scattering effects in our simulations are assessed by examining attenuation of peak ground acceleration. We discover (1) that seismic scattering is proportional to the standard deviation of velocity variations in all three regimes, (2) that scattering is inversely proportional to the correlation length for the regime where seismic wavelengths are shorter than correlation length, but directly proportional to the correlation length in the other two regimes, and (3) that scattering effects are weak due to heterogeneities characterized by a gentle decay of the von Karman ACF for regimes where seismic wavelengths are similar or much longer than the correlation length.

Dynamic Stress Analysis of a Circular-Lined Tunnel in Composite Strata-SH Wave Incidence

It is necessary to study the problem of seismic wave scattering in composite stratum for tunnel engineering because the existence of composite strata will make the stress of tunnels more complicated during earthquakes. In this thesis, a series solution of the scattering wave field of the composite strata and lining is obtained using the complex function method. According to the stress and displacement boundary conditions between the composite stratum and the lining, a series of equations are established and are solved by means of Fourier transformation and finite term truncation, and the calculation errors are also discussed. Through programming calculations, the dynamic stress concentration factor (DSCF) of circular tunnels in the two types of composite strata, “hard-over-soft” and “soft-over-hard,” is analyzed when SH waves propagate, and certain conclusions on the scattering of SH waves that are distinguished from the case of single homogeneous layers are reached. The research in this article reveals some phenomena. For the Q345 steel lining in the calculation examples, it is found in this paper that increasing the thickness of the lining is effective to reduce the influence of the DSCF. But, for C30 concrete, increasing the thickness of the lining reduces the DSCF of the outer surface while increasing the DSCF of the inner surface.

Mathematical interpretation of seismic wave scattering and refraction on tunnel structures of circular cross-section

Mathematical interpretation of the elastic wave diffraction in circular cylinder coordinates is in the focus of this paper. Firstly, some of the most important properties of Bessel functions, pertinent to the elastic wave scattering problem, have been introduced. Afterwards, basic equations, upon which the method of wave function expansions is established, are given for cylindrical coordinates and for plane-wave representation. In addition, steady-state solutions for the cases of a single cavity and a single tunnel are presented, with respect to the wave scattering and refraction phenomena, considering both incident plane harmonic compressional and shear waves. The last part of the work is dealing with the translational addition theorems having an important role in the problems of diffraction of waves on a pair of circular cylinders.