Seismic wave propagation analysis in the framework of generalized continuum mechanics theory

Abstract

For the problems of seismic wave propagation, scale effects will appear while considering the microstructures of medium. Scale effects mean that new components of wave fields appear in the seismograms due to the microstructure interactions in the medium and vary with the change of the characteristic length scale parameters. The generalized continuum mechanics (GCM) theory which introduces the intrinsic length scales of the microstructures is suitable for analyzing the scale effects of seismic wave propagation. We adopt the concept of multi-scale microstructure interactions, that is, the modified couple stress theory, and the one-parameter second strain gradient theory, as two branches of the GCM theory, have the same definition characteristic length scale parameters of medium, to describe the microstructure interactions at different scales. Through the quantitative relationship between the characteristic length scale parameters of the medium and the micropore, the layered model of the characteristic length scale parameters of the micropore is constructed for numerical modeling in a unified framework, and the scale effects of seismic wave propagation is analyzed. More specifically, the asymmetric elastic wave equations under a unified framework are derived, and the physical definition of the characteristic length scale parameters of medium is given. And the influence of the characteristic length scale parameter of the micropore on the seismic wave propagation is focused on. Finally, the scale effects of seismic waves excited by high-speed trains under the viaduct system are analyzed, and some conclusions are drawn.