Numerical modelling for elastic wave equations including rotational deformation and strain gradient

Abstract

In this work, through introducing the first and second derivatives of strain gradient into the strain energy density function that depends only on the classical strain in conventional continuum mechanics theory to describe the microscopic interactions, the elastic wave equations including rotational deformation and strain gradient based on the Aifantis’s strain gradient theory is derived. The elastic wave equations including rotational deformation and strain gradient with consideration of the scale effects caused by the microscopic interactions will make seismograms appear obvious changes, which are reflected in amplitude attenuation and dispersion, especially P-wave and S-wave propagate in a dispersive manner based on this theory. The results of numerical modelling and theoretical analysis verify this conclusion. The closer the wavelength is to the characteristic scale of the media (lattice size and interparticle distance), the macroscopic response which results from the microscopic interactions becomes more prominent. To further study the effects of microstructure interactions, we compare the results of numerical modelling with the real data when high-speed train passed the piers in Dingxing County in both time and frequency domains, some conclusions are drawn from the comparison.