Scattering of plane SH waves by a circular tunnel in nonlocal fractional-order viscoelastic half-space

Abstract

This paper proposed a complex function solution to the scattering of plane SH waves by circular tunnels in nonlocal fractional-order viscoelastic half-space. The nonlocal theory and the fractional order viscoelastic model are used to describe the viscoelastic properties and nonlocal effects of the soil, respectively. The basic equations are expressed in the complex domain based on the theory of complex functions, and then the scattering displacement potential function of plane SH waves is obtained using the wave function expansion method. The correctness of the presented method is verified by degrading it to the classical local elastic solution. Finally, the effects of non-local parameters, soil viscosity and fractional order on the distribution of dynamic stress concentration factors inside the tunnel were analyzed, and it was found that they had significant effects on the dynamic stress concentration factors under high-frequency wave incidence.