Dynamic response of an infinite body with a cylindrical tunnel cavity under fractional-order thermoviscoelastic diffusion theory with various shock loads

Abstract

Underground tunnels serve as vital infrastructure for road and rail transportation, oil and gas pipelines, power grids, and military applications; they are inherently subject to harsh environments characterized by extreme temperatures, chemical erosion, and sudden impacts. To address these challenges, the sophisticated coupled thermoelastic diffusion dynamic model has been developed based on Biot’s wave equation, Fick’s law, viscoelastic theory, and Ezzat’s fractional-order thermoelastic theory. The research presented here delves into the intricate thermoviscoelastic diffusion dynamic response of the system, exploring how it reacts when simultaneously confronted with a thermal source, normal load, and chemical shock directly applied to the surface of the cylindrical tunnel cavity. The Laplace transform and the Crump numerical inversion method have been used to obtain the non-dimensional displacement, temperature, chemical potential, concentration, radial stress, hoop stress, and axial stress. A meticulous analysis reveals the intricate interplay between the fractional coefficient, temporal evolution, and diverse shock load types on these variables. The fractional-order coefficients have a certain effect on the analysis of all physical variables except the non-dimensional chemical potential. The action time has a significant effect on all non-dimensional physical variables. The two different viscoelastic relaxation time factors have no significant effect on non-dimensional temperature and chemical potential, however, have obvious effects on non-dimensional concentration, radial stress, hoop stress, and axial stress.