Dynamic response of the fractional order thermoelastic diffusion problem of an infinite body with a cylindrical tunnel cavity under different shock loads

Abstract

Underground tunnels, widely used for road and rail transit, oil and gas transportation, and military engineering, are often subjected to harsh environments such as high temperature, chemical corrosion, and shocking. Based on Ezzat’s fractional order thermoelastic theory, a coupled thermoelastic diffusion dynamic problem for an isotropic, uniform infinite body with a cylindrical tunnel cavity which subjected to a thermal source, normal load, and chemical shock simultaneously on its surface is investigated. Analytical expressions for the non-dimensional displacement, temperature, chemical potential, and radial stress are obtained using the Laplace transform method. The effects of the fractional coefficient, time, and different kinds of shock loads on the considered variables are presented and discussed. The results show that the fractional coefficients have significant effects on all physical variables except the chemical potential. These effects can be seen in the peaks and valleys of the curves that are presented. An increase of action time not only increases the size of the region disturbed by each physical variables, but also increase the influence of the fractional coefficient on each physical variables when the three shock loads are considered together. Chemical shock has little effect on the physical variables other than the chemical potential.