Fractional derivative modelling for rheological characteristics of multilayered saturated porous rock with interfacial thermal contact resistance

Abstract In this paper, the one‐dimensional rheological characteristics of multilayered saturated porous rock subjected to a ramp‐type heating is investigated. By introducing the fractional order parameter and material parameters, a viscoelastic constitutive model is proposed to describe the rheological characteristics of multilayered saturated porous rock. The general incomplete thermal contact model is established to predict the interfacial thermal contact resistance of multilayered saturated porous rock. Based on the coupled thermo‐hydro‐mechanical theory, the semi‐analytical solutions of the excess pore water pressure, temperature increment and displacement are obtained by using the Laplace transform method. The accuracy of the present solutions is verified by comparing with the classic elastic and viscoelastic models, and existing solutions. In addition, the influence of fractional order parameter, material parameter ratio, thermal contact transfer coefficient and thermal partition coefficient on the excess pore water pressure, temperature increment and displacement of multilayered saturated porous rock are investigated.