A fractional order theory of poroelasticity. (September 2019) - Alaimo, G.; Piccolo, V.; Cutolo, A.; Deseri, L.; Fraldi, M.; Zingales, M.
Highlights: A time memory formalism in the flux-pressure constitutive relation, ruling fluids diffusion phenomenon occurring in several classes of porous media is studied. The memory formalism, useful to capture non-Darcy behavior, is modeled by the Caputo's fractional derivative. The resulting flux-pressure law is applied to the classic confined compression test problem of a sand sample. In such a case, the classical Darcy equation may lead to inaccurate estimates of the settlement time. It is shown that the time-evolution of both the degree of settlement and the pressure field is strongly influenced by the order of Caputo's fractional derivative. Abstract: We introduce a time memory formalism in the flux-pressure constitutive relation, ruling the fluid diffusion phenomenon occurring in several classes of porous media. The resulting flux-pressure law is adopted into the Biot's formulation of the poroelasticity problem. The time memory formalism, useful to capture non-Darcy behavior, is modeled by the Caputo's fractional derivative. We show that the time-evolution of both the degree of settlement and the pressure field is strongly influenced by the order of Caputo's fractional derivative. Also a numerical experiment aiming at simulating the confined compression test poroelasticity problem of a sand sample is performed. In such a case, the classical Darcy equation may lead to inaccurate estimates of the settlement time.