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.

A fractional order theory of poroelasticity / Alaimo, G.; Piccolo, V.; Cutolo, A.; Deseri, L.; Fraldi, M.; Zingales, M.. - In: MECHANICS RESEARCH COMMUNICATIONS. - ISSN 0093-6413. - ELETTRONICO. - 100:(2019), p. 103395. [10.1016/j.mechrescom.2019.103395]

A fractional order theory of poroelasticity

Piccolo V.;Deseri L.;Fraldi M.;Zingales M.
2019

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.
Alaimo, G.; Piccolo, V.; Cutolo, A.; Deseri, L.; Fraldi, M.; Zingales, M.
A fractional order theory of poroelasticity / Alaimo, G.; Piccolo, V.; Cutolo, A.; Deseri, L.; Fraldi, M.; Zingales, M.. - In: MECHANICS RESEARCH COMMUNICATIONS. - ISSN 0093-6413. - ELETTRONICO. - 100:(2019), p. 103395. [10.1016/j.mechrescom.2019.103395]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/267028
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