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A fractional order theory of poroelasticity

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… Click to show full abstract

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.

Keywords: time; poroelasticity; fractional order; order theory; theory poroelasticity

Journal Title: Mechanics Research Communications
Year Published: 2019

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