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RESEARCH PRODUCT

A fractional order theory of poroelasticity

Luca DeseriGianluca AlaimoA. CutoloMassimiliano FraldiMassimiliano ZingalesValentina Piccolo

subject

Constitutive equationPoromechanics02 engineering and technology01 natural sciencesPressure fieldDarcy–Weisbach equationPhysics::Geophysics010305 fluids & plasmas0203 mechanical engineeringFractional operators0103 physical sciencesCaputo's fractional derivative; Fractional operators; PoroelasticityApplied mathematicsGeneral Materials ScienceCaputo's fractional derivative Fractional operators PoroelasticityCaputo's fractional derivativeCivil and Structural EngineeringMathematicsOrder theoryBiot numberMechanical EngineeringPoroelasticityCondensed Matter PhysicsFractional calculus020303 mechanical engineering & transportsMechanics of MaterialsFractional operatorSettore ICAR/08 - Scienza Delle CostruzioniPorous medium

description

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.

yearjournalcountryeditionlanguage
2019-09-01
10.1016/j.mechrescom.2019.103395http://hdl.handle.net/11588/773509