Mathematical framework for unsaturated flow in the finite deformation range

Abstract

SUMMARYThe presence of fluid in the pores of a solid imposes a volume constraint on the deformation of the solid. Finite changes in the pore volume alter the degree of saturation of a porous material, impacting its fluid flow and water retention properties. This intricate interdependence between the hydromechanical properties related to solid deformation and fluid flow is amplified when the deformation of the solid matrix is large. In this paper, we present a mathematical framework for coupled solid‐deformation/fluid‐diffusion in unsaturated porous material considering geometric nonlinearity in the solid matrix. The framework relies on the continuum principle of thermodynamics to identify an effective or constitutive stress for the solid matrix, and a water‐retention law that highlights the interdependence of the degree of saturation, suction, and porosity of the material. Porous materials are typically heterogeneous, making them susceptible to localized deformation. In this work, we consider random heterogeneities in density and degree of saturation as triggers of localized deformation in a porous material. Copyright © 2013 John Wiley & Sons, Ltd.

A unified mechanical and retention model for saturated and unsaturated soil behaviour

“…local level). This is the common procedure used in the literature for finite element analysis involving unsaturated soils [5,38,43], because these two increments (i.e. , s) can be easily approximated at the corresponding integration points, once the nodal displacements and pore fluid pressures increments have been found from the discretized global equations.…”

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“…Adopting the same framework as that of Barcelona Basic Model, several authors provide a characterization of the stress state in terms of net stress and suction; see, for example, , , and references therein. Alternatively, models have been developed on the basis on the concept of Bishop's effective stress and suction; see, for a review, and , or some recent contribution as , and . In particular, the modified Cam‐Clay model adopted in this work has been extended to unsaturated conditions following this last approach; see and .…”

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