No abstract

No abstract

This article presents poroelastic laws accounting for a retention behavior dependent also on porosity, as suggested by experimental evidence. Motivated by the numerical formulation of the corresponding boundary-value problem presented in a companion article, these constitutive equations employ displacements and fluid pressures as primary variables. The thermodynamic admissibility of the proposed rate laws for stress and fluid contents is assessed by means of symmetry and Maxwell conditions obtained from the Biot theory. In the case of strain-dependent saturation, the two elasticity tensors describing the drained response in saturated and unsaturated conditions, respectively, are proven to be in general not coincident, with their difference depending on capillary pressure and porosity. Furthermore, it is shown that besides the stress decomposition proposed by Coussy, also the stress split proposed by Lewis and Schrefler is consistent with the Biot framework. The former decomposition is obtained for retention laws depending only on capillary pressure, as expected. The Lewis-Schrefler split is proven to be consistent with retention models depending also on porosity. In these developments, the compressibility of all the phases is taken into account, in order to assess the thermodynamic consistency of an extension of the Biot's coefficient to partially saturated anisotropic porous media.

This paper presents the numerical resolution of unilateral boundary conditions able to effectively model several problems of unsaturated flow, as those involving rainfall infiltration and seepage faces. Besides the penalty technique, we also consider the novel regularization of these conditions by means of the more effective augmented Lagrangian method. The performance of the so-obtained finite element method is carefully investigated in terms of accuracy and ill-conditioning effects, including comparisons with analytical solutions and a complete identification of the analogies with the problem of frictionless contact. In this way, we provide a priori estimates of optimal and admissible ranges for the penalty coefficient as functions of permeability and spatial discretization. The proposed method and the estimated coefficient ranges are validated in further numerical examples, involving the propagation of a wetting front due to rainfall and the partial saturation of an aged concrete dam. These applications show that the proposed regularizations do not induce any detrimental effect on solution accuracy and on convergence rate of the employed Newton-Raphson method. Hence, the present approach should be preferred to the commonly used iterative switching between the imposed-flow and the imposed-pressure conditions, which often leads to spurious oscillations and convergence failures.

No abstract