Hydromechanical Modeling of Unsaturated Flow in Double Porosity Media

Abstract

Geomaterials with aggregated structure or containing fissures often exhibit a bimodal pore size distribution that can be viewed as two coexisting pore regions of different scales. The double-porosity concept enables continuum modeling of such materials by considering two interacting pore scales satisfying relevant conservation laws. This paper develops a thermodynamically consistent framework for hydromechanical modeling of unsaturated flow in double-porosity media. With an explicit treatment of the two pore scales, conservation laws are formulated incorporating an effective stress tensor that is energy-conjugate to the rate of deformation tensor of the solid matrix. A constitutive framework is developed on the basis of energy-conjugate pairs identified in the first law of thermodynamics, which is then incorporated into a three-field mixed finite-element formulation for double-porosity media. Numerical simulations of laboratory-and field-scale problems are presented to demonstrate the impact of double porosity on the resulting hydromechanical responses.

Effects of spatial heterogeneity and material anisotropy on the fracture pattern and macroscopic effective toughness of Mancos Shale in Brazilian tests

“…The implementation of the numerical model leverages the open source finite element library, deal.II [ Bangerth et al ., , ] interfaced with p4est mesh handling library [ Burstedde et al ., ], and Trilinos project—a growing collection of mathematical software libraries for solving a large‐scale, complex multiphysics engineering and scientific problems [ Heroux and Willenbring , ; Salinger et al ., ]. Recently, deal.II has been adopted as a finite element library for geomechanics applications to resolve solid deformation and fluid diffusion coupling problems [ White and Borja , , ] as well as different poromechanics problems including pressurized fracture propagation [e.g., Heister et al ., ; Choo and Borja , ; Choo et al ., ; Na and Sun , ]. In this study, we slightly modify the phase field model published in Heister et al .…”

“…Recently, deal.II has been adopted as a finite element library for geomechanics applications to resolve solid deformation and fluid diffusion coupling problems Borja, 2008, 2011] as well as different poromechanics problems including pressurized fracture propagation [e.g., Heister et al, 2015;Choo and Borja, 2015;Choo et al, 2016;Na and Sun, 2017]. In this study, we slightly modify the phase field model published in Heister et al [2015] by introducing the spatial heterogeneity and anisotropy.…”

Mixed Arlequin method for multiscale poromechanics problems

“…We formulate a discrete Lagrangian such that the updated solid displacement and fluid pressure ( u n +1 , p n +1 ) satisfying the time‐discrete versions of and are the saddle point of the the discrete energy functional. The total (discrete) free energy functional of the solid matrix Π s at time t n +1 is the total free energy of the porous media subtracted by the total free energy contributed by the pore fluid of the same control volume , Under the quasi‐static and isothermal conditions, the internal energy of the solid matrix at time t = t n +1 is given by where Δ t = t n +1 − t n is the time increment. The energy contribution of the pore fluid at time t = t n +1 is given by …”

A fully coupled simple model for unsaturated soils

“…In the last 15 years, many hydro‐mechanical coupled models for unsaturated soils have been developed using the effective stress concept. Some recent examples of models developed to solve different problems can be found in the literature . Some models use non‐normal flow rules requiring a plastic potential function in addition to a yield surface.…”