A bridge between dual porosity and multiscale models of heterogeneous deformable porous media

Hajiabadi, Mohammad Reza; Khoei, A.R.

doi:10.1002/nag.2860

Cited by 15 publications

(18 citation statements)

References 38 publications

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“…5.3.2 Case 2: Implicit decoupling assumptions For Case 2 we investigate the impact of implicit decoupling assumptions. This is particularly poignant considering the use of such decoupled constitutive models in the recent works of Alberto et al (2019) and Hajiabadi and Khoei (2019). To mimic implicit assumptions we consider 1 Q = 0 and A 23 = 0 and make no acknowledgement of these assumptions with respect to relations between mechanical properties.…”

Section: Case 1: Intrinsic Fracture Propertiesmentioning

confidence: 99%

Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models

Ashworth

Doster

2019

Transp Porous Med

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A dual-continuum model can offer a practical approach to understanding first order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to 1 arXiv:1903.11361v2 [physics.geo-ph] 25 Oct 2019 end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromehcanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein we offer recommendations for how and when to use different coefficient modelling concepts.

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Section: Case 1: Intrinsic Fracture Propertiesmentioning

confidence: 99%

Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models

Ashworth

Doster

2019

Transp Porous Med

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“…It is noteworthy that in this study for the sake of simplicity, the elasticity modulus of the fracture area is assumed to be equal to that of the matrix domain in consistent with. 31,55 The fluid flow problem is solved using the finite element analysis with the FE mesh shown in Figure 3. The fracture and matrix pressures are computed at each time step and the hydraulic shape factor is evaluated using Equation (9).…”

Section: Hydraulic Shape Factormentioning

confidence: 99%

“…Furthermore, there are various investigations performed in the literature based on a bridge between the dual-porosity approach and other techniques to enhance the accuracy of the dual-porosity results. [54][55][56][57][58][59][60][61][62][63] However, in most of the aforementioned studies, the applied shape factor is assumed to be constant in both unsteady and steady-state situations and only depends on the geometry of blocks. Accordingly, these assumptions lead to significant errors in the simulations, especially in the transient stages.…”

Section: Introductionmentioning

confidence: 99%

A computational dual‐porosity approach for the coupled hydro‐mechanical analysis of fractured porous media

Khoei,

Taghvaei

2024

Num Anal Meth Geomechanics

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Dual‐porosity simulation is one of the most used and efficient approaches in modeling fractured porous media. The performance of this approach is highly dependent on the accuracy of the definition of matrix‐fracture transfer shape factor. In this paper, a two‐step computational algorithm is developed to enhance the accuracy of the dual‐porosity method in modeling large‐scale deformable porous media, particularly in the transient stage when the conventional dual‐porosity models are associated with some errors. Moreover, in the proposed finite element method (FEM)‐based algorithm, the interaction between the fluid and solid phases is taken into account using a modified expression for the conventional shape factor. To this end, an extended relationship is derived to calculate the hydro‐mechanical shape factor for deformable saturated porous media. An appropriate unit cell along with the consistent boundary conditions is introduced, and the corresponding hydro‐mechanical shape factor is numerically evaluated for the unit cell at each time step. Finally, the calculated time‐varying shape factors are employed in a dual‐porosity framework to simulate various case studies and investigate the influence of different parameters, including the boundary conditions, the fracture to matrix permeability ratio, and the fracture compressibility coefficient on the hydraulic and hydro‐mechanical time‐varying shape factors. Numerical simulations are carried out by employing the proposed dual‐porosity algorithm through two general problems and the results are compared with the fine‐grid direct numerical simulation. The results are promising and show that the present algorithm effectively and efficiently increases the precision of the dual‐porosity method in modeling large‐scale deformable problems.

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“…where i, j, l = 1, 2, 3. It follows from (20) that the stabilized term for the effective force state accounting for the non-uniformed deformation state can be written as…”

Section: Two-phase Stabilization Formulationmentioning

confidence: 99%

“…Shahbodagh et al 18 proposed an elasto‐viscoplastic model for dynamic analysis of strain localization in fully saturated clay. Enriched finite element methods such as the extended finite element and multiscale models have been applied to model saturated porous media (e.g., References 20‐23, among others). For example, Khoei 21 proposed an enriched finite element technique for numerical simulation of interacting discontinuities in naturally fractured porous media.…”

Section: Introductionmentioning

confidence: 99%

A stabilized computational nonlocal poromechanics model for dynamic analysis of saturated porous media

Menon

Song

2021

Numerical Meth Engineering

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In this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero-energy modes associated with the original multiphase correspondence constitutive models in the coupled nonlocal poromechanics model. The two-phase stabilization scheme is formulated based on an energy method that incorporates inhomogeneous solid deformation and fluid flow. In this method, the nonlocal formulations of skeleton strain energy and fluid flow dissipation energy equate to their local formulations. The stable coupled nonlocal poromechanics model is solved for dynamic analysis by an implicit time integration scheme. As a new contribution, we validate the coupled stabilization formulation by comparing numerical results with analytical and finite element solutions for one-dimensional and two-dimensional dynamic problems in saturated porous media. Numerical examples of dynamic strain localization in saturated porous media are presented to demonstrate the efficacy of the stable coupled poromechanics framework for localized failure under dynamic loads.

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A bridge between dual porosity and multiscale models of heterogeneous deformable porous media

Cited by 15 publications

References 38 publications

Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models

Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models

A computational dual‐porosity approach for the coupled hydro‐mechanical analysis of fractured porous media

A stabilized computational nonlocal poromechanics model for dynamic analysis of saturated porous media

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