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International audience; Crack nucleation has been the subject of important contributions in the two last decades. However, it seems that few attention has been granted to the case of saturated porous media. This is the question adressed in the present paper which is devoted to nucleation in traction mode. From a physical point of view, nucleation is a sudden phenomenon, so that the material response is both adiabatic and undrained. In the spirit of the variational approach, the nucleated crack is viewed as the final state of a region of space in which the material undergoes a full damage process. In traction mode, the opening of a saturated crack in undrained condition induces a drop of fluid pressure. In case of low fluid compressibility, the presence of the fluid delays the brittle failure usually associated with nucleation, as long as the fluid pressure remains above the saturation vapour pressure. Nucleation is therefore possible only if a partial vaporization of the fluid takes place.

International audience; Crack nucleation has been the subject of important contributions in the two last decades. Starting from the double criterion of Leguillon (2002), the present paper suggests that an energy criterion is sufficient for the prediction of the loading level that triggers nucleation as well as its geometrical characteristics. In view of application to saturated porous materials, the role of the pore fluid during nucleation is considered. In case of low fluid compressibility, the presence of the fluid delays the brittle failure usually associated with nucleation, as long as the fluid pressure remains above the saturation vapour pressure. The energy nucleation criterion is then applied to discuss the formation of breakouts around wellbores subjected to remote compressive stresses.

The constitutive equations of finite strain poroelasticity at the macroscopic level are recovered from an analysis conducted on a representative elementary volume of porous material open to fluid mass exchanges. The change of scale procedure relies upon the solution of a boundary value problem defined on the solid domain of the representative volume undergoing large elastic strains. Such a micro-macro procedure makes it possible to establish necessary and sufficient conditions ensuring the validity of an “effective stress” formulation of the constitutive equations of finite strain poroelasticity. The particular but important case of an incompressible solid matrix is shown to satisfy these conditions.

This paper is concerned with the change in stress, pore pressure, and salt concentration taking place in a chemically active shale around a borehole filled with a drilling fluid which is not in thermodynamic equilibrium with the saturating fluid. We first derive a phenomenological Biot type theory of chemoporoelasticity. This theory can be degenerated into two limiting cases, one corresponding to the absence of any chemical interaction, and the other one which can be characterized as a perfect ion exclusion membrane theory. The equations are then specialized to solve initial boundary value problems, characterized by an irrotational displacement field. Finally, the Laplace transformed field equations are solved explicitly for the borehole problem.

The macroscopic mechanical behaviour of unsaturated porous media under isothermal conditions is studied within the framework of upscaling techniques. First the main features of the homogenization method are recalled. Then, the macroscopic state equation including the capillary effects is derived. Finally, a morphological model is used in order to clarify the link between the sorbtion-desorbtion hysteretic phenomena and the macroscopic mechanical behaviour.

This study focuses on the poroelastic behaviour and permeability of tight sandstones, which are characterized by a low porosity, a low gas permeability and a strong sensitivity to in-situ stress. Experimentally the Biot coefficient takes a value close to 1 at low confinement and decreases with increasing confining pressure; the permeability shows an important reduction with increasing confining pressure. This behaviour can be attributed to pore entrapment and to the closure of cracks and joints. Micromechanical models, considering low permeable sandstones as made up of an assemblage of grains with interfaces and pores, reproduce well the observed trends of Biot coefficient and permeability.

Comprehensive modeling of sedimentary basins should integrate the coupled nature of different phenomena such as sediment compaction, pore-fluid flow and heat transport. In this context, the thermal evolution of the basin plays an important role in the mechanical and chemo-mechanical deformation processes as heat modifies fluids viscosity and minerals physicochemical properties, thus affecting pore fluid expulsion and mineral stability. The present paper describes a three-dimensional constitutive and numerical model specifically devised for dealing with thermo-poromechanical deformation processes during diagenesis. The sedimentary basin is modeled as a fully saturated thermo-poro-elastoplastic-viscoplastic medium undergoing large strains. A key feature of the model is related to the evolution of the sediment material properties associated with temperature and large irreversible porosity changes. The computational model, which integrates both poroplastic and poroviscoplastic components of deformation at large strains, relies upon a parallel implementation of the finite element method with a shared memory multiprocessing interface. Numerical simulations of gravitational compaction during the sediment accretion phase as well as along geological period of pore pressure dissipation are performed in the context of oedometric setting. Special emphasis is given to temperature effects on the deformation history of the basin.

This paper is devoted to the modelling of stress-sensitive Biot coefficient experimentally observed in low permeable sandstones. Sandstones are described as an assemblage of rigid inclusions surrounded by poroelastic interfaces representing joints between grains and pores. A micromechanical model of Biot coefficient under loading is developed, which highlights the role of interfaces closure on the poroelastic macroscopic behaviour. Experimental results available concerning low permeability sandstones are analyzed in view of this model.

In this paper, the strength properties of a ductile nanoporous material are investigated by means of a non-linear homogenization approach based on the modified secant method. The material is described as a rigid-ideal-plastic solid matrix, obeying to a von Mises strength criterion, and containing isotropically-distributed spherical nanovoids. Aiming to properly account for local strain-rate heterogeneities, a 3-layered model is adopted. A novel closed-form macroscopic strength criterion is established, and successfully compared with available numerical data. Proposed approach results in an effective enhancement of the non-linear homogenization-based model recently provided by Dormieux and Kondo (2013).

International audience; Crack nucleation issue is addressed in a comprehensive micromechanics-based framework allowing to bridge the 2D model with the more realistic 3D representation of a crack. The sudden and abrupt nature of the nucleation process argues in favour of adiabatic conditions rather than isothermal so that the formulation of the energy balance is formulated in terms of internal energy instead of Helmholtz free energy. The proposed theory provides the mean to evaluate the temperature rise as a function of the created entropy at the microscopic scale and the internal energy crack density at the macroscopic one.

International audience; Several experimental studies, carried out on anisotropic rocks, have evidenced that even though strains, due to isotropic loading and/or internal fluid pressure, are strongly anisotropic, the resulting Biot’s tensor is almost isotropic. Those results were found on two different rocks: a clay rock (France—Bure argillite) and a sandstone from the Vosges region (France). Such (a priori) surprising results led us to develop micromechanical modelling in which anisotropy comes either from an anisotropic solid matrix (and isotropic pore space) or from an anisotropic pore space (and isotropic solid matrix). The obtained results have shown that for both cases the Biot’s tensor is virtually isotropic or presents a very weak anisotropy. This unambiguously supports the fact that a strongly anisotropic porous material is compatible with experimental measurements of isotropic (or quasi isotropic) Biot’s tensor

In this paper, hydrostatic strength properties of nanoporous materials are investigated by addressing the limit state of a hollow sphere undergoing isotropic loading conditions. Void-size effects are modelled by treating the cavity boundary as a coherent-imperfect homogeneous interface. The hollow sphere is assumed to be comprised of a rigid-ideal-plastic material obeying to a general isotropic yield criterion. The latter is defined by considering a simplified form of the yield function proposed by Bigoni and Piccolroaz in [Int J Solids Struct; 41: 2855–2878], resulting able to account for a broad class of pressure-sensitive materials whose plastic response is also affected by the stress Lode angle. The corresponding support function is consistently derived and discussed. The exact solution of the limit-state problem is fully determined, providing a closed-form description of stress, strain-rate and velocity fields, as well as the macroscopic hydrostatic strength of nanoporous media. Proposed approach allows to consistently generalise available analytical solutions for porous and nanoporous materials, by accounting for a general plastic response of the solid matrix and for void-size effects. Finally, present exact solution, as well as the identification of the support function for the adopted general strength criterion, open towards novel kinematic limit-analysis approaches for describing macroscale strength properties of nanoporous materials under arbitrary triaxial loadings.

International audience; An efficient numerical method is proposed to upscale the strength properties of heterogeneous media with periodic boundary conditions. The method relies on a formal analogy between strength homoge-nization and non-linear elasticity homogenization. The non-linear problems are solved on a regular discretiza-tion grid using the Augmented Lagrangian version of Fast Fourier Transform based schemes initially introduced for elasticity upscaling. The method is implemented for microstructures with local strength properties governed either by a Green criterion or a Von Mises criterion, including pores or rigid inclusions. A thorough comparison with available analytical results or finite element elasto-plastic simulations is proposed to validate the method on simple microstructures. As an application, the strength of complex microstructures such as the random Boolean model of spheres is then studied, including a comparison to closed-form Gurson and Eshelby based strength estimates. The effects of the microstructure morphology and the third invariant of the macroscopic stress tensor on the homogenized strength are quantitatively discussed.

Summary Compaction and associated fluid flow are fundamental processes in sedimentary basin deformation. Purely mechanical compaction originates mainly from pore fluid expulsion and rearrangement of solid particles during burial, while chemo-mechanical compaction results from Intergranular Pressure-Solution (IPS) and represents a major mechanism of deformation in sedimentary basins during diagenesis. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modeling of purely mechanical and chemo-mechanical compaction in sedimentary basins. Extending the concepts that have been previously proposed for the modeling of purely mechanical compaction in finite poroplasticity, deformation by IPS is addressed herein by means of additional viscoplastic terms in the state equations of the porous material. The finite element model integrates the poroplastic and poroviscoplastic components of deformation at large strains. The corresponding implementation allows for numerical simulation of sediments accretion/erosion periods by progressive activation/deactivation of the gravity forces within a fictitious closed material system. Validation of the numerical approach is assessed by means of comparison with closed-form solutions derived in the context of a simplified compaction model. The last part of the paper presents the results of numerical basin simulation performed in one dimensional setting, demonstrating the ability of the modeling to capture the main features in elastoplastic and viscoplastic compaction. Copyright © 2016 John Wiley & Sons, Ltd.

Summary This paper addresses the open question of the effect of the third invariant in the definition of the strength criterion of porous media. This is here achieved in the context of a porous medium made up of a solid phase, in which strength criterion appears as an explicit function of Lode's angle. Application is provided from the Gurson hollow sphere model for which the macroscopic strength exhibits a lack of symmetry for axisymmetric macroscopic strain rate loadings. Copyright © 2015 John Wiley & Sons, Ltd.

The aim of this paper is to model the viscoelastic properties of micro-cracked materials based on the homogenization micro-macro approach. The isotropic case with random orientation distribution of micro-crack in Burgers non-ageing linear viscoelastic solid was previously modeled. However, in many cases, micro-cracks appear to be parallel and the macroscopic behavior is transversely isotropic. An alternative effective transversely isotropic Burgers model is developed to model the behavior of such materials for the cases of open cracks. For this anisotropic case, the Burgers model for the macroscopic viscoelastic behavior of the micro-cracked materials depends on 20 viscoelastic parameters which are functions of the damage parameter and of the viscoelastic properties of the solid phase. In this study, the evolution of all 20 damage viscoelastic parameters as functions of the crack density is detailed based on a dilute-stress homogenization approach. The use of the same Burgers viscoelastic model as non-cracked material to model the viscoelastic behavior of micro-cracked material is an approximation. This approximation is carried out in short- and long-term behaviors. However, the comparison of this approximation with the exact solution in the case of 1D traction loading showed an excellent validation of this approach in transient situation.

International audience; In this paper, we first recall some available Eshelby-based homogenization schemes applied to microcracked materials. An emphasis is put on models accounting for interacting opened or closed microcracks and their spatial distribution. On the basis of these schemes, we briefly present a class of isotropic damage models. The main part of the study is devoted to the derivation of exact solutions for mechanical fields (damage distribution, displacement, stress fields) in a hollow sphere subjected to a radial loading and made up of an elastic damageable material. The solutions, discussed in link with the different homogenization schemes, may serve as a reference for assessment of numerical predictions of brittle damage models. Interestingly, it is shown that the existence of physically meaningful solutions strongly depends on the model under consideration. Finally, we establish explicit solution to the hollow sphere problem in unloading regime.

In the case of micro-cracked viscoelastic materials, the numerical approach is required to solve the problem of crack propagation. The step-by-step method is used to model, using the finite element method, a morphologically representative pattern of the media. The computation of the effective behaviour of the material in the case without crack propagation shows a very good validation with respect to the Burger effective model obtained by the analytical method. The case of crack propagation is solved numerically considering a morphologically representative pattern containing a single crack. We also develop the concept of critical rate of kinematic loading and of asymptotic damage.

A numerical scheme for the computation of the permeability of complex microstructures is presented. As a darcean counterpart of the FFT-based scheme in elasticity, the method is designed to be directly coupled with 3D imaging techniques of porous samples, without meshing or definition of an equivalent pore network. The method relies on the variational principle of Hashin and Shtrikman which ensures a rigorous upper bound status to the estimated permeabilities and provides an energetically consistent rule for heterogeneous voxels comprising both the solid and fluid phases.

International audience; In the present study, we investigate the strength properties of ductile porous materials reinforced by rigid particles. The microporous medium is constituted of a Drucker-Prager solid phase containing spherical voids; its behavior is described by means of an elliptic criterion (issued from a modified secant moduli approach) whose corresponding support function is determined. The latter is then implemented in a limit analysis approach in which a careful attention is paid for the contribution of the inclusion matrix-interface. This delivers parametric equations of the effective strength properties of the porous material reinforced by rigid particles. The predictions are compared to available results obtained by means of variational homogenization methods successively applied for micro-to-meso and then for meso-to-macro scales transitions. Moreover, additional static solutions are derived and compared to the kinematics limit analysis ones in order to prove the accuracy of the strength predictions under isotropic loading. Thereafter, the theoretical predictions (by the two methods) under shear loading are assessed by comparison with experimental data. The influences of mineralogical compositions and porosity are also discussed. Finally, we derive an approximate closed-form expression of the macroscopic strength which proves to be very accurate. Then, we examine in Appendix the particular case of a von Mises solid phase of the porous matrix for which our results are compared to the available estimates.

SUMMARY The paper deals with the modeling of some aspects, such as the formulation of constitutive equations for sediment material or finite element approach for basin analysis, related to mechanical compaction in sedimentary basins. In addition to compaction due to gravity forces and pore-pressure dissipation, particular emphasis is given to the study of deformation induced by tectonic sequences. The numerical model relies upon the implementation of a comprehensive constitutive model for the sediment material formulated within the framework of finite poroplasticity. The theoretical model accounts for both hydromechanical and elasticity–plasticity coupling due to the effects of irreversible large strains. From the numerical viewpoint, a finite element procedure specifically devised for dealing with sedimentary basins as open systems allows to simulate within a two-dimensional setting the process of sediment accretion or erosion. Several basin simulations are presented. The main objective is to analyze the behavior of a sedimentary basin during the different phases of its life cycle: accretion phase, pore-pressure dissipation phase and compressive/extensional tectonic motions. Copyright © 2013 John Wiley & Sons, Ltd.

International audience; The development of nanocomposites and nanoporous materials in the last two decades has stimulated tremendous researches aiming particularly to predict particles or voids size effects on the mechanical behavior. However, few studies have been devoted to nonlinear behavior of this class of materials. The present paper investigates the strength property of ductile (plastic) nanoporous materials by means of a non linear homogenization approach. The material under stake is composed of a rigid-ideal plastic solid matrix (assumed to obey to von Mises criterion) and of spherical nanosized voids. The theoretical procedure consists in an extension of the so-called modified secant moduli method in which an interfacial strength is appropriately accounted. It delivers a general equation giving the macroscopic strength, from which is derived a closed-form expression which explicitly accounts for voids size effects. Finally, we take advantage of these new results to discuss the validity of some recent models available in literature. © 2013 Elsevier Ltd. All rights reserved.

This study aims at determining the macroscopic strength of porous materials having a Drucker–Prager solid phase at microscale and two populations of saturated pores with different pressures at both micro and meso scales. To this end, and taking account of the available results by Maghous et al. (2009), we first derive a closed-form expression of approximate criterion for a dry porous medium whose matrix obeys to a general elliptic criterion. The methodology to formulate this criterion is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. The obtained results are then implemented in a two-step homogenization procedure, which interestingly delivers analytical expression of the macroscopic criterion for dry double porous media whose solid phase at microscale obeys to a Drucker–Prager criterion. After a brief discussion of the results, we propose an extension to double porous saturated media, allowing therefore to quantify the simultaneous effects of the different pore pressures applied on each voids population. The results are discussed in terms of the existence or not of effective stresses. Finally, they are assessed by comparing them to recently available results.

In this paper, deviatoric strength properties of nanoporous materials are investigated by addressing the limit state of a hollow sphere undergoing axisymmetric deviatoric strain-rate based loading conditions. The hollow sphere is assumed to be comprised of a rigid ideal-plastic matrix obeying to a von Mises strength criterion. Void-size effects are consistently described by introducing a coherent-imperfect homogeneous interface at the cavity boundary. In the framework of a kinematic approach, the limit-analysis problem on the hollow sphere is solved by referring to a particular trial velocity field, expressed in terms of some free model parameters, chosen as a result of an optimization strategy. A closed-form expression for estimating the macroscopic deviatoric strength is obtained and successfully compared with available benchmarking data.

International audience; Classical micromechanics approaches for heterogeneous media assume perfect bonding between phases, implying that both displacement and stress vectors are continuous across the interface between the phases. When nanoinclusions are involved, a stress vector discontinuity in the local equilibrium has to be accounted for. In this framework, this paper derives an approximate solution of the Lippmann-Schwinger (L-S) equation, which accounts for these surface stresses. This approach suggests introducing the concept of an equivalent particle that combines the particle with the surrounding interface, which can be directly implemented in any standard homogenization procedure, such as the Mori-Tanaka scheme. Analytical expressions for the stiffness tensor of the equivalent particle is derived for spheroidal inclusions, accounting for a wide range of nanoinclusion shapes and dimensions. Finally, an energy-based analysis proves how the dramatic increase of the elastic properties is controlled, for a given volume fraction, by the smallest size of the nanoinclusions.

International audience; In the framework of limit analysis theory, we derive closed-form expressions of approximate criteria for ductile porous materials whose plastically compressible matrix obeys to an elliptic criterion. The general methodology is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. We first consider a porous medium with a Green type matrix and establish the corresponding macroscopic yield function. Then, the obtained results are used in order to investigate double porous materials whose solid phase at the microscale (the smallest scale) obeys a von Mises criterion. The results are assessed by comparing them with numerical data, and with recently published results.

The formulation of macroscopic poroelastic behavior of a jointed rock is investigated within the framework of a micro–macro approach. The joints are modeled as interfaces, and their behavior is modeled by means of generalized poroelastic state equations. Starting from Hill's lemma extended for a jointed medium and extending the concept of strain concentration to relate the joint displacement jump to macroscopic strain, the overall poroelastic constitutive equations for the jointed rock are formulated. The analysis emphasizes the main differences and similarities of the resulting behavior with respect to that characterizing ordinary porous media. It is shown that, unlike ordinary porous media, conditions on the poroelastic parameters of joints are required for the macroscopic drained stiffness to entirely define the poroelastic behavior. This is achieved, for instance, if the joint network is characterized by a unique Biot coefficient. Extension of the analysis to non-linear poroelasticity is also outlined. Finally, the theoretical formulation is applied to two particular cases of jointed rock for which explicit expressions of the overall poroelastic parameters are derived.

This article aims at the determination of the effective behavior of a microcracked linear viscoelastic solid. Due to the nonlinearity of the strain concentration in the cracks, the latter cannot be derived directly from a combination of the correspondence theorem with the Eshelby-based homogenization schemes. The proposed alternative approach is based on the linear relationship between the macroscopic strain and the local displacement discontinuity across the crack. An approximation of the effective behavior in the framework of a Burger model is derived analytically.