The present work falls within the framework of linear fracture mechanics extended to saturated porous media. It aims at generalizing the classical crack propagation criteria by accounting for poromechanical coupling. The main objective is to identify the driving force of propagation which now depends on the pore pressure. The result is applied in particular to the two limit cases of drained and undrained regimes. It is shown on the example of the 3-points bending test that significantly different propagation thresholds can be obtained.

Crack nucleation has been the subject of important contributions in the two last decades. Starting from the energy criterion of Leguillon (Eur. J. Mech.—A/Solids 21 (2002)), the present paper examines some consequences that follow directly from the perfectly brittle model. This enables to discuss whether a quasi-static modelling of nucleation is possible. Rigorous bounds for the loading level that triggers nucleation as well as for the set of observable crack lengths under dynamic conditions are established.

The purpose of this study is to investigate the effective behaviour of a micro-cracked material whose matrix bulk and shear moduli are ruled by a linear viscoelastic Burgers model. The analysis includes a detailed study of randomly oriented and distributed cracks displaying an overall isotropic behaviour, as well as aligned cracks resulting in a transversely isotropic medium. Effective material properties are approximated with the assumption that the homogenized equivalent medium exhibits the characteristics of a Burgers model, leading to the identification of short-term and long-term homogenized modules in the Laplace–Carson space through simplified formulations. The crucial advantage of this analytical technique consists in avoiding calculations of the inverse Laplace–Carson transform. The micromechanical estimates are validated through comparisons with FE numerical simulations on 3D microstructures generated with zero-thickness void cracks of disc shape. Intersections between randomly oriented cracks are accounted for, thereby highlighting a potential percolation phenomenon. The effects of micro-cracks on the material’s behaviour are then studied with the aim of providing high-performance creep models for macrostructure calculations at a moderate computation cost through the application of analytical homogenization techniques.

Crack nucleation has been the subject of important contributions in the two last decades. Starting from the double criterion of Leguillon (Eur J Mech A 21:61–72, 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.

Homogenization theory is increasingly applied to coupled phenomena, i.e. when different physical processes have to be modeled in order to correctly describe a system. The reason is that this methodology provides the means to propose a consistent morphological description of the system irrespective of the different phenomena involved, which is deemed to be physically sound. Here, we perform numerical simulations of both mechanical and transport processes in a linear context, so as to identify the best homogenization scheme out of five classical ones. The goal is to eventually apply the result to cracked rocks, which present complex structures, but this study is restricted to the case of parallel disks in an otherwise isotropic matrix. Since cracks in rocks present a vanishing stiffness but an infinite conductivity with respect to the rock, both types of contrast will be considered, and the reverse cases as well (infinite stiffness and vanishing conductivity) for the sake of completeness. After detailing the motivations behind this work, the theoretical background necessary to derive all the analytical estimates is laid down. The derivations given are somewhat improved over previously published ones, and the framework is extended to deal with vanishing as well as infinite contrast. The methodology is explained for the 3D numerical simulations, and the results are presented and discussed. Two different numerical strategies have been used: an FEM software and an FFT-based code. This allows to lessen potential biases of a particular method, and increases the credibility of the results. All in all, the differential scheme is identified as the best fit, which confirms the results of previous studies, but this time in several different cases. (C) 2021 Elsevier Ltd. All rights reserved.

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.

3D finite element simulations have been performed in order to assess the ability of five classical micromechanical estimates to model the elastic behavior of solids with parallel cracks, namely the dilute, Mori-Tanaka, selfconsistent and differential schemes and the Ponte-Castaneda and Willis bounds. The cracks have been represented in the simulations by right circular cylinders with aspect ratios as low as 10(-3) and with centroids randomly located in the REV. Special attention has been paid to the crack aspect ratio variation predicted by the different schemes, since the goal is ultimately to propose a non-linear micromechanical model of a cracked solid, taking complete crack closure into account. The results confirm earlier studies which showed that the differential scheme was best suited for this kind of morphology when computing elastic moduli, but additionally, we show that changes in crack aperture are also accurately predicted. It is however noted that the randomness in the positions of the cracks leads to significant scatter in the magnitude of the aperture variation inside a given simulation, which suggests that the cracks do not close simultaneously. As a consequence, non-linear numerical simulations accounting for contact between the crack lips should be performed in order to completely validate a non-linear micromechanical model in alternate tension/compression loading cases.

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.

SummaryCrack nucleation has been the subject of important contributions in the last two last decades. However, it seems that few attention has been granted to the case of saturated porous media. This is the question addressed 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 vapor pressure. Nucleation is therefore possible only if a partial vaporization of the fluid takes place.

A theoretical model of the Compression of the Damaged Zone experiment is proposed. The tools of micromechanics are used to represent the fractured zone. Assuming an elastic behavior of the sound COx claystone and a simplified geometry of the drift, an analytical solution is presented and the crack closure is determined as a function of distance from the drift wall for two loading cases: a prescribed 4 MPa pressure and a stress-free strain with 1 % average value to describe the swelling due to resaturation. The results are in agreement with experimental observations and give insights into the heterogeneous character of self-sealing in the damaged zone.

Extensive preliminary studies have led the National RadioactiveWaste Management Agency (ANDRA) to thechoice of the Callovo-Oxfordian (COx) claystone of the Meuse/Haute-Marne as a host rock for a radioactive wasterepository because of its very low permeability and adequate mechanical properties, which allow for the geologicallayer to act as a natural barrier against the spreading of radionuclides in the biosphere. However, the concept ofunderground storage relies on the excavation of a network of wells and drifts, which damages the surrounding rock,leading to the creation of a so-called excavation damaged zone (EDZ) along the gallery walls. As a consequence,the overall water permeability is increased by several orders of magnitude. This EDZ is important in the context ofperformance assessment because it might represent a preferential pathway for dissolved radionuclides which couldreach prematurely the surrounding more permeable geological layers. Thankfully, existing fractures tend to closewhen this rock is wetted, mainly because of swelling phenomena and delayed deformations, which is referred toas self-sealing.We propose here to model the hydromechanical couplings that take place during self-sealing so that the progressiveresaturation of a drift may be studied from a theoretical standpoint. The swelling phenomena are first studied ina simplified linear elastic context to analyse the influence of geometry and boundary conditions on self-sealing,first at the scale of the sample using the finite element code Cast3M (CEA) to simulate the progressive resaturationaround a set of periodic elliptical cracks. Non trivial effects are brought to light, and lead to the conclusion that selfsealingneeds to be investigated at the level of the structure and not only at the level of the material. Thus, furtherinvestigations are performed at the scale of the underground drift. Using micromechanics, the EDZ is represented asa medium composed of a homogeneous matrix in which microcracks are distributed with preferential orientations.It should be noted that since the operation phase and the resaturation process take place over a hundred years anda few thousands of years respectively, delayed deformations are bound to develop, leading to convergence of thedrift walls. This first model provides insights that may be useful for understanding the response of the EDZ, butalso when developing a more elaborate model taking into account the viscoplastic behaviour of the rock in relationwith the water content. Both aspects indeed appear to have a significant impact on the macroscopic response ofthe COx claystone subject to swelling phenomena. We then propose to develop a model based on micromechanicsto describe the long-term response of the claystone. In this model, viscoplasticity is introduced at the interfacebetween the clay particles, and a homogenisation scheme is used to determine the behaviour of the clay matrix. Asecond homogenisation step is then required to introduce the quartz and calcite inclusions, and their damageableinterfaces with the matrix. The material response is then analysed and discussed as well as its implications withregards to self-sealing.

The creep response measured on a test at 3 months cannot be directly transposed to a structural calculation for a load at 3 years. It is also excluded to wait several years to perform a creep test on a specimen. To develop a model of material behavior incorporating aging creep, given the multi-scale and multi-physics nature of concrete, the micro-mechanical approach is attractive. The modeling part of the paper aims to estimate the aging viscoelastic behavior of cement paste from information on the chemical evolutions, extending an already developed approach to an evolving cement paste morphological model. These micromechanical models are derived semianalytically. We discuss the suitability of the self-consistent homogenization scheme to describe the setting phase of cement paste. This approach helps to check the applicability of the tools. In parallel, an experimental campaign is carried out to characterize the aging behavior at the cement paste scale.

The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundary value problem defined on a representative elementary volume（REV）. The principle of nonlinear homogenization is illustrated based on the case of a solid phase having a Green’s strength criterion. An original refinement of the so-called secant method（based on two reference strains） is also provided. The paper also describes the main feature of the Gurson’s model which implements the principle of limit analysis on a conceptual model of hollow sphere. The last part of the paper gives some ideas concerning poromechanical couplings.

Materials such as concrete exhibit a strong evolution of their microstructure as a function of time, mainly due to chemical processes such as hydration. This induces a time-dependence of physical and mechanical properties. When the considered behaviour does not involve time, such as elasticity, homogenization techniques can be readily used, on a time by time basis, to estimate the effective properties evolution. But when the behaviour is by nature time-dependent, such as creep, modelling is much more involved as two processes coexist: microstructure evolution and the time-dependent individual behaviour of phases. Taking advantage of recent advances in micromechanics, and focusing on mean field homogenization, the influence of microstructure evolution on the effective ageing viscoelastic behaviour of porous materials can be investigated. A porous material undergoing massive precipitation in pores is considered as illustration, and the effective behaviour is, whenever possible, approximated from a relaxation tensor similar to Bazant solidification theory result.

Prediction of the permeability of porous media is of vital importance to such fields as petroleum engineering, agricultural engineering and civil engineering. The liquid water within unsaturated granular materials is distinguished as the intergranular layer, the wetting layer and the water film. By means of the micromechanics approach, a physical conceptual model is developed to predict the permeability (intrinsic and relative permeabilities) of the monodisperse granular materials. The proposed model has been validated by comparing the available experimental data and the empirical models, and has been used to re-interpret the Kozeny–Carman's relation in particular. The results obtained with this model show that the intergranular water will dominate the flow transport when the saturation degree is higher than the residual saturation degree; when the saturation degree is below the residual saturation degree, the wetting layer will govern the flow transport and the relative permeability will decrease by 3 to 8 orders of magnitude depending on the connectivity of the wetting layer.

A new micromechanics analysis of solute diffusion in unsaturated granular materials is put forward. This permits predicting the percolation effect. To do so, the pore water is divided up into four phases that account for the different spatial distributions and diffusion properties: interconnected capillary water, isolated capillary water, wetting layer and water film. A parameter denoted as connectivity ratio is introduced to account for the connectivity of the capillary pore water. Our model agrees well with experimental results on unsaturated sands and glass beads from literature. It also permits interpreting the physical meaning of the saturation exponent of Archie’s law: The latter is found to be correlated with the connectivity ratio of the unsaturated granular materials.

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. (C) 2016 American Society of Civil Engineers.