3‐D mesoscale simulation of crack‐permeability coupling in the Brazilian splitting test

In this paper, mesoscale hydromechanical simulations are performed to study (1) fracture features and (2) crack‐gas permeability coupling evolution in the context of the tensile splitting test. The mesostructure is based on a 2‐phase 3‐D representation of heterogeneous materials, such as concrete, where stiff aggregates are embedded into a mortar matrix. To take into account these heterogeneities without any mesh adaptation, a weak discontinuity is introduced into the strain field. In addition, a strong discontinuity is also added to take into account microcracking. This mechanical model is cast into the framework of the enhanced finite element method. Concerning the coupling with gas permeability, a double‐porosity method is used to simulate the flow through the cracks and the porosity. The apparent gas permeability is afterwards evaluated by a homogenization method. On the basis of finite element simulations, influence of aggregate size on ultimate crack opening, macroscopic ultimate tensile stress, total dissipated energy, and gas permeability evolution is numerically investigated. Furthermore, gas permeability evolution is also compared with experimental results from the literature. In addition, in the spirit of a sequential multiscale approach, macroscale gas permeability equations are identified from the hydromechanical results coming from the mesoscale computations. These equations lead to a relation between macroscale gas permeability evolution and crack opening. Besides, we show how the aggregate size influences the percolation threshold and that after this threshold, a cubic relation between macroscale gas permeability and crack opening is obtained.     

Homogenization of anisotropic elastoplastic behaviors of a porous polycrystal with interface effects

This paper is devoted to develop a theoretical framework to predict the macroscopic transversely isotropic elastoplastic behavior of clay‐like material, which is viewed as a porous polycrystal. We consider evolutions of two local plastic mechanisms of grains and interface simultaneously, for which a Schmid criterion is used for the strength of sheet‐like grains and a Tresca criterion for the strength of interfaces between particles. By adapting the standard incremental method, we propose firstly a classic self‐consistent model, which does not consider the effect of interface, then a generalized self‐consistent model in which the solid phase is represented by laminated (or isotropic) spherical grains surrounded by interfaces. Comparisons of numerical predictions between these two methods are performed and have demonstrated the validity of the generalized self‐consistent model taking account of interface effects. Numerical simulations of uniaxial compression tests have shown that the macroscopic elastoplastic behavior of polycrystalline (clay‐like) material can be successfully predicted by the way of considering the two local plastic mechanisms at microscopic scale. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical modelling of the hydro‐chemo‐mechanical behaviour of geomaterials in the context of CO2 injection

Safety assessment of geosequestration of CO₂ into deep saline aquifers requires a precise understanding of the study of hydro‐chemo‐mechanical couplings occurring in the rocks and the cement well. To this aim, a coupled chemo‐poromechanical model has been developed and implemented into a research code well‐suited to the resolution of fully coupled problems. This code is based on the finite volume methods. In a 1D axisymmetrical configuration, this study aims to simulate the chemo‐poromechanical behaviour of a system composed by the cement well and the caprock during CO₂ injection. Major chemical reactions of carbonation occurring into cement paste and rocks are considered in order to evaluate the consequences of the presence of CO₂ on the amount of dissolved matrix and precipitated calcium carbonates. The dissolution of the solid matrix is taken into account through the use of a chemical porosity. Matrix leaching and carbonation lead, as expected, to important variations of porosity, permeability and to alterations of transport properties and mechanical stiffness. These results justify the importance of considering a coupled analysis accounting for the main chemical reactions. It is worth noting that the modelling framework proposed in the present study could be extended to model the chemo‐poromechanical behaviour of the reservoir rock and the caprock when subjected to the presence of an acidic pore fluid (CO₂‐rich brine). Copyright © 2013 John Wiley & Sons, Ltd.     

Effective properties of a cemented or an injected granular material

In this paper the macroscopic elastic properties of injected or cemented sands are derived from the characteristics of the constituents and the analysis of the microstructure using a multi‐scale modelling approach. Particular interest is given to the choice of the representative elementary volume, by relying on existing microstructural data. The periodic homogenization is adopted and required numerical solutions are performed by the finite element method. An assessment of the validity of the multi‐scale approach is achieved through comparison with theoretical and experimental results on cemented and injected granular media reported in the literature. The capabilities of the model are also used to investigate the influence of geometrical and mechanical microscale parameters on the macroscopic behaviour of the treated materials. Copyright © 2004 John Wiley & Sons, Ltd.     

Compressibility and permeability of sand–kaolin mixtures. Experiments versus non‐linear homogenization schemes

This study deals with the behaviour of mixtures of sand and saturated kaolin paste considered as composite materials made of permeable and deformable (with non‐linear behaviour) matrix (the kaolin paste) with rigid and impervious inclusions (the sand grains). Oedometric and permeability tests highlight the key role of the state of the clay paste, and show the existence of a threshold of sand grain concentration above which a structuring effect influences both compressibility and permeability. At the light of these experiments two homogenization schemes (with simplifying assumptions to make the problem manageable) are considered to model these two parameters. Qualitative and quantitative comparisons with experimental data point out their respective domain of interest and limitations: a tangent homogenization scheme is shown to be sufficient to describe the macroscopic properties for dilute sand concentration; above the concentration threshold, the structuring effect is captured by the new homogenization scheme developed in this paper. Copyright © 2010 John Wiley & Sons, Ltd.     

Meso‐scale particle modeling of concrete deterioration caused by alkali‐aggregate reaction

A meso‐scale particle model is presented to simulate the expansion of concrete subjected to alkali‐aggregate reaction (AAR) and to analyze the AAR‐induced degradation of the mechanical properties. It is the first attempt to evaluate the deterioration mechanism due to AAR using the discrete‐element method. A three‐phase meso‐scale model for concrete composed of aggregates, mortar and the interface is established with the combination of a pre‐processing approach and the particle flow code, PFC2D. A homogeneous aggregate expansion approach is applied to model the AAR expansion. Uniaxial compression tests are conducted for the AAR‐affected concrete to examine the effects on the mechanical properties. Two specimens with different aggregate sizes are analyzed to consider the effects of aggregate size on AAR. The results show that the meso‐scale particle model is valid to predict the expansion and the internal micro‐cracking patterns caused by AAR. The two different specimens exhibit similar behavior. The Young's modulus and compressive strength are significantly reduced with the increase of AAR expansion. The shape of the stress–strain curves obtained from the compression tests clearly reflects the influence of internal micro‐cracks: an increased nonlinearity before the peak loading and a more gradual softening for more severely affected specimens. Similar macroscopic failure patterns of the specimens under compression are observed in terms of diagonal macroscopic cracks splitting the specimen into several triangular pieces, whereas localized micro‐cracks forming in slightly affected specimens are different from branching and diffusing cracks in severely affected ones, demonstrating different failure mechanisms. Copyright © 2012 John Wiley & Sons, Ltd.     

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

This paper studies the chemo‐mechanics of cemented granular solids in the context of continuum thermodynamics for fluid‐saturated porous media. For this purpose, an existing constitutive model formulated in the frame of the Breakage Mechanics theory is augmented to cope with reactive processes. Chemical state variables accounting for the reactions between the solid constituents and the solutes in the pore fluid are introduced to enrich the interactions among the microstructural units simulated by the model (i.e., grains and cement bonds). Two different reactive processes are studied (i.e., grain dissolution and cement precipitation), using the chemical variables to describe the progression of the reactions and track changes in the size of grains and bonds. Finally, a homogenization strategy is used to derive the energy potentials of the solid mixture, adopting probability density functions that depend on both mechanical and chemical indices. It is shown that the connection between the statistics of the micro‐scale attributes and the continuum properties of the solid enables the mathematical capture of numerous mechanical effects of lithification and chemical deterioration, such as changes in stiffness, expansion/contraction of the elastic domain, and development of inelastic strains during reaction. In particular, the model offers an interpretation of the plastic strains generated by aggressive environments, which are here interpreted as an outcome of chemically driven debonding and comminution. As a result, the model explains widely observed macroscopic signatures of geomaterial degradation by reconciling the energetics of the deformation/reaction processes with the evolving geometry of the microstructural attributes. Copyright © 2015 John Wiley & Sons, Ltd.     

Two‐scale modeling of solute dispersion in unsaturated double‐porosity media: Homogenization and experimental validation

A two‐scale modeling of solute transport in double‐porosity (DP) media under unsaturated water flow conditions is presented. The macroscopic model was developed by applying the asymptotic homogenization method. It is based on theoretical and empirical considerations dealing with the orders of magnitude of characteristic quantities involved in the process. For this purpose a physical model that mimics the behavior of DP medium was built. The resulting two‐equation model relies on a coupling exchange term between micro‐ and macro‐porosity subdomains associated with local non‐equilibrium solute concentrations. The model was numerically implemented (Comsol Multiphysics^®) to simulate the macroscopic one‐dimensional physical process taking place into the porous medium of 3D periodic microstructure. A series of dispersion experiments of NaCl solution under unsaturated steady‐state flow conditions were performed. The experimental results were used first to calibrate the dispersion coefficient of the model, and second to validate it through two other independent experiments. The excellent agreement between the numerical simulations and the measurements of the time evolution of the non‐symmetrical breakthrough curves provides a proof of predictive capacity of the developed model. Copyright © 2010 John Wiley & Sons, Ltd.     

Macro‐and Microstructural,Textural Fabrics and Deformation Mechanism of Calcite Mylonites from Xar Moron‐Changchun Dextral Shear Zone,Northeast China

The calcite mylonites in the Xar Moron-Changchun shear zone show a significance dextral shearing characteristics. The asymmetric(σ-structure) calcite/quartz grains or aggregates, asymmetry of calcite c-axes fabric diagrams and the oblique foliation of recrystallized calcite grains correspond to a top-to-E shearing. Mineral deformation behaviors, twin morphology, C-axis EBSD fabrics, and quartz grain size-frequency diagrams demonstrate that the ductile shear zone was developed under conditions of greenschist facies, with the range of deformation temperatures from 200 to 300°C. These subgrains of host grains and surrounding recrystallized grains, strong undulose extinction, and slightly curved grain boundaries are probably results of intracrystalline deformation and dynamic recrystallization implying that the deformation took place within the dislocation-creep regime at shallow crustal levels. The calculated paleo-strain rates are between 10~(–7.87)s~(–1) and 10~(–11.49)s~(–1) with differential stresses of 32.63–63.94 MPa lying at the higher bound of typical strain rates in shear zones at crustal levels, and may indicate a relatively rapid deformation. The S-L-calcite tectonites have undergone a component of uplift which led to subhorizontal lifting in an already non-coaxial compressional deformation regime with a bulk pure shear-dominated general shear. This E-W large-scale dextral strike-slip movement is a consequence of the eastward extrusion of the Xing'an-Mongolian Orogenic Belt, and results from far-field forces associated with Late Triassic convergence domains after the final closure of the Paleo-Asian Ocean.     

Reaction mechanism for the replacement of calcite by dolomite and siderite: implications for geochemistry, microstructure and porosity evolution during hydrothermal mineralisation

Carbonate reactions are common in mineral deposits due to CO₂-rich mineralising fluids. This study presents the first in-depth, integrated analysis of microstructure and microchemistry of fluid-mediated carbonate reaction textures at hydrothermal conditions. In doing so, we describe the mechanisms by which carbonate phases replace one another, and the implications for the evolution of geochemistry, rock microstructures and porosity. The sample from the 1.95 Moz Junction gold deposit, Western Australia, contains calcite derived from carbonation of a metamorphic amphibole—plagioclase assemblage that has further altered to siderite and dolomite. The calcite is porous and contains iron-rich calcite blebs interpreted to have resulted from fluid-mediated replacement of compositionally heterogeneous amphiboles. The siderite is polycrystalline but nucleates topotactically on the calcite. As a result, the boundaries between adjacent grains are low-angle boundaries (<10°), which are geometrically similar to those formed by crystal–plastic deformation and recovery. Growth zoning within individual siderite grains shows that the low-angle boundaries are growth features and not due to deformation. Low-angle boundaries develop due to the propagation of defects at grain faces and zone boundaries and by impingement of grains that nucleated with small misorientations relative to each other during grain growth. The cores of siderite grains are aligned with the twin planes in the parent calcite crystal showing that the reactant Fe entered the crystal along the twin boundaries. Dolomite grains, many of which appear to in-fill space generated by the siderite replacement, also show alignment of cores along the calcite twin planes, suggesting that they did not grow into space but replaced the calcite. Where dolomite is seen directly replacing calcite, it nucleates on the Fe-rich calcite due to the increased compatibility of the Fe-bearing calcite lattice relative to the pure calcite. Both reactions are interpreted as fluid-mediated replacement reactions which use the crystallography and elemental chemistry of the calcite. Experiments of fluid-mediated replacement reactions show that they proceed much faster than diffusion-based reactions. This is important when considering the rates of reactions relative to fluid flow in mineralising systems.     

A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching

Based on relevant experimental data of a petroleum cement paste under mechanical loading and chemical leaching, an elastic‐plastic model is first proposed by taking into account plastic shearing and pore collapse. The degradation of mechanical properties induced by the chemical leaching is characterized by a chemical damage variable which is defined as the increase of porosity. Both elastic and plastic properties of the cement paste are affected by the chemical damage. The proposed model is calibrated from and applied to describe mechanical responses in triaxial compression tests respectively on sound and fully leached samples. In the second part, a phenomenological chemical model is defined to establish the relationship between porosity change and calcium dissolution process. The dissolution kinetics is governed by a diffusion law taking into account the variation of diffusion coefficient with calcium concentration. The chemical model is coupled with the mechanical model, and both are applied to describe mechanical response of cement paste samples subjected to progressive chemical leaching and compressive stresses. Comparisons between experimental data and numerical results are presented.     

On incremental non‐linearity in granular media: phenomenological and multi‐scale views (Part I)

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto‐viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro‐mechanical models based on multi‐scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro‐mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non‐linear character of their behaviour. It is shown that both phenomenological and micro‐mechanical models exhibit an incremental non‐linearity. In addition, the multi‐scale approach reveals that the macroscopic incremental non‐linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.     

Formation of bed‐scale spatial patterns in dolomite abundance during early dolomitization: Part I. Mechanisms and feedbacks revealed by reaction–transport modelling

Dolomites of varied ages exhibit metre‐scale nested patterns of lateral periodic variation in permeability and porosity and, by inference, dolomite abundance as most examples are 100% dolomite. Two‐dimensional reaction–transport modelling simulations of bed‐scale dolomitization were used to assess whether those patterns in dolomite abundance could form during near‐surface replacement dolomitization. Simulations used a 2 m high and 18 m long model domain, a low‐Mg calcite grainstone precursor and an evaporated Mississippian seawater brine (430 parts per thousand salinity) as the dolomitizing fluid. The domain was initially populated with random variations in porosity and/or grain size. Results reveal that spatial patterns in dolomite abundance emerge when there is as little as 1% dolomite formed, with similarities between the modelled patterns and outcrop‐documented patterns. The nested patterns include a near‐random component that constitutes ≤40% of the total variance, short‐range correlation ranging from 1·5 to 3·3 m and a longer‐range periodic trend with a wavelength up to 6·5 m. The emergence of pattern in dolomite abundance is the result of an autogenic self‐organizing phenomenon. It is triggered by variation in initial calcite reactive surface area that occurs due to the random heterogeneities in initial porosity and/or grain sizes. The pattern develops due to a combination of kinetic disequilibrium reactions (dolomite precipitation and calcite dissolution) and positive feedbacks between dolomite growth, calcite dissolution and fluid flow. Flow is around loci of higher dolomite, lower porosity and higher reactive surface areas, but through loci of lower dolomite, higher porosity and lower reactive surface areas. The resulting less porous/more dolomite and more porous/less dolomite structures at the metre‐scale arise from those localized interactions. This self‐organizing mechanism for pattern formation constitutes a new model for geochemical self‐organization during dolomitization and is the only self‐organization model that is proven applicable to the formation of metre‐scale patterns during early, near‐surface dolomitization.     

A dual-porosity model for ionic solute transport in expansive clays

A microstructure model of dual-porosity type is proposed to describe contaminant transport in fully-saturated swelling clays. The swelling medium is characterized by three separate-length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the nanoscale, the medium is composed of charged clay particles saturated by a binary monovalent aqueous electrolyte solution. At the intermediate (micro) scale, the two-phase homogenized system is represented by swollen clay clusters (or aggregates) with the nanoscale electrohydrodynamics, local charge distribution, and disjoining pressure effects incorporated in the averaged constitutive laws of the electro-chemo-mechanical coefficients and the swelling pressure, which appear in Onsager’s reciprocity relations and in a modified form of Terzaghi’s effective principle, respectively. The microscopic coupling between aggregates and a bulk solution lying in the micropores is ruled by a slip boundary condition on the tangential velocity of the fluid, which captures the effects of the thin electrical double layers surrounding each clay cluster. At the macroscale, the system of clay clusters is homogenized with the bulk fluid. The resultant macroscopic picture is governed by a dual-porosity model wherein macroscopic flow and ion transport take place in the bulk solution and the clay clusters act as sources/sinks of mass of water and solutes to the bulk fluid. The homogenization procedure yields a three-scale model of the swelling medium by providing new nano and micro closure problems, which are solved numerically to construct constitutive laws for the effective electro-chemo-hydro-mechanical coefficients. Considering local instantaneous equilibrium between the clay aggregates and micropores, a quasisteady version of the dual-porosity model is proposed. When combined with the three-scale portrait of the swelling medium, the quasisteady model allows us to build-up numerically the constitutive law of the equilibrium adsorption isotherm, which governs the instantaneous immobilization of the solutes in the clay clusters. Moreover, the constitutive behavior of the retardation coefficient is also constructed by exploring its representation in terms of the local profile of the electrical double layer potential of the electrolyte solution, which satisfies the Poisson–Boltzmann problem at the nanoscale.     

Assessment of the physico-mechanical behaviour of gypsum-lime repair mortars as a function of curing time

Gypsum-based mortars were widely used during the Mudejar artistic period in Spain from the 12th to 16th century. During restoration works, compatibility between the new repair mortars and the original components is essential for an adequate intervention on the monument. The increasing interest of knowing the properties of the gypsum-lime-based mortars for restoration purposes justifies the research carried out. Different mortars compatible with traditional building materials were elaborated by varying the binder proportions, the type of aggregates, the binder/aggregate ratios and the curing time. The main goal of this paper is to characterize the mechanical behaviour and the pore structure of the mortars as a function of curing time. The influence between the different variables used to prepare the mortars and the development of the carbonation process over time is also considered. Mechanical strength and porosity measurements as well as X-ray diffraction and thermal analysis were performed after curing times of 1, 28 and 90 days. The results obtained confirmed a progressive increase in mechanical strength linked to the carbonation of the mortars prepared. Less lime binder and also aggregate contents showed the highest rise in strength over time, related to the highest initial porosity which favoured the carbon dioxide flow. The use of siliceous aggregates (GL-QS mortars) obtained the best results in the development of physico-mechanical properties over curing time. The knowledge obtained from the studied mortars provides practical information to establish a suitable mortar mixture for restoration works on historic buildings and modern architecture where gypsum-lime-based mortars are used.     

A water retention model accounting for void ratio changes in double porosity clays

This paper presents a constitutive model that predicts the water retention behaviour of compacted clays with evolving bimodal pore size distributions. In line with previous research, the model differentiates between the water present inside the saturated pores of the clay aggregates (the microstructure) and the water present inside the pores between clay aggregates (the macrostructure). A new formulation is then introduced to account for the effect of the macrostructural porosity changes on the retention behaviour of the soil, which results in a consistent evolution of the air-entry value of suction with volumetric deformations. Data from wetting tests on three different active clays (i.e. MX-80 bentonite, FEBEX bentonite, and Boom clay), subjected to distinct mechanical restraints, were used to formulate, calibrate, and validate the proposed model. Results from free swelling tests were also modelled by using both the proposed double porosity model and a published single porosity model, which confirmed the improvement in the predictions of degree of saturation by the present approach. The proposed retention model might be applied, for example, to the simulation of the hydromechanical behaviour of engineered bentonite barriers in underground nuclear waste repositories, where compacted active clays are subjected to changes of both suction and porosity structure under restrained volume conditions.

     

Numerical determination of the tensile response and the dissipated fracture energy of concrete: role of the mesostructure and influence of the loading rate

At the mesoscopic scale, concrete can be considered as a mix of coarse aggregates with a mortar paste matrix. In this paper, we investigate numerically the influence of aggregates arrangements and loading rate on the tensile response of concrete. Each coarse aggregate is assumed to be circular with six different radiuses following the aggregates size distribution of real gravel. Rate‐independent cohesive elements are used to model failure within the mesostructure. Our results show that the spatial distribution of heterogeneities does not influence the peak strength, while it changes the post‐peak macroscopic response. This implies that our specimen size is large enough for strength computation but that larger mesostructures should be considered to obtain fully reliable toughness predictions. Although the cohesive approach is able to capture the transition from one macro‐crack in quasi‐static to multiple micro‐cracks in fast dynamics, which increases the dissipated fracture energy, our results suggest that the full extent of the high‐rate strengthening of concrete observed experimentally for loading rates greater than 1/s cannot be captured with rate independent constitutive laws.Copyright © 2013 John Wiley & Sons, Ltd.     

Diagenesis in the Middle Jurassic Khatatba Formation sandstones in the Shoushan Basin,northern Western Desert,Egypt

The Middle Jurassic Khatatba Formation acts as a hydrocarbon reservoir in the subsurface in the Western Desert, Egypt. This study, which is based on core samples from two exploration boreholes, describes the lithological and diagenetic characteristics of the Khatatba Formation sandstones. The sandstones are fine‐ to coarse‐grained, moderately to well‐sorted quartz arenites, deposited in fluvial channels and in a shallow‐marine setting. Diagenetic components include mechanical and chemical compaction, cementation (calcite, clay minerals, quartz overgrowths, and a minor amount of pyrite), and dissolution of calcite cements and feldspar grains. The widespread occurrence of an early calcite cement suggests that the Khatatba sandstones lost a significant amount of primary porosity at an early stage of its diagenetic history. In addition to calcite, several different cements including kaolinite and syntaxial quartz overgrowth occur as pore‐filling and pore‐lining cements. Kaolinite (largely vermicular) fills pore spaces and causes reduction in the permeability of the reservoir. Based on framework grain–cement relationships, precipitation of the early calcite cement was either accompanied by or followed the development of part of the pore‐lining and pore‐filling cements. Secondary porosity development occurred due to partial to complete dissolution of early calcite cements and feldspar. Late kaolinite clay cement occurs due to dissolved feldspar and has an impact on the reservoir quality of the Khatatba sandstones. Open hydraulic fractures also generated significant secondary porosity in sandstone reservoirs, where both fractures and dissolution took place in multiple phases during late diagenetic stages. The diagenesis and sedimentary facies help control the reservoir quality of the Khatatba sandstones. Fluvial channel sandstones have the highest porosities and permeabilities, in part because of calcite cementation, which inhibited authigenic clays or was later dissolved, creating intergranular secondary porosity. Fluvial crevasse‐splay and marine sandstones have the lowest reservoir quality because of an abundance of depositional kaolinite matrix and pervasive, shallow‐burial calcite and quartz overgrowth cements, respectively. Copyright © 2013 John Wiley & Sons, Ltd.