Poromechanics VI: Proceedings of the Sixth Biot Conference on Poromechanics

The hydraulic fracturing of shale, as well as the fracturing of concrete due to the alkali-silica reaction (ASR), require some interesting generalizations of Biot concept of two-phase medium. In both, the fracturing due to pore pressure if the salient physical phenomenon. The lecture explains how the concept of a three-phase medium—solid-percolating nanopores-hydraulic cracks—makes it possible to predict the lateral branching of hydraulic cracks, provided that the body forces due to gradients of pressure in nanopores are included. Some similar phenomena exist in the alkali-silica reaction (ASR) as affected by ASR gel diffusion and pore water diffusion and are important in assessing the structural damage due to ASR.

We synthesize the framework reported in previous works for hydromechanical analysis of coupled fluid flow-solid deformation in shale accommodating the following important features: (a) double porosity concept allowing Darcy flow to occur through the distributed microfractures and non-Darcy flow to prevail through the much smaller nanopores, (b) structural anisotropy in the mechanical response, and (c) thermal effects in the mechanical constitutive description. The work involves coupling of fluid flow with solid deformation by idealizing the shale as a deformable mixture of two overlapping porosity subdomains.

Under a high pressure of helium, the volume change of amorphous silica is much smaller than expected from its elastic properties. This is due to helium insertion in the free volume of the glass network. Here, we report spectroscopic experiments using either helium or neon as penetrating pressurizing media and molecular simulation that indicate a relationship between the amount of gas adsorbed and the strain of the network. A generalized poromechanical approach, describing the elastic properties of microporous materials upon adsorption, is shown to successfully describe the physics of deformation of such silica glasses in which the free volume exists only at the sub-nanometer scale.

Dispersion and attenuation of elastic waves have been observed in crustal rocks. Existing theories and experimental measurements evidenced the existence of different energy-loss mechanisms. In rocks fully saturated by a Newtonian fluid, one major candidate is fluid flow at different scales, separating three regimes: the drained, undrained, and unrelaxed regimes. Here, two elastic transitions, between these three regimes, are investigated in two porous rocks: a Fontainebleau sandstone and a Lavoux limestone. Both the cause and the consequence of the drained/undrained transition are evidenced. Because the second transition measured occurs at higher frequency, where no global fluid flow occurs, it in turn is associated to the undrained/unrelaxed transition (or squirt flow). This second transition is only observed in the Fontainebleau sandstone. For the second transition, the amount of open microcracks seems to be the major contributor to the magnitudes of dispersion and attenuation.

Introduction of infinitely many solid phases in continuum micromechanical representations of hierarchical porous media, in combination with rigorous consideration of free strains and stresses (which arise in the material microstructures as plastic or viscous strains, or as pore pressures). This turned out as the major key to providing reliable (“nano-micro-macroscopic” or “micro-meso-macroscopic”) structure-mechanical property predictions of complex material systems such as concrete, wood, bone, porous ceramics, or paper.

Whether it concerns the understanding of cementitious materials, the derivation of new test methods or the development of new products and systems, poromecahnics always come into play. Some recent examples of activities at the LafargeHolcim R&D Center are presented, covering topics as curing and drying of concrete with highly substituted cement, cementitious foam hardening, admixtures to control shrinkage, external sulfate attack, or thermal behavior of massive structure.

Numerous geomaterials, manufactured porous materials have a complex structure with a multiscale organization of the pore network, ranging from nm to μm and above. A good knowledge of the structure at these different scales is a cornerstone to properly understand transport properties (diffusion-permeation) and mechanical strength. In this context, micro and nano X ray microcopies and small angle X ray and neutron scattering (SAXS and SANS) are two attractive and no destructive tools for the investigation of the structure these strongly disordered systems. In the first part of this presentation, we present some strategies to probe at different length scales the structure and the evolution of a multiscale porous material. In some specific case, such as the cement paste, we will show how comparison between imaging techniques and small angle scattering approach allows to test and to discard some microstructure hypothesizes. In the second part of this talk, we focus on a long and slow dynamics inside multiscale porous materials essentially driven by the molecular diffusion. This mechanism plays a major role to estimate the sustainability over a long period of time of numerous manufactured multiscale porous materials. We analyze the interplay between pore structure, adsorption and diffusion and how these different processes act in the long term molecular transport.

The paper presents a rigorous thermodynamic derivation of the augmented Biot equations for a general case of adsorbing fluid mixture confined to nanoporous solid. The proposed approach extends the Gibbs excess adsorption thermodynamics to poroelastic nanomaterials. The augmented Biot equations contain additional terms associated with the adsorption stress, which represents the derivative of the excess grand thermodynamic potential of the adsorbed phase. The adsorption stress depends on the geometrical specifics of the material under consideration (pore size, shape, etc.) and the potential of fluid-solid intermolecular interactions. It can be calculated by using the density functional theory and/or Monte Carlo simulations, as well as empirical or classical thermodynamics theories. Special attention is paid to the specifics of adsorption deformation in micropores of molecular dimensions and the interpretation of the strain measurements in situ XRD and dilatometry experiments. Examples include micro- and mesoporous carbons and metal-organic frameworks.

A theory of semi-coupled Maxwell and Biot equations is discussed in which the coupling in electrokinetic in nature and arises from the existence of a streaming current in Ampère’s law. This electrical current is in turn associated with the existence of an electrical double layer coating the surface of reactive minerals in contact with water and the resulting effect of an excess of charge in the pore water. This model is developed both for saturated and unsaturated conditions, water being the wetting fluid for the minerals. The constitutive equations for the transport of the pore water and electrical charges are developed based on a volume-averaging procedure. An extensive comparison with experimental data is made to evaluate the heuristic power of this model, which is for instance able to explain the saturation dependence of the coupling terms (streaming potential and electroosmotic terms) in a way that is consistent with the saturation dependence of the conductivity terms (electrical conductivity and permeability). The resulting field equations are then solved using the finite element approach. Two applications are discussed to geophysical imaging by using a seismic beamforming method and to the electrical field radiation associated with hydrofracturing of porous media.

Mixed fluid phenomena in porous media have profound implications on soil-atmosphere interaction, energy geotechnology, environmental engineering and infrastructure design. Surface tension varies with pressure, temperature, solute concentration, and surfactant concentration; on the other hand, the contact angle responds to interfacial tensions, surface topography, invasion velocity, and chemical interactions. Interfaces are not isolated but interact through the fluid pressure and respond to external fields. Jumps, snap-offs and percolating wetting liquids along edges and crevices are ubiquitous in real, non-cylindrical porous networks. Pore- and macroscale instabilities together with pore structure variability-and-correlation favor fluid trapping and hinder recovery efficiency. The saturation-pressure characteristic curve is affected by the saturation-history, flow-rate, the mechanical response of the porous medium, and time-dependent reactive and diffusive processes; in addition, there are salient differences between unsaturation by internal gas nucleation and gas invasion. Capillary forces add to other skeletal forces in the porous medium and can generate open-mode discontinuities when the capillary entry pressure is high relative to the effective stress. Time emerges as an important variable in mixed-fluid conditions and common quasi-static analyses may fail to capture the system response.

The paper presents the features of novel mathematical solutions developed to examine the mechanics of a fluid saturated porous medium where the porous skeleton can undergo hyper-elastic deformations. The modelling has potential applications in the study of highly deformable biological tissues including brain matter, synthetic materials impregnated with fluids and highly deformable porous solids used as tactile sensors, where the fluid can be the air present in the void space. The presence of the saturating fluid entirely changes the character of the approach in that the load partitioning between the fluid and the porous skeleton needs to be addressed, in addition to the provision for fluid flow induced by hydraulic gradients. The paper summarizes recent analytical results for canonical problems involving one-dimensional strains and pure shear. The role of these developments in the validation of computational schemes that can ultimately be used in the solution of problems with complex geometries is also discussed.

In this paper we propose a new approach for coupling flow and geomechanics in poroelastic jointed rocks. The model is developed within the framework of the discrete fracture modeling (DFM) combined with an iteratively coupled formulation seated on the fixed stress split algorithm. The response of the rock matrix is described by the classical Biot’s theory of poroelasticity whereas, rather than considering fractures as traction-free, we also include a nonlinear hyperbolic elastic response in the sense of Barton and Bandis under compression stresses. In this context we construct a new pressure equation including generalized nonlinear Biot parameters for the fracture-filling material. Numerical simulations illustrate the potential of the new approach proposed herein in constructing upscaled properties in coarser cells, such as permeability and porosity, strongly dependent on the local stress state. Such results can be further explored within the context of pseudo-coupling formulations in order to incorporate the features of complex fracture networks susceptible to geomechanical effects in a simplified manner which can be implemented in reservoir simulators.

Soil liquefaction is a devastating earthquake hazard, commonly causing tilting, sinking and floating of infrastructure. The classical mechanism for liquefaction requires undrained and loosely packed soil, that upon shear experiences elevated, lithostatic, pore pressure and consequently zero effective stress. However, some field and experimental observations cannot be explained by this mechanism. These include liquefaction of pre-compacted soils, liquefaction under drained conditions, repeated liquefaction events, and liquefaction triggered by small seismic energy density. A recent study suggests a new mechanism for soil liquefaction that arises only from buoyancy effects of fluids plus grain accelerations, where the term “liquefaction”, used as its phenomenological field definition, refers to a macroscopic transition from rigid to fluid-like behavior. We extend that study and seek a unifying mechanism for field observed liquefaction that accounts both for the buoyancy effect and for elevated pore pressure, though not necessarily with lithostatic values. To achieve this goal, we use a coupled fluid flow and granular dynamics numerical model to study the effect of pore pressure on the sinking of a large object (“intruder”) into a drained densely packed granular system, undergoing cyclic shearing. Results show that despite the drained conditions pore pressure rises during shaking. Although pore pressure remains well below lithostatic values, the soil liquefies, as identified macroscopically by intruder sinking to its isostatic position. Even simulations with buoyancy effects alone show liquefaction and intruder sinking under certain conditions, yet inclusion of pore-pressure effects add to the buoyancy effect, and is seen to enhance liquefaction and promote intruder sinking.

Non-homogeneity of the pore pressure field is an issue when testing low permeability geomaterials, as in the case of the Callovo Oxfordian claystone (k < 10^-19 m²), a possible host rock for radioactive waste disposal. Excess pore pressure can result in significant errors in the measured material parameters. An analytical solution for the pore pressure field evolution in a sample under various loading paths with different loading rates is presented. These solutions permit an estimation of the necessary testing procedures and applicable measurement corrections for reliable evaluation of poroelastic material properties. The proposed methods are applied in a parameter study on the Callovo Oxfordian claystone.

Fluid-structure interaction problems are known to be very difficult to solve due to nonlinear and complex fluid-solid interactions. This complexity is exacerbated by having to simulate these interactions in complex geometries on small scales. However, using homogenization theory it is possible to upscale these complex fluid-solid interactions into effective equations. A classical example of this is supposing an infinitesimal pore-scale deformation, and yielding the classical Biot equations from rock microstructure physics. However, with nonlinear interfacial forces, and thus non-trivial pore-scale deformations, the resulting homogenization problems become highly non-linear and yield, formally, a set of nonlinear Biot equations. This work aims to give better theoretical underpinnings to this idea by applying the homogenization technique of two-scale convergence to domains that have been deformed, e.g. in a previous time-step, and thus are non periodic. Utilizing a mapping technique, we obtain an augmented Stokes equation and two-scale homogenize them rigorously.

Measurements made with vibrating wire piezometers of the rates of change of pore pressures in a clay aquitard during loading revealed a complex behavior over short time periods. Pore pressure velocities were found to progress in evenly-spaced steps rather than in a smoothly continuous manner. This was duplicated in a numerical poroelastic model and is a result of the strong coupling of strains and pore pressures. Pore pressure velocities in the field data were found to exhibit deterministically chaotic behavior in the form of a strange attractor, whose basic shape was duplicated by the model. The velocity histories demonstrate a fractal nature as they repeat when the data is examined on a finer scale. For poroelastic systems, attractor construction offers a supplemental means to verify mathematically correct modeling and may be useful for field studies.

A polymeric gel is a polymer network swollen by a fluid. Here, we report on a model and numerical simulation capability for the coupled deformation-diffusion behavior of gels that are mechanically anisotropic, but diffusively isotropic. A thermodynamically consistent model for the coupled behavior is summarized for large deformation rubber like materials that absorb a solvent. The model has been implemented numerically as in finite element method for the robust simulation of boundary value problems.

In this work, a closed form solution was presented to investigate the behavior of horizontal borehole in anisotropic saturated media taking into account the transient flow of groundwater. More precisely, the focus lies on the effect of transient state of pore pressure on the mechanical response of borehole through the one-way hydro-mechanical coupling (H→M). The complex potential approach, largely discussed in anisotropic elastic medium, was extended in this work to account for the time effect of hydraulic diffusion in the anisotropic poro-elastic media.

The study of stick-slip in granular fault gouge is important since slips observed in laboratory or numerical studies are understood to mimic earthquakes, allowing to better understand the governing mechanisms of earthquake dynamics. Granular fault gouge is the central part of a fault, where intact rocks have been crushed to granular particles due to erosion and fragmentation. These faults may be dry or saturated with fluids. When the gouge is saturated with a fluid, fluid-particle interactions arise which may influence the size and occurrence rate of slip events. Therefore, we conduct 3D coupled CFD-DEM simulations modelling the frictional behavior of fluid-saturated granular fault gouge. We observe that fluids can extend the stick phase leading to an increase in slip event size. This observation is confirmed by statistical analysis on a large number of stick-slip events.

In order to explore the hydro-thermo-mechanical behaviour of compacted earth, triaxial apparatus at controlled temperature and equipped with non-contacted sensors measuring system, was developed. The results show that the relative humidity at which the samples were stored have a strong impact on the mechanical characteristics of earthen material: both the maximum deviator stress f_c and Young’s modulus E decrease with the increase of relative humidity, meanwhile, more plastic characteristics are observed. Along with the development of stress level, a degradation of secant Young’s modulus and accumulation of residual strain appear. The magnitude of both depends on the relative humidity and on the confinement pressure. Finally, the mechanical behaviour (including strength and deformation) does not seem to be affected by temperature modifications between 23°C and 30°C.

Finite element solutions of Biot’s equations may be characterized by unphysical oscillations for small time-steps or low permeabilities. We analyse these numerical wiggles by comparing the Schur complement of the system with an equivalent reaction-diffusion problem. We show that the non-physical behaviour of the discrete solution is due to the fact that the discrete maximum principle is not satisfied. We provide a sufficient condition for two-dimensional problems of this kind to ensure monotonic solutions on triangular meshes.

A coupled Biot model based on a three-field formulation, namely displacement-pressure-velocity, is set-up and used for the prediction of land subsidence in the Chaobai River alluvial fan, China, north-east of Beijing. The area has a regional size and has been recently characterized by a detailed statistical distribution of hydrofacies. The resulting model totals about 5 million unknowns with strong heterogeneities in the hydraulic and geomechanical properties distribution. The proposed numerical formulation allows for an efficient and accurate solution for a sample discharge from an existing well field, thus proving a robust computational tool for the forecast and management of the land subsidence risk in the area.

A nonlinear meshfree method is proposed based on the weakened weak formulation for capturing the coupled hydromechanical behaviour of saturated elastoplastic porous media. The problem domain is spatially discretised by a triangular background mesh, and point interpolation method is adopted for creating the shape functions. A smoothed strain is assigned to each of the smoothing domains which are formed on top of the background mesh. A novel approach is offered for taking the coupling effect of solid and fluid phases into account.

Ice streams are corridors of fast flowing ice that drain the interiors of the large Antarctic and Greenlandic ice sheets. The abrupt transition from the fast flowing ice of the streams to the almost stagnant ice to their side occurs along narrow shear margins, which experience intense internal deformation. This deformation can lead to warming and weakening of the ice, which makes shear margins prone to migration. Previous studies have suggested that efficient drainage of meltwater at the interface between the ice and the underlying weak sediment layer might control the stability of shear margins. However, weak sediment deformation is expected to be tightly coupled to meltwater drainage, and therefore the feedbacks between them are likely of great importance for ice stream stability, while they remain little understood. Here, we use a 3D model to capture the dynamic interactions between meltwater percolation and granular deformation.We solve for the granular mechanics using a discrete element algorithm, and compute the flow in the deforming porous media on a superimposed Eulerian grid. The model intends to represent the upper portion of the weak and unconsolidated sediment layer directly beneath the ice in the shear margin. We use it to study (1) how spatial variations in the shearing velocity affect meltwater percolation, and (2) to what degree the till grains are stable in the presence of horizontal gradients in water pressure. Our simulation results show that horizontal variations in shear velocity enhance the local porosity and permeability, leading to a potentially significant increase in the horizontal water transmissivity. Results further demonstrate that grain stability depends on the magnitude of the horizontal pressure gradient, and cascading events of grain mobilization precede bulk instability flows.

The pore pressure evolution induced by excavation of drifts is analyzed by means of a fully coupled hydro-mechanical finite element simulation. The main goal is to simulate the principal trends of the pore pressure evolution with a simple model taking into account the inherent anisotropy of the material and the anisotropy of the initial stress state. The influence of the degree of anisotropy of the rock on the overpressures induced by the excavation is analyzed. The influence of the hydro-mechanical coupling on the development of the failed zone around drifts is also discussed.

Explicit techniques have been used for simulating coupled fluid flow and geomechanical interactions in porous media. Still, the techniques are conditionally stable and require small time steps, affecting their efficiency for long-term simulations. To remove these restrictions, an unconditionally stable alternating direction explicit (ADE) scheme could be used to solve the flow problem. However, the standard ADE scheme is only moderately accurate and is restricted to uniform grids, thus impractical for large-scale domains. This paper introduces high-order ADE schemes capable of solving flow problems in non-uniform grids. The new schemes are derived from non-uniform fourth-order approximations to the spatial derivatives of the fluid-diffusion equations. The flow solutions are then sequentially coupled with a geomechanical simulator in the computer code Fast Lagrangian Analysis of Continua (FLAC). Validations on consolidation problems show that the new sequential coupling technique reduces simulation runtimes by 46-66% of FLAC’s basic scheme without numerical instability and with maximum errors < 4%.

The variation in pore pressure and stress may cause sand production during the service life of underground gas storages into sandstones. As such a sand production is generally linked to the rock failure or intense damage, experimental investigations were made to better understand the coupled effects between pore pressure and stress applied to a Vosges sandstone. A series of tri-axial compression tests was firstly conducted to investigate this rock basic mechanical responses until failure from which a simple failure criterion was derived. Following hydrostatic compression tests were also performed to measure the Biot’s coefficient. The critical pore pressure that can be sustained under confining pressure and deviatoric stress can then be predicted with the help of these preliminary tests and under the assumption of a constant Biot’s coefficient (i.e. not affected by the deviatoric stress). Three validation tests were carried out to measure the critical pore pressure which turned out to be close to the predicted one.

This study examines wave-induced response of seabed around a buried pipeline in silty soil. The response of the seabed is simulated with a numerical model based on the u-p approximation of the Biot formulation and the UBC3D-PLM soil model. The pipeline is modeled as a non-porous elastic material with a rigid interface between the pipe and the soil. The linear wave theory is implemented to simulate wave-induced water pressures on the surface of the seabed. A series of analyses are conducted to investigate the effects of wave height on the seabed response and its liquefaction potential. The effect of the pipe presence in the seabed on the development of pore pressures is examined by comparing pore pressures in the proximity of the pipe and in the far field. The results demonstrate that the implemented model captures the main mechanisms of the wave-induced liquefaction around a buried pipeline.

The discrete element method (DEM) coupled with the Lattice Boltzmann Method (LBM) is emerging as a viable tool for modeling multi physics problems in geomechanics. By coupling two explicit solvers, the DEM-LBM model can be used as a robust and computationally efficient tool to model the micromechanics of coupled thermo-hydro-mechanical processes in granular media. In this study, a coupled DEM-LBM model is developed and used for micromechanical modeling of hydro-mechanical processes in various geomechanical problems. The DEM models the solid particle phase by treating each particle as a discrete rigid body, and the LBM solves the incompressible Navier Stokes equations. To demonstrate the capabilities of the DEM-LBM model, results are presented for two problems of a two-dimensional biaxial test on dilative material and shear thickening in a solid-fluid mixture. The biaxial test provides a study of the ability of the LBM to model pore pressure response based on the apparent compressibility of the immersed fluid. Comparison with the experimental test results showed that the DEM-LBM model is able to accurately model the shear thickening behavior of a suspension undergoing shear loading.

The results of simulations of indentation and chamber tests focused on analysis of mobilization of interstitial fluid and residual deformations in lymphoedematous tissues are presented. The cylindrical, leyrered geometry of a fragment of a limb composed of skin modeled as hyperelastic solid and subcataneous tissue modeled as hyperporoelastic material filled with fluid are considered. The model assumes the effective stress principle and the flow rule with constant and matrix deformation depenedent permeability. The model predictions for different stifness of matrix representing stages of lymphoedema and their comparison with clinical data are discussed.

Three different variational formulations of Biot consolidation are presented: a mixed principle reminiscent of the Hellinger-Reissner principle of elastostatics as well as two principles similar to the upper and lower bound principles of plasticity. The two latter principles can be used for computing rigorous bounds to the energy of the system, thereby providing a possibility for verification of numerical solutions to problems involving Biot consolidation.

The linear theory of multiple-porosity and multiple-permeability poroelasticity is presented; a self-consistent extension to Biot’s formulation of a single-porosity, homogenous, isotropic, fluid-saturated, and linearly elastic material is made to obtain the constitutive relations and poroelastic constants of a material with an arbitrary number of N systems or scales of porosity and permeability. Sudden and continued confinement of a spherical sample of porous material while allowing for the pore fluid drainage from the surface boundary is known as Cryer’s problem in the poromechanics literature. The closed-form solution to this problem is developed in Laplace transform domain for the general case of N-porosity and N-permeability poroelasticity with full inter-porosity fluid exchange property. Numerical results in the time domain are presented for single-porosity, double-porosity, triple-porosity, quadruple-porosity, and quintuple-porosity poroelastic models of organic-rich shale.

The definition of an elastic potential energy used by Biot to construct poroelastic constitutive relations has been subject to examination employing various theoretical approaches. This continued interest is also driven by the fact that in Biot’s original formulation the role of porosity as a kinematic measure of deformation is obscured. We compare and contrast several elastic potential energy expressions with the way it appears in the volume-averaging poroelasticity approach. In the latter approach the elastic potential energy of the solid and fluid phase is a function of its own measure of deformation, that is the phasic solid and fluid strain. The kinematic porosity variable appears therein naturally as the deformation of one phase is made known to the other phase through the change of porosity. This way more general deformation processes can be incorporated which appear not to be adequately captured in other poroelasticity frameworks.

The 2D geomechanical model of a test on confined adsorption deformation of cylindrical rock specimens and the numerical–analytical method to solve the related boundary problem based on coordinate-wise averaging of a system of equations of poroelasticity for orthotropic media have been developed. It is shown that the axial and radial strains measured in the test are proportional to the volume-average adsorption stresses. Using the test results, the authors formulate and solve the coefficient inverse problem “determination of deformation characteristics and permeability of coal matrix”. It is found that the matrix permeability is lower than efficient permeability of a core by three orders of magnitude, which is conditioned by the natural damage structure of coal.

The authors have developed the geomechanical–geodynamic model of multi-phase fluid flow and deformation in the near-well zone in the fractured porous reservoir based on the concepts of representative equivalent volume and double porosity. The axially symmetrical modeling uses the original numerical–analytical method when the mass transfer equations are solved using the implicit finite difference scheme and the matrix elimination method, whereas the poroelasticity and poroelastoplasticity equations are solved in quadratures. The derived transcendental equation enables determination of the radius R of the irreversible strain zone at any time point. The numerical experiments at different well production regimes have shown that: R grows with an increase in the lateral earth pressure coefficient, Biot parameter and Poisson’s ratio (depletion regime); the pressure grows much faster in the fractures than in the blocks (pressure recovery); water saturation of the blocks decreases with time (depletion).

We build transient, large-strain, evolutionary geomechanical models of salt basins that couple deformation with sedimentation and fluid flow. We study how pore pressures develop near salt and how such excess pressures affect the strength of basin sediments and the evolution of the salt system. The rising of a salt wall and the emplacement of a salt sheet both contribute to significant excess pressures near salt. We find that excess pore pressures cause the effective stresses to remain low within the wall rocks and sediments below salt. As a result, the strength of these sediments also remains low, facilitating salt growth. Our transient evolutionary models incorporate sedimentation and salt deformation, and provide the complete stress tensor as well as pore pressure prediction over time. We show that coupling pore-fluid flow with salt flow significantly affects the macro-scale geological evolution: salt structures and associated geometries are impacted by the pore pressure developed in the sediments. Our modeling provides the foundation for a technical approach that can address many geological systems where large strains, pore fluids, and sedimentation interact.

In this work, we present an isogeometric (IGA) finite element implementation for hydro–mechanical coupled problems within the framework of (small–strain) second gradient plasticity. Higher-order continuity across elements is one of the interesting properties of IGA basis functions that allows a straightforward implementation of second gradient formulations, which restores objectivity when strain localization occurs. As compared to traditional implementation of second gradient poromechanics, the proposed approach results in a decrease of the total number of degrees of freedom required for a given discretization density, and thus in a higher computational efficiency. Smoothness of the approximating functions is another desirable feature of IGA which mitigates significantly the requirements for minimum time steps in transient poromechanics problems. A serie of biaxial tests on a fully saturated porous media are simulated in order to demonstrate the capabilities of the enriched hydro–mechanical second gradient formulation using IGA, as well as showing effective regularization of the localization patterns.

We propose an extension of Biot’s poroelasticity that allows for absorption of the permeating fluid from the channeling pores into the solid skeleton.We frame our theory in a non-conventional virtual power format, where a key role is played by compatibility of test velocities with mass balance, no matter whether mass exchanges between interstitial and absorbed fluid are allowed. Granted suitable constitutive prescriptions, our theory covers a variety of imbibition/syneresis phenomena, and is susceptible of diverse applications. We proceed in three steps, describing the kinematics, balance laws, and constitutive theory, of a saturated porous solid exchanging mass with an incompressible interstitial fluid. Our general format can accommodate fluid compressibility and partial saturation, but we here exclude these and other effects to focus on mass exchanges and to concentrate on the foundational structure of the theory. Constitutive modeling issues are touched upon in the concluding remarks.

Characterization of hydrocarbon deposits and monitoring of tectonic stresses require understanding of stress dependences of elastic moduli of rocks. The third-order non-linear elasticity theory, usually applied for this, is restricted for rocks to small stress variations. Another approach is the piezosensitivity theory explicitly considering strains of the rock pore space as the main reason of the elastic non-linearity. Here we generalize the piezosensitivity approach to arbitrarily anisotropic rocks.We assume the isotropy of the tensor describing sensitivity of elasticity to small strains of the pore space and derive explicit stress dependencies of the elastic compliances. The resulting stress dependencies are expected to be valid up to several 100 MPa. The theory’s predictions of mutual relations between isotropic third-order elastic moduli is in a rather good quantitative agreement with literature data on corresponding laboratory measurements.

In swelling materials, the hydraulic parameters, such as porosity, permeability, and retention properties depend on the degree of swelling. An example of swelling granular materials are super absorbent polymer (SAP) particles, which can absorb 30-40 times their initial weight of saline fluids within a few minutes. Due to their fast absorption rate, measurements of the hydraulic parameters of a bed of SAP particles is complex or not feasible unless a quasi-static approach is used. An alternative is to use a grain-scale model to estimate hydraulic properties for various packings. We have performed compaction simulations of SAP particles, at the grain-scale, to reconstruct various packings with varying degrees of swelling and varying mechanical parameters, using the discrete element method (DEM). DEM models are commonly based on packings of spheres. But, SAP particles have very irregular shapes and this affect their hydraulic properties significantly. Therefore, the shapes of particles were represented by sets of overlapping spheres also known as clumps. An algorithm was developed to make realistic clumps that are representative of real SAP particles. An inventory of real shapes was obtained using micro-CT scans of individual SAP particles. In DEM, particles were randomly generated based on 20 clumps and the particle size distribution. The particles were then compacted under a constant confining stress in order to obtain a packing. The resulting pore geometry was used to obtain the porosity value which was compared to experimental data.

Desiccation cracking in clayey soils is the cause of significant damage to structures supported by the soils as it can create fluid path ways leading to internal erosion in earth structures, or trigger slope failures and landslides. This paper presents a continuum computational framework to investigate soil cracking undergoing drying shrinkage. The proposed framework combines an advanced meshfree smoothed particle hydrodynamics (SPH) computational method and a size-dependent constitutive model that allows modelling soil cracking at the particle level. The potential of the proposed approach is demonstrated through two examples of a single cracking problem, and a more complex one that involves complex cracking patterns.

This paper is focused on the simulation of the lateral spreading phenomenon and the anticipated maximum surface displacements of sloping ground. An innovative numerical methodology is proposed employing a generalized plasticity model implemented in a finite element code which has been thoroughly validated against VELACS centrifuge liquefaction experiments. The results of numerical analysis compared with experimental measurements indicate that the proposed numerical model has the capability to simulate the lateral spreading phenomenon. This model has been used for a parametric study. In parametric analyses, different factors have been investigated and their effects on magnitude of soil deformation have been studied.

This paper presents a numerical model of internal erosion based on the approach of continuous porous media. The soil skeleton saturated by a pore fluid is treated as the superposition of four constituents in interaction: solid skeleton, erodible fines, fluidized particles, and fluid. The detachment and transport of fine particles are modeled by the mass exchange between solid and fluid phases. In order to take into account the influence of the change of void ratio induced by internal erosion on the soil skeleton, a critical state based constitutive model is used to calculate the effective stress-strain response of the soil skeleton. This coupled hydro-mechanical analysis is applied to study the impact of erosion on a dike. The numerical simulations show the progressive development of internal erosion within the foundation of the dyke. The effect of the mechanical degradation due to internal erosion is demonstrated by evaluating the factor of safety of the dyke slope by means of the shear strength reduction method.

Superabsorbent polymers (SAPs) are cross-linked polymer networks with large negatively charged ion groups attached to the solid matrix (polymer chains). By the presence of these large negatively charged ion groups, Donnan osmotic pressure difference rises in and outside of the gel. The Donnan osmotic pressure difference is, as a matter of fact, the main cause for the exceptional swelling ability of SAPs. In this study, we present a dynamic mixed hybrid finite element (MHFE) model in three dimensional setting for the simulation of the finite swelling of SAPs. In this model, the normal flux is approximated using Raviart-Thomas elements, which conserve mass both locally and globally. The solid part is assumed to be isotropic and hyperelastic under isothermal conditions. The transient simulation results are verified with a semi-analytical solution in one dimension; while the 3D equilibrium results in the case of a spherical geometry are verified against the analytical solutions.

The experimental results of two centrifuge test replicas of a sloping (saturated-soil) deposit are used to assess the predictions of the (open source) software OpenSees. The discrepancy between recorded and computed acceleration time histories is expressed as a unique aggregate of three measures associated with shape, phase and frequency-shift. This decomposition sheds light on the level of consistency between computed and recorded soil accelerations and the likely source of inaccuracies in the used model prediction.

In this work, the shrinkage-swelling of a porous medium having an elastic solid phase is addressed within the framework of numerical homogenization. In the proposed approach, an explicit description of the porous microstructure, as well as the distribution of the capillary liquid phase during drying is taken into account. In this context, the shrinkage/swelling is a consequence of the capillary pressure and surface tension effects on the elastic skeleton. A hybrid Lattice-Boltzmann method (LBM) and finite element method (FEM) is developed to perform the micro-scale simulations. The LBM is used to describe the distribution of the capillary liquid water within the microstructure, while the FEM is employed to simulate the elastic deformation of the skeleton under the action of the liquid phase, for arbitrary morphologies of microstructures. The expected hysteresis of capillary pressure as a function of water saturation observed during drying and wetting in experiments can be reproduced by the LBM. The parameters of the derived macroscopic unsaturated constitutive equations can be identified without any assumption about the morphology of the liquid and vapor phases. Finally, the effects of capillary pressure and surface tension to the macroscopic shrinkage or swelling are compared and discussed.

When an oak board is exposed to moisture on only one of its surfaces, an asymmetric moisture content profile induces differential expansion over the thickness. Consequently, a bending moment causes the board to curve. Meanwhile, moisture transport takes place, which results in a continuously changing bending moment. When exposed to a step change in the moisture content, the end of the board deflects to a maximum, after which the board, due to moisture transport, deflects back to its initial x-position. The y-position of the free end of the board changes continuously too, but reaches a different value eventually due to a different moisture content. In real-life applications, however, objects are most often exposed to continuous or cyclic changes in the relative humidity. It is shown that the deflective step response of the board contains information about its frequency behavior. When assuming linear system behavior, the frequency response can be predicted from the step response. Experiments with a sinusoidal fluctuation in relative humidity at different frequencies confirm the prediction from the step response.

Different approaches can be considered to use nanoporous materials for mechanical energy storage. First the most well known is founded on the use of hydrophobic porous solids in which water is forced to enter into the pores by mechanical pressure. To study this mechanical to surface energy transformation a specific device has been settled relying on the use of a high pressure pump. Moreover the system’s compression and decompression is studied in a microcalorimeter to be able to calculate the total energy balance. Different zeolitic imidazolate frameworks (ZIF) are thus studied and their energetic performances can be compared to those obtained with a second approach systems consisting in flexible metal organic frameworks (MOF) that are submitted to a mechanical pressure with a transmitting fluid. This later should not penetrate in the pores.

Swelling/shrinkage behavior of wood induced by relative humidity variations is anisotropic and influenced by its multi-scale and heterogeneous structure. In this study, 3D characterization of the structure and the hygromechanical behavior of earlywood, latewood and growth-ring samples is performed by X-ray microtomography. Samples are subjected to a relative humidity increase (44% to 97% RH) and imaged once they have reached their equilibrium moisture content. Digital volume correlation is used to measure the global and local strains. Earlywood and latewood exhibit different macroscopic hygromechanical behavior. Strains are not similarly distributed in the two types of wood. The local distribution of the strains related to the microstructure and interactions between earlywood and latewood are discussed.

This work concerns the linearization of a three-field discretization of generalized Biot’s equations describing coupled fluid flow and mechanical deformation in unsaturated porous media. The model of interest employs the effective stress based on the so-called equivalent pore pressure and can be interpreted as linear mechanics nonlinearly coupled with Richards’ equation. As linearization, we apply simultaneously the L-scheme and the fixed stress splitting scheme, which have been established and analyzed for Richards’ equation and the linear Biot’s equations, respectively. Numerical results demonstrate robustness and mesh independent convergence rates, whereas the popular, locally convergent Newton’s method does not display robust convergence for the numerical examples we present.

The changes of free energy in deforming systems of spherical grains in partial saturation are analyzed with the help of numerical simulations. In such system and in the elastic regime we obtain the effective stress as the work conjugate of the macroscopic deformation. It is found that the Love-Weber stress-which is frequently supposed to play the role of effective stress in multiphase systems-is equal to the effective stress only in regular packings. In random packings on the other hand, it does not compare consistently with the numerical results. Further, the results show that some changes of the elastic free energy associated to the micro-scale deformation occur independently of the macroscopic deformation, in contrast with a classical assumption of energy separation.

A two scale study is conducted on the sorption-induced deformation of nano-porous materials. At the micro-scale, an atomistic single pore model is built, based on which a hybrid grand canonical Monte Carlo (GCMC)/molecular dynamics (MD) simulation is performed to study the coupling between sorption and deformation. We find that the sorption process shows a film forming phase, followed by a significant jump in adsorbed fluid during condensation, whereafter the capillary meniscus further flattens until total filling. Each stage corresponds to a distinct deformation behavior, shrinkage during film formation and condensation and swelling during meniscus flattening. Sorption hysteresis is observed between adsorption and desorption over a small range in chemical potential around the condensation point, where mechanical hysteresis is also observed. At the meso-scale, the porous system is represented by a collection of nano-pores with different pore sizes embedded in a solid matrix, as found for example in MCM-41. The sorption-induced deformation of the porous system is modeled by the dependent domain theory, taking into account the mechanical interaction between neighboring pores. We find that the progressive condensation and evaporation in pores with different diameters results in unevenly distributed local deformations, which reversely have an impact on the sorption process and turn the hysteresis loop into type H2 (the IUPAC classification). This micro-scale/meso-scale modeling provides a valuable framework for the investigation of the behavior of sorption and deformation in nano-porous materials.

This work aims to understand the hygromechanical coupled behavior of the wood cell wall S2 layer, a nanoporous composite material, as displayed by the co-occurrence of swelling and adsorption. We use an upscaling from molecular dynamics simulations (MD) at the atomistic scale to a poroelastic model, which is implemented in finite-element modeling (FEM) at the cell wall scale. We study this coupling in detail, document its co-occurrence and propose the vocable “perfect hygromechanical coupling”, as applicable to such systems.

This paper investigates whether an effective stress possibly exists in partially saturated idealized granular media, based on a detailed micro-mechanics computation of spherical particle assemblies wetted at low moisture. Attention is focused on the contact stress tensor, the part of the total stresses of wet granular materials that stems from intergranular contact forces. While this stress contribution is known to unify the failure description of wet and dry granular materials, it is also verified against stress-strain constitutive description using the discrete element method. Comparing the associated strain and contact stress paths during wet and dry simulations, it is shown that the pseudo-elastic behaviors of dense and loose granular soils can be described using the contact stress as an effective stress within a unique framework for dry and wet conditions. However, once interparticle plastic sliding is mobilized and becomes dominant in the elasto-plastic regime, the effective nature of the contact stress tensor is lost.

The homogenized stress-strain behavior of partially saturated expansive clays is mathematically derived as a multi-phase system by highlighting the underlying physics at the nanoscale. The condition of partial saturation in the clay material results into a complex three-phase system involving three scales. At the finest scale, the pore space between the electrically charged clay particles is assumed to be saturated by an electrolyte solution. The deformational behavior at equilibrium is up-scaled through a homogenization procedure based on average-field theory. The source of macroscopic swelling stress is described by the electro-chemical interactions at the nanoscale, herein governed by the Poisson-Boltzmann problem. The proposed derivation is restricted to the elastic regime and ultimately leads to a tensorial stress partitioning that elucidates the existence of a Bishop-like effective stress measure. It is shown how the interaction between fluid phases at the different scales contributes to the capillary stress with a surface tension term that is dependent on pore size and morphology.

Soil water characteristic curves, defining the correlation between water content and suction, are essential for investigating the constitutive behaviour of unsaturated soils. The SWCC during wetting is known to differ from that during drainage, demonstrating a feature of hysteresis. The contact angle effect is one of the main causes for this hysteretic behaviour. By analysing the topological configurations of liquid bridges presented between soil particles, a grain-scale model is presented to quantitatively evaluate the corresponding contributions of the intrinsic liquid pressure and surface tension. Verified with available experimental results, the analytical solution obtained from the model for soils with varied advanced and receding angles shows a good consistency. Furthermore, comparisons are made to analyse matric suction arising from different sized soil particles. The intrinsic liquid pressure is also compared with the matric suction that accounts for the additional interfacial energy determined by the surface tension and interfacial area between water and air phases. This study provides a first attempt to construct a constitutive framework to explicitly connect measurable physical quantities at the grain-scale to the effective hydro-mechanical properties of soils.

The velocity of ultrasonic waves in fluid-saturated porous media is a function of elastic moduli of solid and fluid constituents. Therefore, when the properties of a solid are known, ultrasonic measurements can provide information on the elastic modulus of the fluid in the pores. Recent ultrasonic experiments on fluid-saturated nanoporous glasses suggested that the elastic modulus of fluids in the pores is affected by confinement. Here we present theoretical predictions for the elastic modulus of liquid-like argon confined in spherical silica nanopores. We calculate the modulus using two different approaches. First we use the macroscopic thermodynamic definition of the modulus and calculate the modulus based on the derivative of the average fluid density, where the density of confined fluid is predicted by density functional theory. Second, we use the statistical mechanics approach and calculate the modulus from the fluctuations of number of molecules in the pore modeled using Monte Carlo molecular simulations in the grand canonical ensemble. We show that the predictions of the two approaches are consistent and close to the experimental results. Performing the calculations for a range of pore sizes we show that both methods predict that the modulus of confined argon is a linear function of the inverse pore size. Additionally we vary the solid-fluid interaction parameter, to represent solids other than silica. We show that the strong solid-fluid interactions (solvophilic confinement) make the fluid effectively stiffer, while the weak solid-fluid interactions (solvophobic confinement) make the fluid softer.

In this paper, we present the method used to investigate the drying behavior of the Resorcinol (R) formaldehyde (F) hydrogels and the tools needed for its numerical modeling. First, the studied material is introduced. Then the experiments are briefly presented and some preliminary results are given. Drying tests have been first carried out to characterize the drying kinetics of RF hydrogels. The experiments are used to calibrate the transfer parameters of a convective drying law based on the boundary layer model. Ultimately, the goal is to model the Hydromechanical behavior of the RF gels during drying and predict crack genesis. To do so, a thermo-hydro-mechanical coupled model including a tensile failure criterion is suggested. The tensile failure criterion is based on the existence of a tension cut-off expressed in terms of a minimum mean effective stress.

Multiscale modeling is an important tool to predict complex physical processes with a manageable framework, e.g., using averaged densities or velocities. The objective of a simplified description is also known in mathematical statistics, e.g., using probability distributions. There, the statistical concept of sufficiency and the Rao-Blackwell-Kolmogorov theorem are utilized to decrease the complexity and increase the accuracy of an estimator. Following this idea, the present work adapts the concept of sufficiency to multiscale modeling. Using the example of capillary rise, a set of sufficient parameters is determined to predict the saturation by interfacial areas and an averaged pore radius. Information about the sufficient set and the physical processes transferred to the macroscale will then yield a successful improvement of a crude estimator based on only one measurement in a single pore. The discussion covers the analytical solution as well as peculiarities arising for numerical and experimental studies.

The alveolar structure of cork confers to this natural material specific physical properties such as low permeability to liquids and gases, thermal and acoustic insulation, high elasticity. These properties make this material particularly interesting for sealing wine. We focused in this study on the compression properties of cork along the radial and tangential direction at 25°C when cork is stored in various relative humidity environments, from 0% to 100%. The direction of compression significantly affected the Young’s modulus, with a higher value for the radial direction. More surprising is the effect of water sorption on its mechanical property. Both directions exhibit the same behavior when the relative humidity is increasing. First the Young’s modulus is constant up to 50% relative humidity. Then above this point, the increase in water content leads to a decrease in material rigidity which is attributed to water clusters formations.

In this work we consider the coupling between multiphase flow of binary-gas components (CH₄ and CO₂) and water in cleats coupled with the swelling of a poroelastic matrix leading to the closure of the cleats induced by the simultaneous methane desorption and carbon dioxide adsorption. Macroscopic governing equations are derived within the framework of the formal homogenization procedure where we upscale the anomalous behavior of the binary gas mixture in the nanopores. The adsorption isotherm is constructed rigorously by exploring the thermodynamics of inhomogeneous gases in nanopores. More precisely we consider spherical nanopores and apply the density functional theory (DFT) to compute the gas density profiles incorporating both hard-sphere repulsion and Lennard-Jones attractive intermolecular interactions supplemented by a fluid-solid external potential. In addition we consider the mechanics of the matrix by computing the solvation force which induces the volume strain of the matrix. Finally a 2D reservoir simulation of methane production enhanced by CO₂ injection is presented to illustrate the potential of the multiscale model proposed herein.

Several multi-scale extensions of Terzaghi’s effective stress principle to saturated and unsaturated expansive clays have been derived by our group using periodic homogenization. Starting from nano- and micro-mechanical analyses, the total stress at the macro-scale is the result of three terms: fluid pressure, contact and disjoining stresses. The advantage of this representation is its ability to clearly discriminate between the contributions of these terms to the effective stress. An application to numerically simulate the hydro-mechanical behavior of bentonites during hydration however pointed out that the medium stiffness might be linked rather to disjoining forces than to the solid phase connectivity. The present work proposes therefore a reformulation of the total stress including disjoining stress contributions in the medium stiffness. The potential of this reformulation in capturing the impact of the two porosity levels as well as ion concentration on the rigidity tensor of expansive clays is shown by numerical analyses.

The present contribution specifically considers the tensile stress exerted by in-pore (or confined) capillary liquids and the role it possibly plays on the host solid mechanics, in absence of significant confining pressure. This situation stands for any unsaturated porous systems submitted to drying-wetting cycles. An original combination of micro-thermometric procedures applied to liquids occluded inside quartz closed cavity, with Raman scattering data collected in the solid quartz lattice, leads to conclude that not only tensile guest liquid can act on its host solid, but can result in solid cracking in subcritical conditions. These processes are of importance for natural or man-made materials present in the Earth’s environment, where water and other active species are present, for which various combination of pore fluid and confining pressure/tension are possible, and displacements and stresses are small.

Porous anodized aluminum oxide (AAO) is an ideal playground for fundamental studies on adsorption. Straight, not-interconnected pores having diameter of a few tens of nanometers with a relative dispersion below 1% and lengths up to hundreds of microns can be easily produced on large surface areas. Apart from standard uniform pores, more complex geometries can be accurately tailored including modulated pores, duplex layers and conical pores. Here we summarize the adsorption isotherms taken on these different AAO pores with a torsional microbalance.

The goal of the paper is to generalize our previous result concerning the derivation of a non-equilibrium matrix imbibition equation for the homogenized Kondaurov double porosity model in the case of small relaxation times τ_m, where the index m stands for the matrix part of the fractured porous reservoir. This equation is given in terms of the real saturation and the Barenblatt parameter. In this paper we obtain a general form of the of the non-equilibrium matrix imbibition equation involving the real saturation and Kondaurov’s non-equilibrium parameter, i.e., the principal unknowns of the model. This equation is now valid for arbitrary relaxation times τ_m including the case τ_m = +∞. The numerical tests of the model are also presented.

Natural and synthetic porous media are generally composed of different and disctinct porosities: the microporosity where the fluid is trapped as an adsorbed phase (called the adsorption porosity in this study) and a meso or a macro porosity required to ensure the transport of fluids to and from the smaller pores (called the transport porosity). The different porosities are defined following the IUPAC classification. This study aims at characterizing the influence of an adsorbed phase on the instantaneous deformation of micro-to-macro porous media. In very small pores, the molecules of fluid are confined. This effect, denoted as molecular packing, includes fluid-fluid and fluid-solid interactions and has significant consequences at the macroscale, such as instantaneous swelling. If adsorption in nanopores induces instantaneous deformations at a higher scale, the matrix swelling may close the transport porosity, reducing the global permeability of the material. For instance, in-situ adsorption-induced coal swelling has been identified as the principal factor leading to a rapid decrease in CO₂ injectivity during enhanced coal bed methane production. Theoretically, classical poromechanics predicts the shrinkage of a porous media when it is saturated by a gas. This framework has to be extended to take into account of adsorption phenomena. In this study, a new poromechanical framework is developed allowing adsorption-induced strain estimations by taking into account the incremental variations of the different porosities upon swelling for isotropic and homogeneous materials saturated by a single fluid. A new experimental procedure is proposed for simultaneous measurement of both adsorption and swelling quantities by respectively a manometric technique and a full-field digital image correlation technique. This procedure is applied to compared the model predictions for natural coal samples saturated with pure CH₄ and pure CO₂. A good agreement is obtained in term of adsorption induced swelling quantities.

The adsorption of a fluid in a nanoporous material induces deformations of the solid. The saturating regime, where the solid is filled with liquid, generally exhibits a linear relationship between the liquid pressure and the solid strain. This provides an experimental way to measure the elastic moduli of the solid walls. For large pores, the strain is determined by the pressure of the liquid saturating the pores and the mechanical properties of the porous solid. What happens at the nanometric scale, where liquid/matrix interfacial effects dominate? We have performed molecular simulations of a simple Lennard-Jones fluid confined between deformable nanoplatelets. The simulations provide the deformation of the nanopore as a function of the liquid pressure, in a way similar to what is done experimentally. The results show unexpected interface effects, which could be relevant to experimental data analysis.

Confined fluids in mesoporous solids induce deformations of porous matrices. In stiff materials, porous glass and silicon, we show that the pore-load modulus deduced from adsorption and strain measurements on the saturating regime does not depend on the nature of fluid. Thus, the mechanical stress due to the liquid can be described in terms of an isotropic pore pressure derived from macroscopic thermodynamics. Then, we use the framework of anisotropic poroelasticity to get for the first time the whole set of elastic coefficients of porous silicon for various porosities. The elastic constants are in agreement with direct stress-strain tests. We have performed a 2D finite element modeling of porous silicon honeycombs with a geometry transverse to the pore axis as determined by electron microscopy. The calculated moduli are smaller than experimental ones, indicating finite size effect. However, the data cannot be accounted for by a rescaling of Young’s modulus of walls, probably due to the lack of invariance along the pore axis.

The phase field model of unsaturated poromechanics recently introduced by one of the authors is numerically implemented within CODE_BRIGHT, focusing attention, at the moment, only on the behavior of the air-water mixture saturating the pore space. The model is formulated within the framework of gradient poromechanics, which implies the Darcy law, to be generalised into a fourth order partial differential equation with respect to saturation degree. From the numerical point of view this enriched structure of the differential problem is faced adopting a mixed finite element approach which means that not only the pore water pressure but also the saturation degree must be regarded as nodal unknowns. Within this framework a problem related to gravity driven segregation, say the counter-current flow, is addressed reproducing in a natural way the formation and the propagation of a bulge in the vertical saturation.

We present hybrid data-driven approach to model multi-physical process in fluid-infiltrating porous media across length scales. Unlike single-physical problems where data-driven model is often used as a replacement of the solid constitutive law, a hydro-mechanical problem often leads to more complex hierarchical relations among physical quantities which in return complicate the design of the data-driven solver. When artificial neural network is used, additional issues may arise when constraints and rules, such as material frame indifference, cannot be explicitly enforced without artificially expanding the training dataset. In this work, we introduce a component-based strategy in which a multiphysical problem is viewed as a directed graph, a network consisting of inter-connected vertices representing physical quantities. This strategy enables modelers to couple data-driven model with conventional math-ematical expression methods by considering different hierarchical relations among data. Depending on the availability of data, hybridization of data-driven and mathematical models may take different forms. To enforce material frame indifference efficiently, we employ spectral decomposition to handle the invariant and spin terms via Lie algebra.

Poromechanical descriptions of drying shrinkage are based on the changes of pore fluid pressure acting on the solid skeleton as driving mechanism of bulk deformations. In this paper, different poroelastic models of drying shrinkage are applied for prediction of shrinkage of a cement-based mortar and compared to experimental data. A comprehensive analysis of the model parameters is presented, in particular regarding the influence of the degree of saturation on the predicted shrinkage. Further, the propagation of uncertainty is studied, i.e. the effects of random errors of experimentally-determined input parameters on the uncertainty of the final model predictions are analyzed by means of the bootstrapping technique.

The main purpose of this contribution is to study the effects of adsorption-induced swelling on the porosity, permeability and poromechanical properties of Callovo-Oxfordian (COx) argillite. To verify the adsorption effects, three kinds of gases with different adsorption capacities, helium, argon, carbon dioxide, were used. The results show that the porosity measured by helium is around 13.5%, and is not affected by gas pressure. Values obtained with argon and CO₂ are higher and sensitive to gas pressure. The gas permeability is also greatly modified when the type of gas is changed. It can be very low when measured with CO₂, around 10^-20m² or quite high with helium (around 10^-17m2). These results are first evidence that the different adsorption capacities of the gases plays a significant role on these properties. On another hand, poromechanical tests showed that the values of Biot’s tensor components strongly depend on the gas used to control the pore pressure. This may also be linked to the different adsorption-induced swellings of the gases in the clay minerals.

This paper presents a micromechanical model for unsaturated granular soils based on thermodynamics. The dissipation of energy is examined at the level of the particle contacts. The total Helmholtz free energy is separated between a mechanical and a hydraulic part, each of which is a function of either the elastic displacement or the degree of saturation at the micro scale. The dissipation of energy, assumed to be frictional in origin, is a function of the plastic displacements at the micro scale. Both the Helmholtz free energy and the dissipative energy are volumetrically averaged from the micro to the macro scale. The Chang-Hicher micromechanical model has been adopted for the deformation of the skeleton, whereas a hydraulic potential dependent on the size of the particles has been chosen for the expression of the water retention.

Geothermal systems are identified as either open-loop geothermal systems (OLGS) or closed-loop geothermal systems (CLGS). In OLGS, fluid is produced from the subsurface, while there might be concurrent fluid injection into the reservoir. The loss of working fluid, surface subsidence, and formation compaction are major challenges in OLGS. To address the indicated challenges, closed-loop geothermal systems can be considered as an alternative option. In CLGS, a working fluid with low boiling point is circulated through the coaxial sealed pipes to extract heat from the geothermal reservoir. Conduction is the main heat transfer mechanism in the CLGS; however, available mere-conduction configurations are not capable to quickly transfer heat from the reservoir to the wellbore. To improve conductive heat extraction from this system, we suggest induced thermal-conductive fractures for CLGS to enhance conductive heat transfer into the wellbore. Comprehensive analysis of this problem requires simultaneous modeling of fluid flow, heat transfer and rock deformation. A finite element thermo-poroelastic model represents CLGS. The numerical results suggest that fractures significantly improve thermal power and cumulative extracted heat for the proposed configuration. Thermal conductivity of the proppants filling the induced fractures is the key parameter affecting the heat extraction. Negligible surface subsidence in the proposed technique suggests this configuration is suitable for the areas where surface subsidence or induced seismicity restricts the application of OLGS.

Bituminous mixtures can be seen as granular media composed by particles (larger aggregates) and a viscoelastic bonding phase (a mix of smaller aggregates and bitumen, called bituminous mastic). During fatigue experiments, a decrease in norm of complex modulus, increases in phase angle and in temperature are observed. This stiffness change is commonly misinterpreted as damage, supposedly irreversible. Literature proposed an explanation for that initial modulus decrease based on local thermal effects (local self-heating, creating a thermomechanical coupling), but considering no thermal diffusion. This work investigates thermal diffusion in the mastic phase. A non-uniform (local) heat production in the mastic is considered with simplified geometry (monodisperse rigid particles in a mastic phase). The local effects of temperature on stiffness were analyzed for the first 100 cycles of loading at 10 Hz (10 s). Results showed that the calculated modulus decrease is not sufficient to explain the changes during fatigue tests observed experimentally. That suggests the existence of another phenomenon (consistent with the definition of thixotropy) responsible for the reversible modulus decrease in bituminous mixtures.

This article introduces the development of a numerical model, suitable for simulating geological storage applications of carbon dioxide. The governing equations cover twophase flow of immiscible fluids, strongly coupled with heat transport and solid deformation. Although immiscible, component-based phase transitions between the fluids are considered, governed by thermodynamic relations. This choice of processes allows the description of CO₂ propagation in the reservoir, reservoir temperature evolution, the safety assessment of rock integrity, and the quantification of structural, residual and solubility trapping mechanisms in geological CCS applications. For the description of the vapour-liquid and solution equilibria, a non-iterative method was developed, following well-known and established thermodynamic relations and empirical models. By avoiding iterative computations, this method is very efficient and thus well-suited for simulations exhibiting many degrees of freedom.

Clays thermo-mechanics are complex with thermal expansions or contractions, reversible or irreversible, depending on the loading history and the range of temperature. Some key experimental observations are well captured by a recent thermomechanical model considering water adsorption at the heart of the thermo-mechanical couplings. In this paper, we investigate a peculiar experiment that shows an effect of temperature on preconsolidation pressure. This experiment is interesting because it highlights a significant effect on the plastic behavior whereas the temperature change is applied after unloading in the elastic domain and induces only small reversible deformations. Accordingly, the phenomenon cannot be attributed to any change of microstructure. The model based on adsorption reproduces this experimental result and offers a nanoscopic interpretation of the effect of temperature on preconsolidation pressure. This finding further supports adsorption as central to the physical origin of the thermo-mechanical couplings in clays.

The influence of salt type and content on the behavior under water of simplified bituminized waste products (BWP) has been evaluated by measuring the amount of water uptake and ions released during leaching experiments. For BWP containing highly soluble salt such as sodium sulfate, the amount of water uptake increases simultaneously with the amount of released ionic species. For BWP containing poorly soluble salt such as barium sulfate, it has been observed that the amount of water uptake increases drastically beyond a threshold content of salts, despite the low release of ionic species in leachates. Such results would support the existence of a second phenomenon responsible for water uptake, different from the already described osmotic one.

The study presents results of measurements of thermo-physical properties and hygro-thermal behavior of two types of materials: the cement mortar which is used as reference material and the polystyrene concrete. In parallel to the experimental study, a model representative of heat and mass transfer is developed in order to predict hygro-thermal behavior of the wall. This model is validated by confrontation of simulated and experimental results. The study showed the advantage of using polystyrene concrete compared to ordinary concrete. It is possible to improve the thermal performance of the building walls, saving energy used mainly in heating and air conditioning.

Ionized porous media, such as hydrogels, soft tissues, are considered as a saturated two-phase mixture, consist of a charged deformable solid skeleton and an interstitial fluid of opposite charge. Hydrogels subjected to changes of salt concentrations often develop cracks during swelling or shrinking. In return, the presence of discontinuities influences the swelling mechanics of the porous media, like swelling capacity. Therefore, it is strongly desirable to study the coupling between the fluid pressure and crack propagation. In biomedical engineering, hydrogel is a common physical model for soft tissues and consists of cross-linked ionized polymers. In this paper, we present a swelling driven fracture model for porous media in large deformation. Flow of fluid within the crack, within the medium and between the crack and the medium are accounted for. The partition of unity method is used to describe the displacement field and chemical potential field respectively. In order to capture the chemical potential gradient between the gel and the crack, an enhanced local pressure model is applied. A crack opening example is used to test the accuracy of the current model without the influence of the complexity of the crack propagation.

In this study the hydration/dehydration kinetics are studied of a thermochemical material (TCM), CaCl₂, stabilized with aramide. The experiments show that the TCM can be stabilized with help of aramide within three cycles. The material show constant hydration/dehydration rate over seven cycles, but that the hydration/dehydration characteristics are slower than for pure material after 10 cycles.

The aim of this study is to assess the mechanical behavior of earthen materials when submitted to spatial and temporal variations of temperature and hygrometry. The first step of this study is to quantify the effects of heat and mass transports, including the phase changes occurring within the pores, on the hygrothermal behavior. This information is imported into a poromechanical model that allows calculating the local strain induced by the sorption-desorption processes. Model predictions are finally compared to an experimental result.

To guarantee the durability of new cement and concrete formulations, we need to understand the long-term degradation mechanisms and how they relate to the evolution of the microstructure. Inside a porous medium, the different phenomena are coupled by the microstructure and its evolution. For example, in coupled simulation of drying and carbonation, the entry of CO₂ and release of water will occur through the carbonated layer which has distinct properties from the non-carbonated core. To solve this problem, we propose a new reactive transport implementation which can integrate a custom-made microstructure model adapted to the problem at hand. This feature has many strong numerical challenges and it leads to a robust and flexible reactive transport framework. We demonstrate its capabilities through coupled carbonation and drying simulation of cement pastes. We show that the water transport properties are key elements in the rate of propagation of the carbonation reaction. To reach quantitative prediction abilities, the capillary pressure and the relative transport properties must be computed accurately in both the carbonated and the non-carbonated layers.

Heat extraction from sedimentary rocks at a depth of 3800 m has been tested in an abandoned gas well, Horstberg, in the North German Basin. The Horstberg geothermal well was completed in a multilayer sandstone reservoir and a massive hydraulic fracturing test was performed. As a result the upper and lower reservoir formations (Solling and Detfurth) were hydraulically connected along a vertical distance of around 125 m. In a forthcoming field campaign, the produced water from Solling of approximately 144 °C will be injected into the Detfurth formation. For this procedure the borehole is completed with a tubing pipe and a sealing packer seated between two formations that allows injection and production through annulus. The current interpretation of 3D seismic data mapped the nearby faults in the vicinity of the Horstberg wellbore where the major faults strike east-west direction. A reevaluation of performed tests shows that in-situ stress has a significant impact on the behavior of the induced hydraulic fracture. In a normal stress regime the hydraulically induced fracture is vertical and propagates parallel to the nearby fault plane. However, in a strike-slip stress regime the hydraulically induced fracture may intersect the nearby fault. The values of vertical stress components in Solling and Detfurth formations are as high as 86 and 89 MPa, and the values of minimum horizontal stress components are approximately 65 and 66.5 MPa, respectively. The calculated stress field for the Horstberg geothermal reservoir suggests a normal to strike slip stress regimes for Buntsandstein formation. A 3D structural model that includes the major faults and induced hydraulic fracture provides the input mesh into a finite element software that will be populated with physical and hydraulic parameters. This model aims at simulating of the thermo-hydro-mechanical behavior of the reservoir and comparing the thermal breakthroughs in a normal stress and strike-slip stress regime. The model also considers the effect of the vertical stress profile on the permeability of the fracture over time. That is, the permeability of the hydraulically induced fracture changes as the stress changes.

Clays adsorb water following discrete steps in which water is roughly structured in layers. The resulting discrete hydration states can be viewed as phases separated by unstable domains and the change of hydration state can be viewed as a phase transformation. Here, we identify stable basal spacings and the domains of (meta-) stability through the analysis of confining pressure isotherms obtained from molecular simulations performed in grand canonical ensemble. This ensemble mimics drained conditions. Through thermodynamic analysis, we can explain the coexistence of different hydration states at clay particle scale and provide kinetics arguments to the hysteresis observed with respect to traction and compression. The gained insights into the mechanical behavior of the elementary constituents of clays may lead to a better understanding of the behavior of clay-rich rocks and soils.

The disposal of heat-generating nuclear waste establishes a thermal gradient, therefore may cause brine-filled inclusions in the salt grains to migrate toward the heat source, and may slowly corrode the waste package. In this study a fully coupled thermal-hydro-mechanical (THM) model based on the finite volume method (FVM) is developed to study and analyze such a phenomenon. For fluid flow, a dual-continuum model considering flow in the interconnected pore space and also in the salt grains is established. The mass balance of salt and water in these two continuum is separately considered, and their coupling is represented by flux associated with brine migration. Together with energy balance, such a system produces a coupled TH model with strong nonlinear feature. For mechanical analysis, a new formulation different from traditional FVM is developed based on the Voronoi tessellated mesh. By relating each cell to several connected triangles, first-order approximation is constructed. The coupling between thermal and mechanical fields is only considered in terms of thermal expansion. And the coupling between the hydraulic and mechanical fields in terms of pore-volume effects is derived consistent with the Biot’s equation. Therefore, a fully coupled THM model is developed. The model was verified by a consolidation example for HM coupling and good agreement with the analytical solution was achieved.

Ion chromatographic (IC) analysis of effluents show that compaction rates on outcrop chalk flooded by divalent anion and cations are controlled by sorption processes. Effluent analyses give information whether the dominating sorption process is adsorption of ions on the chalk surface and/or absorption or ion exchange in the chalk bulk phase. The dominating sorption process with the divalent anion SO₄^2- shows to be adsorption. After three days of flow, SO₄^2- effluent concentration was the same as the injected concentration. During adsorption, rapid increase in the strain rate was recorded followed by a deceleration when no more adsorption took place at the rock surface. For the divalent cation brine, Mg²⁺, Ca²⁺, Sr²⁺ or Ba²⁺, the effluent concentration of injected cation never achieved its original value, while an equal concentration of divalent cations were produced from the core. This implies that the dominating sorption process for divalent cations show to be absorption and/or due to ion exchange. The absorption driven processes led to decreasing creep strain rates with increasing cation size.

This paper aims at providing a numerical simulation for coupled heat and mass transfer within soils surrounding building foundations subjected to seasonal freezing and thawing. The mass conservation is derived by considering the phase change and the seepage flux. Also, the heat conservation is derived considering phase change, conduction and convection of heat. The water and ice contents in the soil are obtained by combining a generalised form of the Clapeyron equation with the soil water retention curve (SWRC). The developed solution is validated by comparison with experimental data obtained from literature. A case study is then carried out to show the impact of the thermal insulation around the foundation wall on the distributions of temperature and ice water content in soil.

The paper considers the technique of determining effective characteristics of microporous piezoceramic material with random porosity and local alloying (metallized) pore surfaces. The presented investigation is based on a complex approach, which included the effective moduli method for the mechanics of composites, modeling of representative volumes with closed porosity and with local metallized pore surfaces and the finite element method. Static problems of the piezoelectricity theory for an inhomogeneous representative volume were solved numerically with the help of ANSYS finite element package and special programs written in ANSYS APDL. To simulate the metallization of the parts of porous borders the boundary conditions of free electrodes were used. The influence of the local alloying pore surfaces on the values of the most important effective moduli was investigated numerically for microporous piezoceramic PZT-4. The computation results have shown that microporous piezoceramics with local metalized pore surfaces has a range of extreme properties perspective for practical applications.

The present study explores the variation in mechanical and index properties of reactive granular materials through a systematic chemical dissolution exercise. Series of mineral dissolution tests were conducted on calcite granules under confined condition up to a certain level of mass reduction followed by mechanical testing with the degraded specimens. Two sets of conventional drained triaxial tests,–at constant relative density and at constant initial void ratio–were carried out on the degraded particles at different initial degree of dissolution. The results show that for degraded granular materials the shear strength properties are influenced by the granular material packing (density) in terms of initial void ratio, while current void ratio regulates the elastic response. Based on such experimental observation we enhance the extended Mohr-Coulomb constitutive relationship. Additionally we propose a novel coupled (volume-shear) nonlinear elastic model for granular materials taking into account the variation in void ratio during deformation.

In this study, the frequency-dependent electrokinetic coupling coefficient (ECC) for cylindrical capillaries is derived. Compared with the Packard’s model which is limited to the thin EDL assumption, this expression is available for both the thin and the thick EDL assumptions and also for arbitrary scales between of them. The identical expression obtained from the two different electrokinetic mechanisms indicates that the Onsager reciprocity is applicable not only for the thin EDL assumption.

Quasi-instantaneous thermal expansion coefficients of mature cement pastes follow a non-symmetric bell-shaped function of the internal relative humidity. This is related to the experimentally proved fact that a temperature increase, ΔT, results in a quasi-instantaneous increase of the internal relative humidity, ΔRH. The present contribution establishes a quantitative link between macroscopically measured thermal expansion coefficients and microscopically measured hygrothermic coefficients ΔRH/ΔT. Multiscale poroelasticity is applied to mature cement pastes, exhibiting an initial water-to-cement mass ratio that amounts to 0.40. Their microstructures are resolved down to nanoscopic scales. The pore space is assumed to consist of wellconnected gel and capillary pores. Both are idealized as spherical, and their pore sizes are modeled on the basis of exponential distributions. Consideration of capillary pressure together with adsorbed water layers at the surface of air-filled pores provides the sought quantitative link between macroscopic thermal expansion coefficients and microscopic hygrothermic coefficients.

The Callovo-Oxfordian claystone (COx) is considered as the potential host formation for the disposal of radioactive waste at great depth in France. The temperature rise due to heat emitted from the waste induces a pore pressure increase in a low permeability porous medium such as COx claystone. Since 2000, an important research program has been launched by Andra to investigate the thermo-hydro-mechanical (THM) response of the COx to thermal loads. The program comprises laboratory and in situ experiments, as well as theoretical and model developments. The THM parameters of the COx are investigated within the program. The determination of the COx thermal pressurization coefficient within the laboratory and in situ experiments is discussed. The effect of the thermomechanical stresses induced due to boundary conditions within the repository architecture is finally discussed. A thermo-mechanical pressurization coefficient is proposed to account for the total stress change.

The growth of a small spherical void within a polymeric gel is viewed through the prism of micromechanics and finite element analysis. An attempt is made towards obtaining an estimation of the effective behaviour of porous polymeric gels where microvoids are already present. The present computational study addresses the numerical simulations of a cylindrical representative volume containing an initially spherical void, immersed in a solvent, and then subjected to axial and lateral overall stresses under conditions of constant prescribed overall stress triaxiality. For fixed values of the Flory-Huggins parameter and the nominal concentration of the solvent, the overall stress-strain behaviour of the RVE and the influence of the initial porosity on the RVE behaviour have been highlighted.

The purpose of this study is to discuss the long-term load bearing capacity of RC beams under sustained loads by using multi-scale analysis incorporating alkali-silica reaction (ASR) gel in motion through cracked concrete pores. Coupling of ASR and varying loads over the life of RC are underlined. Firstly, enhanced capacity of RC beams with coupled silicate chemical reaction and mechanical loads is investigated with different failure modes. Varying external loads over the life are also studied in considering real infrastructures subjected to soil pressure. It is computationally pointed out that alkali-silicate gels in cracks may upgrade the long-term capacity owing to arrested shear crack propagation due to crack-to-crack interaction.

The effect of preceding cracks on expansion of concrete by alkali silica reaction (ASR) is investigated. First, the authors examine the scale-effect of ASR expansion of concrete under different boundary conditions of alkalinity with preceding cracks by utilizing chemo-hygral poro-mechanics. Furthermore, ASR expansion of RC beams and slabs with preceding cracks, through which silica gels may migrate, is simulated as a highly coupled event. A possible scenario is computationally shown to exist as such pre-cracking induced by pre-loads may influence on the following anisotropic expansion of structural concrete. For performance assessment of ASR damaged structures in practice, it is suggested that ASR gel’s migration through cracks and micro-pores shall be incorporated with multi-directional crack modeling for considering interaction of gels in pore and structures.

This study uses a thermal uncoupled thermal-hydraulic-mechanical (THM) model to investigate the interactive behavior of change in pore water pressure, displacement, and temperature of a buffer material in the near-field of the nuclear waste repository. The variation of pore water pressure is contributed to both the deformations of porous space and the swelling of pore water. The deformations are controlled by the thermal expansion coefficients of solid and fluid. Stochastic analysis is performed by using Monte Carlo simulations. The variances of displacement and change in pore water pressure vary spatial-temporally. The variances expresses the variation of displacement and change in pore water pressure in the domain and provides the uncertainty information. The proposed stochastic THM analysis provides a tool for the uncertainty assessment of the nuclear waste repository.

Microseismicity is often assumed to be directly linked to the pore pressure increase by shifting stress conditions onto the Mohr-Coulomb yield surface. In addition, a large proportion of seismic events occurs mainly within the reservoir and have tensile opening component, characteristic of fluid-filled fractures. However, there are observations of injection-induced microseismicity at large offset distances from the operation site. Such seismic events often occur at some distance from the reservoir or pressure front and are characterized by mainly double couple source mechanism. We discuss mechanisms that might trigger such events and show that in deformable porous rocks stress changes and subsequent induced seismicity might happen ahead of the fluid pressure diffusion front. Localization of the fluid flow that might occur in rocks exhibiting time-dependent creep, e.g. shales, might lead to out-of-zone seismicity that continues even after injection has been stopped.

Much less electroosmotic pressure experiments were conducted than streaming potential experiments on rock samples in laboratory. This is because the electroosmotic pressure signal is rather weak and usually covered by stronger background noise. In this work, two pressure transducers are used with a differential method to improve the signal-to-noise ratio of the electroosmotic pressure. The measurement transducer records the electroosmotic pressure signal when an electric voltage is applied on the sample. A reference transducer is used to record the background noise. To account for the response difference between the measurement and the reference transducers, an algorithm is proposed to get correlation coefficient between them. By deducting the noise from the recorded electroosmotic pressure, the resultant signal has a much more prominent resonant point in the frequency domain, which is the valid result of the electroosmotic pressure. This two transducer method greatly enhances signal-to-noise ratio and can be used in laboratory electroosmotic pressure measurements for different kinds of rock samples.

Lignin is a biopolymeric porous material, which plays a crucial role in binding the different cell wall constituents in wood, thus providing the material its mechanical stiffness. In this study, we focus on uncondensed lignin, one of the softwood lignins, which forms with xylan the matrix of wood cell wall S2 layer. Using molecular dynamics and grand canonical Monte Carlo simulations, we show that both moisture adsorption and temperature strongly affect the structural and mechanical behavior of softwood lignin. As moisture content increases, the material adsorbs moisture, causing swelling and mechanical weakening. With a temperature rise, lignin weakens. The understanding of this hygro-thermo-mechanical coupling problem is required to unravel not only the physical processes ongoing in lignin, such as water diffusion, percolation and etc, but also the moisture and temperature dependent behavior of wood at macroscopic scale. The atomistic simulations are upscaled into a higher order poromechanical model. Together with mechanical properties such as moduli and Poisson’s ratio, poromechanical parameters are implemented into a continuum model.

Poroelastic moduli of rocks are difficult to measure in the laboratory setting. Digital rock technology has the potential to support the interpretation of laboratory results and to provide insights into pore-scale deformation patterns. We apply a digital rock workflow to images obtained for a sand pack to estimate the Biot coefficient and the drained pore modulus by exploiting its relation to the drained bulk modulus and the solid phase bulk modulus. Comparison with measured values of sandstone of similar porosities indicate that the simulated value of the Biot coefficient is plausible but the drained pore modulus appears too high. The reason for this discrepancy is likely the existence of compliant grain contact areas in rocks which are not properly resolved in the digitized images of the sand pack.

In engineering geology and classification of rock masses for civil engineering purposes, the degree of induration for a rock serves as a useful classification parameter. Induration is a measure of how well the grains of a sedimentary rock are cemented together–from loosely cemented/soft rock to very competent/slightly metamorphic rock. The Biot coefficient links to the degree of cementation in the capacity of how it relates the elastic deformations with the change in pore pressure. A hypothesis is that the degree of induration could be correlated to the magnitude of the Biot coefficient. This is tested on 11 Copenhagen Limestone specimens of varying porosity and densities obtained from one borehole with a limestone interval of 30 m. Their induration varies from H2 to H5. Elastic wave propagation measurements are used to establish the Biot coefficient and determination of the mineralogy for H5 specimens aids in performing fluid substitution with Gassmann’s equation. For the soft H2 specimens the shear wave could not be obtained and isoframe modelling is applied. A correlation is found; although, the Biot coefficient for the intermediate indurations H3 and H4 overlap. The dry density is found to adequately correlate with the Biot coefficient.

A careful determination of the poroelastic parameters of the Callovo-Oxfordian (COx) claystone, a potential host rock for the deep underground repository of radioactive waste in France, was conducted in an isotropic compression cell. Fully saturated specimens were tested by carrying out drained, undrained and unjacketed compression tests. Due to the low permeability (10^-20 m²), small loading rates were used to ensure full drainage conditions in drained and pore pressure tests (0.5 kPa/min) and in the unjacketed test (2 kPa/min). Strains were precisely measured by ensuring direct contact between the LVDTs’ stems and the specimen. A transverse isotropic poroelasticity analysis provided the anisotropic Biot’s effective stress coefficients b₁ (perpendicular to bedding) and b₂ (parallel to bedding) with b₁ between 0.85 and 0.87 and b₂ between 0.90 and 0.98. An unjacketed modulus K_s = 21.7 GPa was also determined directly and by an indirect evaluation. A set of equivalent isotropic poroelastic parameters was derived and a good compatibility between the results of different tests was found.

The Callovo-Oxfordian (COx) claystone is considered as a possible host rock for radioactive waste disposal in France (Andra). Temperature elevation, expected to reach 100°C, will affect the rock. Thermal volumetric response of the COx claystone is studied in this work by using a thermal isotropic compression cell. Full saturation of the sample and fully drained conditions during heating are carefully achieved thanks to the short drainage length (10 mm). A drained heating test under constant stress carried out up to 80°C exhibited a thermo-elastic expansion followed by thermo-plastic contraction. The transition appeared at a temperature of 48°C, close to the maximum burial temperature supported during the geological history of the material, estimated at 50°C. A volumetric creep enhanced by temperature is observed under in-situ stress conditions. Creep volume changes were modelled by using a Kelvin-Voigt viscoelastic model, so as to correct the measured strains and evaluate the thermal expansion coefficients.

Recently, THz waves shows to be a good technique to investigate the water diffusion within porous media such as biomaterial or insulation materials. This is due to the sufficient resolution for such applications and safe radiation. In this study, a calibration method is developed in order to demonstrate the relationship between the absorption coefficient of maritime pine sample and its water content. An analytical model is built, based on the Beer-Lambert law, linking the absorption coefficient, the density of solid and its water content.

Rammed-earth (RE) material has been the focus of scientific research in the last decade because of the significant heritage of RE buildings throughout the world. Moreover, a renaissance of RE constructions has recently been observed due to this material’s sustainable properties. Nondestructive methods are now needed to assess the mechanical behavior of this material, for both old and new RE constructions. This paper presents how in-situ vibrational measurements can be used to identify the dynamic behavior of RE walls and to determine the Young’s modulus of the RE walls measured. To determine Young’s modulus from the dynamic characteristics, an analytical model based on Timoshenko’s beam theory was developed, both for flexural and torsional modes. The proposed analytical model was then verified with measurements on a wall. The comparison showed that the result from the proposed method provided high accuracy and was better than that obtained on the usual specimens (prismatic and cylindrical).

Rammed earth (RE) is a construction material which is manufactured by dynamically compacting the soil in a formwork. The RE wall is composed of several earthen layers about 12-15 cm thick. This material has been attracting numerous scientific researches because of its low embodied energy and a positive hygrothermal behavior. Several recent studies tried to identify mechanical characteristics of this material, however, there have been few studies which identified the cohesion c and friction angle φ directly by experiments. This paper presents an investigation on c and φ of RE through shear box tests (within the earthen layer). The specimens were directly taken from RE walls. Two types of specimens were taken: specimens at the upper part of the layers and specimens at the middle part of the layers. Then, the obtained experimental values were used in a numerical model (with Drucker-Prager’s criterion) to simulate pushover tests on two RE walls. The results showed the interfaces were needed to get better results. The best values identified for earthen layers were φ_layer = 44° and c_layer = 135kPa and the interfaces having 50-70% of the corresponding earthen layer characteristics.

We report on the poroelastic indentation response of thin hydrogel films geometrically confined within contacts with rigid spherical probes. Grafted networks differing in their glass transition temperature in the dried state were considered. Time-dependent changes in the indentation depth under a constant applied load were monitored over time as a function of the film thickness and of the radius of curvature of the probe using optical interferometry. The results are analysed within the framework of an approximate contact model derived within the limits of confined contact geometries. From this approach, scaling laws for the characteristic poroelastic time and the equilibrium depth are obtained. We show that this model adequately describes the poroelastic indentation behavior of the hydrogel films as far as the glass transition of the water plasticized network is not lowered below room temperature.

Tissue engineering scaffolds are very promising technologies in regenerative medicine for replacement of many hard and soft tissues. This methodology consists of seeding patient’s cells onto porous mesh like structures called scaffolds that are made of degradable and biocompatible synthetic and biological materials. The scaffolds themselves have two-tiered interconnected porosities; one forming the overall microstructure and the other being wall porosities of the membranes that form the microstructure. Transport of fluids and bio-molecular entities assisting in mineralization and tissue formation through interconnected porosities is vital for the regeneration of tissue. The specific hierarchical porosities of scaffolds enable biomineralization and growth of a bone-mimetic environment. In this study, we demonstrated that when osteotropic cancer cells such as prostate and breast cancer are seeded on these scaffolds, they form tumoroids that mimic in vivo like early stage of cancer cell colonization at the metastatic bone site. We demonstrate the use of nanoindentation technique to evaluate mechanical properties of live cancer cells that may be used to describe disease progression in the future. We also demonstrate use of finite element methods to develop robust cancer cell models. These studies suggest the use of mechanics-based approaches that may be used in future to evaluate biochemical behaviors of cancer progression.

Drying process of cementitious materials leads to cracks, especially in the presence of aggregates restraint, which has important consequences on transport and mechanical properties. This paper presents different effect on cracks generated in the drying process of cementitious composites under different conditions of inclusions. The non-destructive method, X-ray microtomography, is used to visualise the crack propagation. Two conditions of inclusions, the surface roughness of the aggregates and the Young’s modulus of aggregates, are considered to evaluate their influences on degree of cracking during drying. Based on the microtomographic observation, the distribution of cracks is identified and the characteristics of cracking in samples with different inclusions are well distinguished and analysed.

Experimental techniques have been developed to measure two poroelastic parameters: unjacketed bulk modulus K_s′ and unjacketed pore modulus K_s″. K_s′ is measured on samples with no jacket that are instrumented with strain gages, confining fluid (oil) penetrates inside the material and hydrostatic mean stress is equal to pore pressure, so the overal unjacketed bulk modulus can be calculated. K_s″ is measured on water-saturated rock by determining the change in pore volume of the specimen from accurate measurements on pore pressure controller, while the difference between mean stress and pore pressure is preserved constant. K_s′ and K_s″ are measured to be pressure-independent for Berea sandstone and Opalinus clay (shale). K_s′ ≈ K_s″ for the clay-rich shale, but K_s″ is smaller than K_s″ and bulk modulus of quartz for quartz-rich Berea sandstone. This result is explained by the presence of non-connected porosity.

Earth material was used for millennia, later abandoned by many communities, appear today as an alternative to face climate change and resource limitations. The objectives of this study were to 1) characterize earth readily available in large quantity for building construction, 2) formulate mix design stabilized with cement and unstabilized, and 3) do the mechanical tests to get the strengths in order. The soil was taken in Mascouche north from Montreal Island, in Quebec, Canada. The earth characterization was performed according to Canadian Standards Association and American Society for Testing and Materials. According to the results the sample contains 4% clay and organic materials, 8% silt, 85% sand, and 9 % gravel. The texture of this sandy soil was composed of fine homogeneous particles giving a very well graded earth. The soil fineness modulus of 0.58 was low compared to concrete sands which are usually between 2.2 and 2.8. The organic material content was high in the fine part of the material (10%). The coarse aggregate used in concrete are natural stones and angular aggregates. Three different sizes were tested and mixed in appropriate proportions to obtain a uniformly graded aggregate. The constituent materials of earth concrete (water, cement, earth and gravel) was determined by absolute volume. Six earth mixes were tested, stabilized, or unstabilized. The slump, density, air content, and compressive strength of these mixes were determined. Due to the presence of organic matter, the stabilized earth underperformed, but still represents a stabilization success. Adding clay to the sandy earth increased its strength. Metakaolin further increased the compressive strength.

Small strain shear modulus (G_max) is an important parameter used in geotechnical earthquake engineering. While most of the previous studies on G_max of sands have focused on isotropic stress state, there exist innumerable situations in geotechnical engineering where the soil is experiencing stress anisotropy. In this study, the influence of stress anisotropy on G_max of sands is evaluated using the results of a comprehensive set of bender element tests conducted on saturated sand samples under anisotropic loading conditions. It is generally shown that at a given mean effective stress, G_max increases with stress anisotropy. It is also observed that the influence of stress anisotropy on small-strain shear modulus is more pronounced for well-graded angular sands. This is attributed to the higher structural stability and non-homogeneous distribution of contact forces among the sand particles due to shearing. Finally, a new model for the prediction of small-strain shear modulus of sands subjected to stress anisotropy is developed.

Fluid-saturated sedimentary rocks are porous materials which elastic properties were shown to depend on the experimental conditions such as strain amplitude or strain rate. Similarly, poroelastic properties and compressibility coefficients should also depend on those two aspects. Moreover, under undrained conditions, it has been shown that the role of the experimental boundary conditions could play a role. Accounting for these considerations, we present a new methodology to attain accurately several compressibility and poroelastic coefficients. The method relies on forced confining or pore fluid pressure oscillations, and is designed to apply well in porous and permeable rocks.

In nuclear industry, huge quantity of liquid radioactive waste coming from reprocessing plant or unluckily Fukushima disaster, has to be treated in order to minimize the volume of these effluents. One way to decontaminate these waste is to synthesize inorganic monolithic filters that are less sensitive to radiolysis phenomena than organic ones. Geopolymer cements are good candidate to fulfill these specifications since intrinsically they are mesoporous with high specific surface area, and compatible with specific grafting agents which allow to trap selectively radionucleides of interest (especially the cesium). This work aims to synthesize monolithic geopolymer foams to produce some columns of filtration for decontamination process. A sodium geopolymer is studied and hydrogen peroxide is used as blowing agent. The results show that monolithic materials with hierarchical porous network are obtained. The bubble size distribution is controlled by the H₂O₂ concentration, the nature and the concentration of surfactants and the chemical composition of the geopolymer which control rheological behavior of the paste. In parallel, the basis of a swelling model of a geopolymer foam, taking into account physical phenomena such as the source term, the nucleation and growth process and the rheological behavior will be presented.

In this paper, the 3D-morphology of the porous structure in dentin is investigated by confocal laser scanning microscopy (CLSM). The porous microstructure near the dentino-enamel junction (DEJ), which consists of tubules partly connected by lateral branches, was found to exhibit a complex geometry. We revisit and challenge previous 2D studies by focusing on the 3D morphology (tubule and branching geometry) and quantification of porosity. Our work provides fundamental insight into the microstructure of dentin which could be used to study the effect of age and pathologies. Furthermore, such information is essential for the design of biomaterials used in dentistry, e.g., to ensure more efficient bonding to dentin. Finally, our analysis of the tubular network structure provides valuable data that could be used directly as inputs in a numerical model.

Increased usage of porous solids in the aerospace, automobile and infrastructure sectors necessitates understanding of the mechanics of large deformation processes. We present the results of a comparative experimental study of evolving deformation fields in porous brittle and porous ductile solids under plane-strain indentation. Gypsum (porosity = 37%) and sintered copper (porosity = 15%) have been used as model materials. A wedge indenter with apical angle of 120° was used to perform the indentation experiments. Images of the region surrounding the indenter were captured using a high-speed camera and microscope assembly. Images captured during the experiments were analysed using particle image velocimetry (PIV) algorithm in order to obtain velocity, strain-rate and strain field maps. Studies using indentation platforms provide a theoretical backing for many manufacturing processes such as drilling and machining.

Advances in additive manufacturing technology have enabled the use of sand as a 3D printing material. This has allowed 3D printed sandstone analogues to be produced that significantly reduce specimen-to-specimen heterogeneity and conversely, provides exacting control over the explicit inclusion of heterogeneity, such as fractures, within a specimen. By knowing and controlling inter-sample variability in terms of porosity, fracture networks, grain size distribution, and density distribution, 3D printing of geomaterials provides a valuable tool to validate numerical models, develop scaling laws and constitutive relationships, quantify the degree of influence of pore geometry, fracture network characteristics, and structural heterogeneity on macroscopic properties. Extensive research efforts are underway to fully characterize the thermo-hydro-mechanical properties of 3D printed sandstone specimens. Parallel to this study, tests such as shear strength, compressibility, permeability, wettability and pore size distribution have been conducted under various 3D printing configurations such as binder saturation, specimen orientation relative to build layer orientation and layer thickness. A range of testing results with a particular focus on the compressibility characteristics of the specimens are presented in this paper to demonstrate that 3D printed sandstone specimens has the potential to serve as the foundation for the next generation of experimental investigations of multi-scale, multi-physics reservoir geomechanical processes.

For cementitious materials, the time-dependent strain of a non-loaded specimen exchanging no water with the outside is called autogenous shrinkage. Whether this autogenous shrinkage is asymptotic or not at large times has not been systematically studied. The first objective of the present work is to study how autogenous shrinkage evolves over time at long term by analyzing experimental data that are available in literature. In these experimental data, autogenous shrinkage showed logarithmic evolution over time at large times, from which we characterized the long-term kinetics by a long-term slope of the deformations plotted on a log scale. In the second part, we are interested in the origin of autogenous shrinkage. Considering concrete as a multiscale material, by three steps of downscaling, we linked the long-term log-slope of autogenous shrinkage to the creep modulus of calcium silicate hydrates (C-S-H) gel. Then we computed at this scale an equivalent mechanical stress that should act in order to explain the measured long-term rate of autogenous shrinkage of the concrete. This mechanical stress is of the same magnitude as the effective pore water pressure due to self-desiccation and computed from the theory of poromechanics. Hence, we may consider autogenous shrinkage as creep induced by capillary forces due to self-desiccation.

Ideal flows are solenoidal smooth plastic flows in which an eigenvector field associated everywhere with the greatest principal strain rate and stress is fixed in the material. The technological value of the ideal flow theory comes from its potential to provide rapid preliminary designs of deformation processes. The available theory of ideal flows is restricted to the rigid perfectly plastic Tresca solid (i.e. the constitutive equations of this solid are the Tresca yield criterion and its associated flow rule). The objective of the present work is to demonstrate the existence of steady planar ideal flows for the double slip and rotation model of pressure-dependent plasticity. This model is known to be applicable to several different types of material, for example soils and granular materials.

This paper presents a bounding surface plasticity model to capture the behaviour of soils under multiaxial loading conditions. A 3D mapping rule is described to locate the image point on the bounding surface in the principal stress space. To demonstrate the performance of the model in predicting the behaviour of soils, under 3D loading conditions, examples of drained true triaxial tests under constant mean effective stress are simulated. The numerical results are compared with the existing experimental data to confirm the validity of the proposed model.

The impact of impurities on salt healing properties is studied through creep tests performed on brine saturated granular salt with various quartz contents. Quartz grains act as shields that reduce dissolution at salt grain contacts and decrease the creep rate. Non-smooth creep curves are obtained for specimens with 50% quartz contents, due to sequential pore collapse. Micro-CT images acquired before creep, after creep, and after unloading, show that pore-to-pore distances decrease with quartz contents and that the creep rate decreases as the mean area of the salt grain contacts increases. Based on grain scale thermodynamic models, we show that creep deformation is controlled by diffusion-not dissolution-precipitation. Permeability evolution is less sensitive to porosity than to void radius and spacing, which control pore connectivity. The proposed modeling framework can be used in any crystalline material to relate microscopic reaction rates to macroscopic deformation rates.

The time-dependent response of rocks is strongly influenced by saturating pore fluids. This paper presents a theoretical framework for the modelling of the time-dependent behaviour of unsaturated rocks. This framework is constructed based on the theory of poromechanics combined with irreversible thermodynamics. Delayed inelastic deformation is modelled using the theory of viscoplasticity and isotropic creep damage which both are governed by a plastic effective stress. This framework strikes a balance between different requirements in constitutive modelling: capability to reproduce the rock behaviour, simplicity for engineering applications and thermodynamic consistency. Its applicability is illustrated by formulating a specific constitutive model which has been validated against experimental data.

For a part of the concrete containment buildings of French nuclear power plants, the leak-tightness depends vastly on the pre-stress of the building which can decrease due to concrete delayed strains. Therefore, EDF has developed a large experimental program in the early 2000 in order to study the biaxial creep of concrete. In this paper phenomenological drying, shrinkage and creep model is used to model these biaxial tests. The identification of the parameters of the drying model is first presented. Then, the parameters relative to a parasite mass-loss which occurred in the sealed tests and to the creep model are identified. The model is shown unable to reproduce correctly the biaxial strains observed in the tests. A change of the part of the model accounting for the desiccation creep is therefore proposed. Assuming that the desiccation creep Poisson’s ratio is identical to the basic creep and the elasticity ones allows for a better reproduction of long-term multiaxial concrete creep.

In this paper a two stress-state variables model with solid phase stress and cryogenic suction is introduced for simulating the long-term behavior of frozen soils. The solid phase stress is introduced as the combined stress of soil grains and ice. The model is able to represent the behavior of frozen soils in different temperatures and ice contents with a single set of parameters. It is also able to simulate the transition between frozen and unfrozen states. The so-called over-stress method is applied for simulating the elastic-viscoplastic deformation of the material due to variation of solid phase stress, while an elastic-plastic formulation is applied for the suction induced deformation. In unfrozen state, the model becomes a conventional elastic-viscoplastic critical state model. The model is implemented in PLAXIS and results are compared with the available test data and reasonable agreement is achieved.

In this research, an experimental campaign was carried out to investigate the elastic and viscoelastic behaviour of cement pastes. For this purpose, uniaxial creep tests and elastic modulus tests with elasticity modulus measurement through ambient response method were performed on cement pastes with water to cement ratio of 0.35 at early ages, and autogenous shrinkage was measured in parallel. After subtracting the measured autogenous shrinkage from the total measured deformation under load, the early-age evolution of basic creep was obtained. The kinetics of the elastic and visco-elastic properties was formulated based on Tikhonov regularization. The results show that the kinetics of basic creep compliance and creep recovery at all loading ages had log-linear trend. Therefore a power law function was established to express the specific basic creep. It was found the amplitude and the slope of the kinetics were linked to the loading ages and the hydration evolution.

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 semi-analytically. 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.

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 Bažant solidification theory result.

The Callovo-Oxfordian (COx) claystone, due to its low permeability, self-sealing ability and the absence of cracks, will be the hosted rocks for underground disposal of high- and intermediate-level long-life radioactive wastes in France. This paper characterises gas permeability change of the COx claystone in process of triaxial creep. The effect of differential stress on permeability change is investigated by stress loadings in four successive steps. Unloading and reloading cycles are carried out to characterise the variation of elastic modulus during triaxial creep process. It is found that lower differential stresses induce a decrease of the gas permeability and higher differential stresses however induce an increase of the gas permeability during the multi-step creep process. The transition of gas permeability from the decrease phase to the increase phase corresponds well to the evolution of volume strains. The scatter-measured elastic moduli during the creep process however mainly show a monotonic feature. It is concluded that the gas permeability is more sensitive than the elastic modulus to identify the micro cracking process of the COx claystone during triaxial creep process.

A viscoplastic constitutive model for describing the time-dependent stress-strain behaviour of unsaturated geomaterials is presented. The proposed model is formulated within the framework of viscoplastic consistency and the bounding surface plasticity model. The model provides a continuous transition from rate-independent plasticity to rate-dependent viscoplasticity. The hardening parameter representing the size of the bounding surface is defined as a function of viscoplastic strain, viscoplastic strain rate, and suction. The suction hardening effect is described using the coupled influence approach where suction has a multiplicative effect to the viscoplastic volumetric hardening. Numerical results are presented to demonstrate the capability of the proposed model in simulating the behaviour of saturated and unsaturated geomaterials.

The thermodynamic framework for continuum mechanics can be applied to model granular and porous materials. Broadly speaking, there exists two approaches: the French school approach and Ziegler’s approach. Despite the fact that they both have the same foundations, differences between them emerge regarding the way in which stored energy is accounted for. This is illustrated here by applying the two approaches to the classical Von Mises kinematic and isotropic hardening models. In Ziegler’s approach, the stored energy is solely used for the kinematic hardening, as opposed to the French school approach in which the stored energy is allowed in both cases of hardening. In spite of which modelling approach is taken, we will show how certain modifications to these theories have to be made in order to develop the classical modified Cam Clay model, which emphasises the difference between the classical and the thermodynamic formulations.

The paper presents an advanced plasticity formulation for modelling partially saturated geomaterials based on the effective stress principle. The bounding surface plasticity framework is adopted for development of the proposed model. The bounding surface is assumed to undergo isotropic hardening due to increase in the volumetric strain and suction. A unique feature of the presented model is explicit incorporation of the influence of the soil density on the soil water retention curve and analytically correlating this dependency to the effective stress parameter without introducing additional material parameters. To validate the presented model, several experimental data including constant suction and wetting tests are simulated and the capability of the model to predict the experimental results is discussed.

This paper presents a novel, exact, theoretical solution for the quasi-static expansion of a cylindrical cavity in anisotropic incompressible fine-grained geomaterials under undrained condition. The solution is based on the rotated and distorted elliptical yield surface of the S-CLAY1 model to account for inherent anisotropic behavior without rotational hardening. The solution is rigorously developed by introducing new stress invariants to deal with the inherent anisotropy. The theoretical solution requires numerical evaluation of a system of three first-order ordinary differential equations. The presented solution is verified against finite element analyses.

The concept of rotational hardening (RH) was introduced into constitutive model formulations in order to rotate a yield or bounding surface from the isotropic axis during either anisotropic consolidation or shearing. To properly account for the evolution of stress induced anisotropy during shearing, a suitable RH rule must be used. An improved RH rule is presented in this work. Although it incorporates aspects of several previous formulations, the improved RH rule includes provisions that allow it to more accurately simulate the response of anisotropically consolidated cohesive soils. This is especially true for overconsolidated specimens tested in extension. It was found that in order to properly match the experimental effective stress paths in such tests, it is necessary to accelerate the pace of rotation of the plastic potential towards the critical state line in extension; the higher the overconsolidation ratio, the faster should be the pace of rotation.

This paper focuses on the coupling between the microcracking and shrinkage in the secondary creep of concrete in bending under a high sustained load. Based on an interaction between the cracking and the diffusion of moisture, microcracks can drive the growth of a crack in concrete at high stress level. This effect has been modeled in a simplified poromechanical model in the framework of continuum damage mechanic. The proposed model has been implemented in a discrete lattice code which uses Voronoi discretization for the conduit elements and Delaunay triangulation for the dual mechanical elements. The model has been validated against recent experimental tests on creep of fiber reinforced concretes in bending.

The homogenization techniques recently developed for the numerical study of the elastic behavior of snow are adapted to its non-linear visco-plastic behavior. Based on the definition of kinematically uniform boundary conditions, homogenization problems are applied to 3D-images obtained by X-ray tomography, and the mechanical response of snow samples of different densities is explored. An original post-processing approach in terms of viscous dissipated powers is defined in order to formulate the macroscopic behavior of snow as an Abouaf model based on a density parameterization.

Due to the complex microstructure and properties of cement-based materials, the influences of pores on concrete mechanical and creep properties are still in debate. This study conducts research both experimentally and numerically at the microscale to take a further look at the mechanism of porosity effects. In addition to adopting the analytical homogenization schemes based on continuum micromechanics, a finite element model is developed to simulate the porosity effect by considering the pore volume and pore size distribution. The simulated results show that the elastic modulus decreases with increasing volume fraction of pore, while the relationship between the creep property and the volume fraction of pore exhibits an opposite trend. The pore size distribution also affects the mechanical and creep properties to some extent. The simulated results are then compared to the results measured by microindentation. It is found that the simulated results agree well with the experimental measurement, validating the feasibility of the numerical simulation for porosity effect.

We address Hydro-Mechanical (H-M) feed-back coupling in a fluid-filled fractured rock, whereby the hydraulic conductivity of the fractured rock is modified by its deformation. We present an upscaled description of this coupling based on previous work on tensorial macro-permeability (Kij) of fractured rock. The H-M feed-back coupling effects are expressed for the 2D case with fractures as straight line cracks, and for the 3D case with fractures as planar disc cracks. We assume at first that the deformable rock matrix remains impervious: feed-back effects are then due solely to crack deformation, while the effect of matrix deformation on Kij is neglected. The resulting tensorial H-M sensitivity coefficients, (K′ijkl) and (Φ′kl), are expressed explicitly. Extensions of this work are indicated in the conclusive section, e.g.: strain of the permeable porous matrix; thermal expansion; and combining all types of H-M couplings (stress/pressure/fluid production coupling, as well as feed-back coupling).

Gas permeability experiments were performed on partially and fully water-saturated tight gas sandstone samples. The tests were conducted at confining pressures of 15, 20, and 30 MPa and at different mean gas (He, N₂) pressures up to 6 MPa in order to account for the slip-flow effect. With increasing water content gas permeability coefficients decreased by up to three orders of magnitude. Furthermore, in the plot of apparent permeability vs. reciprocal mean pressure the usually observed “Klinkenberg trend” was found to become non-linear and exhibited negative intercepts with increasing water saturation and differential pressure. This can either be due to capillary pressure-controlled water drainage or dilatation of the pore network. Effective gas permeability is therefore not simply controlled by the absolute water-content of the pore system but additionally by the effective and differential pressure. This may have important implications for gas productivity, as water content and fluid pressure and effective stress change dynamically during dry and wet gas production.

Cirrhosis is a life-threatening condition that represents a leading cause of death in the western world. In this condition the structure of the liver tissue is altered by the development of fibrosis, which means it becomes stiffer and its permeability to blood and interstitial flow within the tissue that are vital to its function are reduced. We develop a new mathematical model based on those, which we use to investigate the changes in liver volume, blood flow and lymphatic uptake, which measures interstitial flow, that occur as the tissue becomes progressively stiffer. Our results suggest that the typical changes that develop during cirrhosis have a significant effect on the permeability properties, highlighting the seriousness of this condition.

Coal fines are small coal particles produced during coal seam gas (CSG) production and may plug fluid flow paths, resulting in significant reduction in CSG productivity. This study aims to employ laboratory experiments to examine coal permeability variation induced by coal fines generation and migration during the dewatering stage. One coal sample from Bowen Basin, Australia, was tested under different pressure differences. The evolution of coal permeability and the amount of produced coal fines were monitored during the experiments. The pressure difference was increased from the initial 0.8 MPa to 1.5 MPa through 7 steps to investigate its impact on the characteristics of coal fines and the corresponding permeability change, and to obtain the critical velocities for a range of particle sizes. Every 5 mL effluent was collected and analysed in terms of particle size distribution and volume. The results revealed that for this sample, the sizes of coal fines ranged from 1 μm to 14 μm. Initially the coal permeability dropped dramatically due to excessive coal fines generation, with 74.1% reduction for the case of 0.8 MPa pressure difference, followed by gradual decline with fluctuations. It was observed that the production of large coal fine particles was accompanied by significant permeability fluctuations. This was attributed to the counteraction between formation damage (cleats plugging and coal fines settlement) and coal fines removal from the samples (widened cleats). Although no clear correlation between particle size and pressure difference was observed, the critical particle size was positively related to the flow velocity. The velocity followed parabolic fashion against the pressure difference. For this sample, keeping the differential pressure between 1.1-1.3 MPa can reduce the permeability damage induced by coal fines. This study delivers fundamental understandings of coal fines generation and migration behaviours during the dewatering stage, which can provide useful guidelines to implement effective dewatering strategies to minimize production loss induced by coal fines.

MX-80 granular bentonite is expected to be used as a buffer material for high level nuclear waste storage in Switzerland. This material is composed of 85% of smectite clay and exhibits a particular structure with four different scales. MX-80 macroscopic properties can therefore be investigated using upscaling techniques, but this approach needs a comprehensive understanding of the material fabric. In the present work, intrinsic permeability of MX-80 has been derived from available data on the structure arrangement with three upscaling steps. The missing structural parameters (permeability of clay stacks, their shape and the shape of micropores) can be estimated and it is shown that the permeability derived using a self-consistent scheme is in good agreement with experimental measurements for reasonable values of these parameters. The influences of these parameters variations have been investigated. The ranges of values in which they play a key role on the permeability derivation for structures like the one of MX-80 have been highlighted.

A benchmarking exercise of low permeability measurements was organized with 30 laboratories from 8 different countries. The contribution of each team was to measure the intrinsic permeability of a common low permeability material with the technique of their choice. The selected material was the Grimsel granodiorite and the benchmark was called KG²B (K for Grimsel granodiorite benchmark). The different methods used can be classified into direct methods, including steady-state, transient and pore pressure oscillating techniques, and indirect permeability estimation, mostly models using microstructural data. Within the allowed time frame of one year we collected the results from 24 laboratories. We present the different stages of the benchmarking project and the general profile of the data set in terms of methods, experimental conditions and sample size. The complete analysis is still going on, but our preliminary results on the statistics of the raw permeability measurements are presented.

This research aims at understanding fluid transport through the pore network of a pure Portland-based high performance concrete (HPC). Pores are characterized by direct imaging at the mesoscale (tens of nanometers). We combine two imaging techniques, 3D FIB/SEM (focused ion beam/scanning electron microscopy) and 2D STEM (scanning transmission electron microscopy). Voxel sizes are on the order of 10 nm for FIB/SEM (with sample volumes on the order of 60-120 micron³) and 1.57 nm for STEM (with sample volumes on the order of 1.5-2.6 micron²). STEM images are selected within the cement hydrates by using energy dispersive spectroscopy (EDS). With both imaging methods, porosity is on the order of the macroscopic porosity (10%). The pore network is quantified, so that its main features are used to assess fluid permeability by the Katz-Thompson equation. Predicted permeability (on the order of 10^-19 m²) is found in good agreement with macroscopic permeability measurements, at both pore scales.

In order to assess the performance of radioactive waste repository, the investigation of gas migration process through the formation of fully water-saturated Cox argillite is indispensable. Traditional methods, based on macroscopic approaches or homogeneous transport properties, are inappropriate to analyze this issue at the meso/microscopic scale. In this study, using the experimental pore size distribution curve, the morphological aspect of porous network is represented by the excursion of Gaussian Random Field. Essentially, the extraction of accessible pores for a given gas pressure is feasible via the morpho-mathematical transformations. This modeling work focuses on the estimation of capillary induced breakthrough pressure and the identification of adequate gas transport mechanisms for breakthrough process.

A model capable of predicting transport properties based solely on the pore size distribution of the material and the fluid characteristics has been developed previously by the authors. This model combines a Darcy description of the fluid flow at the macroscale with a Poiseuille/Knudsen flow at the micro-scale. A stochastic approach is then used with regards to pore network generation, in a manner consistent with mercury intrusion porosimetry (MIP). The present paper extends this model to multi-phase flow in an attempt to model partially saturated porous media. Kelvin’s law defines which pore sizes are invaded with liquid and rules for accounting contributions of the pore network to liquid and vapour flows are introduced. The extended model provides data that are consistent with the Van Genuchten approach to liquid and gas relative permeabilities, compares well with experimental data and provides information of the relative permeability to vapour and liquid water upon damage.

The general description of solute transport in multiphase environments depends on assumptions not only concerning the interphase exchange, but also concerning transport processes within the phases. In case of equilibrium between phase concentrations the formulation can be simplified significantly by the introduction of additional factors (R-factors) for advection, diffusion and degradation processes. The mathematical derivation is a generalization of the concept of retardation factors, which is well established in porous medium studies. In the given description of general multiphase situation the characterizing Péclet number is determined by the interphase equilibrium - in contrast to the common concept of retardation factors. An application demonstration is given for a two-domain system, in which both sub-domains obey transport equations with different Péclet-numbers. It is shown that the concentration profile is very different in the sub-domains on both sides of the interface.

Sustainable energy production is key for today’s energy and heat demand and relies on the successful stimulation of low-permeable oil, gas or geothermal reservoirs. Fracture permeability is a substantial topic in recent laboratory and numerical studies. Our aim is to study the sustainability of fracture permeability at varying effective stress with a focus on the fracture mechanism involved. We aim to further characterize the permeability evolution for different modes, mode I tensile fractures, saw-cut fractures, mode I tensile fractures with shear displacement and mode II shear fractures, in the laboratory, covering all fracture modes commonly observed in EGS. The hydraulic experiments are carried out in a triaxial compression cell. To simulate production and injection procedures in a geothermal reservoir, the effective pressure is varied and permeability is continuously measured. The permeability development of different fracture types at high effective stresses has been investigated and a general decrease of permeability at already low effective stress was observed in all tests. Shearing does not lead to a sustainable permeability increase for the tested sandstone. Conclusively, any reduction in pore pressure after stimulation will damage the fracture permeability irrecoverably.

Permeability and mechanical behavior of fracture-damaged shale is investigated through a recently developed three-dimensional discrete dual lattice model. The mechanical lattice model simulates the granular internal structure of material at the grain level, and describes the heterogeneous deformation by means of discrete compatibility and equilibrium equations. Fluid flow along intergranular pores and cracks is simulated through a fluid transport network. The variation of permeability for cracked material is captured by coupling mechanical and transport lattice models. The formulated framework is used to simulate fluid flow along cylindrical shale specimens fractured during splitting test. The results show that the simulated effect of cracking on the overall permeability is in general qualitative agreement with available experimental data.

An NMR logging-based permeability estimator was implemented for chalk. Several authors have identified the inability of accurate prediction of permeability from NMR logs in carbonates. Current models (namely Coates and SDR) may yield unreliable permeability data and require extensive calibration of parameters. Also, calibration requires data from core analysis, which undermines one of the key advantages of the technology: minimizing the need of expensive coring runs. A modified Kozeny method is used for permeability estimation from NMR logs. Unlike the model of Coates and SDR, does not require calibration. To translate the T₂ relaxation distribution into pore size, an analogy is made between the NMR T₂ data and the MICP output. Specific surface data acquired by the Brunauer Emmett Teller method (BET) was used to aid the interpretation of the surface relaxivity. The model was tested in a chalk reservoir borehole in the North Sea, for which NMR logs and permeability data for 4 core plugs are available. Results achieved using the modified Kozeny equation are in better agreement with the Klinkenberg permeability of core plugs than both the SDR and Coates methods. They are also superior to the results found by the application of Kozeny’s equation when used without input from NMR data.

Electromagnetic field excites acoustic field in a porous elastic medium saturated with fluid electrolyte due to electrokinetic conversion effect. Our solution of finite-difference equations, obtained from Pride’s equations describing this process, showed that acoustic field consists of the same types of waves as in the process of traditional acoustic logging plus fast wave, which propagates almost instantly. Amplitude of this wave is sensitive to the formation permeability and can be registered, if proper electric emitter is used. Modified Pride’s equations, which take into account the effect of Joule heating on the propagation of acoustic waves, are used in this work. It follows from numerical results that Joule heating can make significant contribution to the acoustic field.

Using a finite-difference code for Biot-Pride’s equations of acoustical and electromagnetic propagation in a saturated porous medium, we show a flexural acoustic wave attenuation can be used for formation permeability estimation. It is also shown that the ratio of spectral amplitudes of acoustic and electromagnetic flexural waves can be used for formation permeability evaluation. The last approach is applicable even in the case of sealed pores on the borehole wall.

The phenomenon of coupled porous media deformation and solute transport occurs in a variety of geoenvironmental engineering applications. This paper presents an extensively verified numerical model (named CST3) for coupled large strain deformation and solute transport in saturated, multi-layer porous media. The deformation algorithm accounts for vertical strain, media self-weight, general constitutive relationships, relative velocity of fluid and solid phases, changing compressibility and hydraulic conductivity during deformation, unloading/reloading effect, time-dependent loading and boundary conditions, external hydraulic gradient, and multiple layers of porous media with different material properties. Large strain can be considered such that the nonlinearity of material properties such as compressibility and hydraulic conductivity can be accounted for. The solute transport algorithm accounts for advection, diffusion, mechanical dispersion, linear and nonlinear sorption, equilibrium and non-equilibrium sorption, media porosity-dependent effective diffusion coefficient, and first-order decay reactions. A hypothetical problem is simulated using CST3, and to illustrate the importance of coupling between deformation and transport, two simulation cases are considered: one case takes into account the coupling effect between soil deformation and solute transport whereas the other ignores such coupling effect and assumes soil media does not deform. Simulation results indicate that soil deformation can have significant impact on the solute transport process for a long period of time. For relevant engineering applications, ignoring such coupling effect can lead to significant errors in the associated design and analysis.

To model a creeping flow through closed cracks in cracked materials we study a normal mechanical contact between two elastic half-spaces with rough surfaces is studied. The roughness is modeled using a filtering technique in Fourier space: the root mean squared roughness, the spectral content and the fractal dimension are prescribed. The non-linear contact problem is solved using a spectral boundary element method. A general transmissivity laws for incompressible fluid linking roughness parameters and applied load are deduced up to the percolation limit. In this analysis it is assumed that hydrostatic pressure is much smaller than contact pressures. It is shown that the transmissivity decreases exponentially with the effective contact area, which in turn grows linearly with the contact pressure. The effective contact area includes both contact clusters and zones of trapped fluid. A strongly coupled problem of trapped fluid in the wavy contact interface is also considered for compressible and incompressible fluid. The influence of the trapped fluid on the friction angle is studied.

The hydration temperature has a considerable effect on the microstructure of cement paste and its mechanical properties. The present work aims to study the influence of hydration temperature on the mechanical properties of cement paste via micromechanical modelling. We will first characterize the microstructure of a class G cement paste hydrated at different temperatures, between 7 and 90°C. Then, the influence of the microstructure variations on the elastic properties of the hardened cement paste will be explored. The analysis of the microstructure enabled determining accurately the volume fractions of different phases present in the microstructure which is an essential input for the micromechanical modelling of its elastic properties. A multiscale self-consistent homogenization model is used based on these results to simulate the variations of the mechanical properties of hardened cement paste with hydration temperature. The results are compared with macro-scale experimental results of uniaxial compression tests.

The aim of this paper is to present a methodology of determining the thermal conductivity of the straw fibers used to elaborate an insulating material concrete developed in the framework of the PROMETHE research program. In order to identify the transversal thermal conductivity of straw fiber a simple periodic microstructure with a unidirectional orientation of the fibers incorporated in a silicone rubber matrix is considered. This rubber matrix, with high thermal conductivity is chosen in order to, one hand, maximize the contrast with thermal properties of straw, and on the other hand to manufacture easily the specimens. Thermal conductivity of the straw-silicone composite is measured using the hot wire technique. The effective thermal conductivity is evaluated using analytical homogenization method based on Mori-Tanaka scheme. The upscaling technique uses the information on the straw fibers volume fraction, fiber orientation, and components properties. The inverse method is based on the error minimization between experimental and analytical results.

Saturated, isotropic, poroelastic materials are classically described by their elastic stiffiness, one Biot coefficient and one Biot modulus. The situation becomes more complex for unsaturated, isotropic, poroelastic materials that require multiple Biot coefficients and moduli. These poroelastic coefficients are dependent and linked by several linear relationships. Micromechanical estimates of these coefficients have been proposed by several authors. However, these estimates may fail to fulfill the linear relationships that relate the exact poroelastic coefficients. This might be regarded as an undesirable inconsistency of the model. In this work, we propose new, consistent (in the sense that the above mentioned linear relationships are preserved) estimates of the poroelastic coefficients. Our point of departure is the principle of Hashin and Shtrikman, suitably extended to eigenstressed materials. Adopting stress-polarization fields that are similar to the eigenstress-free case allows us to derive variational estimates of the poroelastic coefficients, which can be shown to fulfill all known linear relationships required from the exact values. After outlining the derivation within the general framework of eigenstressed, heterogeneous materials, the results will be specialized to poroelasticity. This will lead to a variational justification of the ad-hoc pore isodeformation assumption.

A methodology for upscaling 3D coupled hydro-mechanical (HM) properties of fractured porous rocks is developed theoretically and tested on synthetic fractured rock samples. We consider the case of water-saturated elastic rock modeled as a deformable porous matrix with deformable cracks filled with compressible water. The upscaling is a strain superposition method, in which the local strains in the matrix and in the cracks are superimposed under the effect of a frozen “effective” stress field. Given the geometric and coupled hydro-mechanical properties of the matrix and cracks, the superposition method yields a system of upscaled continuum laws with equivalent tensorial mechanical and HM coefficients. We obtain in the fluid production equation a “second” Biot coefficient, B_ij^(II) and two distinct Biot moduli, M^(I) and M^(II). The theoretical tensorial expressions are then specialized to the case of isotropic crack systems and are tested by running 3D upscaling “experiments” on synthetic, statistically homogeneous and isotropic, Poissonian crack systems.

Clay-rocks often named shales are considered as a two-phase mixture consisting of non-clay grains and an anisotropic clay matrix whose the spatial organization obeys to a “local simplicity” assumption. Under this assumption, the complexity of spatial clay distribution can be captured by two local functions, namely, the local clay distribution μ and the local percolation probability λ which are calculated by partitioning a mineral map. This approach is applied to a mineral map made from a Callovo-Oxfordian mudstone sample for which petrophysical data are available. The results of a sensitivity analysis illustrate the significant impact of the complexity of spatial clay fluctuations on the effective elastic wave velocities and the corresponding Thomsen parameters. They also show that the elastic anisotropy of clay rocks is significantly overestimated when spatial clay fluctuations are not taken into account.

This paper describes a simple (idealized) lattice-type model of porous materials, and uses that model to derive analytical expressions that determine interactions between the pore fluid and the material framework. The examples included here address the change in horizontal stress associated with fluid depletion, and also the way that fracture apertures are changed due to alterations of fluid pressure. The predictions agree in magnitude with observations and large-scale inferences. Analysis of the model’s behavior leads to questions concerning the validity, or not, of the scale-independence of stress, along with posing questions about the use of continuum ideas for porous materials. The notion of effective stress is considered within the framework of the model, which reveals that the so-called poro-elastic coefficient is not a material property.

The Paleozoic shales exposed on the island of Bornholm contain intervals with more than 10% organic matter which is post mature with respect to the formation of hydrocarbons. Four shallow bore holes have been drilled through the 250 m thick shale interval and partly cored and logged with geophysical probes. We studied how the organic content and mineralogical composition influence mass density and elastic properties as measured from core analysis and logging data. The shales have porosity in the range of 1%-10% and modelled permeability (from porosity and BET) of generally less than 0.1 μDarcy. We found that solid density and elastic stiffness parameters only vary insignificantly with solid composition, when TOC is lower than 5%, but that mass density and TOC are correlated when TOC is higher than 5%. A similar correlation was not seen for TOC and Sonic logging data. A reason can be that the content of low-density kerogen and high-density pyrite is correlated. According to our data, the shales have weak to medium degree anisotropy of stiffness and compare well with other studied shales.

In this paper, a micromechanical model is proposed to describe the elastoplastic behavior of a typical shale gas reservoir. According to petrographical observations, the studied material is seen as a heterogeneous rock with complex and multi-scale microstructure. At mesoscale, different types of inclusions are seen embedded in a composite matrix. In the latter, different constituents can be distinguished at smallest scales: organic inclusions and fine calcite grains are immersed in a porous medium whose solid phase obeys to Drucker-Prager criterion. Thus, in order to estimate the macroscopic elastoplastic behavior of the shale rock, a three-step homogenization procedure is adopted to consider the constituents effect on the macroscopic behavior. At the end, a comparison between numerical simulations and experimental data is conducted in order to highlight the capacity of the model to capture the main features of the mechanical behavior of this material.

This paper focuses on effective poroelastic properties of materials constituted by an isotropic homogeneous solid matrix containing non ellipsoidal pores. In the frame of effective media theory (EMT), property contribution tensor approach extended to non ellipsoidal inhomogeneities is used to estimate effective poroelastic properties. On the basis of recent results obtained by the authors, two reference 3D shapes are considered: supersphere and superspheroid, characterized by a concavity parameter and being convex or concave. Related compliance contribution tensors respectively verify cubic and transversely isotropic symmetries have been characterized thanks to 3D finite element modellings and obtained analytical approximation formula are used in this paper. Analysis is focused on the effect of the parameter characterizing concavity on effective poroelastic coefficients. Non interaction approximation (NIA), Mori Tanaka, and Maxwell homogenization schemes are compared. It is shown that concavity parameter is of major importance as may be aspect ratio of spheroidal pores.

Analytical estimations of stresses and strains fluctuations (or statistical variability) in elasticity at early-age are provided according to different scales of interest of cement-based materials (CBM). The estimations are obtained by means of relations between square means and effective properties for isotropic medium. Mori-Tanaka (MT), self-consistent (SC) and generalized self-consistent (GSC) schemes are combined to represent the multiscale microstructure of CBM. In the estimations, the evolution of volume fractions of phases due to cement hydration processes is accounted for at the cement paste level. Interfacial transition zone (ITZ) is considered at mortar level. These estimations provide important information regarding the heterogeneity of the mechanical fields in cement-based materials, which can be used, for instance, in the definitions of failure or onset of damage criteria. The distributions of stress and strains are provided for the phases of interest at a given scale for different loadings.

The paper describes an experimental study investigating the effect of natural fibres on the mechanical properties of adobe bricks. Six laboratory-designed and produced adobe mixtures, containing different amounts of straw fibre, were examined in this study. The samples prepared were subjected to direct tension, bending and compression tests. The results show that the addition of fibres does not affect the mode of failure sustained under the loading conditions imposed. Mixtures with high fibre content tend to develop lower mechanical strength. However, straw fibres can increase deformability under compression and flexure, precluding sudden failure when the load-bearing capacity of the material is exceeded. The effect of fibre reinforcement on post-cracking tensile response was found to be rather limited, since all specimens tested exhibited brittle behaviour.

The dentinal tissue is made of tubules surrounded by peri-tubular dentin (PTD), embedded in a matrix of inter-tubular dentin (ITD). Hashin and Rosen found exact stiffness bounds for hexagonal patterns of hollow fibers. But state of-the-art micro-macro models rely on simplified microstructure representations and lack experimental validation. The Poisson’s ratios of dentin microstructure components cannot be determined by direct experimental methods. By contrast, we apply Hashin’s homogenization scheme to a non-uniform PTD distribution, determined from image analysis. According to finite element simulations, a cube containing 60 tubules is a representative elementary volume. Microscopy, nanoindentation and resonant ultrasound spectroscopy data were collected from each dentin sample studied for model calibration. Despite the high variability of microstructure descriptors and mechanical properties, statistical analyses show that Hashins bounds converge and that the proposed model can be used for backcalculating the microscopic mechanical properties of dentin constituents.

We investigate the numerical modeling and simulation of mechanical effective properties of disordered foams in 3D. We consider the elasticity, the thermal conductivity as well as the permeability. We present a meshing procedure for the microstructure of randomly disordered wet foams. The material behavior is modeled by constitutive equations and a boundary value problem is set on the microstructure. We present and implement the homogenization approach for the determination of the effective mechanical properties. The local problems are discretized and solved with the finite element method. We investigate the monodisperse and disordered configuration of a wet foam by varying the volume fraction.

An efficient numerical method for solution of elasticity and poroelasticity problems for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Cracks and inclusions occupy a finite region of the medium that is subjected to arbitrary external forces. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. The method is mesh free. Stress fields inside inclusions and crack opening vectors are approximated by Gaussian functions centered at a system of nodes. The elements of this matrix are calculated in closed analytical forms (for inclusions) or expressed in terms of five standard 1D-integrals (for cracks) that can be tabulated. For regular node grids, the matrix of discretized system has Toeplitz’s structure, and a Fast Fourier Transform technique can be used for calculation of matrixvector products with such matrices. In the present work, the problem for media with both heterogeneous inclusions and cracks are solved in the framework of a general numerical scheme.

A discrete framework to reformulate poroelasticity of heterogeneous media is proposed using lattice element method (LEM). In congruence with μVT and NPT ensembles of statistical mechanics, discrete expressions for Biot poroelastic coefficients are derived. The exchange of mechanical information between pore and solid(s) is captured by means of force field potentials for these domains, which eliminate the requirement of scale separability of continuum-based poromechanics approaches. Furthermore, this formulation accounts for the presence of interfaces as well as local microtextural and elastic variations. The theory is validated against continuum based expressions of Biot poroelastic coefficients for porous media with isotropic and tranversely isotropic elastic solid behavior.

This study aims to numerically investigate the effect of particle size distribution (PSD) of asphalt mixtures on their load carrying capacity measured in three point bending test. Discrete element method (DEM) is employed as the numerical framework to simulate asphalt mixtures. The PSD feature of asphalt mixtures is replicated in DEM by an assembly of polydisperse particles with identical gradation. A cohesive damage-plasticity model characterising the fracturing processes of binder matrix within the materials is also incorporated in the inter-particle contacts to collectively model their macro-behaviour. This discrete-based modelling approach is validated to capture well the mechanical response of asphalt mixtures in three point bending test. It is then applied to investigate the PSD effects, in which numerous simulations of three point bending test are conducted and material PSD is varied while other model parameters remain constant. The influence of PSD on material load carrying capacity obtained from the simulations is discussed and interpreted via further micromechanical analysis on numerical specimens.

The aim of this study is to numerically investigate the effect of air void structure on the mechanical behaviour of a highly porous foamed concrete using the discrete element method (DEM). In the DEM simulation, the foamed concrete, which features high porosity and a complicated internal structure, is represented by an assembly of spherical particles randomly generated in a given space predefined by a void matrix. To simulate the cementitious phase of the foamed concrete, a cohesive-frictional model with parameters calibrated from experiments is adopted. The numerical results obtained from the validated DEM model show that the air-void structure has a significant effect on the compressive strength and the fracture of the material.

Soil water retention curve (SWRC) is a fundamental relationship for unsaturated soils. Its knowledge is essential for constitutive modeling of unsaturated soils. Furthermore, it carries important information about the soil internal structure. When soil deforms, its porous network changes and its water retention properties are consequently affected. Thus, one can employ the measured SWRCs under different stress levels to acquire insights on the soil porous network at each stress level. In this study, the values of pore fractal dimension are determined from SWRCs which are experimentally obtained at different stress levels. In this study, the variation of pore fractal dimension under different net stress levels has been analyzed and the results have been interpreted in terms of changes in soil porous structure. Furthermore, suggestions on the potential usage of the method for formulating various hydraulic and mechanical parameters in unsaturated soils have been made.

A theoretical model for prediction of effective thermal conductivity with application to sedimentary rocks is presented. Effective thermal conductivity of sedimentary rocks can be estimated from empirical relations or theoretically modelled. Empirical relations are limited to the empirical conditions and should be applied with caution. Theoretical models are typically porosity-based and unable to capture the complexity of sedimentary rocks. We propose a theoretical model, derived from measurable para-meters including both quantity and connectivity of the constituents. Because the thermal conductivity of solids is typically orders of magnitude larger than that of fluids, grain contacts constituting the solid connectivity governs the heat transfer of sedi-mentary rocks and hence should be the basis for modelling effective thermal con-ductivity. By introducing Biot’s coefficient, α, we propose (1–α) as a measure of the solid connectivity and show how effective thermal conductivity of water saturated and dry sandstones can be modelled.

In this study, we show how milli-fluidic tools can be used to elaborate polymer foams with tunable microstructural parameters, such as the size and the connectivity of the pores. We produce several samples having the same density and the same monodisperse pore size but different values of the closure rate of the windows separating the foam pores, which is estimated by measuring the proportion of closed cells and the size distribution of apertures for open-wall cells. This distribution is based on a distinction between the windows counting four or less edges from the windows counting more than four edges. Then a representative unit cell is reconstructed to mimic the main feature of microstructure information and serves as the basis to the computation of the sound absorbing parameter, using numerical homogenization techniques. Very good correspondences between numerical results and experimental measurements were observed. Our analysis reveals a significant dependence of membrane level on the sound absorption behavior of these foams.

The paper describes the influence of the as-compacted state on air permeability of kaolin specimens. Air permeability was estimated using the gas pressure decay method. Two different compaction densities and three degrees of saturation were selected in this study to reproduce a wide range of initial soil fabrics. The experimental results show a strong influence of the as-compacted state on gas permeability. Mercury intrusion porosimetry tests, performed on ‘post-mortem’ specimens, have been used to estimate variations in pore size distribution. MIP results show the strong influence of the degree of saturation on the PSD which is reflected as well in different micro and macro void ratios (e_m and e_M). Preliminary results presented here do not show a unique relationship between air permeability with air void ratio and macro void ratio.

Modern interpretation of seismic surveys aims at going beyond structural characterization of reservoirs on the basis of the spatial distribution of velocity. In particular, hydraulic properties of fluid-filled reservoirs are of prime interest for hydrocarbon exploration or water-reservoir management. Such analyses require a physics-based understanding of the processes involved with the propagation of seismic waves in fractured rocks. The main objective of this work is the investigation of the hydro-mechanics of fluid-filled fracture networks and the related diffusion of fluid pressure in the conduits. We apply methods of computational homogenization to discuss an effective Skempton coefficient and analyze it for different setups in time as well as in frequency domain. In the first setup we investigate a modified version of Cryer’s problem embedding a spherical sample in a mantle of constant thickness. The kernel and the mantle constitute porous media but with different material properties. The second setup aims to investigate the hydro-mechanical properties of stochastically generated fracture networks. In both setups we apply Biot’s theory of linear consolidation. Evaluating the effective Skempton coefficient predicted by computational homogenization for those cases we can show limitations of previously performed laboratory measurements of the Skempton coefficient.

New poroelastic solutions for substitution of elastic properties of the frame mineral are derived. These accurately predict the change in rock stiffness (or seismic velocities) upon change in the frame mineral, assuming no change in microstructure or mineral volume fraction. With the aid of laboratory and numerical examples, we show that this technique can be applied to separate the effects of composition (mineralogy and pore-fill) on the rock stiffness from the effects of microstructure (i.e., porosity, pore shape). Upon application of the new mineral substitution technique on laboratory data, we find that the technique can be used to correct for the mineralogical bias on seismic velocities so as to analyze the effects of microstructure. This is important for many reservoir rocks, including limestones and dolomites. Using mineral substitution, we also analyzed the impact of change in mineralogy on Vp-Vs trends. We find that if the original minerals making up the sandstones are substituted with the calcite mineral, the newly predicted Vp-Vs trend for the modified sandstones is very similar to the previously known Vp-Vs empirical trends for limestones, and vice-versa. Therefore, we conclude that the Vp-Vs trends are generally dominated by mineralogy and the impact of microstructure on the Vp-Vs trends is relatively less significant. This technique can also be applied to predict Vp-Vs trends corresponding to rocks of mixed mineralogy, for which reliable core data are not often available.

Granular packing is one of the long-standing problems that have been studied for decades. Most of the current methods are trying to infer some statistical properties to describe and then regenerate a granular medium. These techniques, however, remain at the lower orders and cannot extract very complex information and, thus, they produce unrealistic models that are physically unlikely. The texture of the generated particles using these techniques are mostly different from the real sharpness of granular materials. In this paper, a new technique for direct modeling of granular materials (DGM) based on using high-order statistics is introduced that can extract more information and, finally generate very accurate models. This method, indeed, does not employ any particle descriptor and uses the existing 2D/3D images directly. The results indicate a very good agreement between the simulated and original data. The computational cost of this method is very low.

The paper presents a framework to include the effect of change of soil microfabric under load and suction changes on its hydro-mechanical response It is based on a new derivation of Bishop’s χ parameter from changes in pore size distribution proposed by Vaunat and Casini (2017), that proves to encompass the different proposal currently considered for Bishop’s effective stress. Use of Bishop’s parameter as a bi-directional coupling parameter expressing both the effect of partial saturation on material mechanical response and of volumetric strain on water retention curve allows to develop a fully uncoupled hydro-mechanical in the space of Bishop effective stress, corrected suction, volumetric strain and effective hydraulic strain, which naturally incorporate microfabric effect. Preliminary results show an encouraging capability of the model to predict material response under load and changes in suction.

A non-invasive technique for deriving permeability and porosity values for spinal cord tissue is described. Poroelastic models of the spinal cord are becoming increasingly important in a range of research areas such as drug delivery and disease. Physical properties of the spinal cord are difficult to obtain due to the complex nature of biological tissues. Neurite orientation dispersion and density imaging (NODDI) is a popular diffusion-weighted MRI technique designed to reveal the microstructure of central nervous system tissues. This microstructural information is used to calculate permeability and porosity values for spinal cord tissue. Permeability values for grey matter were found to be approximately ~2 × 10⁻¹³ m², whilst for white matter permeability values were in the region of ~5 × 10⁻¹⁴ m² perpendicular to tissue fibres and ~2.5 × 10⁻¹³ m² parallel to tissue fibres. Spinal cord permeability and porosity properties obtained are suitable for use in poroelastic models of the spinal cord.

Argillaceous rock is encountered in a variety of engineering circumstances such as civil engineering and petroleum engineering; a good understanding of the hydromechanical behavior of the involved rock is of crucial importance. However, characterization of this rock is challenging: it exhibits complex coupled thermo-hydro-chemo-mechanical behavior and a multi-heterogeneity, the description of which would strongly benefit from an improved experimental insight on their deformation and damage mechanisms at micro-scale. We propose here an experimental method for micro-scale characterization, consisting of in situ tests within the chamber of an environmental scanning electron microscope (ESEM), and quantification at micrometric scale of the induced local strains through analyzing high resolution imaging by digital image correlation techniques (DIC). On the basis of this method, the hydromechanical behavior of argillaceous rock can be investigated at their inclusion-matrix-composite microstructure: this scale is of particular interest because the complex matrix-inclusion interactions are a key mechanisms governing the deformation and damage of such rocks. We present some recent observations of the evolution of argillaceous rock subject to mechanical load, in particular the key role of the microstructure on its macroscopic behavior.

Structural anisotropy in peat is induced by the presence of fibres. This paper presents laboratory test results of the fibre effect in peat on pre-failure compression behaviour and failure modes originating from both tensile and compressive stresses supported by fibres. Furthermore, a hyperviscoplastic constitutive model for peat is extended to account for structural anisotropy. Undrained triaxial compression tests were carried out with vertical and horizontal undisturbed peat specimens. Additional oedometer tests on vertical and horizontal undisturbed peat specimens were used to compare the fibre effect on the failure mechanism of fibrous peat in undrained triaxial compression. The experimental results quantified the tensile and compressive effects of fibres in peat and also indicated that the strain softening in horizontal specimens resulted in the development of cracks rather than a mere buckling of fibres under compressive loads. The structural cross-anisotropy was modelled by extending a hyperviscoplastic model proposed for peat with a fibre layer characterized by a vector field.

The evaluation of mechanical properties is critical to the fracability analysis for hydraulic fracturing in shale reservoirs. This work provides a multiscale approach for the characterization and prediction of mechanical properties in shale. At the mineral scale, scanning electron microscopy (SEM) and nanoindentation are applied to measure Young’s modulus and hardness of different minerals and organic matter. At the core scale, microindentation is performed to investigate the mechanical behavior of shale samples. Besides, Mori-Tanaka model is applied to predict the macroscopic properties. At the well scale, conventional and advanced logs can help us collect porosity, mineral composition and organic matter content data. We utilize these data to estimate the mechanical properties of the stratum along the whole well via the prediction model. The results indicate that the prediction model agrees well with the experimental results. Furthermore, a new brittleness index (BI) based on the composition and the mechanical properties of each composition is proposed. This new BI has a similar trend with the macroscopic mechanical properties along the well, which also indicates that the approach presented here is effective for the fracability analysis for shale reservoirs.

This paper investigates mass transfer and sound propagation in permeo-elastic porous materials. The microstructure of this type of materials is composed of a connected fluid network saturated with a Newtonian fluid and a solid frame made of a stiff skeleton onto which highly-flexible thin films are fixed. Contrarily to the case of Biot poroelastic materials where the fluid flow is not affected by the deformation of the solid frame, the presence of the films can significantly modify the mass transfer of the fluid in permanent and harmonic regime. As a consequence of the fluid-film interaction, and in particular of the local fluid-film resonances, the acoustic behaviour departs from the classical physics leading to the Biot macroscopic description.

We present a nodal discontinuous Galerkin scheme for solving the poroelastic wave equation for materials saturated by one or two immiscible fluids. The presented wave equation is based on Biot’s theory and accounts for macroscopic flow. Using an example of a numerical simulation we show the existence of the third P-wave. The velocity and amplitude of this wave are significantly smaller than the velocities and amplitudes of the first and second P-wave. The numerical codes can be applied to various scientific questions related to unsaturated soils or rocks like exploration and monitoring of hydrocarbon or geothermal reservoirs or CO₂ storage sites.

Several mechanisms can cause wave attenuation and velocity dispersion in fluid-saturated fractured porous media comprising, on the one hand, pressure diffusion phenomena, such as fracture-to-background (FB) and fracture-to-fracture (FF) wave-induced flow (WIFF), and, on the other hand, dynamic effects, such as scattering and Biot global flow. In this study, we compare attenuation estimates from wave propagation simulations based on Biot’s dynamic equations with corresponding estimates from a numerical upscaling approach based on quasi-static poroelasticity. The former is able to capture all aforementioned attenuation mechanisms and their interplay, though detailed interpretations tend to be difficult. The latter only accounts for pressure diffusion phenomena and thus will be guiding the physical interpretation. We verify that the attenuation behavior caused by pressure diffusion due to FB WIFF is equivalent for both approaches. The results for FF WIFF are less conclusive. We also observe that scattering may be affected by pressure diffusion phenomena.

A combination of physical model tests and numerical analyses was utilized to study the effects of an explosion on an underground tunnel, located below a body of water. Strains induced on the tunnel because of the explosion were measured in centrifuge model tests conducted at 70 g. Three-dimensional numerical analyses using an explicit dynamic hydrocode were also conducted. The results of the numerical analyses showed favorable comparison with those from centrifuge model tests. The results indicated that, for the same mass of explosives, the damage to the tunnel increased with increasing height of water up to a certain maximum height. When the water level was increased beyond this height, the magnitude of damage remained relatively unchanged and did not appear to increase further.

Biot investigated wave attenuation and dispersion in a porous medium under laminar flow assumption. However, wave induced turbulent flow might occur in pores at frequencies higher than some threshold value. In this study, an oscillatory capillary turbulent flow model is developed to quantify the turbulent flow effect on wave attenuation and velocity dispersion in an isotropic porous medium. Prandtl’s mixing length theory, the hydraulic smooth pipe model and the viscous skin depth concept are combined to analyze the turbulent resistance in a pipe and its influences on overall dynamic properties. We obtain a fully analytic, frequency-dependent viscosity correction factor, which is then used to modify generalized Darcy’s formula for filtration under turbulence flow condition. The wave attenuation predicted by the modified model is greater than that predicted by Biot’s model when frequency is higher than a threshold frequency. Numerical calculations show that this model degenerates into the Biot model when the frequency is lower than the threshold frequency. The modified model has potential application in sound absorption and transmission in air saturated porous media.

The objective of the paper is the study of the influence of fluid saturation on guided and body wave propagation in two kinds of poroelastic waveguide structures: a multilayered half-space under dynamic surface load and a multi-domain coaxial cylindrical waveguide with a monopole source in the intratube fluid. The effect of additional guided wave emergence due to the fluid-saturation of interlayers have been revealed and studied in the both structures.

We analyze wave propagation in heterogeneous brittle materials modeled by a linear elastic body with micro-cracks. The problem is nonlinear due to the boundary conditions on the cracks, such as non-penetration and friction. A numerical upscaling homogenization technique and a discontinuous Galerkin space discretization method are applied to find the effective properties of the damaged material. The wave propagation (speed, amplitude and pulse length) of micro-cracked materials in configurations of varying complexity is studied. While theoretical and numerical wave velocities are found to be very close for small values of the crack density parameter, large values exhibit remarkable differences. Furthermore, we observe that amplitude and speed of the transmitted (damaged) wave are affected by its length when it is close to the length of the micro-cracks.

In this study, we propose a finite-difference (FD) algorithm for calculating the seismoelectric logging in a horizontally-stratified fluid-saturated porous formation and/or with a mud cake neighbouring the borehole. Without considering the negligible feedback influence of the seismic-wave-induced electric field, the seismic waves in the borehole, the mud cake, and the formation are calculated by the identical FD discrete formula for fluid, solid and porous media. And then the distribution of the induced electric potential is calculated at each discrete time by considering the known seismic field as the source of the electric field.

Seismic dispersion and attenuation are important attributes for the detection and characterization of saturated fractured formations. An important mechanism for this is the wave-induced fluid flow (WIFF) between the fractures and the host rock. While many theoretical models have been proposed to describe this mechanism, most of them have the assumptions of infinitesimal fracture thickness and dilute fracture concentration. Hence, in this work, we extend the model for the rocks with aligned penny-shaped cracks by considering the effect of finite fracture thickness and then test its validity by comparing with the numerical simulations. The results show good agreement between the theoretical prediction and the numerical simulations even under the relatively high fracture density. Furthermore, it is shown that the finite fracture thickness effect is small at low frequencies but significant at high frequencies.

In porous media, P-wave propagations may be associated to conversions of mechanical into electrical energy known as seismoelectric (SE) effects. SE phenomena may be expressed as a dynamic transfer function linking coseismic SE field (E) to seismic acceleration (ü) through numerous porous medium properties. To measure transfer function E/ü, we developed a laboratory experiment in unconsolidated sediment (quartz sand). Investigations focused on the impact of water saturation over the coseismic SE field. While varying saturation, the E/ü ratio experienced a switch in polarity at a particular saturation S* due to a mechanical coupling β, identified as the fluid/matrix relative displacement ratio. This particular behaviour at critical saturation S* appears to be a direct observation of Biot’s dynamic compatibility, causing the coseismic electric field to drop to zero in the absence of relative pore/fluid displacements. Hence the coseismic SE field, that allowed to electrically observe the signature of a poroelastic phenomenon, seems a relevant indicator of dynamically compatible states. In the meanwhile, the transfer functions could become a new tool for characterization of fluid distribution within pores.

Using our newly developed finite-element solution of the quasi-static frequency-domain poroelastic equations, we conduct compressibility tests on synthetic fractured rock samples to study P-wave attenuation and velocity dispersion related to wave-induced fluid flow (WIFF). Our algorithm allows to generate realistic stochastic fracture networks and to mesh them without any user-interaction. Experiments on sets of fracture networks randomly drawn from a power-law distribution show that attenuation due to WIFF between the fractures and the background shifts to lower frequencies with decreasing fracture density, because the average distance between the fractures increases. Furthermore, we observe that attenuation due to WIFF between connected fractures shifts to higher frequencies when the average fracture length decreases, because the average distance between a fracture tip and an intersection with another fracture decreases. Our results also show that attenuation increases in magnitude with increasing average fracture length. Finally, there is preliminary evidence to suggest that attenuation may decrease for percolating fracture networks.

Fluid-saturated fractured rock is well-known to exhibit a pronounced attenuation of elastic waves at low seismic frequencies due to the equilibration of wave-induced pressure gradients by pressure diffusion. At low seismic frequencies, the Poiseuille flow model results in a Darcy-type behavior for the pressure diffusion along the fractures. Moreover, it is reasonable to assume that pressure diffusion occurs on a length scale much smaller than the seismic wave length, and we, therefore, consider it as a local process. On the geological scale the material can then be interpreted as a viscoelastic medium. In the present contribution we aim to develop a computational homogenization scheme substituting the heterogeneous fractured medium by a homogeneous viscoelastic substitute model. We make use of the system’s linearity and derive a reduced order formulation for the upscaling problem. Hence, we detect a reduced basis for the fluid pressure field and superimpose the stress response due to transient external loadings. Altogether, the viscoelastic substitute model can be identified at reasonable numerical costs and can be validated by numerical simulations at full mesoscopic resolution.

We have simultaneously observed two distinct kinds of Biot’s compressional waves in air-filled dense glass bead packs under weak loading. The velocity of the sound wave propagating through the solid-frame increases with increasing the external load, while the velocity of the wave travelling through the saturating fluid remains constant. We find that this airborne wave, usually termed as slow wave, may propagate faster than the frame wave. These unusual results are shown to agree with the Biot theory in the weak-frame limit for high frequencies. The attenuation of the airborne wave increases when the air pressure is lowered.

In two well-know papers published in 1956 M. A. Biot developed a theory of acoustics in porous fluid-filled media which predicted the existence of two longitudinal/compressional waves, fast and slow, as well as a transverse/shear wave. The relevance of this theory to real materials was long discounted by many researchers because no one had observed two distinct compressional waves in any porous medium. This changed with the publication in 1980 of Plona’s seminal paper in which he reported fast and slow compressional waves, as well as the shear wave, in a number of man-made samples saturated with water. This result led immediately to an explosion in the understanding of acoustics in porous media, which I will review. Furthermore, this understanding led directly to the development of of a commercial service whereby the fluid flow resistance of an oilfield formation can be determined by means of acoustic measurements taken within the borehole.

This paper is concerned with the propagation of plane longitudinal waves in a liquid saturated porous medium with cavities. The wave energy dissipation in the medium is disregarded. Since non-linear stationary waves are of the greatest interest for the study, there are herein examined peculiarities of the propagation of periodic (cnoidal) waves and solitons in a porous medium with cavities. To simplify analysis, the dependencies of the equation are reduced to dimensionless form. The effect of system parameters is examined, in particular the size of the spherical cavities on the basic parameters of solitary waves at the wave amplitude and width. The results of which are compared with the classic behaviour of solitons. The influence of nonlinear periodic rate (cnoidal) waves on the amplitude and the wave number is analysed. The dispersion properties of system are also investigated, by analysing the behaviour of the dispersion curves depending on changes in certain system parameters.

In this paper we consider the propagation of elastic waves in gas-filled porous media at small but non-zero Knudsen numbers 0 < Kn ≤ 0.3 (the so-called slip regime). In this case, it is possible to apply the classic equations of hydrodynamics with modified boundary conditions. Here we consider the problem of modelling of oscillation of a system of gas-filled infinite cylindrical capillaries for the slip flow mode. We have obtained the expressions for drag and added mass coefficients for the Biot equations. We have found that drag coefficient and added mass depend considerably on the Knudsen number and accommodation coefficients. The influence of interfacial slip effect on the velocities of first kind compressional and shear waves is small, but the velocity and attenuation of the longitudinal wave of the second kind are considerably influenced by this effect. The results obtained show the fundamental possibility of solving the important inverse problem: the definition of the accommodation coefficient by measuring the velocity of longitudinal wave of the second kind for different values of gas pressure (or the Knudsen number).

In this proposal, we present a global sensitivity analysis method applied to the study of wave propagation occurring in a poroelastic material. The global aim is to get relevant information in the investigation of the most influential poroelastic parameters. A sensitivity analysis allows to quantify the impact of the input parameter uncertainties on the mechanical model outputs. The analysis is based on the calculation of the Sobol indices or the partial variances that quantify the influence of each independent parameters, but also the possible interactions between these parameters, on the simulated pore pressure or solid displacement fields. The Extended FAST method is handled in combination with an efficient forward solution. The configuration under study concerns a fluid overlying a poroelastic two-dimensional halfspace ground submitted to a transient excitation. A line source emits cylindrical waves. The problem is first solved analytically with the stiffness matrix method, to get a forward solution. Since the global sensitivity analysis is based on the repetition of numerous forward problems, these ones have to be efficient from the numerical point of view. Excitation type and receiver locations concern laboratory experiment simulations, of typical distance about 1 meter. A 10% uniform distribution of uncertainties has been taken into account. The same kind of approach can be applied in civil engineering, aquifer or soil auscultation, or biomechanics, involving larger typical dimensions or other uncertainty distributions. Moreover, this approach is part of a broader methodology that aims at constructing an inversion procedure involving only the parameters of interest. Four influential parameters have been identified in the specific studied configuration, ρS, μ, φ and K_F. The methodology is generic but the results are linked to the characteristics of the problem under study.

In this work an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is traversed by a pure SH wave, is derived. The considered model assumes a one-dimensional soil constituted by two homogeneous media in contact at the water table, and a shearing force located at the earth’s surface as the wave source. The model also considers that the electroosmotic feedback can be neglected in Biot’s equations, as it is usually assumed. The upper medium represents a partially saturated porous rock whose porous space contains the minimum amount of water, while the lower medium is completely saturated with water, representing the saturated zone. The analytical expressions for both electric and magnetic fields are analyzed for a hypothetical scenario. The main result shows that a sharp contrast in water saturation at the water table can induce strong interfacial responces in both fields.

The second bulk compressional (slow P-) wave is perhaps the most intriguing feature in the acoustics of fluid-saturated porous media. According to Biot’s theory the slow P-wave becomes a propagating wave mode in the so-called high-frequency range. Since its first experimental observation by Plona in 1980 using ultrasound it become soon clear that slow P-waves are hard to observe directly in porous media with complex internal structure. We argue that one reason for this low level of observability is that slow P-waves become partially localized (attenuated) in the high-frequency range due to the presence of viscous boundary layers. We model slow P-wave attenuation in the high-frequency range due to conversion scattering into the diffusive slow shear wave with the latter being a proxy for the vorticity diffusion within the viscous boundary layer.

We use Biot’s quasi-static equations to numerically simulate oscillatory compression tests on 3D models representative of laboratory samples. Simulations are performed on cylindrical models that have equally a total 99% water saturation but distinct fluid distributions; their curved boundaries are either open (drained) or closed (undrained). For undrained tests, a gradual change in water saturation with the sample length yields a frequency-dependent attenuation that reasonably agrees with laboratory data. Meanwhile, results for drained tests yield attenuation curves that are shifted by two orders of magnitude to higher frequencies. Our results indicate that the seismic attenuation observed in the laboratory was caused by pressure diffusion associated with a fluid saturation change within the sample and at the sample scale. They also indicate that flow out of the sample is unlikely to have occurred. This study provides useful insights for interpretation and quality control of attenuation measurements in fluid-saturated rock.

The paper deals with the modelling of dynamics and wave propagation in fluidsaturated periodic media with large contrasts in the permeability and other poroelastic coefficients. The effective behaviour is described using a model obtained using the homogenization of the heterogeneous Biot continuum relevant to the mesoscopic level at which the dual porosity is featured by low permeability, whereas the primary porosity is very compliant. All material coefficients of the homogenized model depend on the frequency of incident waves. Although this effect is low at the effective elasticity, it is more important at the Biot compressibility and the pressure-strain coupling coefficients. Numerical examples illustrate comparison between the standard single porosity and the proposed double porosity models.

We study here the propagation of nonlinear thermo-elastic transients in a thin boundary layer between two adjacent rocks. Attention is focused on convection and its effects on transients crossing such thin boundary. In early models this boundary was assumed to be a sharp,” mathematical” plane between the two rocks, but here we develop a more realistic view of such boundary. Therefore, we discuss a novel nonlinear model. It describes quick and sharp transients, which are characterized by a velocity drift and by amplitude variations. This model can be fruitfully applied also to volcanic, hydrologic, hydrothermal… systems and to deep oil drilling. Moreover we investigate the effect of a pressure dependent permeability in a very thin boundary, very similar to the above treatment but with a different “time” θ(t).

We here discuss a novel model of the dynamics of fluid pressure and fluid/rock temperature during extensional earthquakes, with application to the L’Aquila 2009 earthquake. We follow a recent interpretation of the dynamics of this system of faults, i.e. a main fault and a dilational band (formed during the interseismic period and antithetic to the seismogenic fault) finally causing the sudden fall of a suspended wedge. We focus on a non linear thermo-poro-elastic model, i.e. also considering the heat convection, of this system evolution, before and after the suspended wedge fall. We therefore obtain a novel model of the temperature and pressure evolution, along these two faults during the L’Aquila 2009 earthquake. A reasonable agreement with field data is discussed critically.

Biot theory considers wave propagation in a poroelastic solid saturated by a single-phase fluid. This paper generalizes the theory to the case of multiphase fluids including capillary pressure and relative permeability functions. To determine the constitutive relations, capillary forces are included as constrains using Lagrange multipliers in the virtual complementary work principle. The lagrangian equations of motion are formulated using multiphase Darcy’s law in terms of relative permeabilities. For two-phase fluids, a plane wave analysis shows the existence of three compressional waves (P1, P2, P3) and one shear (S) wave. For three-phase fluids, an additional compressional P4 wave exists. The numerical examples analyze the behavior of all waves in a saturated sandstone as function of saturation, frequency and wetting phase pressure. While the P1, P2 and S waves behave similar to those in the classical Biot theory, the P3 and P4 compressional waves are additional slow waves whose behavior is ruled by the motion of the non-wetting phases.

The acoustic properties of fractured hydrocarbon reservoirs vary with formation depth and pore pressure, with seismic velocity and attenuation being function of the effective pressure, the difference between confining and pore pressure. This work analyzes variations in velocity and attenuation in a Biot medium containing a dense set of aligned fractures due to changes in pore pressures. Fractures are modeled as boundary conditions imposing discontinuity of pore pressures and solid and fluid displacements along fractures. Using numerical experiments and for wavelengths much larger than the average fracture distance and aperture, it is possibly to determine a viscoelastic transversely isotropic (VTI) medium long-wave equivalent to the original fractured Biot medium. It is shown that velocity and attenuation of the equivalent VTI medium are noticeable sensitive to variations in pore pressure.

This work is about ultrasonic wave propagation in microstructured porous media. The classic Biot model is here enriched using a strain gradient approach to be able to capture high order effects when the wavelength approaches to the characteristic size of the microstructure. In order to reproduce actual transmission/reflection experiments performed on poroelastic samples, and to validate the choice of the model, the time domain response is necessary. In this paper, the time domain solutions are computed via the closed form solution and the finite element method. The effects introduced by the strain gradient terms are visible in the time response. The results can be exploited in the characterization of mechanical properties of poroelastic media by enhancing the reliability of quantitative ultrasound techniques.

Wave propagation phenomena occur in reality often in semi-infinite two-phase (porous) regions. Such problems can be handled well with the poroelastodynamic boundary element method (BEM). But, it is well known that the BEM with its dense matrices becomes prohibitive with respect to storage and computing time. This is especially true for poroelastodynamics, where in the best case four degrees of freedom (dofs) per node are required. Additionally to this efficiency problem also numerical problems occure due to the different physical nature of the matrix entries, which vary over several orders of magnitude. Last, the fundamental solution of poroelastodynamics is computationally expensive. A fast multipole BEM is proposed to circumvent those points. The Chebyshev interpolation-based FMM reduces the memory consumption to Ο(N log⁷N). As well, it requires fewer evaluations of the fundamental solution. To employ an iterative solver, the use of a transformation of the material data is mandatory. Numerical tests show the behavior of the proposed method.

In the present paper, a problem on the Rayleigh type surface wave at a traction free surface of a generalized porothermoelastic solid half-space is considered. The governing equations of generalized porothermoelastcity are specialized for x₁ − x₂ plane. The surface wave solutions in x₁ − x₂ plane are obtained which satisfy the required radiation conditions in porothermoelastic half-space. These solutions satisfy the boundary conditions at free surface of the half-space and a secular equation for wave speed of Rayleigh wave is obtained. The wave speed of Rayleigh wave is computed for an experimental data of water-saturated sandstone. The effects of porosity, frequency, thermal relaxation times, coefficients of thermal expansion and thermoelastic coupling are observed on the wave speed of the Rayleigh wave.

The elastic bulk modulus of a sandstone is affected by the fluid saturation as compression induces a pressure in the fluid thus increasing the bulk modulus of the sandstone as a whole. Assuming a uniform induced pressure and no interaction between the saturating fluid and the solid rock the fluid contribution to the elastic bulk modulus is quantified by Gassmann’s equations. Experimental measurements of the fluid contribution to the elastic moduli are, however often much larger than predicted within the assumptions of Gassmann. Clay-rich low-mobility sandstones are especially prone to having elastic moduli highly sensitive to the fluid saturation. The presence of clay in a sandstone can affect two of the underlying assumptions to Gassmann’s equations: decreased fluid mobility can cause pressure gradients and fluid-clay interactions are common. The elastic and petrophysical properties of clay are not well defined and the consequent parameter fitting makes both effects viable when modelling elastic moduli measured on fully saturated sandstones. To address this question, we conduct a thorough characterization of a suite of sandstones and measure their elastic moduli at different saturations. We supplement the data with low field NMR spectra at each saturation step to determine if any anomalous effects are associated with the fluid mobility and distribution in the pore-space. We find anomalous fluid contributions to the elastic moduli in sandstones with high clay contents. We also find that the anomalous fluid contributions are closely linked to the fluid distribution in the pore-space, meaning that pressure gradients associated with the presence of clay is more significant than fluid-clay interactions.

An analytical solution is presented for the effective shear modulus in a heterogeneous fluid-filled poroelastic medium containing spherical inclusions. Our model consists of three phases: a spherical inclusion, a shell of matrix material with different mechanical and/or hydraulic properties and an outer region of effective homogeneous medium of infinite extent. The behavior of the inclusion and the matrix is described by Biot’s equations, while the outer medium is regarded as an equivalent elastic or viscoelastic material with complex and frequency-dependent moduli to be determined. It is shown that for the double porosity structure (inclusions having a different solid frame than the matrix but the same pore fluid as the matrix), the mesoscopic-scale wave-induced fluid flow gives arise to a complex and frequency-dependent shear modulus. The mixed heterogeneity in the solid frame and pore fluid has important influences on the frequency-dependent shear wave attenuation.

We present a new model for elastic wave dispersion and attenuation in porous rocks saturated with viscous fluids and viscoelastic substances. The main idea is that the dispersion is mainly caused by frequency dependence of the normal and tangential stiffness of compliant pores that are hydraulically connected to stiff pores. First, we assume that the compliant pore (microcrack or grain-to-grain contact) is filled with an elastic solid. This allows us to obtain the stiffness of the compliant pore using a known solution of the elastic problem for a circular interlayer sandwiched between two parallel plates. The solution is then extended to viscoelastic pore fill using elastic/viscoelastic correspondence principle. The model predicts both, squirt-flow and viscous shear relaxation, and substantial increase in the rock rigidity with increasing frequency (or decreasing temperature) for rocks saturated with viscoelastic substances. The results are illustrated by an example of a typical rock saturated with water and with heavy oil.

The concept of frequency-dependent permeability is tracing back to various investigations in the last 60 years. Aim of the contribution is to review and discuss the basic modelling concepts beyond dynamic permeability and to compare modelling results derived from poroelasticity in the time-domain with well-known results in frequency-domain. We show that the basic sigmoidal character of dynamic permeability, i.e. a smooth transition from a viscous- to a inertia-dominated momentum coupling can be prescribed by classical poroelasticity. Results in dynamic permeability deviate only by a factor from the dynamic permeability function proposed by Johnson and coworkers.

Piezoelectric layers are embedded or surface bonded to composite materials to render self-sensing and actuation capabilities for various applications such as shape control, health monitoring and non-destructive evaluation/testing of materials. In comparison to monolithic piezoelectric materials, porous piezoelectric materials are preferred in some applications as to have enhanced acoustic impedance hydrostatic figure of merits and design flexibility. The scattering phenomenon of electro-elastic waves in a laminated porous piezoelectric plate sandwiched between two half spaces (elastic and dielectric) is investigated in this paper. The dispersion and reflection-transmission phenomena of shear horizontal waves, both for electrically open and shorted boundaries, are studied. The dispersion equations for particular cases, when half-spaces are considered as air or vacuum, are also studied. Three kind of unit cells forms i.e. PZT-5H, PZT-5H/PZT-7H and PZT-5H/Polythene/PZT-5H are considered for numerical computation and further investigations of the results. The effects of incidence, frequency, porosity, piezoelectricity and number of layers on the different dispersion modes and on the reflection and transmission coefficients are studied. The phase velocity is less in the case of polythene in comparison to that in vacuum while the number of modes remains the same. With the inclusion of porosity in the piezoelectric plate, the number of modes decreases. Simulated reflective spectra are also obtained. The SH waves in the multi layered composite plate are forbidden for the frequency in the band gaps. The number of stop bands and pass bands are also studied and are found to increase with the increase in the number of cells.

This paper investigates sound propagation in multiscale sorptive porous materials saturated with a pure gas. An example of this type of materials is a packing of porous grains where a mesoscopic, microscopic, and nanoscopic scale can be identified. These scales are associated with the grain size, and the micrometric and nanometric pores inside the grains, respectively. Assuming that the inner-grain and inter-granular viscous permeabilities are highly contrasted, the macroscopic description of sound propagation through the material is derived by upscaling a local mesoscopic description using the two-scale asymptotic method of homogenisation for periodic media. The local mesoscopic description is given by i) an homogenised model of the grains that accounts for fluid flow and heat conduction in the micropores, inner-grain interscale mass diffusion, and sorption occurring on the nanpore walls, ii) the equations describing the fluid flow and heat conduction in the mesoscopic fluid network, and iii) boundary conditions of continuity of mass flux and pressure, and of negligible temperature variations on the pore surfaces. It is concluded that the compressibility of the effective saturating fluid becomes significantly affected by sorption and interscale pressure and mass diffusion processes. This leads to a decrease in sound speed and an increase in sound attenuation, particularly around the characteristic frequencies associated with the diffusion processes.

Both fabric heterogeneity and patchy-saturation are the significant factors causing seismic wave dispersion and attenuation, and most previous studies on rock anelasticity focus on a single aspect of the two types of heterogeneities. In this work, we present a double double-porosity model which can model the overlapping effect of the two heterogeneities on wave dispersion and attenuation. Comparisons between experimental data in the siltstone sample and theoretical results show good agreements. The new theory allows for a comprehensive description of wave propagation process in the highly complex reservoir rocks.

The common algorithms for the interaction between the soil skeleton and the pore fluid pressure are based on the u-p element proposed by Zienkiewicz. These algorithms are mostly implicit and the inverse of singular matrix is solved frequently, which makes the computation time-consuming for dynamic analysis with many steps. In this paper, a simple 4-node quadrilateral plane-strain element for dynamic analysis of saturated porous media is presented. The pore pressure is taken not as a degree of node freedom but as a variable of central integration point, and a corresponding explicit algorithm based on the difference equations is proposed, which is more efficient than common implicit algorithm for dynamic problems. The drained and undrained boundary conditions are implemented in the permeable matrix. In order to verify the accuracy of this algorithm, several numerical examples are put on. The calculated results are compared with the numerical results of the other researchers. The comparisons demonstrate that this explicit algorithm is accurate. Finally, the dynamic analysis of an embankment is carried out as an example application.

We studied the brittle-ductile transition in three porous carbonates, Indiana, USA, Majella, Italy, and Leitha, Austria, with porosity ranging between 16 and 31%. A series of triaxial experiments were performed at room temperature, constant strain rate, and at effective pressures ranging from 5 to 150 MPa. Several sets of X-ray Tomography images were acquired before and after deformation. 3D digital image correlation (DIC) was performed on the images of the intact and deformed samples. The use of 3D-volumetric DIC allowed us to map out the subtle development of strain localization associated with the transition from brittle faulting to cataclastic flow in the three limestones. Our observations showed that strain localization may develop at relatively small axial strains of ~1%, in both the brittle faulting and transitional regimes. In Majella limestone (porosity = 31%), the localized deformation involved both shear and compaction. Compaction bands were only observed in less cemented samples of Leitha limestone.

Failure modeling of quasi-brittle materials in terms of continuum damage mechanics model and finite element approach is presented in this paper. A stress-based implicit gradient-enhanced damage model using low-order finite elements is developed in which the characteristic length is a stress level dependent parameter. A simple formula for the calculation of the characteristic length of failure localization in the spatial discretization of materials is also taken, which is to additionally suppress the sensitivity of geometrical meshes. The displacements and nonlocal equivalent strain fields are approximated in the framework of low-order finite elements, i.e., the same interpolation functions are used for both primary variables. The spurious damaged zones and stress oscillation induced by the standard strain-based gradient damage can be overcome by using the proposed damage approach. Quasi-brittle materials such as concrete and limestone are considered and some numerical examples with different configuration are examined. The obtained numerical results are analyzed and are validated against reference solutions including experimental data and other existing numerical approaches.

Some granular materials may exhibit stick-slip behaviour. In order to determine the factors leading to such instabilities, an experimental study was conducted and presented in this paper. The effects of particle size distribution, strain rate and confining pressure on stick-slip mechanism were investigated. Cylindrical specimens consisting of dry spherical glass beads were tested in triaxial compression. The results show that particle size distribution of spherical glass beads has a strong effect on stick-slip behaviour. Frequency of slip cycles is greater for the samples including wider range of particle sizes than that of relatively monodisperse ones. It was also observed that, as the strain rate was increased, deviatoric stress amplitudes generally decreased. However, the oscillation amplitudes seem to be less sensitive to strain rate changes. The effect of confining pressure on stick-slip behaviour is also considerable. When the confining pressure is increased, both the deviatoric stress amplitude and the oscillation amplitude increase.

This paper reports the dynamic instabilities of model granular materials under isotropic consolidation and triaxial drained axisymmetric compression. Loose and fully saturated samples of mono sized glass beads exhibit in isotropic drained compression a series of local collapses under undetermined stress and even liquefaction in some rare cases. Stick-slip phenomenon occurs in drained compression, and even rare liquefaction happens for the first slip. These dynamic instabilities (collapse, liquefaction and stick-slip) of loose granular assembly can share the same physical driving mechanisms with strong links to geometrical features, i.e. the collapse of the structural metastable honeycombed macropores or the propagation of the local failures of the force chains; even if the unambiguous identification of the triggering mechanisms is still unknown. The experimental data eliminates the excess pore fluid as the primary cause.

The slow movement of rock can be modeled by non-Newtonian viscous flow which developing quasi exponentially after reaching of the yield strength. This flow closer to the ideal plasticity rather than to the Newtonian viscosity and in the limit can be considered as viscoplastic current. Was studied the bifurcation of the uniform flow of viscoplastic medium with internal dry friction. The condition when the disturbed flow equations lose ellipticity was found. It is shown that the adjacent flow forms can be realized in the form of linear or cell structures. It is shown that increase of pore pressure reduces the instability interval of flow velocity.

The formation of shear-enhanced compaction bands is of interest for various geological reservoir applications such as energy storage, geothermal energy production or enhanced oil recovery. These localized features can indeed have great impacts on the transport properties of reservoir rocks and therefore on the reservoir productivity. In this study, we report experimental and numerical results aiming at identifying and quantifying the processes responsible for localization of deformation and their impacts on porosity evolution. Axial loading experiments in a triaxial setting at three different confining pressures were conducted on Bentheim sandstone with continuous porosity measurements. In a second step, the experimental results were used as constraints for numerical modeling using a Drucker-Prager yield criterion with data-derived hardening and softening rules.

Saturated porous materials can be abstractly simplified as homogeneous two phase media. In the two phase media, the displacements and micro rotations of skeleton particles as well as the pore pressure are assumed as basic unknowns in the finite element discretized equations. A coupled fluid-solid elastoplastic model has been implemented within the framework of micro-polar theory using ABAQUS which provides users an interface to define a new element (UEL) in this article. From the numerical simulated results of biaxial tests, it is shown that the nearly unique finite thickness of shear bands and similar load-displacement curves can be obtained regardless of different mesh sizes; larger rotations of particles in the shear band region are observed obviously, which can explain clearly the occurrence and development of shear bands; incompressible fluid in saturated porous material can affect significantly the peak load carrying capacity, at the same time the occurrence of shear bands is delayed compared with single solid phase media.

Calibration and validation of constitutive models and numerical modeling techniques used in analysis of soil liquefaction and its effects are often based on extensive comparisons with the results of element tests and centrifuge experiments. While good quality experimental data are available to understand and quantify the stress-strain-strength response of liquefiable soils in monotonic and cyclic drained/undrained element (triaxial and direct simple shear) tests, the results of these experiments are often less repeatable when the soil approaches liquefaction state and relatively large deviatoric strains suddenly develop within a few cycles of loading. The main source of these less repeatable patterns of soil behavior appears to be instability rather than the attainment of a state of material failure. The goal of this paper is to investigate the role of instability on the stress-strain response of liquefiable soils by using a critical state sand plasticity model that is enriched with an internal length scale representing the potential shear bands that may develop during monotonic or cyclic loading conditions. Through a series of numerical simulations, it is shown that the global stress-strain response measured in the element tests is a good approximation of the soil constitutive response before an unstable condition such as shear banding or liquefaction develops in the soil specimen.

In this work, the stability of radial jet drilled (RJD) laterals in both injection and production wells are studied. Thermo-elastoplastic and poro-elastoplastic finite element models are developed in a robust software (ABAQUS) and used to simulate the injector and producer laterals. Several cases with varying in situ stresses are considered. The temperature and pressure gradients of 60°C and 10 MPa are applied. The simulation results show that both hydraulic and thermal stresses can affect the stability of a lateral by increasing the plastic region near the lateral. The thermal effect increases the plastic region around the producer, while the hydraulic effect increases the plastic region and its magnitude at the producer.

Frictional heating has long been considered as a mechanism responsible for the high velocities and long run-out of some large-scale landslides. In the shear zone, complex processes such as heat production and diffusion, pore-fluid pressure generation and dissipation, and soil skeleton deformation are coupled to each other. However the amount of heat produced by frictional heating is closely related to the relevant velocity in the shear zone. In this work, different vertical velocity profiles in the shear zone are used in the thermo-poro-elastic modeling of landslides. Their influences on heat production and diffusion process as well as pore pressure evolution have been analyzed. The results show that velocity profiles influence the generation of heat, hence the pore pressure profiles in the shear zone, which may lead to different sliding behaviors of landslides.

In this paper, a fault zone is modelled as a saturated infinite layer under shear. In order to study the stability of this layer under undrained adiabatic shear and access to the shear localization thickness, a Cosserat continuum is used. Furthermore, thermo-hydro-mechanical (THM) couplings are considered. In particular, we show the strong influence of the thermal expansions and compressibilities of the skeleton and water on the bifurcation state and the thickness of the localized zone of deformation. The results for the shear band thickness are compared with field observations and finite element (FE) analyses and show a good agreement.

This paper presents a finite element analysis of non-isothermal elasto-plastic multiphase geomaterials in dynamics including frictional heating generation. A fully coupled mathematical model is developed within the Hybrid Mixture theory. A computationally efficient reduced formulation is derived following the u-p-T approach. Two strain localization problems are simulated. The first one is a plain strain compression test of globally undrained water saturated dense sand. The second test concerns a rapid strain localization example inspired by the Vajont landslide. The numerical results show that cavitation occurs at strain localization in the first test and the frictional heating increases slightly the temperature in the shear band, anticipating the onset of cavitation in comparison with the case neglecting the heating generated by friction. The second numerical test shows a temperature increase in the shear band much higher than the boiling temperature of the liquid water, with consequent formation of a vapor cushion and loss of shear strength. These simulations show that frictional heating generation may have a role in dynamic strain localization, in particular during the development of rapid catastrophic landslides.

It is well known that classical continuum models for softening materials suffer from stability issues that lead to mesh dependent numerical solutions and their regularisation is needed for the analysis of boundary value problems. In this work, a Perzyna’s type viscous regularisation was applied to a plasticity model for use with the smoothed particle hydrodynamics (SPH) to analyse strain localisation in porous geomaterials. The proposed approach was first verified against an analytical solution for a plane strain compression test and then employed for the investigation of size dependent effects in localised failure of geomaterials. It is found that the proposed SPH-based approach, combined with visco-plastic constitutive relation, is an effective and simple way to capture both the onset and post-localisation behaviour.

The characterization, modeling and production of many carbonate reservoirs pose significant challenges due to multiscale geological heterogeneities resulting from the combination of sedimentary and diagenetic processes. This paper proposes an integrated geological, petrophysical and petroacoustic workflow designed to derive correlations between the petrophysical and petroacoustic signature of key reservoir facies and their microstructure. The ultimate objective of this workflow is to provide a reservoir model populated with petrophysical and petroacoustic properties consistent with geological description. First results obtained on a well-preserved Oligo-Miocene succession of mixed carbonate–siliciclastic facies outcropping in the South-East of France have been used as a guiding line to discuss the successive workflow steps and their interrelations.

We present recent argon gas permeability experiments conducted in a partially fractured Eagle Ford Shale sample using the transient pulse decay method at in-situ stress conditions. Permeability decreases by almost an order of magnitude while cycling the confining pressure (P_c) between 27.6 to 51.6 MPa at a constant pore pressure (P_p) of 14.4 MPa. Most of the permeability decrease is within the first loading and unloading cycle. Three subsequent P_c cycles show only a marginal decrease in permeability (less than 10% variation between the start and the end of each cycle). We interpret that the permeability loss is due to the closing of micro-fractures in the rock caused by stress-relief during sample retrieval from the subsurface and/or during the sample preparation process. Permeability of the sample after three P_c cycles varies between 18 and 37 nD (1nD ≈ 10^-21 m²), depending on the effective stress (P_c – P_p), and follows a power-law-type relationship. The permeability at the lowest P_c – P_p, where we observed a persistent dual-timescale pressure response behavior indicating dual permeability structure, is approximately an order of magnitude higher than our intact Eagle Ford samples. We interpret that the higher permeability is mainly due to partial closure of a pre-existing fracture that extends nearly half the sample length. We next explore the permeability behavior of this sample under different P_c and P_p conditions to examine their relative effect on permeability. The preliminary results suggest that the effective stress coefficient for permeability (n_k) is close to 1, slightly higher than our intact Eagle Ford samples (0.7 to 0.9 ± 0.2). This is significantly different from the values reported in literature for Eagle Ford Shale. A more thorough understanding of how permeability changes with confining stress and pore pressure evolution will help to inform optimal production strategies for the gas shale reservoirs.

While cutting metals is a well-studied problem, rock cutting due to its inherent complexity and more complicated physics due to its granular structure is less-known. The substantial role of the pore fluid pressure and confining pressure in the cutting process is one of these differences that may surface in practical engineering problems especially in deep subsurface drilling. Two sets of experiments were conducted in this research using single polycrystalline diamond compact (PDC) cutters. Regular scratch tests conducted in atmospheric pressure on Carthage Marble were compared with scratch/cutting tests performed under pressure. Finite element analysis (FEA) is then carried out to determine failure parameters by match lab measurement to investigate any potential changes in rock failure properties. It has been observed that pressurized conditions as low as 250 psi may convert the cutting process from intuitive fracture initiation and coalescence phenomenon to rock scooping. More ductile failure, formation of cutting ribbons and the size of cracks are some of these characteristics which are not observed in low confining pressures.

This paper considers the plane strain problem of a hydraulic fracture propagating in a poroelastic medium, as a result of injection of fluid from a well. It describes an asymptotic solution that is applicable provided that four conditions are met: (i) the material toughness is negligible; (ii) the viscosity of the injected fluid is similar to that of the native pore-fluid; (iii) the medium has a large permeability relative to the fracture conductivity; and (iv) the injection rate is small enough that the fracture propagates inside the growing region around the well, where the pore pressure field is quasi-stationary. If these conditions are met, the fracture propagates stably in a self-similar manner, with its length and aperture growing as square root of time. Because the fracture remains in the quasi steady-state region, poroelastic effects are fully developed and significantly impact crack growth.

Reservoir stress changes associated with pore-pressure depletion are wellknown to have significant impact on permeability in reservoirs with abundant natural fractures. In most fractured reservoirs depletion induces increases of effective stresses and therefore a decrease in permeability. However, some reservoirs that accommodate significant amounts of gas adsorbed in organic micropores in the rock matrix can manifest opposite trends with increases in permeability during depletion. This permeability enhancement occurs due to stress relaxation and opening of fractures induced by rock matrix shrinkage during gas desorption. Additionally, pore pressure drawdown results in increased stress anisotropy potentially leading to reactivation of criticallyoriented fractures and shear failure. Fracture and rock matrix depletion have different time scales which depend on fracture permeability, rock matrix permeability, surface area of fractures in contact with the rock matrix, and fracture connectivity among others. The objective of this paper is to present a FEM solution of a double-porosity coupled poromechanical model that discriminates fracture pressure and rock matrix pressure and accounts for desorption-induced stresses. The results of the study show that implications from desorption such as gas production and stress relaxation can be significantly delayed with respect to fracture depletion, and therefore, wellhead pressure. We highlight the importance of multiple-porosity approach in calculating the timing of sorption stresses, which is crucial when modeling production in stress-sensitive unconventional reservoirs.

Organic-rich shale reservoirs contain substantial amounts of hydrocarbons. Because of extremely low matrix permeability, they require special treatments such a slick-water hydraulic fracturing. Many shale reservoirs accommodate a significant amount of carbonates, minerals that can be easily dissolved in acid solutions suggesting acid hydraulic fracturing as an enhanced-recovery stimulation technology. Calcite and dolomite in shales can be either embedded into the rock matrix or deposited and localized within natural fractures (so-called veins). In this study we focus on: the effect of carbonate veins dissolution on post-fracturing stresses and the effect of mineral dissolution at the tip on fracture propagation. Reactive transport and mechanics are solved using a FEM-based formulation. Fracture propagation is modeled using the phase-field approach. We propose to link the phase-field variable that usually represents rock damage due to creation of fractures also as an indicator of the damage related to mineral dissolution. Experimental evidence is used to validate developed models. Results indicate that the phase-field variable acts as a diffusive zone and therefore can be assimilated as a mineral dissolution front in predicting fracture propagation. After acid leak-off, the dissolution of mineralized natural fractures can result in stress relaxation and potentially to shear failure within the reservoir. Overall, the results show that combining mineral dissolution and hydraulic fracturing can offer new approaches to hydraulic fracturing.