Modelling chemo‐hydro‐mechanical behaviour of unsaturated clays: a feasibility study

Effective capabilities of combined chemo‐elasto‐plastic and unsaturated soil models to simulate chemo‐hydro‐mechanical (CHM) behaviour of clays are examined in numerical simulations through selected boundary value problems. The objective is to investigate the feasibility of approaching such complex material behaviour numerically by combining two existing models. The chemo‐mechanical effects are described using the concept of chemical softening consisting of reduction of the pre‐consolidation pressure proposed originally by Hueckel (Can. Geotech. J. 1992; 29 :1071–1086; Int. J. Numer. Anal. Methods Geomech. 1997; 21 :43–72). An additional chemical softening mechanism is considered, consisting in a decrease of cohesion with an increase in contaminant concentration. The influence of partial saturation on the constitutive behaviour is modelled following Barcelona basic model (BBM) formulation (Géotech. 1990; 40 (3):405–430; Can. Geotech. J. 1992; 29 :1013–1032). The equilibrium equations combined with the CHM constitutive relations, and the governing equations for flow of fluids and contaminant transport, are solved numerically using finite element. The emphasis is laid on understanding the role that the individual chemical effects such as chemo‐elastic swelling, or chemo‐plastic consolidation, or finally, chemical loss of cohesion have in the overall response of the soil mass. The numerical problems analysed concern the chemical effects in response to wetting of a clay specimen with an organic liquid in rigid wall consolidometer, during biaxial loading up to failure, and in response to fresh water influx during tunnel excavation in swelling clay. Copyright © 2005 John Wiley & Sons, Ltd.     

A coupled chemo‐thermo‐hygro‐mechanical model of concrete at high temperature and failure analysis

A hierarchical mathematical model for analyses of coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible–miscible levels. The thermo‐induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo‐thermo‐hygro‐mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non‐self‐adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes subjected to fire and thermal radiation. Copyright © 2005 John Wiley & Sons, Ltd.     

Formulation of a three‐dimensional rate‐dependent constitutive model for chalk and porous rocks

Rate‐dependent behaviour of chalk and other porous rocks has undergone widespread study in geomechanics due to its implications on the performance of engineering structures. We present a rate‐dependent constitutive model for chalk and other porous rocks with several new features. The model formulation is based on a viscoplastic rate‐lines approach in which the axial strain rate depends on the proximity of the stress point to an elliptical reference surface. A non‐associated viscoplastic potential surface and an axial scaling algorithm are used to determine the viscoplastic strain components. The model predicts that axial yields stress varies as a power function of applied axial strain rate, as shown by published laboratory data. Comparisons with published experimental data indicate that the model is capable of reproducing observed rate‐dependent behaviour of chalk under a variety of loading conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

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

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

A constitutive model for mechanical and chemo‐mechanical compaction in sedimentary basins and finite element analysis

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

A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation

The mechanical behaviour of bonded geomaterials is described by means of an elastoplastic strain‐hardening model. The internal variables, taking into account the ‘history’ of the material, depend on the plastic strains experienced and on a conveniently defined scalar measure of damage induced by weathering and/or chemical degradation. For the sake of simplicity, it is assumed that only internal variables are affected by mechanical and chemical history of the material. Despite this simplifying assumption, it can be shown that many interesting phenomena exhibited by weathered bonded geomaterials can be successfully described. For instance, (i) the transition from brittle to ductile behaviour with increasing pressure of a calcarenite with collapsing internal structure, (ii) the complex behaviour of chalk and other calcareous materials in oedometric tests, (iii) the chemically induced variation of the stress and strain state of such kind of materials, are all phenomena that can be qualitatively reproduced. Several comparisons with experimental data show that the model can capture the observed behaviour also quantitatively. Copyright © 2003 John Wiley & Sons, Ltd.     

Creep of saturated materials as a chemically enhanced rate‐dependent damage process

Material behaviour that exhibits characteristics of creep induced by a spontaneous mineral dissolution enhanced by material damage is studied. It is believed that the characteristic rates of the chemical processes involved determine the time‐rate dependence of the resulting strain. A basic model of a combined chemo‐plastic softening and chemically enhanced deviatoric strain hardening for saturated geomaterials is presented. Chemical softening is postulated to occur as a consequence of the net mass removal resulting from dissolution and precipitation of specific minerals occurring at the damage‐generated inter‐phase interfaces. Closed and open systems are discussed. In the former case, deformation at constant stress results entirely from a local compensation mechanism between the chemical softening and strain hardening. The classical three stages of creep are interpreted in terms of mechanisms of dissolution and precipitation, as well as the variation in the reaction surface areas involved in the mass exchange. In an open system, the above local mechanism is enhanced by the removal of mass via diffusion of species affecting the mass balance. Such a system is addressed via a boundary value problem as shown in an example. Copyright © 2007 John Wiley & Sons, Ltd.     

Mechanical behaviour of Lixhe chalk partly saturated by oil and water: experiment and modelling

Two or more different fluids generally saturate chalk in oil reservoir, and therefore its behaviour can be very complicated. In this paper, a constitutive law is proposed for modelling the mechanical behaviour of a chalk saturated by two non‐miscible fluids, water and oil. The effects of the capillary pressure or suction are taken into account. They are considered as an independent variable, as in the Barcelona's basic model developed for unsaturated soils. On the other hand, internal friction and pore collapse are modelled as independent mechanisms. The determination of the parameters is based on triaxial and oedometer tests. Finally, in order to validate the model, predictions are compared with experimental results of water‐flooding test. Copyright © 2002 John Wiley & Sons, Ltd.     

Laminated–bioturbated cycles in Maastrichtian chalk of the North Sea: oxygenation fluctuations within the Milankovitch frequency band

The Maastrichtian chalk of the southern Central Graben, Danish North Sea, is a homogeneous pure white coccolithic chalk mudstone deposited in a deep epeiric shelf sea, which covered large parts of northern Europe. The sediment displays a pronounced cyclicity marked by decimetre‐thick bioturbated beds alternating with slightly thinner non‐bioturbated, mainly laminated beds. The laminated half‐cycles consist of alternating millimetre‐thick, graded, high‐porosity laminae and non‐graded, low‐porosity laminae. The cyclicity has been interpreted previously as caused by periods of slow background sedimentation and bioturbation interrupted by periods of rapid deposition of laminated beds, with the latter reflecting random and local resedimentation processes. Based on textural and structural analysis, the millimetre‐scale, non‐graded laminae are interpreted as having been deposited directly from pelagic rain of pelleted coccoliths representing the primary production. The graded laminae were deposited from small‐volume, low‐density turbidity currents and suspension clouds. The sedimentation rates of the cyclical chalk are similar to those known elsewhere, and the lamination is interpreted as having been preserved from destruction through bioturbation by anoxic conditions at the seafloor. Bioturbated–laminated cycles are thus formed by slow sedimentation during alternating seafloor redox conditions probably on a Milankovitch scale. A direct implication of this interpretation is that the cycles are areally widespread, probably extending throughout the southern Central Graben area and may be useful for correlation and high‐resolution cyclostratigraphy in the chalk fields of the Danish North sea. If the laminated half‐cycles represent a few rapid resedimentation events, with a high sedimentation rate as suggested by most workers, then the sediment would not be truly cyclic, but would represent event sedimentation within a pelagic background represented by the bioturbated beds. In this case, the cycles would have very limited potential for correlation.     

Responses of chemically active and naturally fractured shale under time‐dependent mechanical loading and ionic solution exposure

In this paper, the analytical dual‐porosity dual‐permeability poromechanics solution for saturated cylinders is extended to account for electrokinetic effects and material transverse isotropy, which simulate the responses of chemically active naturally fractured shale under time‐dependent mechanical loading and ionic solution exposure. The solution addresses the stresses, fracture pore pressure, matrix pore pressure, fluid fluxes, ion concentration evolution, and displacements due to the applied stress, pore pressure, and solute concentration difference between the sample and the circulation fluid. The presented solution will not only help validate numerical simulations but also assist in calibrating and interpreting laboratory results on dual‐porosity dual‐permeability shale. It is recommended that the analytical solutions of radial and axial displacements be used to match the corresponding laboratory‐recorded data to determine shale dual permeability and chemo‐electrical parameters including membrane coefficient, ions diffusion coefficients, and electro‐osmotic permeability.     

Steady‐state analytical solutions of flow and deformation coupling due to a point sink within a finite fluid‐saturated poroelastic layer

An exact steady‐state closed‐form solution is presented for coupled flow and deformation of an axisymmetric isotropic homogeneous fluid‐saturated poroelastic layer with a finite radius due to a point sink. The hydromechanical behavior of the poroelastic layer is governed by Biot's consolidation theory. Boundary conditions on the lateral surface are specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of the governing equations. Ordinary differential equations in the transformed domain are solved, and then the analytical solutions in the physical space for the pore pressure and the displacements are finally obtained by using finite Hankel inversions. The analytical solutions at some special locations such as the top and bottom surfaces, lateral surface, and the symmetrical axis are given and analyzed. And a case study for the consolidation of a water‐saturated soft clay layer due to pumping is conducted. The analytical solution is verified against the finite element solution. Meanwhile, an analysis of coupled hydromechanical behavior is carried out herein. The presented analytical solution is an exact solution to the practical poroelastic problem within an axisymmetric finite layer. It can provide us a better understanding of the poroelastic behavior of the finite layer due to fluid extraction. Besides, it can be applied to calibrate numerical schemes of axisymmetric poroelasticity within finite domains. Copyright © 2017 John Wiley & Sons, Ltd.     

Micromechanical viscoelasto‐plastic models and finite element implementation for rate‐independent and rate‐dependent permanent deformation of stone‐based materials

This paper presents parallel and serial viscoelasto‐plastic models to simulate the rate‐independent and the rate‐dependent permanent deformation of stone‐based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto‐plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement‐based incremental formulation for the viscoelastic part and an elastic predictor—plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto‐plastic model employed a viscoelastic predictor—plastic corrector algorithm. The stone‐based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto‐plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto‐plastic matrix models. The simulation results showed that the serial viscoelasto‐plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto‐plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate‐independent and rate‐dependent viscoelasto‐plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto‐plastic behaviors of the stone‐based materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Fast planar slides. A closed‐form thermo‐hydro‐mechanical solution

Heat‐induced excess pore pressures on the failure surface of a planar slide have been calculated by solving the mass and heat balance equations on the shear band. The set of differential equations and the equation of motion of the slide have been solved in closed form for the case of incompressible fluid and incompressible soil skeleton. The solution describes the accelerated motion of the slide. It has been compared with the numerical solution when soil and water stiffness terms are not disregarded. A case study, based on a well‐known translational slide (Cortes slide) has been solved. Numerical and analytical solutions are compared. Results of a sensitivity analysis indicate that the permeability of the shear band is the key parameter to control the onset of a rapid motion. For a band permeability above a threshold value, in the vicinity of 10^?15m² (10^?8m/s), fast accelerated motions are very unlikely. Copyright © 2009 John Wiley & Sons, Ltd.     

Hydro‐mechanical erosion models for sand production

Sand production is a complex physical process that depends on the external stress and flow rate conditions as well as on the state of the material. Models developed for the prediction of sand production are usually solved numerically because of the complexity of the governing equations. Testing of new sand production models can very well be performed through calibration with laboratory experiments, which by construction possess geometric symmetry facilitating explicit mathematical analysis. We introduce an erosion model that is built upon the physics (poro‐mechanical coupling of the fluid‐solid system) usually incorporated in erosion models for the prediction of sand production. Around this model, we set up a mathematical framework in which sand production models because of erosion can be tested and calibrated without having to resort to complex numerical work or specialised software. The model is validated by data of volumetric sand production from a hollow cylinder test on synthetic sandstone. Generalisations of the model, which are naturally incorporated in the same framework and have useful phenomenological features, are discussed. Copyright © 2015 John Wiley & Sons, Ltd.     

Poro‐elasto‐plastic response of an unconsolidated formation confined with stiff seal rocks under radial injection

In this article, we evaluate geomechanics of fluid injection from a fully penetrating vertical well into an unconsolidated formation confined with stiff seal rocks. The coupled behavior of an isotropic, homogeneous sand layer is studied under injection pressures that are high enough to induce plasticity yet not fracturing. Propagation of the significant influence zone surrounding the injection borehole, quantified by the extent of the plastic domain in the elasto‐plastic model, is examined for the first time. First, a new fully coupled axisymmetric numerical model is developed. A comprehensive assessment is performed on pore pressures, stresses/strains, and failure planes during the entire transient period of an injection cycle. Results anticipate existence of five distinctive zones in terms of plasticity state: liquefaction at wellbore; two inner plastic domains surrounding the wellbore, where failure occurs along two planes and major principal stress is in vertical direction; remaining of the plastic domain, where formation fails along one plane and major principal stress is in radial direction; and a non‐plastic region. Failure mechanism at the wellbore is found to be shear followed by liquefaction. Next, a novel methodology is proposed based on which new weakly coupled poro‐elasto‐plastic analytical solutions are derived for all three stress/strain components. Unlike previous studies, extension of the plastic zone is obtained as a function of injection pressure, incorporating plasticity effects on the subsequent elastic domain. Solutions, proven to be a good approximation of numerical simulations, offer a huge advantage as the run time of coupled numerical simulations is considerably long. Copyright © 2016 John Wiley & Sons, Ltd.     

Modelling of coupled fluid‐mechanical problems in fractured geological media using enriched finite elements

Geological environments, such as petroleum reservoirs, normally exhibit physical discontinuities, for example, fractures and faults. Because of the reduced thickness of these discontinuities, finite element formulations with strong discontinuity have been applied to the numerical modelling of geological environments. Until now, two relevant characteristics of petroleum reservoirs have not been addressed by these formulations. The first is the pore pressure jump in the direction normal to a discontinuity in a fluid‐mechanical coupling condition, which is present primarily in sealing faults owing to the contrast of permeability with the porous medium. The absence of this jump can affect the prediction of the deformability of a physical discontinuity. Furthermore, reservoir models frequently use coarse meshes. Thus, the method used to evaluate the pore pressure in the discontinuity may exhibit a strong dependence relative to the mesh refinement. Based on these characteristics, in this study, a formulation of an enriched finite element for application to coupled fluid‐mechanical problems with pre‐existing physical discontinuities saturated by a single fluid is presented. The formulation employs discontinuous interpolation functions and enables the reproduction of jumps of displacement and pore pressure associated with a discontinuity inside the element without the need to discretise it. An approximation to estimate the pore pressure in the discontinuity was developed, one which seeks to minimise the influence of refinement. The element's response is verified by comparison with a one‐dimensional analytical solution and simple examples that are simulated using commercial software. Copyright © 2015 John Wiley & Sons, Ltd.     

On finite volume method implementation of poro‐elasto‐plasticity soil model

Accurate prediction of the interactions between the nonlinear soil skeleton and the pore fluid under loading plays a vital role in many geotechnical applications. It is therefore important to develop a numerical method that can effectively capture this nonlinear soil‐pore fluid coupling effect. This paper presents the implementation of a new finite volume method code of poro‐elasto‐plasticity soil model. The model is formulated on the basis of Biot's consolidation theory and combined with a perfect plasticity Mohr‐Coulomb constitutive relation. The governing equation system is discretized in a segregated manner, namely, those conventional linear and uncoupled terms are treated implicitly, while those nonlinear and coupled terms are treated explicitly by using any available values from previous time or iteration step. The implicit–explicit discretization leads to a linearized and decoupled algebraic system, which is solved using the fixed‐point iteration method. Upon the convergence of the iterative method, fully nonlinear coupled solutions are obtained. Also explored in this paper is the special way of treating traction boundary in finite volume method compared with FEM. Finally, three numerical test cases are simulated to verify the implementation procedure. It is shown in the simulation results that the implemented solver is capable of and efficient at predicting reasonable soil responses with pore pressure coupling under different loading situations. Copyright © 2015 John Wiley & Sons, Ltd.