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 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.     

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.     

Chemical and physical responses to deformation in micaceous quartzites from the Tauern Window, Eastern Alps

Micaceous quartzites from a subvertical shear zone in the Tauern Window contain abundant quartz clasts derived from dismembered quartz‐tourmaline veins. Bulk plane strain deformation affected these rocks at amphibolite facies conditions. Shape changes suggest net shortening of the clasts by 11–64%, with a mean value of 35%. Quartz within the clasts accommodated this strain largely via dislocation creep processes. On the high‐stress flanks of the clasts, however, quartz was removed via solution mass transfer (pressure solution) processes; the resulting change in bulk composition allowed growth of porphyroblastic staurolite + chlorite ± kyanite on the clast flanks. Matrix SiO₂ contents decrease from c. 83 wt% away from the clasts to 49–58% in the selvages on the clast flanks. The chemical changes are consistent with c. 70% volume loss in the high‐stress zones. Calculated shortening values within the clast flanks are similar to the volume‐loss estimates, and are greatly in excess of the shortening values calculated from the clasts themselves. Flow laws for dislocation creep versus pressure solution imply large strain‐rate gradients and/or differential stress gradients between the matrix and the clast selvages. In a rock containing a large proportion of semirigid clasts, weakening within the clast flanks could dominate rock rheology. In our samples, however, weakening within the selvages was self limiting: (1) growth of strong staurolite porphyroblasts in the selvages protected remaining quartz from dissolution; and (2) overall flattening of the quartz clasts probably decreased the resolved shear stress on the flanks to values near those of the matrix, which would have reduced the driving force for solution‐transfer creep. Extreme chemical changes nonetheless occurred over short distances. The necessity of maintaining strain compatibility may lead to significant localized dissolution in rocks containing rheologic heterogeneities, and overall weakening of the rocks may result. Solution‐transfer creep may be a major process whereby weakening and strain localization occur during deep‐crustal metamorphism of polymineralic rocks.     

Three‐dimensional transient thermo‐hydro‐mechanical fundamental solutions of unsaturated soils

The governing differential equations of unsaturated soils considering the thermo‐poro‐mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three‐dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed‐form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed‐form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution. Copyright © 2009 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.     

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.     

压力溶解对颗粒聚集岩体中热-水-应力耦合影响的数值模拟

在自主研制的孔隙介质热-水-应力耦合有限元程序中引入Taron等提出的颗粒聚集体的压力溶解模型,针对一个假设的实验室尺度且位于非饱和石英颗粒聚集岩体中的高放废物地质处置模型,拟定两种计算工况：（1）孔隙率和渗透系数是压力溶解的函数;（2）孔隙率和渗透系数均为常数,进行4 a处置时段的数值模拟,考察了岩体中的温度、颗粒界面水膜及孔隙中的溶质浓度、迁移和沉淀质量、孔隙率及渗透系数、孔隙水压力、地下水流速和应力的变化、分布情况。研究结果表明：工况1计算终了时,压力溶解使得孔隙率和渗透系数分别下降到初始值的43%～54%、4.4%～9.1%。在核废料释热温度场的作用下,工况1、2中的负孔隙水压力分别为初始值的1.00～1.25倍、1.00～1.10倍,前者表现了压力溶解的明显影响;两种工况的岩体中的应力量值及分布基本相同。     

A micromechanical modeling of ductile behavior of a porous chalk: Formulation,identification, and validation

Porosity strongly affects the overall ductile behavior of cohesive geomaterials undergoing plastic deformation. In the present paper, we proposed an original micromechanical approach that suitably couples Drucker–Prager‐type plasticity, evolving porosity under general triaxial loadings. The resulting model has the advantage to be based on a single macroscopic yield function, which also plays the role of plastic potential. It is shown that this yield function is particularly appropriate to account for the pore collapse and plastic shearing mechanisms that govern the mechanical behavior of the studied Lixhe chalk. Finally, the new model is implemented and validated by comparison to triaxial tests data, covering a wide range of confining pressures. Copyright © 2011 John Wiley & Sons, Ltd.