Influence of gas generation in electro‐osmosis consolidation

This paper presents a numerical model for the elasto‐plastic electro‐osmosis consolidation of unsaturated clays experiencing large strains, by considering electro‐osmosis and hydro‐mechanical flows in a deformable multiphase porous medium. The coupled governing equations involving the pore water flow, pore gas flow, electric flow and mechanical deformation in unsaturated clays are derived within the framework of averaging theory and solved numerically using finite elements. The displacements of the solid phase, the pressure of the water phase, the pressure of the gas phase and the electric potential are taken as the primary unknowns in the proposed model. The nonlinear variation of transport parameters during electro‐osmosis consolidation are incorporated into the model using empirical expressions that strongly depend on the degree of water saturation, whereas the Barcelona Basic Model is employed to simulate the elasto‐plastic mechanical behaviour of unsaturated clays. The accuracy of the proposed model is evaluated by validating it against two well‐known numerical examples, involving electro‐osmosis and unsaturated soil behaviour respectively. Two further examples are then investigated to study the capability of the computational algorithm in modelling multiphase flow in electro‐osmosis consolidation. Finally, the effects of gas generation at the anode, the deformation characteristics, the degree of saturation and the time dependent evolution of the excess pore pressure are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

A coupled poroplastic damage model accounting for cracking effects on both hydraulic and mechanical properties of unsaturated media

Damage induced by microcracking affects not only the mechanical behaviour of geomaterials but also their hydraulic properties. Evaluating these impacts is important for many engineering applications, such as the safety assessment of radioactive waste disposal facilities. This paper presents a new constitutive model accounting simultaneously for the impact of damage on hydraulic and mechanical properties of unsaturated poroplastic geomaterials. The hydro‐mechanical coupling is formulated by means of the thermodynamic framework for partially saturated media, extended by taking into account isotropic damage and plasticity. State and complementary laws are governed by the so‐called plastic effective stress and equivalent pore pressure. Assuming a bimodal pore size distribution for cracked porous media, the hydraulic part (water retention curve and hydraulic conductivity) is modelled using phenomenological functions of damage variable. The participation of damage on both mechanical and hydraulic part enables this model to describe bilateral couplings between them. This coupled model is then validated against a number of experimental data obtained from Callovo‐Oxfordian argillite, which is the possible host rock for a radioactive waste disposal in France. Parametric studies are also carried out to check the consistency and to better demonstrate the bilateral couplings in the model. Copyright © 2015 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.     

Two‐dimensional finite element analysis of gravitational and lateral‐driven deformation in sedimentary basins

The paper deals with the modeling of some aspects, such as the formulation of constitutive equations for sediment material or finite element approach for basin analysis, related to mechanical compaction in sedimentary basins. In addition to compaction due to gravity forces and pore‐pressure dissipation, particular emphasis is given to the study of deformation induced by tectonic sequences. The numerical model relies upon the implementation of a comprehensive constitutive model for the sediment material formulated within the framework of finite poroplasticity. The theoretical model accounts for both hydromechanical and elasticity–plasticity coupling due to the effects of irreversible large strains. From the numerical viewpoint, a finite element procedure specifically devised for dealing with sedimentary basins as open systems allows to simulate within a two‐dimensional setting the process of sediment accretion or erosion. Several basin simulations are presented. The main objective is to analyze the behavior of a sedimentary basin during the different phases of its life cycle: accretion phase, pore‐pressure dissipation phase and compressive/extensional tectonic motions. Copyright © 2013 John Wiley & Sons, Ltd.     

A micromechanics model for molecular diffusion in materials with complex pore structure

Molecular diffusion in fully saturated porous materials is strongly influenced by the pore space, which, in general, is characterized by a complex topological structure. Hence, information on macroscopic diffusion properties requires up‐scaling of transport processes within nano‐pores and micro‐pores over several spatial scales. A new model in the framework of continuum micromechanics is proposed for predicting the effective molecular diffusivity in porous materials. Considering a representative volume element, characterizing a porous material without any information about the pore space microstructure complexity, the uniform flux is perturbed by recursively embedding shape information hierarchically in the form of the ESHELBY matrix‐inclusion morphology to obtain the effective diffusivity as a function of the recurrence level and the porosity. The model predicts a threshold value for the porosity, below which no molecular diffusion can occur because of the presence of isolated pore clusters that are not connected and unavailable for transport. The maximum porosity, below which no molecular transport is possible, is predicted as one‐third for spherical inclusions. The model allows for extensions to more complex morphologies of the inclusions. We also identify, that the effects of the micro‐structure on molecular transport are characterized by porosity dependent long‐range and short‐range interactions. The developed framework is extended to incorporate realistic pore size distributions across several spatial scales by means of a distribution function within the hierarchical homogenization scheme. Available experimental results assert the model predictions. Copyright © 2015 John Wiley & Sons, Ltd.     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.     

A model for pore‐fluid‐sensitive rock behavior using a weathering state parameter

Chalk and other porous rocks are known to behave differently when saturated with different pore fluids. The behavior of these rocks varies with different pore fluids and additional deformation occurs when the pore fluid composition changes. In this article, we review the evidence that behavior in porous rocks is pore‐fluid‐dependent, present a constitutive model for pore‐fluid‐dependent porous rocks, and present a compilation of previously published data to develop quantitative relationships between various pore fluids and mechanical behavior. The model proposed here is based on a state parameter approach for weathering and has similarities to models previously proposed for weathering‐sensitive rocks in that the values for parameters that characterize material behavior vary as a function of weathering. Comparisons with published experimental data indicate that the model is capable of reproducing observed behavior of chalk under a variety of loading conditions and changes in pore fluid composition. Copyright © 2008 John Wiley & Sons, Ltd.     

不同温-压条件下含水合物沉积物的损伤本构关系

环境温度和孔隙压力对含水合物沉积物的力学特性存在重要影响,深刻揭示温度和孔隙压力对含水合物沉积物力学特性的影响机制并对其进行有效地模拟是含水合物地层稳定性评估的前提。在分析温度和孔隙压力变化对含水合物沉积物的力学特性影响机制的基础上,引入温压条件参数来考虑温度和孔隙压力变化对含水合物沉积物力学特性的影响,建立了考虑温度和孔隙压力影响的损伤本构模型。模型假设含水合物沉积物微元强度服从Weibull分布,采用Drucker-Prager强度准则描述微元强度,建立了损伤因子的演化规律。此外,还提供了一套模型参数的确定方法。通过一系列不同温度压力条件下的含水合物沉积物的三轴压缩试验结果对模型进行校核和验证,结果表明,该模型能很好地模拟含水合物沉积物的应力-应变关系,并且能较好地考虑水合物含量、环境温度和孔隙压力对含水合物沉积物的力学特性的影响。     

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

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

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Chlorite meniscus cement – implications for diagenetic mineral growth after oil emplacement

The possible influence on diagenesis of oil migration into reservoir sandstones is important for understanding their development. Although many studies have addressed the question of continued growth of diagenetic minerals after oil emplacement, there is little clear evidence of the timing of mineral growth relative to oil emplacement, nor of the possible mechanisms of continued mineral growth. This study presents an example of continued cementation by pore‐lining chlorite during and after the migration of oil into a Palaeocene turbidite sandstone reservoir near the Faroe Islands. Chlorite developed in two different textures. One texture occurs on framework grain surfaces adjacent to open pore space in contact with oil. The other texture occurs close to framework grain contacts where contact with oil appears to have been prevented by residual pore‐water menisci. The meniscus crystals are larger than those from open pore, implying that diagenetic clay mineral growth has continued after oil emplacement.     

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.     

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.     

A thermo‐mechanical model for the catastrophic collapse of large landslides

In this work, a new thermo‐mechanical model is developed, applicable to large‐scale, deep‐seated landslides consisting of a coherent mass sliding on a thin clayey layer. The considered time window is that of catastrophic acceleration, starting at incipient failure and ending when the acquired displacement and velocity are such that the sliding material begins to break up into pieces. The model accounts for temperature rise in the slip zone due to the heat produced by friction, leading to water expansion, thermoplastic collapse of the soil skeleton, and subsequent increase of pore water pressure. The model incorporates the processes of heat production and diffusion, pore pressure generation and diffusion, and an advanced constitutive law for the thermo‐mechanical behavior of soil. An analysis of the Vajont landslide is presented as an example. A sensitivity analysis shows that friction softening is the mechanism most affecting the timescale of the final collapse of a slide, but also that the mechanism of thermal pressurization alone can cause a comparably catastrophic dynamic evolution. It is also shown that, all other factors being equal, thermo‐mechanical collapse will cause thicker slides to accelerate faster than shallow ones. Copyright © 2010 John Wiley & Sons, Ltd.     

Similarity solution for cavity expansion in thermoplastic soil

This paper presents an analytical solution for cavity expansion in thermoplastic soil considering non‐isothermal conditions. The constitutive relationship of thermoplasticity is described by Laloui's advanced and unified constitutive model for environmental geomechanical thermal effect (ACMEG‐T), which is based on multi‐mechanism plasticity and bounding surface theory. The problem is formulated by incorporating ACMEG‐T into the theoretical framework of cavity expansion, yielding a series of partial differential equations (PDEs). Subsequently, the PDEs are transformed into a system of first‐order ordinary differential equations (ODEs) using a similarity solution technique. Solutions to the response parameters of cavity expansion (stress, excess pore pressure, and displacement) can then be obtained by solving the ODEs numerically using mathematical software. The results suggest that soil temperature has a significant influence on the pressure‐expansion relationships and distributions of stress and excess pore pressure around the cavity wall. The proposed solution quantifies the influence of temperature on cavity expansion for the first time and provides a theoretical framework for predicting thermoplastic soil behavior around the cavity wall. The solution found in this paper can be used as a theoretical tool that can potentially be employed in geotechnical engineering problems, such as thermal cone penetration tests, and nuclear waste disposal problems.     

Size and shape evolution of pores in a viscoplastic matrix under compression

The frequent use of soils and earth materials for hydraulic capping and for geo‐environmental waste containment motivated our interest in detailed modelling of changes in size and shape of macro‐pores to establish links between soil mechanical behaviour and concurrent changes in hydraulic and transport properties. The objective of this study was to use finite element analysis (FEA) to test and extend previous analytical solutions proposed by the authors describing deformation of a single macro‐pore embedded in linear viscoplastic soil material subjected to anisotropic remote stress. The FEA enables to consider more complex pore geometries and provides a detailed picture of matrix yield behaviour to explain shortcomings of approximate analytical solutions. Finite element and analytical calculations agreed very well for linear viscous as well as for viscoplastic materials, only limited for the case of isotropic remote stress due to the simplifications of the analytical model related to patterns and onset of matrix‐yielding behaviour. FEA calculations were compared with experimental data obtained from a compaction experiment in which pore deformation within a uniform modelling clay sample was monitored using CAT scanning. FEA predictions based on independently measured material properties and initial pore geometry provided an excellent match with experimentally determined evolution of pore size and shape hence lending credence to the potential use of FEA for more complex pore geometries and eventually connect macro‐pore deformation with hydraulic properties. Copyright © 2006 John Wiley & Sons, Ltd.     

LBM–DEM modeling of fluid–solid interaction in porous media

Three porous media flow problems, in which the fluid mechanical interactions are critical, are studied in a mesoscopic–microscopic coupling system. In this system, fluid flow in the pore space is explicitly modeled at mesoscopic level by the lattice Boltzmann method, the geometrical representation and the mechanical behavior of the solid skeleton are modeled at microscopic level by the particulate distinct element method (DEM), and the interfacial interaction between the fluid and the solids is resolved by an immersed boundary scheme. In the first benchmark problem, the well‐known and frequently utilized Ergun equation is validated in periodic particle and periodic pore models. In the second problem, the upward seepage problem is simulated over three stages: The settlement of the column of sphere under gravity loading is measured to illustrate the accuracy of the DEM scheme; the system is solved to hydrostatic state with pore space filled with fluid, showing that the buoyancy effect is captured correctly in the mesoscopic–microscopic coupling system; then, the flow with constant rate is supplied at the bottom of the column; the swelling of the ground surface and pore pressure development from the numerical simulation are compared with the predictions of the macroscopic consolidation theory. In the third problem, the fluid‐flow‐induced collapse of a sand arch inside a perforation cavity is tested to illustrate a more practical application of the developed system. Through comparing simulation results with analytical solutions, empirical law and physical laboratory observations, it is demonstrated that the developed lattice Boltzmann–distinct element coupling system is a powerful fundamental research tool for investigating hydromechanical physics in porous media flow. Copyright © 2012 John Wiley & Sons, Ltd.     

Development of an inverse analysis framework for extracting dynamic soil behavior and pore pressure response from downhole array measurements

Observations from earthquakes over the past several decades have highlighted the importance of local site conditions on propagated ground motions. Downhole arrays are deployed to measure motions at the ground surface and within the soil profile, and also to record the pore pressure response within the soft soil profiles during excitation. The degradation of soil stiffness as excess pore pressures are generated during earthquake events has also been observed. An inverse analysis framework is developed and demonstrated to directly extract soil material behavior including pore water pressure (PWP) generation from downhole array measurements that can then be readily used in 1D nonlinear site response analysis. The self‐learning simulations (SelfSim) inverse analysis framework, previously developed for total stress site response analysis, is extended to extract PWP generation behavior of the soil in addition to cyclic response during ground shaking. A Neural Network based constitutive model is introduced to represent PWP generation during cyclic loading. A new analysis scheme is introduced that can use data from co‐located piezometer and accelerometer sensors. The successful performance of the proposed framework is demonstrated using four synthetic vertical array recordings. Copyright © 2013 John Wiley & Sons, Ltd.     

ACMEG‐TS: A constitutive model for unsaturated soils under non‐isothermal conditions

This paper introduces an unconventional constitutive model for soils, which deals with a unified thermo‐mechanical modelling for unsaturated soils. The relevant temperature and suction effects are studied in light of elasto‐plasticity. A generalized effective stress framework is adopted, which includes a number of intrinsic thermo‐hydro‐mechanical connections, to represent the stress state in the soil. Two coupled constitutive aspects are used to fully describe the non‐isothermal behaviour. The mechanical constitutive part is built on the concepts of bounding surface theory and multi‐mechanism plasticity, whereas water retention characteristics are described using elasto‐plasticity to reproduce the hysteretic response and the effect of temperature and dry density on retention properties. The theoretical formulation is supported by comparisons with experimental results on two compacted clays. Copyright © 2008 John Wiley & Sons, Ltd.