A constitutive model based on modified mixture theory for unsaturated rocks

Non-equilibrium thermodynamics and Biot poro-elasticity have been combined to give a coupled hydro-mechanical formulation for unsaturated rock. Darcy’s law for unsaturated flow has been derived from the dissipation process by using standard arguments of non-equilibrium thermodynamics, whereas Helmholtz free energy has been used to derive the relationship between stress and pore pressure changes. The resulting general framework accommodates both large and small deformation theories. When small deformations are assumed, the formulation is comparable with coupled equations derived using an alternative approach. For illustrative purposes, the formulation has been used to analyse a seasonally affected tunnel model. Numerical results for the desaturation in winter and resaturation in summer, of the zone near the tunnel wall, have been evaluated and compared with the findings of other researchers.     

A dual-porosity model for the study of chemical effects on the swelling behaviour of MX-80 bentonite

Significant chemical influence on the swelling potential of MX-80 bentonite was observed during swelling tests where specimens were hydrated with highly concentrated brine. The maximum swelling pressure for specimens hydrated with brine was about 30% of the maximum swelling pressure for the same specimens hydrated with de-ionized water. The maximum swelling pressure was attained within tens of hours of brine infiltration and further decreased by half within a year. A fully coupled hydro–mechanical–chemical (HMC) dual-porosity model is proposed in this paper to interpret the swelling behaviour of MX-80 when infiltrated with brine. The dependence of hydraulic and mechanical properties on such factors as porosity, salinity and water content was investigated. A nonlinear elastic constitutive model was proposed to correlate the swelling pressure with the variation in the microporosity. The chemical effects on the mechanical behaviour were coupled at the micropore level. A number of relationships have been developed for MX-80, i.e. micropore permeability as a function of void ratio, water retention characteristics of micropores and macropores, micropore dependence on water content and the diffusion coefficients of the two types of pore structure. The proposed model was successful in reproducing both quantitatively and qualitatively the experimental results from two sets of infiltration experiments on compacted MX-80 bentonite.

     

Coupled hydro-mechanical model for partially saturated soils predicting small strain stiffness

In the paper, we present newly developed hydro-mechanical hypoplastic model for partially saturated soils predicting small strain stiffness. Hysteretic void ratio dependent water retention model has been incorporated into the existing hypoplastic model. This required thorough revision of the model structure to allow for the hydro-mechanical coupling dependencies. The model is formulated in terms of degree of saturation, rather than of suction. Subsequently, the small strain stiffness effects were incorporated using the intergranular strain concept modified for unsaturated conditions. New features included degree of saturation-dependent size of the elastic range and an updated evolution equation for the intergranular strain. The model has been evaluated using two comprehensive data sets on completely decomposed tuff from Hong-Kong and Zenos Kaolin from Iran. It has been shown that the modified intergranular strain formulation coupled with the hysteretic water retention model correctly reproduces the effects of both the stress and suction histories on small strain stiffness evolution. The model can correctly predict also different other aspects of partially saturated soil behaviour, starting from the very small strain range up to the asymptotic large-strain response.     

Extension of plasticity theory to debonding,grain dissolution,and chemical damage of calcarenites

The mechanical properties of calcarenites are known to be significantly affected by water saturation: both stiffness and strength decrease for wetting in the short term and for chemical dissolution in the long term. Both processes mainly affect bonds among grains: immediately after inundation depositional bonds fall in suspension, whereas diagenetic bonds dissolve more slowly. In this paper, the authors started from the micro‐structural analysis of the weathering processes to conceive a strain hardening hydro‐chemo‐mechanical coupled elastoplastic constitutive model. The concept of extended hardening rules is here enriched: weathering functions have been determined by employing a micro to macro simplified upscaling procedure. Chemical damage is incorporated into the formulation by means of a scalar damage function. Its evolution is also described by using a multiscale approach. A new term is added to the strain rate tensor in order to incorporate the dissolution induced chemical deformations developing once the soft rock is turned into a granular material. A calibration procedure for the constitutive parameters is suggested, and the model is validated by using both coupled and uncoupled chemo‐mechanical experimental test results. Copyright © 2015 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.     

Thermo-Hydro-Mechanical-Chemical Simulation of Methane Hydrate Dissociation in Porous Media

The vast amount of methane deposits in permafrost and oceanic sediments has significant energy and environmental implications. There are increasing interests in the development of numerical simulation techniques to predict the reservoir responses due to natural gas recovery from methane hydrate dissociation. There has been extensive amount of work on modeling the chemo- thermo- hydro-responses associated with hydrate dissociation. The mechanical responses of hydrate bearing ground, however, have largely been overlooked and are just starting to receive more and more attention. From energy recovery perspective, a comprehensive model that includes the mechanical responses of hydrate disassociation is crucial for predicting the mechanical stability of gas hydrate reservoir and potential geohazards. This paper proposes a thermo-hydro-mechanical-chemical model for simulating the dissociation of methane hydrate. The governing equations for the conservation of energy (thermal), mass (hydraulic) and momentum (mechanical) were derived from the local balance equations. The proposed governing equation system for methane hydrate as a four-phase four-component composite was simplified based on reasonable assumptions to facilitate numerical implementations. The dissociation reaction was considered using chemical kinetics. Auxiliary relationships such as the soil water characteristic curve, constitutive correlations, stress formulation based on the mixture theory were employed to mathematically close the formulation. The mathematical model was implemented using the finite element method. The simulation results were evaluated and compared with those obtained by conventional simulators based on thermo-hydro-chemical models. The mechanical module of this new model was applied to predict the geotechnical responses induced by gas recovery in a typical oceanic reservoir.     

Finite element modelling of transport of organic chemicals through soils

Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed.     

A fully coupled hydro‐thermo‐poro‐mechanical model for black oil reservoir simulation

A fully coupled formulation of a hydro‐thermo‐poro‐mechanical model for a three‐phase black oil reservoir model is presented. The model is based upon the approach proposed by one of the authors which fully couples geomechanical effects to multiphase flow. Their work is extended here to include non‐isothermal effects. The gas phase contribution to the energy equation has been neglected based on a set of assumptions. The coupled formulation given herein differs in several ways when compared to the earlier work and an attempt is made to link the flow based formulation and mixture theory. The Finite Element Method is employed for the numerical treatment and essential algorithmic implementation is discussed. Numerical examples are presented to provide further understanding of the current methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

Modeling of self‐desiccation in a cemented backfill structure

After placement of cemented tailings backfill (CTB), which is a mixture of tailings (man‐made soil), water, and binder, into underground mined‐out voids (stopes), the hydration reaction of the binder converts the capillary water into chemically bound water, which results in the reduction of the water content in the pores of the CTB, thereby causing a reduction in the pore‐water pressure in the CTB (self‐desiccation). Self‐desiccation has a significant impact on the pore‐water pressure and effective stress development in CTB and paramount and practical importance for the stability assessment and design of CTB structures and barricades. However, self‐desiccation in CTB structures is complex because it is a function of the multiphysics or coupled (i.e., thermal, hydraulic, mechanical, and chemical) processes that occur in CTB. To understand the self‐desiccation behavior of CTB, an integrated multiphysics model of self‐desiccation is developed in this study, which fully considers the coupled thermal, hydraulic, mechanical, and chemical processes and the consolidation process in CTB. All model coefficients are determined in measurable parameters. Moreover, the predictive ability of the model is verified with extensive case studies. A series of engineering issues are examined with the validated model to investigate the self‐desiccation process in CTB structures with respect to the changes in the mixture recipe, backfilling, and the surrounding rock and curing conditions. The obtained results provide in‐depth insight into the self‐desiccation behavior of CTB structures. The developed multiphysics model is therefore a potential tool for assessing and predicting self‐desiccation in CTB structures.     

The influence of coupled physical swelling and chemical reactions on deformable geomaterials

Coupled thermo‐hydro‐mechanical‐chemical modelling has attracted attention in past decades due to many contemporary geotechnical engineering applications (e.g., waste disposal, carbon capture and storage). However, molecular‐scale interactions within geomaterials (e.g., swelling and dissolution/precipitation) have a significant influence on the mechanical behaviour, yet are rarely incorporated into existing Thermal‐Hydro‐Mechanical‐Chemical (THMC) frameworks. This paper presents a new coupled hydro‐mechanical‐chemical constitutive model to bridge molecular‐scale interactions with macro‐physical deformation by combining the swelling and dissolution/precipitation through an extension of the new mixture‐coupling theory. Entropy analysis of the geomaterial system provides dissipation energy, and Helmholtz free energy gives the relationship between solids and fluids. Numerical simulation is used to compare with the selected recognized models, which demonstrates that the swelling and dissolution/precipitation processes may have a significant influence on the mechanical deformation of the geomaterials.     

A new matrix for multiphase couplings in a membrane porous medium

The empirical Darcy's law of water transport in porous media, Fick's law of chemical diffusion, and Fourier's law of thermal transport have been widely used in geophysics/geochemistry for over 150 years. However, the strong couplings between water, temperature, and chemicals in a membrane porous medium have made these laws inapplicable and present a significant hurdle to the understanding of multiphase flow in such a material. Extensive experiments over the past century have observed chemical osmosis and thermal osmosis, but a model for understanding their underlying physicochemical basis has remained unavailable, because of the highly cross‐disciplinary and multiscale‐multiphase nature of the coupling. Based on the fundamental principles of nonequilibrium thermodynamics and mixture coupling theory, a rigorously theoretical and mathematical framework is proposed and a general model accounting for all of the coupled influences is developed. This leads to a simple and robust mathematical matrix for studying multiphase couplings in a membrane porous medium when all chemical components are electrically neutral.     

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.     

Simulation of excavation in a poro-elastic material

A method is presented which allows the computation of the displacements and pore pressures which are generated in an elastic soil when excavation is carried out. The formulation is based on Biot's theory and is fully coupled, with consideration also given to the effects of the lowering of the water table which often accompanies the excavation of soil. Example problems are solved to illustrate the theory which has been presented.     

On the use of effective stress in three-dimensional hydro-mechanical coupled model

In the last decades, a number of hydro-mechanical elastoplastic constitutive models for unsaturated soils have been proposed. Those models couple the hydraulic and mechanical behaviour of unsaturated soils, and take into account the effects of the degree of saturation on the stress–strain behaviour and the effects of deformation on the soil–water characteristic response with a simple reversible part for the hysteresis. In addition, the influence of the suction on the stress–strain behaviour is considered. However, until now, few models predict the stress–strain and soil–water characteristic responses of unsaturated soils in a fully three-dimensional Finite Element code. This paper presents the predictions of an unsaturated soil model in a Three-dimensional Framework, and develops a study on the effect of partial saturation on the stability of shallow foundation resting on unsaturated silty soil. Qualitative predictions of the constitutive model show that incorporating a special formulation for the effective stress into an elastoplastic coupled hydro-mechanical model opens a full range of possibilities in modelling unsaturated soil behaviour.     

应力-溶解耦合作用下的盐腔水溶建腔机制研究

通过分析岩盐应力-溶解耦合效应对盐腔水溶建腔过程的影响,研究应力-溶解耦合作用下的盐腔水溶建腔机制。研究表明,在盐腔成腔过程中,应力-溶解耦合效应对盐腔形状的影响不可忽略;应力-溶解耦合作用下的盐腔水溶建腔机制在于溶蚀作用下在水的溶蚀影响范围内的腔壁围岩力学性质发生变化,同时,由于腔壁边界处围岩力学性质的改变,造成盐腔内部溶蚀过程发生变化,从而使盐腔形态发生改变;根据应力-溶解耦合作用下的盐腔水溶建腔机制,建立应力-溶解耦合作用下的盐腔水溶建腔计算方法;使用编制的应力-溶解耦合作用下的盐腔形态变化计算程序以及FLAC计算软件对水溶建腔过程进行计算。计算结果表明,相比于纯溶解作用,应力-溶解耦合作用下计算得到的盐腔形状与实际溶腔形状较为符合。该研究成果可为进一步研究储库盐腔水溶建腔机制提供理论依据和分析基础。     

Assessment of slope stability in cohesive soils due to a rainfall

The primary focus in this work is on proposing a methodology for the assessment of stability of natural/engineered slopes in clayey soils subjected to water infiltration. In natural deposits of fine‐grained soils, the presence of water in the vicinity of minerals results in an interparticle bonding. This effect cannot be easily quantified as it involves complex chemical interactions at the micromechanical level. Here, the evolution of strength properties, including the apparent cohesion resulting from initial suction at the irreducible fluid saturation, is described by employing the framework of chemoplasticity. The paper provides first the formulation of the problem; this involves specification of the constitutive relation, development of an implicit return mapping scheme, and the outline of a coupled transient formulation. The framework is then applied to examine the stability of a slope subjected to a prolonged period of intensive rainfall. It is shown that the water infiltration may trigger the loss of stability resulting from the degradation of material properties. Copyright © 2013 John Wiley & Sons, Ltd.     

Large deformation elastic electro-osmosis consolidation of clays

This paper presents the theoretical background of an elastic electro-osmosis consolidation model for saturated soils experiencing large strains, which considers volumetric strains induced by changes in both the hydraulic and electric driven pore water flows. Three fully coupled governing equations, considering the soil mechanical behaviour, pore water transport and electrical field, and their numerical implementation within an updated Lagrangian finite element formulation, are presented. The proposed model is first verified against a classical one-dimensional analytical solution for electro-osmosis consolidation to demonstrate its accuracy and efficiency. Then, various numerical examples are investigated to study the deformation characteristics and time dependent evolution of excess pore pressure. Finally, the importance of considering large strains in a consistent and proper way is demonstrated, and differences compared to models based on small strain theory are highlighted.     

Numerical simulation of evapotranspiration using a root water uptake model

The abstraction of ground water by vegetation and its influence on the behaviour of geotechnical structures such as pavements, foundations and slopes has been researched for many years. In recent years, the use of numerical methods in geotechnical engineering has rapidly increased. A major challenge for numerical modelers involves the specification of the surface flow boundary condition to model root water uptake by vegetation. The abstraction of ground water by roots is a complex process which involves the interaction of the atmosphere, vegetation and the ground. Accurate prediction of the pore water pressure changes induced by vegetation requires the development of algorithms which can mimic the process of transpiration by vegetation in the continuity equation of fluid flow. This paper presents a root water uptake model which has been coded into a finite element program that can perform coupled (mechanical and fluid flow behaviour) analyses. The input data includes rainfall, potential evapotranspiration and maximum root depth. The key features of the model are discussed first, followed by a presentation of results from a series of parametric studies.     

Anionic sorption onto modified natural zeolites using chemical activation

The sorption of arsenate on modified-natural zeolites was investigated at varying chemical pretreatment. Zeolites were used extensively for water softening, however, a few arsenic studies have been conducted with zeolites. Arsenic pollution of the environment has received renewed attention due to toxicological evidence of its potential health hazards to humans. The ability of modified natural zeolites (stilbite and laumontite) to remove inorganic anion was investigated. The zeolites used in this work are stilbite-laumontite from Zeolitic Zone of the Corda Formation. Experiments were conducted to evaluate the relationships of the arsenate in the modified natural zeolites. Laboratory experiments were conducted examining the effect of the sorption of cationic surfactants and coagulant on stilbite-laumontite mixtures and on the subsequent sorption of arsenate by modified zeolites. Removal of arsenate using hexadecyltrimethylammonium (HDTMA)-modified zeolites was satisfactory whereas ethylhexadecyldimethylammonium (EHDDMA) and ALUM-modified zeolites were not removed with the same efficiency.