Chemo‐thermo‐mechanically coupled seismic analysis of methane hydrate‐bearing sediments during a predicted Nankai Trough Earthquake

In the present study, we have developed a numerical method which can simulate the dynamic behaviour of a seabed ground during gas production from methane hydrate‐bearing sediments. The proposed method can describe the chemo‐thermo‐mechanical‐seismic coupled behaviours, such as phase changes from hydrates to water and gas, temperature changes and ground deformation related to the flow of pore fluids during earthquakes. In the first part of the present study, the governing equations for the proposed method and its discretization are presented. Then, numerical analyses are performed for hydrate‐bearing sediments in order to investigate the dynamic behaviour during gas production. The geological conditions and the material parameters are determined using the data of the seabed ground at Daini‐Atsumi knoll, Eastern Nankai Trough, Japan, where the first offshore production test of methane hydrates was conducted. A predicted earthquake at the site is used in the analyses. Regarding the seismic response to the earthquake which occur during gas production process, the wave profiles of horizontal acceleration and horizontal velocity were not extensively affected by the gas production. Hydrate dissociation behaviour is sensitive to changes in the pore pressure during earthquakes. Methane hydrate dissociation temporarily became active in some areas because of the main motion of the earthquake, then methane hydrate dissociation brought about an increase in the average pressure of the fluids during the earthquake. And, it was this increase in average pore pressure that finally caused the methane hydrate dissociation to cease during the earthquake. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

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.     

Thermo‐hydro‐mechanical modeling with Langmuir's adsorption isotherm of the CO2 injection in coal

In this paper, we used a theoretical model for the variation of Eulerian porosity, which takes into account the adsorption process known to be the main mechanism of production or sequestration of gas in many reservoir of coal. This process is classically modeled using Langmuir's isotherm. After implementation in Code_Aster, a fully coupled thermo‐hydro‐mechanical analysis code for structures calculations, we used numerical simulations to investigate the influence of coal's hydro‐mechanical properties (Biot's coefficient, bulk modulus), Langmuir's adsorption parameters, and the initial liquid pressure in rock mass during CO₂ injection in coal. These simulations showed that the increase in the values of Langmuir's parameters and Biot's coefficient promotes a reduction in porosity because of the adsorption process when the gas pressure increases. Low values of bulk modulus increase the positive effect (i.e., increase) of hydro‐mechanical coupling on the porosity evolution. The presence of high initial liquid pressure in the rock mass prevents the progression of injected gas pressure when CO₂ dissolution in water is taken into account. Copyright © 2014 John Wiley & Sons, Ltd.     

Sensitivity analysis applied to finite element method model for coupled multiphase system

Today multiphysics problems applied to various fields of engineering have become increasingly important. Among these, in the areas of civil, environmental and nuclear engineering, the problems related to the behaviour of porous media under extreme conditions in terms of temperature and/or pressure are particularly relevant. The mathematical models used to solve these problems have an increasing complexity leading to increase of computing times. This problem can be solved by using more effective numerical algorithms, or by trying to reduce the complexity of these models. This can be achieved by using a sensitivity analysis to determine the influence of model parameters on the solution. In this paper, the sensitivity analysis of a mathematical/numerical model for the analysis of concrete as multiphase porous medium exposed to high temperatures is presented. This may lead to a reduction of the number of the model parameters, indicating what parameters should be determined in an accurate way and what can be neglected or found directly from the literature. Moreover, the identification parameters influence may allow to proceeding to a simplification of the mathematical model (i.e. model reduction). The technique adopted in this paper to performing the sensitivity analysis is based on the automatic differentiation (AD), which allowed to develop an efficient tool for the computation of the sensitivity coefficients. The results of the application of AD technique have been compared with the results of the more standard finite difference method, showing the superiority of the AD in terms of numerical accuracy and execution times. From the results of the sensitivity analysis, it follows that a drastic simplification of the model for thermo‐chemo‐hygro‐mechanical behaviour of concrete at high temperature, is not possible. Therefore, it is necessary to use different model reduction techniques in order to obtain a simplified version of the model that can be used at industrial level. Copyright © 2012 John Wiley & Sons, Ltd.     

A three‐phase thermo‐hydro‐mechanical finite element model for freezing soils

Artificial ground freezing (AGF) is a commonly used technique in geotechnical engineering for ground improvement such as ground water control and temporary excavation support during tunnel construction in soft soils. The main potential problem connected with this technique is that it may produce heave and settlement at the ground surface, which may cause damage to the surface infrastructure. Additionally, the freezing process and the energy needed to obtain a stable frozen ground may be significantly influenced by seepage flow. Evidently, safe design and execution of AGF require a reliable prediction of the coupled thermo‐hydro‐mechanical behavior of freezing soils. With the theory of poromechanics, a three‐phase finite element soil model is proposed, considering solid particles, liquid water, and crystal ice as separate phases and mixture temperature, liquid pressure, and solid displacement as the primary field variables. In addition to the volume expansion of water transforming into ice, the contribution of the micro‐cryo‐suction mechanism to the frost heave phenomenon is described in the model using the theory of premelting dynamics. Through fundamental physical laws and corresponding state relations, the model captures various couplings among the phase transition, the liquid transport within the pore space, and the accompanying mechanical deformation. The verification and validation of the model are accomplished by means of selected analyses. An application example is related to AGF during tunnel excavation, investigating the influence of seepage flow on the freezing process and the time required to establish a closed supporting frozen arch. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling the flow of self‐compacting concrete

A Lagrangian particle‐based method, smooth particle hydrodynamics (SPH), is used in this paper to model the flow of self‐compacting concretes (SCC) with or without short steel fibres. An incompressible SPH method is presented to simulate the flow of such non‐Newtonian fluids whose behaviour is described by a Bingham‐type model, in which the kink in the shear stress vs shear strain rate diagram is first appropriately smoothed out. The viscosity of the SCC is predicted from the measured viscosity of the paste using micromechanical models in which the second phase aggregates are treated as rigid spheres and the short steel fibres as slender rigid bodies. The basic equations solved in the SPH are the incompressible mass conservation and Navier–Stokes equations. The solution procedure uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting temporal velocity field is then implicitly projected on to a divergence‐free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. The results of the numerical simulation are benchmarked against actual slump tests carried out in the laboratory. The numerical results are in excellent agreement with test results, thus demonstrating the capability of SPH and a proper rheological model to predict SCC flow and mould‐filling behaviour. Copyright © 2010 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.     

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.     

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.     

Experimental study and constitutive modelling of elasto‐plastic damage in heat‐treated mortar

This study investigates the effect of a heat‐treatment upon the thermo‐mechanical behaviour of a model cement‐based material, i.e. a normalized mortar, with a (w/c) ratio of 0.5. First, a whole set of varied experimental results is provided, in order to either identify or validate a thermo‐mechanical constitutive model, presented in the second paper part. Experimental responses of both hydraulic and mechanical behaviour are given after different heating/cooling cycling levels (105, 200, 300, 400^°C). The reference state, used for comparison purposes, is taken after mass stabilization at 60^°C. Typical uniaxial compression tests are provided, and original triaxial deviatoric compressive test responses are also given. Hydraulic behaviour is identified simultaneously to triaxial deviatoric compressive loading through gas permeability K_gas assessment. K_gas is well correlated with volumetric strain evolution: gas permeability increases hugely when ε_v testifies of a dilatant material behaviour, instead of contractile from the test start. Finally, the thermo‐mechanical model, based on a thermodynamics approach, is identified using the experimental results on uniaxial and triaxial deviatoric compression. It is also positively validated at residual state for triaxial deviatoric compression, but also by using a different stress path in lateral extension, which is at the origin of noticeable plasticity. Copyright © 2009 John Wiley & Sons, Ltd.     

Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method

This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical modelling of multiphase immiscible flow in double‐porosity featured groundwater systems

A numerical model describing the flow of multiphase, immiscible fluids in a deformable, double‐porosity featured soil has been developed. The model is focused on the modelling of the secondary porosity features in soil, which is more relevant to groundwater contamination problems. The non‐linear saturation and relative permeabilities were expressed as functions of the capillary pressures. The governing partial differential equations in terms of soil displacement and fluid pressures were solved numerically. Galerkin's weighted‐residual finite element method was employed to obtain the spatial discretization whereas temporal discretization was achieved using a fully implicit scheme. The model was verified against established, peer‐reviewed works, and the assumption that the immiscible fluids (non‐aqueous phase liquids) will flow preferentially through the secondary porosity features in soil was validated. Copyright © 2011 John Wiley & Sons, Ltd.     

On some advanced thermo‐mechanical models for saturated clays

This paper aims to evaluate the performance of several recent constitutive models in simulating the thermo‐mechanical behaviour of saturated clays. A classic thermo‐mechanical test on natural Boom Clay, commonly used in constitutive modelling, was first clarified. Different methods commonly used to measure volumetric strain in drained heating tests were then discussed. Model evaluation was performed in terms of thermodynamic and elasto‐plastic requirements. The capability of the models to capture the observed behaviour was assessed on the basis of the experimental evidence. It was shown that all the models provide reasonable predictions of the thermo‐mechanical behaviour of saturated clays. However, each constitutive model has its own limitations or unclear points from the theoretical point of view. Copyright © 2013 John Wiley & Sons, Ltd.     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 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.     

One‐dimensional analysis of a poroelastic medium during freezing

A solution to the problem of freezing of a poroelastic material is derived and analysed in the case of one‐dimensional deformation. The solution is sought within the framework of thermo‐poroelasticity, with specific account of the behaviour of freezing materials. The governing equations of the problem can be combined into a pair of coupled partial differential equations for the temperature and the fluid pressure, with particular forms in the freezing and the unfrozen regions. In the freezing region, the equations are highly non‐linear, partly due to the dependence of thermal and hydraulic properties on water saturation, which varies with temperature. Consequently, the solution is obtained through numerical methods, with special attention to the propagation of the freezing front boundary. The response to one‐dimensional freezing is illustrated for the case of cement paste. Finally, the influence on the solution of varying selected parameters is analysed, such as the temperature boundary conditions, the parameters characterizing the geometry of the porous system, the ratio of fluid and thermal diffusivities, and the rate of cooling applied at the freezing end. Copyright © 2008 John Wiley & Sons, Ltd.