Diffusive Reactive Transport of Multicomponent Chemicals Under Coupled Thermal, Hydraulic, Chemical and Mechanical Conditions

This paper presents an investigation of the reactive transport of multicomponent chemicals in clays under coupled thermal, hydraulic, chemical and mechanical framework, considering the diffusion processes in detail. More specifically, combined effects due to the electrochemical and the thermal diffusion potentials are investigated. A theoretical framework for coupling thermal diffusion, i.e. the Soret effect, with electrochemical diffusion in a multi-ionic system is provided. An explicit form of a definition for the thermal diffusion coefficient in a multicomponent chemical transport model is developed. Chemical transport is linked to an advanced geochemical model, PHREEQC (version 2), in order to include chemical reactions. The effects of the combined diffusion potentials on the reactive transport of multicomponent chemicals are investigated by a series of numerical simulations of coupled thermal, hydraulic and chemical behaviour.     

Thermoelastic and thermoplastic response of a porous space submitted to a decaying heat source

A general solution scheme is developed for one-dimensional and non-isothermal consolidation problems for fluid-saturated, porous, thermoelastic media. Two fundamental parameters which describe the coupling effects between thermal, hydraulic and mechanical behaviour are: ratio of thermal and hydraulic diffusivity and ratio of thermomechanical deformabilities in drained and undrained conditions. The solution scheme has been applied to the nuclear waste disposal problem. A solution for a thermoporoelastic rock mass containing a decaying heat source is presented. Numerical results show that coupling effects are most pronounced for low permeability and high porosity media such as deep compressible clays. This corresponds to a low value of the ratio of hydraulic and thermal diffusivities and a high value of the ratio of deformabilities in drained and undrained conditions. Comparison with numerical simulations taking into account the non-linear and non-reversible behaviour of the rock mass is presented. It shows that the thermoelastic model is quite correct for temperature and displacement fields, and gives maxima of the pore pressure and stress elevations.     

A thermo-chemo-electro-mechanical framework of unsaturated expansive clays

Prediction of the coupled chemo-mechanical behaviours of porous media is an important problem in many areas, i.e., expansive clays in geotechnical and petroleum engineering, engineered barriers in the underground storage of nuclear wastes, and biological tissues in biological engineering. A further complex condition occurs when the voids are not fully saturated by liquid, such that capillary effects cannot be neglected a priori and might play an important role. Focusing on the modelling of expansive clays in the geotechnical field and based on the modified mixture theory, the work presented in this paper contributes to the construction of a theoretical framework used to model such complex coupling behaviours. The Clausius–Duhem inequality, which governs the dissipation associated with mechanical work, phase transformation, mass transport and thermal transport, is rigorously derived. Based on this theoretical framework, a chemo-poro-elastic unsaturated model is developed. The model is subsequently used to simulate the salt solution infiltration process through an unsaturated expansive clayey soil that induces changes in the mechanical and hydraulic field quantities. The logical tendencies are obtained and provide a preliminary demonstration of the capabilities of the newly developed theoretical framework.     

Experimental Investigations into the Mechanical Behaviour of the Breccias Around the Proposed Gibraltar Strait Tunnel

The proposed Gibraltar Strait tunnel will cross two zones with breccia consisting of a chaotic mixture of blocks and stones embedded in a clay matrix. The breccia is saturated, has a high porosity and exhibits poor mechanical properties in the range between hard soils and weak rocks. The overburden and high in situ pore pressures in combination with the low strength of the breccia may lead to heavy squeezing. The crossing of the breccia zones thus represents one of the key challenges in the construction of the tunnel. In order to improve our understanding of the mechanical behaviour of the breccias, a series of triaxial compressions tests were carried out. Standard rock mechanics test equipment was not adequate for this purpose, because it does not provide pore pressure control, which is important in the case of saturated porous materials. Pore pressure control is routine in soil mechanics tests, but standard soil mechanics equipment allows only for relatively low nominal loads and pressures. In addition, the low hydraulic conductivity of the breccias demands extremely low loading rates and a long test duration. For these reasons, we re-designed several components of the test apparatus to investigate the mechanical behaviour of the breccia by means of consolidated drained and undrained tests. The tests provided important results concerning the strength, volumetric behaviour, consolidation state and hydraulic conductivity of the breccias. The present paper describes the test equipment and procedures, provides an overview of the test results and discusses features of the mechanical behaviour of the breccias which make them qualitatively different from other weak rocks such as kakirites—a typical squeezing rock in alpine tunnelling. The paper also demonstrates the practical importance of the experimental findings for tunnelling in general. More specifically, it investigates the short-term ground response to tunnel excavation from the perspective of elasto-plastic behaviour with the Mohr–Coulomb yield criterion. The computational results indicate that the breccias will probably experience very large deformations already around the advancing tunnel heading, which can be reduced considerably, however, by advance drainage. The analyses additionally show that plastic dilatancy is favourable with respect to the short-term response, thus highlighting the importance of the constitutive model when it comes to theoretical predictions.     

Visco-Plastic Behaviour around Advancing Tunnels in Squeezing Rock

Summary  The visco-plastic behaviour of rocks plays a relevant role in the tunnelling works, especially for deep tunnels subjected to large initial stresses for which squeezing conditions may develop. A rheological model is discussed that accounts for visco-elastic (primary) and visco-plastic (secondary) contributions to rock creep. The effects of tertiary creep are included in the model by way of a gradual mechanical damage governed by the cumulated visco-plastic strains. The parameters of the intact rock are first identified based on laboratory test results presented in the literature. Then, after scaling them to those of the rock mass, the potential applicability of the model is tested through axisymmetric and plane strain finite element analyses of the full face excavation of a deep circular tunnel. The results are discussed with particular reference to the short term redistribution of stresses around the opening and to its convergence. The analyses show the relevant influence of tertiary creep on the tunnel closure. In addition, those based on an axisymmetric scheme turn out to be crucial for the correct long term prediction of the interaction between the rock mass and the supporting structure of the opening.     

On the non-linear ‘squeezing’ effects around circular tunnels

An analysis is presented of the non-linear creep effects around a deep circular tunnel driven in ‘squeezing’ ground. The time-dependent behaviour of the geotechnical medium is described by means of a simple viscoplastic rheological model capable of approximating primary, secondary and tertiary creep behaviours. It is shown that tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the ‘evolutive’ procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered.     

Continuum modelling of jointed porous rock

Constitutive equations for the mechanical and hydraulic behaviour of saturated porous rock with joint sets of specified orientations are developed by superposing continuum representations for the mechanical and hydraulic properties of the intact rock and each of the joint sets. The resulting continuum theory allows for fluid diffusion through and between interconnected rock pores and joint sets of specified orientation, and also accounts for the anisotropy of the mechanical properties due to joint stiffnesses. The accuracy and reliability of this model are verified by finite element simulation of example problems. The first example considers joint orientation-dependent rock deformation in a hypothetical porous medium with one joint set of different dip angles. More realistic examples related to rock slope stability and reservoir-induced seismicity are also considered in which the constitutive law's utility for modelling time-dependent fluid pressures is illustrated.     

Approximate time-dependent analysis of tunnel support structure considering progress of tunnel face

The pressure acting on tunnel support structures generally increases with lapse in time. The pressure increase may be caused by not only the time-dependent mechanical properties of the underground medium, but also by the progression of the tunnel face. In order to clarify these two effects, three-dimensional analysis is required. In this study, however, a method which takes into account the three-dimensional effects of the tunnel face progression in two-dimensional plane strain analyses is proposedby introducing the ‘equivalent intial stress’. The proposed method can be easily applied to time-dependent analyses of the behaviour of tunnel support structures installed in a visco-elastic medium. The tunnels considered here are circular in shape, being driven in homogeneous isotropic linear visco-elastic media having hydrostatic initial stresses. In the first part of this paper, detailed discussions of the proposed equivalent initial stress are given. The second deals with the mathematical formulations for obtaining closed-form solutions for the pressure acting on tunnel support structures. In the third, numerical results and discussions are given, and special attetion is paid to the effects of both the time-dependent mechanical properties of the material and the tunnel face progression. Finally, the theoretical results obtained here are utilized for interpretation of field measurements.     

Experimental study of thermal effects on the mechanical behaviour of a clay

The paper presents the results of an experimental study of thermal effects on the mechanical behaviour of a saturated clay. The study was performed on CM clay (Kaolin) using a temperature-controlled triaxial apparatus. Applied temperatures were between 22 and 90°C. A comprehensive experimental program was carried out, including: (i) triaxial shear tests at ambient and high temperatures for different initial overconsolidation ratios; (ii) consolidation tests at ambient and high temperatures; and (iii) drained thermal heating for different initial overconsolidation ratios. The obtained results provide observations concerning a wide scope of the thermo-mechanical behaviour of clays. Test results obtained at 90°C were compared with tests performed at ambient temperature. Based on these comparisons, thermal effects on a variety of features of behaviour are presented and discussed. Focus is made on: (i) induced thermal volume change during drained heating; (ii) experimental evidence of temperature influence on preconsolidation pressure and on compressibility index; (iii) thermal effects on shear strength and critical state; and (iv) thermal effects on elastic modulus. Thermal yielding is discussed and yield limit evolution with temperature is presented. The directions of the induced plastic strains are also discussed. Several remarks on the difference in the mechanical behaviour at ambient and high temperatures conclude the paper. Copyright © 2004 John Wiley & Sons, Ltd.     

A Non-Isothermal Constitutive Model for Chemically Active Elastoplastic Rocks

Hydration/dehydration of water-active rocks under non-isothermal conditions is encountered in many industries, in particular the drilling industry. Water-active rocks can adsorb water on their basal crystal surfaces on both the external, and, in the case of expanding lattice clays, the inter-layer surfaces. There are two main mechanisms in which the instability may occur for a structure built in water-active rocks. First mechanism is the change in stresses resulted from mechanical, hydraulic, chemical and thermal interaction, which we formulate based on the concept of non-equilibrium thermodynamics. Second mechanism illustrates the change in mechanical properties of the rock due to physic-chemical interaction between the rock and exposed fluid. We postulate the later mechanism in terms of chemically active plastic deformation by using the modified Cam Clay model. The complete governing equations for non-isothermal chemo-poro-elastoplastic rock are therefore presented. A three-dimensional finite element model is then developed to solve the obtained governing equations. From the numerical results, it was found that the effect of temperature coupling term on stress cannot be ignored when non-isothermal conditions are encountered. However, this effect is almost trivial on pore pressure. It was also revealed that the effect of change in the shale’s mechanical properties on stability due to physic-chemical interaction is as important as change in stresses due to mechanical, hydraulic, chemical and thermal interactions.     

A constitutive thermomechanical model for saturated clays

The structural deformation in clays results from microscopic phenomena involving the mechanical contact-stress change, the physico-chemical variation of repulsive forces in expansive clays, and thermal dilatancy of macropores. These textural strains are associated to three plastic mechanisms represented by respectively the yield surfacesf_Tm, f_R-A andf_T. Under a thermal cycle, the sizes of interlamellar spaces between clay platelets are not modified, hence the temperature cycle is expected to have no effect on repulsive forces and thus the second mechanism is not affected by temperature changes.

This paper suggests a formulation of a model of thermo-elasto-plastic behaviour of non-expansive saturated clays characterised by two plastic mechanisms. The mechanical yield surfacef_Tm of the contact-stress mechanism is based on a modified cam-clay model; the thermal softening yield surfacef_T is a plane separating two thermal domains. In normally consolidated conditions, the resulting response to an increase of temperature is compressive. However, in highly overconsolidated conditions, a small irreversible dilative volumetric strain is observed when the temperature is above a threshold value. In intermediate conditions, the material starts with an expansion and tends to a compression.

The constitutive model combines thermo-mechanical hardening, predominant in normally consolidated states (NCS) and absent in overconsolidated states (OCS) where the thermal softening occurs. The characterisation of the model requires information about rheological parameters obtained from oedometric and triaxial paths. Lastly, some numerical simulations of thermo-mechanical tests onremoulded Boom, ‘Bassin Parisien’ andPontida clays are presented, which show satisfactory agreement between experiments and model predictions.     

温度对粘性土介质力学特性的影响

分析了温度效应对粘性土介质若干基本力学特性的影响。对粘性土的热固结问题、温度对粘性土介质渗透特性的影响、粘性土中的热传导规律及热阻抗特性、土-水体系在温度效应下的作用机理、温度作用下粘性土的本构规律等进行了深入研究。特别就温度诱致的孔隙水压力的变化机理及不同性质土类粘性土体积变化的可逆性问题进行了探讨。     

Interpretation of Core Extrusion Measurements When Tunnelling Through Squeezing Ground

Squeezing intensity in tunnelling often varies over short distances, even where there is no change in the excavation method or lithology. Reliable predictions of the ground conditions ahead of the face are thus essential to avoid project setbacks. Such predictions would enable adjustments to be made during construction to the temporary support, to the excavation diameter and also to the final lining. The assessment of the behaviour of the core ahead of the face, as observed by means of extrusion measurements, provides some indications as to the mechanical characteristics of the ground. If the ground exhibits a moderate time-dependent behaviour and the effects of the support measures are taken into account, the prediction of convergence is feasible. If the ground behaviour is pronouncedly time-dependent, however, convergence predictions become very difficult, because core extrusion is governed by the short-term characteristics of the ground, which may be different from the long-term properties that govern final convergence. The case histories of the Gotthard Base Tunnel and of the Vasto tunnel show that there is a weak correlation between the axial extrusions and the convergences of the tunnel. By means of the case histories of the Tartaiguille tunnel and Raticosa tunnel, it is shown that to identify potentially weak zones on the basis of the extrusion measurements, careful processing of the monitoring data is essential: the analysis of the data has to take account of the effects of tunnel support and time, and has to eliminate errors caused by the monitoring process.     

Progressive degradation of rock properties and time-dependent behavior of deep tunnels

Time-dependent response of deep tunnels is studied considering the progressive degradation of the mechanical properties of the rock mass. The constitutive model is based on a rock-aging law for the uniaxial strength of the rock and for the Young’s modulus. A semi-analytical solution is developed for the stresses and displacements around a deep circular tunnel taking into account the face advance. The evolution of the plastic and damage zones over time is determined. Numerical examples are presented for the case of Saint-Martin-La-Porte access adit in France of the Lyon–Turin Base Tunnel. The computed results which are compared with the field data in terms of the convergence of tunnel wall and of the displacements inside the rock mass monitored by multi-point extensometers show the efficiency of the approach to simulate the time-dependent deformation of a tunnel excavated in squeezing ground. Simple relationships are proposed to evaluate the parameters of the constitutive model directly from those of the empirical convergence law presented in previous work.     

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.     

A semianalytic time-resolved poro-elasto-plastic model for wellbore stability and stimulation

Wellbore stability problems and stimulation operations call for models helping in understanding the subsurface behaviour and optimizing engineering performance. We present a fast, iteratively coupled model for the flow and mechanical behaviour that employs a time-sequential approach. Updates of pore pressure are calculated in a timestepping approach and propagated analytically to updates of the mechanical response. This way, the spatial and temporal evolution of pressure and mechanical response around a wellbore can be evaluated. The sequential approach facilitates the incorporation of pressure diffusion and of time-dependent plasticity. Also, it facilitates the implementation of permeability evolving with time, due to plasticity or stimulation. The model has been validated by means of a coupled numerical simulator. Its capabilities are demonstrated with a selection of sensitivity runs for typical parameters. Ongoing investigations target geothermal energy operations through the incorporation of thermo-elastic stresses and more advanced plasticity models.     

The Mechanical Behaviour of Clay Shales and Implications on the Design of Tunnels

Summary  This paper is a contribution to the study of tunnelling in difficult conditions, with attention paid to large time-dependent deformations, which may develop either during construction, causing instabilities of the tunnel heading and of the face, or during the service life of the tunnel. Under these circumstances the construction costs may rise due to the delays in excavation time, the stabilisation and heavy support measures that need be adopted. Following a review of characterisation and modelling of time-dependent behaviour in rock, the mechanical behaviour of Clay Shales (CS), a structurally complex formation of the Apennines (Italy), is described. Then, the key factors involved in the selection of the constitutive model for CS are identified. Two constitutive models are selected and discussed and their specific material parameters determined. A case study of a large size tunnel is presented where numerical modelling by the finite difference method is carried out. The results of modelling are compared with the monitoring data in terms of radial convergence of the tunnel and extrusion of the tunnel face.     

花岗岩隧道脆性破坏的温度效应研究

目前深埋硬岩隧道的岩爆等脆性破坏研究还较少考虑到温度的作用效应。采用精细网格数值模型,提出热-脆性-精细力学计算方法,应用能反映高地应力下硬岩脆性破坏特点的岩体劣化模型,结合能量计算指标,开展了不同温度作用下隧道硬岩脆性破坏的热力耦合分析。以瑞典APSE花岗岩隧洞岩柱为例,进行不同地温下隧道破坏区、能量释放值和应力指标的定量化对比研究。研究结果表明,隧道地温的增加将使岩体产生附加温度应力,进而增大其脆性破坏程度,计算结果与隧道现场的破坏规律基本一致。热-脆性-精细力学计算能合理描述硬岩的损伤和渐进破坏过程,计算结果较好地揭示了花岗岩等硬岩深埋隧道脆性破坏的温度作用效应,对于高应力、高地温下深部工程的稳定性评价具有指导意义。     

Radial Deformations Induced by Groundwater Flow on Deep Circular Tunnels

Summary. The magnitude and distribution of ground deformations around a tunnel are often monitored during construction and provide key information about ground-support interaction and ground behavior. Thus it is important to determine the effects of different parameters on ground deformations to accurately and effectively evaluate what contributes to ground and support behavior observed during excavation. This paper investigates one such relation: the effects of seepage on radial deformations. A number of numerical analyses have been conducted with the following assumptions: deep circular unsupported tunnel, elastic ground, isotropic far field stresses, dry ground or saturated ground with steady-state water seepage. The analyses cover a wide range of tunnel sizes, effective stresses, and pore pressures. Results from the numerical simulations confirm previous analytical solutions for normalized radial deformations behind the face (i.e. on the tunnel side of the face) of a tunnel excavated in dry ground, and have been used to propose a new analytical formulation for normalized radial displacements ahead and behind the tunnel face for both dry and saturated ground with water flow. Water seepage substantially increases the magnitude and distribution of the normalized radial deformations ahead of the face and at the tunnel face, but does not change much the displacement distribution behind the tunnel face.     

泥岩核废料处置库温度-渗流-应力耦合参数敏感性分析

针对比利时HADES地下实验室PRACLAY现场加热试验,应用温度-渗流-应力耦合弹塑性模型,模拟现场加热过程中泥岩核废料处置库的水力学响应特征。采用单因素分析法,就泥岩热、水、力学参数对核废料处置库围岩孔压、温度、有效应力的影响进行了三维有限元分析。并基于参数敏感性分析结果,就温度、渗流、应力三场两两耦合作用对处置库围岩水力学响应的影响程度进行了系统分析。研究结果表明：泥岩热、水、力学参数中,渗透系数、弹性模量以及导热系数对加温所导致的超孔压的值影响较大;凝聚力、内摩擦角以及热膨胀系数对孔压的影响较小,但会显著影响围岩的有效应力;导热系数对围岩温度场的分布有决定性影响,温度传递的差异会显著影响围岩的孔压和有效应力;不同的热、水、力学参数对孔压、温度以及有效应力的影响机制是不同的,温度、渗流、应力三场两两耦合作用对围岩水力学响应的影响程度也存在显著的差异性。温度场对应力场、温度场对渗流场的耦合效应十分显著,加热后,围岩超孔压的产生以及热膨胀导致的有效应力变化会显著影响处置库的稳定。该研究结果在一定程度上可以为核废料处置库泥岩的热、水、力学参数的确定及耦合机制分析提供科学依据。