Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 Journal of Rock Mechanics and GeotechnicalEngineering Journal of Rock Mechanics and Geotechnical Engineering journal homepage: www.rockgeotech.org A thermo-hydro-mechano-chemical formulation for modeling water transport around a ventilated tunnel in an argillaceous rock Chengyuan Zhang a , Xiaoyan Liu b,c,∗ , Quansheng Liu a a Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China College of Civil Engineering, Wuhan University, Wuhan 430072, China c Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of Ministry of Education, Wuhan University, Wuhan 430072, China b a r t i c l e i n f o Article history: Received 22 May 2012 Received in revised form 19 September 2012 Accepted October 2012 Keywords: Nuclear waste disposal Argillaceous clay Unsaturated flow Ventilation experiment Solute transport DECOVALEX a b s t r a c t Argillaceous rocks are being considered as potential host rocks for deep geological disposal For the research work in DECOVALEX-2011, participant research teams performed simulations of a laboratory drying test and a ventilation experiment for Mont Terri underground laboratory built in argillaceous rock formation Our study starts with establishing a coupled thermo-hydro-mechano-chemical (THMC) processes model to simulate water transport in rock around the ventilated tunnel Especially in this THMC formulation, a three-phase and two-constituent hydraulic model is introduced to simulate the processes which occur during tunnel ventilation, including desaturation/resaturation in the rock, phase change and air/rock interface, and to explore the Opalinus clay parameter set It can be found that water content evolution is very sensitive to intrinsic permeability, relative permeability and capillary pressure in clay rock Water loss from surrounding rock is sensitive to the change of permeability in clay which is induced by excavation damaged zone Chemical solute transport in the rock near ventilation experiment tunnel is simulated based on the coupled THMC formulation It can be estimated that chemical osmotic flow has little significance on water flow modeling Comparisons between simulation results from teams and experimental observations show good agreement It increases the confidence in modeling and indicates that it is a good start for fully THMC understanding of the moisture transportation and mechanical behavior in argillaceous rock © 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences Production and hosting by Elsevier B.V All rights reserved Introduction Argillaceous formations are being investigated worldwide as host media for the disposal of high-level radioactive waste, because of their favorable properties In Switzerland, the Mont Terri rock laboratory was created in 1995 in an argillite layer (called Opalinus clay) to characterize and study the geological, hydrogelogical, geochemical and geotechnical properties of this clay formation (Thury and Bossart, 1999) It is located in northwest Switzerland, about ∗ Corresponding author Tel.: +86 27 87199185 E-mail address: liuxiaoyan09202@163.com (X Liu) Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences 1674-7755 © 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences Production and hosting by Elsevier B.V All rights reserved http://dx.doi.org/10.1016/j.jrmge.2013.03.003 500 m beneath the hill, as shown in Fig (Martin and Lanyon, 2003) The Opalinus clay formed in the Jurassic Sea around 180 million years ago, and its name is derived from a key fossil, Leioceras Opalinum whose surface is opalescent In Mont Terri rock laboratory, heavily instrumented experiments have been designed and installed to supply a large amount of data, which can be further used for model validation Among these experiments, the ventilation experiment (VE) has been carried out in a micro-tunnel to study the desaturation process, which may happen because of the forced ventilation in galleries and drifts, during the construction and operation phases of the repository One common interest of DECOVALEX-2011 (D2011), the 5th stage of DECOVALEX project, focused on hydraulic and mechanical behaviors of Opalinus clay of repository tunnel in Mont Terri rock laboratory Specifically the following issues are involved: desaturation/resaturation, phase change, air/rock interface, and damage/microcracking of the host rock due to hydro-mechanical and/or chemical effects (Floría et al., 2002) The significance of the study lies in the fact that all tunnels in the nuclear waste repository will be subjected to ventilation effects to some extent during the operational phase of the facility It is believed that argillaceous rocks may be especially sensitive to this 146 C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 Fig Isometric view and location of the Mont Terri rock laboratory (Martin and Lanyon, 2003) type of actions (Tsang et al., 2008) During the construction and operational phases of a repository, the ventilation of the openings by relatively dry air and the subsequent backfilling with unsaturated materials will lead to evaporation of the pore water from the surrounding rock After closure of the repository, the previously de-hydrated rock returns to its original saturated conditions Tunnel ventilation dehydrates the rock near the tunnel, and the air entry into the rock results in two-phase flow conditions with reduced effective hydraulic conductivity For plastic and indurated clays, tunnel ventilation and rock saturation–resaturation cycles significantly change rock plasticity and strength parameters The rock creep and self-sealing effect, occurring in the clay formations, is a strong function of the water content On the other hand, the hydraulic changes in rocks increase or reduce the effective stress, resulting in fracture–aperture and permeability changes Therefore, it is essential to model the in situ VE (laboratory drying experiment by Floría et al (2002)) and offers the possibility to calibrate Opalinus clay’s parameter set The main objectives of this study are to verify numerical models of the hydraulic processes occurring in surrounding rock during ventilation Coupled thermo-hydro-mechanical formulations 2.1 Summary of the thermo-hydro-mechanical formulations The formulations used by the different D2011 teams aim at the resolution of water, air and heat flow in deformable porous media (Garitte et al., 2013) The five different teams (Chinese Academy of Sciences (CAS), Commissariat l’Energie Atomique (CEA), Japan Atomic Energy Agency (JAEA), Quintessa Ltd (Quintessa), University of Edinburgh (UoE)) used five different codes The formulations used differ slightly from team to team depending on the capacities of each code The code and the balance equations used by each of the teams are summarized in Table 1, in which “×” means the process is implemented in code Further general information is given hereunder We intend to embrace the common features of the different teams and to point out some differences We refer to the teams individual reports for more specific information The description of the water mass balance and the associated constitutive laws was given more importance, as it was found to be the equation governing the most important processes FRT-THM is a finite element simulator used by CAS It is a combination of home-made C codes, Matlab® and its toolbox Femlab® Sequence of solving partial differential equations can be controlled by C codes and script language of Matlab It brings the power of numerical analysis into multiphysics analysis through an interactive environment Some of the main features of combined simulator include easy modeling, improvising and customizing, and the simplicity with which non-standard computations can be run Femlab is a tool for exploration and quick insight into physics, models, and parameters In this study, chemical solute transport is included to model solute osmotic water flow Therefore, the enhanced simulator should be called FRT-THMC CAST3M, used by CEA, is a general purpose object oriented finite element code Development of CAST3M started at the CEA in the early 1980s (Verpeaux et al., 1989) and aimed originally at structural and fluid mechanics problems Any problem is treated as an operation sequence defined by the users More than 300 elementary operators are available in CAST3M They are used for pre-processing tasks (e.g mesh), heat transfer, mechanical and structural analyses, fluid dynamics, magneto-static analyses, and post-processing tasks A wide variety of elements are available The program is widely used in France, and in many universities and research centers, because it offers a real tool-box for solving unconventional problems, often the cases in a research and development environment It has been intensively validated by comparison to analytical solutions, experimental results, international comparative benchmarks, etc THAMES is a finite element code for the analysis of coupled thermo-hydro-mechanical (THM) behaviors of saturated–unsaturated medium THAMES has been extended to take account of the behaviors in the buffer materials such as the water movement due to thermal gradient and the swelling phenomena The unknown variables are total pressure, displacement vector and temperature The mathematical formulation for the model utilizes Biot’s theory, with the Duhamel–Neuman’s form of Hooke’s law, and energy balance equation The governing equations are derived with the fully coupled THM relationships This code has been validated with the data of the laboratory tests (Chijimatsu et al., 1998), the engineered scale tests and the in situ experiments (Chijimatsu et al., 2000) QPAC is Quintessa’s general purpose finite volume code, currently at version 2.0, which can be run under either Windows or Linux operating systems QPAC has been developed under the TickIT quality management system and can be used as a modeling tool to solve a wide range of problems including those with strongly Table Summary of the codes and balance equations used by the D2011 teams Team Code Water balance Solid balance Air balance Energy balance Stress equilibrium CAS CEA JAEA Quintessa UoE FRT-THMC CAST3M THAMES QPAC RockFlow/GeoSys × × × × × × × × × × × × × × × × × × × C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 coupled nonlinear processes It is possible to simultaneously farmout runs to multiple machines, and this can be useful when multiple or probabilistic calculations are undertaken RockFlow/GeoSys is an environmental simulation software tool and a case study involving HTMC coupled processes for geothermal reservoirs The GeoSys/RockFlow code, original RockFlow code, has been developed now for over 30 years It is based on an object orientated approach which allows the easy development of modules specific to modeling requirements for a whole variety of multidisciplinary fields Most common problems are described by a series of partial differential equations, either coupled or uncoupled 2.2 Hydraulic model 2.2.1 Water transport model The most common method of modeling liquid flow in unsaturated media is to combine the equation of linear momentum balance for the liquid phase with the mass balance equation of the fluid The interaction between water and gas flow fields is established through the soil–water characteristic curve describing the dependency of the volume fraction occupied by degree of saturation on suction at a given temperature, and through the phase exchange term, describing the water transfer from liquid phase to gas phase in a vapor form, and vice versa The differential equation governing water flow through an unsaturated porous medium is krl klij ∂Sl ∂(pv + pa − pl ) ∂ − ∂s ∂t ∂xi l ∂pl + ∂xj l gi = jlg (1) where s= 1+ krl = pg − pl P (1/(1− )) Sl [1 − (1 − Sl 1/ ) ] jlg = Ke (es − e) the density and viscosity of water, respectively; Sl is the saturation of matrix; s is the suction, depending on pg − pl ; pg is the pressure of gas; P and Ps are the air entry suctions; and s are the shape factors for pore space; klij is the intrinsic permeability of matrix; krl is the relative permeability of water in two-phase flow system; jlg denotes the rate of moisture transfer between the liquid phase and the gas phase (negative for condensation and positive for evaporation), which can be described using Dalton’s equation (Eq (4)); Ke is the liquid phase change coefficient; e is the vapor pressure; and es is the saturated vapor pressure in contact with liquid over a planar surface, which can be obtained using the psychrometric law: es = es-free exp − In argillaceous rocks around tunnel, rock mass mechanical behaviors are affected by water content in porous media In pore space, water shall transport in liquid phase in response to hydraulic gradients, and also shall transport in the gaseous phase as water vapor due to moisture gradient according to Fick’s law and air convection Then the conceptual hydraulic model used in CAS team’s THM formulation combines three independent processes: (a) advective flow of liquid water, (b) advective and diffusive flow of water vapor, and (c) advective and diffusive flow of dry air Our governing equations are developed using a systematic macroscopic approach Two constituents (water and gas) and three phases (solid, liquid, vapor, and dry air) are identified in this model Each phase is viewed as an independent continuum Total gas pressure equals vapor pressure plus dry air pressure We assume all gas phases obey the ideal gas law In saturated–unsaturated coupled HM framework (solid phase model is independent (Liu et al., 2006)), pore water pressure, pore vapor pressure, pore dry air pressure, matrix displacement vector are introduced as the four primary variables in a three-dimensional (3D) boundary value problem The physical processes, taking into account the purposes of constitutive modeling, include pore fluid transport, phase exchange (evaporation and condensation), matrix deformation due to the changes of mechanical field and water content − 1− pg − pl Ps s (2) (3) (4) where pl , pv and pa are the pore pressures of water, vapor and dry air, respectively; is the medium porosity; t is the time; xi and xj are the space coordinates; gi is the gravity acceleration; l and l are 147 pg − pl T vR (5) where T is the temperature; v is the vapor density; R is the gas constant; and es-free is the saturated pressure on free surface, which is a function of temperature only and can be obtained using empirical vapor pressure data (Maid, 1992): 17.27T 237.3 + T es-free = 611 exp (6) Therefore, water tension effects due to the presence of capillary suction reduce the saturated vapor pressure thus decrease the evaporation rate For liquid phase, the mobility of water is characterized by relative permeability, which is in turn related to suction via saturation, as shown in the Van Genuchten equations The change of saturation due to suction also induces the change of volume fraction occupied by liquid phase We define a storage parameter for the water flow that reflects the effect of porous water storage 2.2.2 Chemical osmotic flow When chemical transport in water is considered, additional driving force should be introduced into water flow model: ∂Sl ∂(pv + pa − pl ) ∂ − ∂s ∂t ∂xi krl klij l = jlg ∂pl + ∂xj l gi − krl k˘ij ∂˘ ∂xj l (7) where ˘ = CRT represents osmotic pressure and obeys the van’t Hoff relationship, in which C is molar concentration of the solute, and R is the gas constant 2.2.3 Vapor model The vapor transport is described as the combination of two processes: (a) diffusion due to vapor gradient, and (b) advection First, advective flux is calculated as qadvection = − krg kvij v ∂pv + ∂xj v gi (8) where kvij is the intrinsic permeability of matrix, krg is the relative permeability of gas phase in two-phase flow system, and v is the dynamic viscosity When the pores are small and the pressure is also low, the mean free path of gas molecules may be comparable to the pore sizes When this happens, slip takes place and the assumption of purely laminar flow is no longer valid (Olivella and Gens, 2000) Knudsen diffusion effect will be introduced in apparent intrinsic permeability with the following form: kvij = k0ij + b pv (9) where k0ij is the initial intrinsic permeability of matrix, and b is the Klinkenberg parameter 148 C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 Second, diffusive flux is calculated as qdiffusion = − Sg D ∂ωv ∂xj (10) where is the tortuosity, Sg is the degree of gas saturation, D is a molecular diffusion coefficient for vapor, and ωv is the mass fraction of vapor in gas mixture For gas phase, another cause of volume change comes from the compressibility of gas includes vapor and dry air The phase exchange between water and vapor is a source and sink term The governing equation of vapor flow is Sg ∂pv − patm + pv ∂t − ∂ ∂xi Sg D ∂Sg ∂(pv + pa − pl ) ∂s ∂t krg kvij ∂ωv + ∂xj v ∂pv + ∂xj v gi =− l v jlg (11) The governing equation of dry air flow is similar to that of vapor flow, without phase exchange term: Sg ∂pa − patm + pa ∂t − ∂ ∂xi Sg D ∂Sg ∂(pv + pa − pl ) ∂s ∂t krg kaij ∂ωa + ∂xj v ∂pa + ∂xj a gi =0 (12) where patm is the pressure of atmosphere; kaij is the intrinsic permeability of matrix, its apparent form also depends on Kundsen diffusion effect; ωa is the mass fraction of dry air in gas mixture, ωa = − ωv assumed that the three phase temperatures are not in local thermal equilibrium, neglecting the increase in the internal energy due to shearing: ∂ ∂xi ns sij ∂Ts ∂xj = ns ∂Ts ∂T + vsi l ∂t ∂xi s Cs − ns lgT ] ∂ ∂xj Dijkl ∂ ∂xi nl lij ∂Tl ∂xj = nl Cl +L l ∂Tl − nl (clT − ∂t l jlg + nl Cl ∂ ∂xi ng gij ∂Tg ∂xj = ng Cg − Cl l vli g l jlg Tl lgT )Tl ∂pl − nl ∂t where uk denotes the displacement component of solid skeleton, which is a 3D vector; Dijkl is the stiffness of rock skeleton; ˛l and ˛g are the dimensionless tangent effective stress parameters, denoting liquid and gas compressibility contribution to matrix deformation, respectively; dTs denotes the thermal expansion of solid skeleton with change of solid temperature dTs ; BSl denotes the moisture expansion of solid skeleton with change of liquid saturation; Fi represents the external forces Hydraulic model is based on two interacting continua: one representing the liquid flow and the other representing the gas flow Thus at every point in simulation space, two pressures are introduced: one denoting the average liquid pressure and the other denoting the average gas pressure The constitutive equation is written in terms of effective stress with advantage of complete expression with single effective stress variable rather than two or three independent stress variables This significantly simplifies the model and reduces model parameters On the other hand, special forces on solid skeleton can be added to this equation easily 2.3.2 Heat transport model Heat transport model includes three equations describing energy balance of solid, liquid and gas phases In this model, it is ∂pg ∂t (14) lgT Tl ∂pg ∂t + Äls (Tl − Ts ) + Älg (Tl − Tg ) ∂Tl ∂xi ∂Tg + ng ∂t − ng (cgT + (15) lgT Tg lgT )Tg ∂pl ∂t ∂pg −L ∂t l jlg + Cg + Ägs (Tg − Ts ) + Ägl (Tg − Tl ) + ng Cg (13) lgT ] where ns is the mass fraction of solid phase; Ts , Tl , Tg are temperatures for solid, liquid and gas phases; s is the density of solid; vsi is the solid skeleton velocity; cT is the isothermal heat capacity; lgT is the change in the pore liquid space due to a change in the curvature of the liquid–gas interface; ng is the mass fraction of gas; ui is the solid deformation; sij is the thermal conductivity of solid phase; Cs is the heat capacity of the solid; Äsl denotes the heat exchange ratio between the solid and liquid phases; and Äsg denotes the heat exchange ratio between the solid and gas phases (Khalili and Khabbaz, 1995) Similarly, energy balance equations of liquid and gas are listed in Eqs (15) and (16), respectively: ∂duk − (˛l dpl + ˛g dpg + BSl + dTs )ıij + dFi = ∂xl (i = 1, , N) ∂pl − Ts [(˛g − ng )cT + ns ∂t ∂2 ui + Äsl (Ts − Tl ) + Äsg (Ts − Tg ) ∂t∂xi + Ts 2.3 Mechanical and thermal models 2.3.1 Mechanical model Mechanical model is deemed based on thermal-elastic framework, which satisfies the equations of equilibrium It is coupled with water flow and heat transfer processes The total equation for mechanical model can be written as − Ts [(˛l − nl )cT l jlg Tg g vgi ∂Tg ∂xi (16) where lij and gij are the thermal conductivities of liquid and gas phases, respectively; clT is the isothermal heat capacity for liquid; Älg is the heat exchange ratio between liquid and gas phases; vli and vgi are the liquid and gas velocities, respectively; g is the density of gas; cgT is the isothermal heat capacity of gas; Cl and Cg are the heat capacities of liquid and gas phases, respectively; L is the latent heat of vaporization Besides heat exchange between solid and liquid, the energy transport due to phase change is considered in these equations by term Simulation of water transport 3.1 Calibration The main objectives of calibration are to verify numerical models of the processes occurring during ventilation and to gain suitable parameters This first-step study concerns a laboratory experiment which was originally designed to offer the possibility to calibrate Opalinus clay’s parameter set, and to provide information to help modeling the in situ VE (laboratory drying experiment by Floría et al (2002)) In order to obtain data about relevant rock hydraulic parameters, rock samples were subjected to desaturation under controlled climatic conditions The drying test was designed to C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 149 Fig Drying chamber for ventilation test (Garitte and Gens, 2008) measure the actual rate of evaporation from three core samples of Opalinus clay The rock samples and a water pan were tested inside a drying chamber under controlled conditions (temperature = 30 ◦ C, relative humidity (RH) = 33% and air flow rate = 0.5 m/s) specifically prepared for this purpose (Fig 2) The core samples were isolated to allow water evaporation exclusively from their top surface We used enhanced FRT-THM simulator (finite element method code developed and applied in DECOVALEX-THMC research (Liu et al., 2006)) to solve the governing equations described above for the analysis of coupled multiphase flow, phase exchange, and capillary suction A 3D model is created with non-flux boundaries except for top boundary in the simulation, and the parameters are shown in Table Top boundary condition represents that air and vapor exchange between core sample and tunnel space Fig presents the evolution of pore pressure (water, vapor and dry air pressure) of rock samples during the drying test It is shown that values of all pressures and their gradients at the top of the sample are less than those at the bottom That means the water moisture transports upward in the form of vapor during the drying process In the early time of drying test, liquid occupies more volume in sample bottom than gas, thus it is more difficult to complete phase exchange from water to vapor and to form effective transportation path from bottom to top ˜ Munoz et al (2001) carried out simulation for water content profile of these three samples Fig presents the comparison of their results and ours It can be seen that both their and our results are quite similar to the long-run measurements Fig 5a shows the comparison for water content profiles between participant research teams in D2011 task A It can be seen that there is a good agreement which gives confidence in modeling the processes occurring during ventilation and identification of the Opalinus clay’s parameters sets We find that simulation results are very sensitive to intrinsic permeability, relative permeability and capillary pressure Fig 5b presents comparison of water loss evolution for different fitting curves of controlled RH data in the drying test One is an exponential function of time and the other is constant RH value of 33% The calculated RH value from exponential function would be 5–14% less than the constant RH value However, the modeling results of water loss evolution for these two different fitting curves of RH data Fig Simulation results of pore pressure evolution (water, vapor and dry air pressure) of samples in drying test not have much difference It means that this hydraulic model is accurate enough, which provides necessary base for THM simulation, since parameters of mechanical model are strong functions of the water content in Opalinus clay After calibration, hydraulic parameters sets for the Opalinus clay were derived on the basis of the laboratory drying test 3.2 Simulation on water transport around ventilation tunnel We carried out simulation on water transport around ventilation tunnel In concept model, the only way moisture exchanges Table Parameters for argillaceous column model Retention curve (modified van Genuchten model) se = 1+ pg −pl Pa (1/(1− )) (0 < se < 1, pa = 3.9 MPa, − 1− = 0.128, pg −pl Ps s s = 2.73, Ps = 700 MPa) Relative permeability (van Genuchten model) krl = √ se [1 − (1 − se 1/ ) ] (0 < Se < 1, = 0.68) Porosity Initial suction 0.16 (fully saturated) 150 C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 200 200 150 Water loss (g) Water loss (g) 150 100 Sample A 100 Sample B CODE_BRIGHT 50 Sample C 50 Sample A Calculated Sample B 0 50 100 200 150 50 100 Time (day) 150 200 Time (day) 0.30 0.30 0.25 0.25 Distance from base (m) Distance from base (m) (a) Water loss (left: work by CAS; right: from Muñoz et al., 2001) 0.20 Calculated-21 days 0.15 Calculated -99 days Calculated -142 days 0.10 Measured - 21 days 0.20 Calculated-21 days 0.15 Calculated-99 days Calculated-142 days 0.10 Measured - 99 days 0.05 Measured-21 days 0.05 Measured - 142 days Measured-99 days Measured-142 days 0.00 0.00 Water content (%) Water content (%) (b) Water content (left: work by CAS; right: from Muñoz et al., 2001) ˜ Fig Measured and computed results for water content, compared with Munoz et al.’s work (water loss at different times and water content evolution for the drying samples) between rock mass and tunnel space is movement of vapor while water can transport through rock pore space in liquid and gas phase (see Fig 6) Gas is a mixture of dry air and vapor The ventilation rate and the humidity of the inflow-air were varied during the three successive desaturation phases The mean RH and the evaporation coefficient of the test section air were estimated and presented in Table In this VE, temperature of inflow air is set to a fixed value, 15 ◦ C, and each part of water–vapor–air system has nearly the same temperature even affected by heat transfer from far field rock Therefore, the influence of temperature on moisture transport can be ignored A 2D hydro-mechanical plane-strain analysis was performed in CAS’s simulation Fig shows the domain size, numerical grids and boundary conditions used It consists of 1566 elements in 2D simulation The vertical total stress ( v ) is assumed to be a principal stress and equal to the lithostatic stress At the tunnel location, the initial field stress is v = 6.4 MPa, horizontal stress H = 2.04 MPa, and the initial water pressure is 1.94 MPa The hydraulic parameters sets which include important water retention and relative permeability properties of Opalinus clay are the same as those used in the calibration modeling The applied RH boundary condition on tunnel surface in our simulation can be seen in Fig Fig shows the simulation results of water content in rock near tunnel surface during several desaturation–resaturation cycles In Fig 9a, some differences can be seen in initial condition between measurements and settings by different teams However, there is a good agreement shown in Fig 9b for the first dry-out, Fig 9c for the second saturation and Fig 9d for the third saturation It shows the key characteristics of water transport process in argillaceous rock around VE tunnel The range of the partially desaturated zone was estimated to 0–30 cm near tunnel surface, no deeper than 50 cm into rock, in the 4-year test 3.3 Mechano-hydraulic coupling When mechano-hydraulic coupling is performed, evolutive displacement on tunnel surface will appear in simulation Relevant parameters for moisture swelling and mechanical properties used in simulation are listed in Table Fig 10 shows the simulation of displacement evolution on tunnel surface during ventilation In general, rock mass tends to expand when saturated and to shrink when desaturated It seems that the total displacement is very limited, less than mm, while C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 151 Table Experimental condition in Mont Terri tunnel test section Phase Starting date to ending date 2/1999 5/7/2002–1/8/2002 1/8/2002–1/4/2003 1/4/2003–12/6/2003 12/6/2003–3/7/2003 3/7/2003–26/1/2004 26/1/2004–29/1/2004 29/1/2004–2/2/2004 2/2/2004–11/7/2005 11/7/2005–22/2/2006 22/2/2006–8/3/2006 8/3/2006–24/9/2006 24/9/2006–8/12/2009 8/12/2009 Temperature in section air (◦ C) Calculated time in our model (day) 15 −1000 85 15 27 270 342 363 570 573 575 1104 1331 1355 1555 2725 85 93 95 84 47 15 60 100 15 50 10 100 100 15 Estimated RH in section air (%) Table Mechanical properties of the Opalinus clay Solid grain density (kg/m3 ) Moisture swelling coefficient Poisson’s ratio Young’s modulus (GPa) 2710 1.1 × 10−4 (when unit of degree of liquid saturation is %) 0.27 compared to large range of RH of air in tunnel However, it should be noticed that results from different research teams are close to each other while measurements show much more scatter It has to be explained by heterogeneous moisture swelling property or permeability in rock mass if measurements are correct Maybe they are the main reasons which cause larger unstable movement of rock mass around tunnel On the other hand, mechanical effect on water flow should be considered in simulation We carried out a comparative simulation, including Case and Case 2, to see how the increase of permeability induced by excavation damaged zone (EDZ) affects water transport in surrounding rock In Case 1, intrinsic permeability is k = 1.1k0 , which is used in former simulation It represents no damage during the desaturation–resaturation cycles In Case 2, intrinsic permeability k is set to 0.7k0 –2.8k0 in EDZ, varying linearly from m deep to tunnel surface, which represents damage zone induced by desaturation–resaturation cycle, as shown in Fig 11 Comparative water flux through vapor into VE tunnel with/without damage by EDZ is shown in Fig 12 Damage induced permeability increase can cause more water flux into tunnel especially in desaturation phase Therefore, total water loss is much higher than the case without increased permeability, which can be seen in Fig 13 Displacement evolution on tunnel surface shows the same trend, but the value of rock shrinkage is limited (Fig 14) 3.4 Hydro-chemical coupling Chemical solute transports via liquid water flow in rock The governing equation for solute chloride (Cl) transport is listed in Eq (17), including diffusion and advection in water In reverse, Fig Simulation results for water content in rock mass Fig Schematic diagram of water transport in rock and interaction with tunnel air 152 C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 Fig Numerical grids and boundary conditions for moisture transport simulation chemical solute gradient provides additional driving force for water flow, which is introduced in Eq (7): Sr ∂c + ∇ · (− Sr De ∇ c + uc) = Sc ∂t (17) where c is the solute concentration, u is the velocity vector of water flow, De is the effective diffusion coefficient, Sr is the degree of saturation, and Sc is the source term We performed a simulation to see how solute Cl transports in porous rock near VE tunnel and how osmotic flow affects solute transportation In simulation, the value of De is set to 10−11 m2 /s, a value from laboratory measurement in OPA sample (De Windt and Palut, 1999) The chemical permeability k˘ is set to 0.1k, representing strong osmotic effect (Harrington and Horseman, 1999) Also we set fixed far field constant boundary and no Cl flux boundary at tunnel surface for solute chloride (see Fig 15, geometry also see Fig 7) C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 153 Fig 10 Displacement on surface of VE tunnel Fig Boundary condition of relative humidity Fig 11 Schematic diagram of increase of permeability induced by EDZ during desaturation–resaturation cycle Fig 12 Water flux into VE tunnel with/without EDZ Fig Water content in rock near tunnel surface BVE 104, BVE 108 and BVE 111 represent measurements in borehole of VE Fig 13 Water loss evolution with/without EDZ 154 C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 Fig 16 shows evolution of solute concentration of chloride at tunnel surface It is strongly related to desaturation–resaturation cycle After a long term of desaturation, concentration of chloride reaches its peak (before 26 January, 2004), and then goes down because of more and more water comes from surface in resaturation phase (before May, 2005) In Fig 17, it can be found that there is very little difference of concentration of chloride between the cases with and without osmotic flow It seems that osmotic flow has little significance on water flow modeling (less than 1% of classical Darcy flow in general) Conclusions and discussion Fig 14 Displacement with/without EDZ Fig 15 Numerical grids and boundary conditions for solute transport simulation with hydro-chemical model (1) Coupled THMC model including a three-phase and twoconstituent hydraulic sub-model is established It is used to simulate the processes occurring during ventilation and to explore the Opalinus clay’s parameter set, including desaturation/resaturation in the rock, real phase change, air/rock interface and chemical solute transportation Simulation results show the effectiveness of the proposed THMC formulation (2) For the research work in D2011, research teams performed simulations of a laboratory drying test and a VE for Mont Terri underground laboratory Comparisons between simulation results and experimental observations show good agreement (3) Simulation results of moisture transportation are very sensitive to intrinsic permeability, relative permeability and capillary pressure The determination of parameters including heterogeneity is important to achieved good agreement between experimental and simulated results (4) Chemical solute transport in the rock near VE tunnel was simulated based on THMC formulation It can be estimated that osmotic flow has little significance on water flow modeling (less than 1% of classical Darcy flow) Acknowledgments Fig 16 Cl concentration evolution in rock near tunnel surface The work described in this paper was conducted within the context of the international DECOVALEX project (DEmonstration of COupled models and their VALidation against EXperiments) This work was supported by National Nature Science Foundation of China under projects 51108356, 40772161 and 41272272 The authors are grateful to the Funding Organisations who supported the work, and to Quintessa, CEA, JAEA and UoE for modeling compare; Quintessa Ltd and University of Edinburgh were supported by the Nuclear Decommissioning Authority (NDA), UK; CEA was supported by 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Garitte B, Bond A, Millard A, Zhang C, McDermott C, Nakama S, et al Analysis of hydro- mechanical processes in a ventilated tunnel in an argillaceous rock on the basis of different modelling approaches... Schematic diagram of water transport in rock and interaction with tunnel air 152 C Zhang et al / Journal of Rock Mechanics and Geotechnical Engineering (2013) 145–155 Fig Numerical grids and boundary