caa a22 4500 463163508 CHVBK 20180406164754.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11242-006-9026-y doi (NATIONALLICENCE)springer-10.1007/s11242-006-9026-y Thermomechanics of porous media - II: thermo-hydro-mechanical model for compacted bentonite [Elektronische Daten] [Petri Jussila, Juha Ruokolainen] The general thermomechanical and mixture theoretical model derived by Jussila [Transport Porous Med 62, 81-107 (2006)] is applied to the fully coupled thermo-hydro-mechanical description of swelling compacted bentonite. The particular form of the free energy of the clay constituent is chosen to take into account non-linear elastic strain and moisture swelling. The model parameters are calibrated by the simulation of various coupled experiments for compacted Almerian bentonite. Numerical implementation is done with the multi-purpose finite element method software ELMER (CSC 2005). Springer Science+Business Media, B.V., 2006 Bentonite nationallicence Engineered barrier nationallicence Nuclear waste disposal nationallicence Swelling nationallicence Suction nationallicence Adsorption nationallicence Phase change nationallicence Mixture theory nationallicence Constitutive equations nationallicence Thermomechanics nationallicence Latin symbols nationallicence a , b : Constant material parameters [-] nationallicence $$\hat{B}$$ : Subgradient component belonging to subdifferential of indicator function I [Pa] nationallicence c : Specific heat [J/(kgK)] nationallicence dx : Constant parameter in the experimental thermal conductivity nationallicence D : Diffusivity [m2/s] nationallicence D : Rate of deformation [1/s] nationallicence e : Specific internal energy [J/kg] nationallicence E : Young's modulus [Pa] nationallicence f : Adsorption function [-] nationallicence f Π : Swelling function [-] nationallicence F : Right hand side vector in numerical time integration scheme nationallicence g : Gravitational acceleration vector [m/s2] nationallicence G : Shear modulus [Pa] nationallicence h : Specific enthalpy [J/kg] nationallicence H : Heat transfer coefficient [J/(Km2)] nationallicence I : Indicator function for the molar volume fraction restrictions nationallicence J : Indicator function for the constant density constituents nationallicence k : Permeability [m2] nationallicence K : Bulk modulus [Pa] nationallicence $$\mathsf{K}$$ : Matrix containing spatial derivative and reaction terms nationallicence l : Latent heat of vaporization [J/kg] nationallicence L : Abbreviation, L=l 0−(c v p −c l p )T 0 [J/kg] nationallicence m : Mass [kg] nationallicence m : Rate of production of linear momentum [N/m3] nationallicence M : Molar mass [kg/mol] nationallicence $$\mathsf{M}$$ : Time derivative coefficient matrix nationallicence n : Mole number [mol] nationallicence n : Normal vector [m] nationallicence p : Pressure, spherical part of Cauchy's stress [Pa] nationallicence q : Heat flux density [W/m2] nationallicence r : Radial coordinate [m] nationallicence R : Universal gas constant [J/(molK)] nationallicence RH : Relative humidity [-] nationallicence s : Specific entropy [J/(kgK)] nationallicence t : Time [s] nationallicence T : Temperature [K] nationallicence u : Displacement [m] nationallicence U : Absolute velocity [m/s] nationallicence v : Volume [m3] nationallicence $$\tilde{v}$$ : Specific volume [m3/kg] nationallicence V : Relative velocity [m/s] nationallicence w : Gravimetric water content [-] nationallicence x : Molar fraction [-] nationallicence X : Numerical solution vector nationallicence z : Height coordinate [m] nationallicence Greek symbols nationallicence α : Constant parameter in the experimental diffusivity [-] nationallicence β : Volume fraction [-] nationallicence Δ t : Time step size [s] nationallicence ε : Numerical convergence tolerance nationallicence $$\mathbf{\epsilon}$$ : Strain [-] nationallicence ɛ : Void ratio [-] nationallicence ζ : Vapor fraction [-] nationallicence η : Porosity [-] nationallicence θ : Rate of production of mass [kg/(m3s)] nationallicence $$\iota$$ : Rate of production of energy [W/m3] nationallicence λ : Thermal conductivity [W/(Km)] nationallicence μ : Dynamic viscosity [kg/(sm)] nationallicence ν : A coefficient related to the maximization of entropy production [-] nationallicence ξ : Molar volume fraction [-] nationallicence Π : Swelling pressure [Pa] nationallicence ρ : Apparent density [kg/m3] nationallicence $$\tilde{\rho}$$ : Intrinsic density [kg/m3] nationallicence $$\mathbf{\sigma}$$ : Cauchy's stress [Pa] nationallicence υ : Poisson's ratio [-] nationallicence ϕ : Dissipation function [W/m3] nationallicence χ : Liquid saturation [-] nationallicence χ′ : Specific value of liquid saturation in the experimental thermal conductivity [-] nationallicence ψ : Specific constituent free energy [J/kg] nationallicence ∂Ω : Boundary nationallicence Superscripts nationallicence D : Deviatoric nationallicence p : Constant pressure nationallicence v : Constant volume nationallicence ξ : Interaction of the mixture constituents nationallicence 0 : Outside the porous medium, a mixture of gas and liquid nationallicence Subscripts nationallicence * : Reference (velocity) nationallicence 0 : Reference state nationallicence a : Air nationallicence c : Capillary, suction nationallicence dry : Value at dry state nationallicence eff : Effective nationallicence g : Gas nationallicence init : Initial value nationallicence j : General phase nationallicence i, k, p, q : General mixture constituents nationallicence l : Liquid nationallicence max : Maximum nationallicence ref : Reference state of the experimental diffusivity nationallicence rev : Representative elementary volume nationallicence s : Solid nationallicence sat : Value at saturated state nationallicence v : Vapor nationallicence V : Vertical nationallicence vg : Relative velocity of vapor and gas nationallicence Jussila Petri Stuk, Box 14, FI-00881, Helsinki, Finland aut Ruokolainen Juha CSC - Scientific Computing Ltd, Box 405, 02101, Espoo, Finland aut Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 275-296 0169-3913 67:2<275 2007 67 11242 https://doi.org/10.1007/s11242-006-9026-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9026-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jussila Petri Stuk, Box 14, FI-00881, Helsinki, Finland aut NATIONALLICENCE 700 1- Ruokolainen Juha CSC - Scientific Computing Ltd, Box 405, 02101, Espoo, Finland aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 275-296 0169-3913 67:2<275 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer