caa a22 4500 46316301X CHVBK 20180406164753.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s11242-006-0013-0 doi (NATIONALLICENCE)springer-10.1007/s11242-006-0013-0 Numerical Modelling of Swelling Pressure in Unsaturated Expansive Elasto-Plastic Porous Media [Elektronische Daten] [Mingliang Xie, Wenqing Wang, Joëlle De Jonge, Olaf Kolditz] The focus of this work is to provide a new concept for accessing the swelling stress in expansive porous media, especially in highly compacted bentonite. The key to the new approach is the simulation with a chemical swelling model of an infinitesimal volume change followed by a back compaction Process. Free extension is allowed in the first step, to calculate the interlayer porosity change (micro) and the induced volume change potential (macro). The object-oriented FEM simulator GeoSys/RockFlow allows the combination of different processes. The hydro-mechanic/chemical (H2M/C) model takes into consideration two phase flow and deformation, as well as chemical swelling effects. The negative displacements on each boundary after the free extension simulation are taken as Dirichlet boundary conditions of the back compaction problem. The deformation step is simulated in the context of elasto-plasticity using the modified Cam-Clay model. The stresses obtained by back compaction represent the swelling pressure. A 2D example of compacted bentonite is analyzed with the new H2M/C model. Springer, 2007 expansive porous media nationallicence two phase flow nationallicence free extension nationallicence back compaction nationallicence swelling pressure nationallicence modified Cam-Clay model nationallicence numerical modelling nationallicence A : Particle surface area (m2) nationallicence B : Strain-displacement matrix (−) nationallicence c i : Concentration of the ith ion (M) nationallicence C e : Fourth order tensor of elasticity (Pa) nationallicence d : Mean diameter of smectite particles (m) nationallicence D : Diffusion coefficient (m2 s−1) nationallicence e : Void ration in Cam-Clay model (−) nationallicence E : Yong's modulus (Pa) nationallicence $${\mathcal{F}}$$ : Yield function (Pa) nationallicence F : Faraday coefficient (=96485.309 C mol−1) nationallicence $${\mathcal{G}}$$ : Plastic potential (Pa) nationallicence g : Gravity Vector (m s−2) nationallicence J : Flux (kg m−1 s−1) nationallicence I : Ionic strength (mol m−3) nationallicence k : Permeability (m2) nationallicence k : Permeability tensor (m2) nationallicence k rel : Relative permeability (−) nationallicence k sw rel : Swelling relative permeability(−) nationallicence M : Slope of critical state line (−) nationallicence m : Effective layer number (−) nationallicence m : Unit projection vector (−) nationallicence N : Finite element shape function (−) nationallicence n : Porosity (−) nationallicence n tot : Total porosity (−) nationallicence n IL : Interlayer porosity (−) nationallicence n ILmax : Maximum interlayer porosity (−) nationallicence n IP : Interparticle porosity (−) nationallicence n IPmin : Minimum interparticle porosity (−) nationallicence n sw : Porosity change potential (−) nationallicence p csl : Preconsolidation pressure (Pa) nationallicence p : Pressure or hydrostatic pressure (Pa) nationallicence p : Pressure vector (Pa) nationallicence p c : Suction (Pa) nationallicence p c : Suction vector (Pa) nationallicence P S : Mean stress (Pa) nationallicence $${\mathcal{Q}}$$ : Source term (m3 s−1) nationallicence q : Norm of deviatoric stress tensor (Pa) nationallicence R : Gas constant (J mol−1 K−1) nationallicence S total : Total specific surface (m2 g−1) nationallicence S 0 : External specific surface (m2 g−1) nationallicence S : Saturation (−) nationallicence S eff : Effective saturation (−) nationallicence S : Saturation vector (−) nationallicence T : Temperature (K) nationallicence u : Displacement vector (−) nationallicence v : Velocity vector (m s−1) nationallicence v s : Solid velocity vector (m s−1) nationallicence X : Mass fraction (−) nationallicence z i : Ionic charge of the ith ion (−) nationallicence β : Volume fraction of expansive minerals (−) nationallicence γ : Phase (−) nationallicence λ : Virgin compression index (−) nationallicence Λ : Plastic multiplier (−) nationallicence κ : Swelling/re-compression index (−) nationallicence μ : Fluid viscosity (Pa s) nationallicence ργ : Density of phase γ (kg m−3) nationallicence ρd : Dry density of compacted bentonite (g m−3) nationallicence σ : stress tensor () nationallicence σ : Stress () nationallicence ε : Strain tensor () nationallicence ε : Strain () nationallicence τ : Mean thickness of the effective sheets (m) nationallicence ν : Poisson ratio (−) nationallicence ε : Dielectric constant (−) nationallicence ε0 : Permittivity of free space (8.854 × 10−12 C V −1 m −1) nationallicence η : Dimensionless coefficient (−) nationallicence θ : Volumetric water content (−) nationallicence θ s : Saturated volumetric water content (−) nationallicence θ r : Residual volumetric water content (−) nationallicence δ : Thickness of diffuse double layer (DDL) (m) nationallicence ξ : van Genuchten parameter (−) nationallicence Ω : Domain (−) nationallicence ϕ : Shape function (−) nationallicence ω : Test function (−) nationallicence Xie Mingliang Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut Wang Wenqing Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut De Jonge Joëlle Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut Kolditz Olaf Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut Transport in Porous Media Kluwer Academic Publishers 66/3(2007-02-01), 311-339 0169-3913 66:3<311 2007 66 11242 https://doi.org/10.1007/s11242-006-0013-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-0013-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Xie Mingliang Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut NATIONALLICENCE 700 1- Wang Wenqing Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut NATIONALLICENCE 700 1- De Jonge Joëlle Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut NATIONALLICENCE 700 1- Kolditz Olaf Center for Applied Geoscience, GeoSystemsResearch, University of Tübingen, Sigwartstr. 10, D-72076, Tübingen, Germany aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 66/3(2007-02-01), 311-339 0169-3913 66:3<311 2007 66 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer