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[en] Document available in extended abstract form only. The aim of this work is to develop a Hydro-Chemo-Mechanical (HcM) model able to consistently reproduce the whole swelling process of both unsaturated and saturated bentonites. The Barcelona Expansive Model (BExM) was taken as a starting point, as it has been satisfactorily applied to model the behaviour of compacted bentonites. However, its suitability for the analysis of free swelling has not been proved, namely for the case when porosities reach values close to and over 0.9 and the soil becomes disarranged. These conditions mean pulling BExM further away from the domain for which it was initially conceived. For this reason, a modified formulation of BExM has been developed. It has been named m/BExM. In order to explain the high swelling ability of bentonites, it is assumed that the distortion of the water structure induced by the clay sheets begins to have a significant effect also in macro water structure when the micro void ratio goes beyond a certain threshold value and the confining forces do not exceed the repulsive forces. Accordingly, macro water will experience a decrease in its chemical potential, and the voids in which this phenomenon takes part will act as sinks, increasing their volume and causing an important raise of macro-porosity (disarrangement of the soil macro skeleton). When this phenomenon starts, the micro strain rate is greater than that of the macro disarrangement. Nonetheless, when the micro void ratio reaches high values, the disarrangement becomes more significant. The variation of the micro void ratio with the swelling pressure is described with an exponential law. The developed formulation takes into account the geochemical effects by using a modified swelling pressure, in keeping with the proposal of Karnland et al. (2005) when working with a saline solution of relevant concentration. The presence of sodium and calcium cations, as well as that of a generic polyvalent anion (by default, Cl-), have been considered. The transport of species is modelled considering different diffusion coefficient for macro and microstructures. The hypothesis of equilibrium between macro and micro water may be too restrictive, as the dehydration processes of microstructural water are not immediate. Consequently, this work includes the transient nature of the mass exchange between macro and microstructural water. It has been verified that the process can be satisfactorily simulated using the formulation presented by Navarro and Alonso (2001) and Alonso and Navarro (2005). When macro-micro water equilibrium is not assumed, the chemical potential of micro water becomes a new state variable of the problem. The micro water mass balance equation must be solved in order to get its value. Besides the mentioned, m/BExM presents two additional features with respect to BExM. First, the microstructural strain is not necessarily taken as isotropic. The possibility of assuming that the orientation of the aggregates strains depends on the orientation of the stress field is introduced. Second, several definitions of the macro plastic strains induced by micro strains are considered. The developed model has been proved to promisingly reproduce the swelling recorded in two laboratory tests carried out by B+TECH using natural MX-80 bentonite samples hydrated with deionised water. Although other existing models, namely BBM and BExM, can also show the swelling trend, m/BExM performs significantly better
[en] Document available in extended abstract form only. The use of numerical methods, especially the Finite Element Method (FEM), for solving boundary problems in Unsaturated Soil Mechanics has experienced significant progress. Several codes, both built mainly for research purposes and commercial software, are now available. In the last years, Multi-physic Partial Differentiation Equation Solvers (MPDES) have turned out to be an interesting proposal. In this family of solvers, the user defines the governing equations and the behaviour models, generally using a computer algebra environment. The code automatically assembles and solves the equation systems, saving the user having to redefine the structures of memory storage or to implement solver algorithms. The user can focus on the definition of the physics of the problem, while it is possible to couple virtually any physical or chemical process that can be described by a PDE. This can be done, for instance, in COMSOL Multiphysics (CM). Nonetheless, the versatility of CM is compromised by the impossibility to implement models with variables defined by implicit functions. Elasto-plastic models involve an implicit coupling among stress increments, plastic strains and plastic variables increments. For this reason, they cannot be implemented in CM in a straightforward way. This means a very relevant limitation for the use of this tool in the analysis of geomechanical boundary value problems. In this work, a strategy to overcome this problem using the multi-physics concept is presented. A mixed method is proposed, considering the constitutive stresses, the pre-consolidation pressure and the plastic variables as main unknowns of the model. Mixed methods usually present stability problems. However, the algorithmics present in CM include several numerical strategies to minimise this kind of problems. Besides, CM is based on the application of the FEM with Lagrange multipliers, an approach that significantly contributes stability when using the mixed method. The constitutive formulation is implemented as a balance equation. This way, the user can freely implement models involving implicit relationships between variables. To illustrate the application of this method, we have analysed the implementation of a modified formulation of the Barcelona Expansive Model, a critical state model (CSM) of reference for expansive clays, as it is the case for bentonite clays for engineered barriers for radioactive nuclear spent fuel confinement. The tool developed was used to satisfactorily model the coupled hydro-mechanical problem of the free-swelling of a MX-80 bentonite disc. The bentonite sample had an initial dry density of 1600 kg/m3 and a water content of 10% in mass. The initial dimensions of the disk were a height of 15.85 mm and a diameter of 100 mm. The hydration with deionised water applied on the top face of the sample was modelled with a saturation boundary condition. Figure 1 illustrates the case modelled and results obtained on pore water pressure and swelling of the sample at an intermediate time in the simulation. In addition, the modelling results have been compared with the experimental results obtained in the laboratory test carried out by B+TECH, as shown in Figure 2. In conclusion, the present proposal means a useful approach for the introduction of advanced Soil Mechanics models to the modelling of bentonite clays in multi-physics partial differential solvers. The use of it enables to overcome the limitations of some MPDES to integrate state functions defined implicitly. This makes it possible to combine the versatility of MPDES with powerful constitutive grounds. (authors)
[en] Highlights: • Numerical model for electrokinetic remediation of polluted soil with 2,4-D is shown. • Periodic polarity reversal processes has been included in the module M4EKR. • Improvements of the application of polarity reversal strategy has been studied. • Periodic polarity reversal at 6 h enhances the yield of EKR a 94.5%. - Abstract: This article presents a numerical study of the transport phenomena involved in the electrokinetic remediation of soils polluted with polar pesticides. 2,4-Dichlorophenoxyacetic acid is used as a representative of this pesticide type. A one-dimensional configuration with two facing electrodes placed in electrolyte compartments and a cathodic overflow pollutant extraction system has been used for that purpose. The conventional electrokinetic remediation process is evaluated by keeping the electrode polarity constant, and to obtain acceptable yields, it is necessary to extend the treatment for more than 250 days. The application of periodic polarity reversals is proposed to improve these results. This strategy maximises the pesticide concentration in the cathodic compartment, thus maximising the pollutant extraction rate. The results show that by applying polarity reversals over 6-h periods, it is possible to accelerate the treatment, thus improving its overall efficiency up to 94.5% compared with the treatment using a constant electrode polarity.