Up-to-date methods of numerical modelling of random fields were applied to investigate some features of solute transport in saturated porous media with stochastic hydraulic conductivity. The paper describes numerical experiments which were performed and presents the first results.

This work is devoted to the numerical analysis of saturated porous media, taking into accountthe damage phenomenon on the solid skeleton. The porous media is taken into poroelasticframework, in full-saturated condition, based on the Biot's Theory. A scalar damage model isassumed for this analysis. An implicit Boundary element Method (BEM) formulation, basedon time-independent fundamental solutions, is developed and implemented to couple thefluid flow and the elasto-damage problems. The integration over boundary elements isevaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case oftriangular domain cells is followed to carry out the relevant domain integrals. The non-linearsystem is solved by a Newton-Raphson procedure. Numerical examples are presented, inorder to validate the implemented formulation and to illustrate its efficiency.

Carbon nanotubes (CNTs) have been one of the most studied nanoparticles and incorporated into various consumer products. It has been reported that CNTs can enter groundwater systems by accidental or intentional release into the subsurface. As transport mechanisms of CNTs are not well understood, investigation on mobility of CNTs in the subsurface will be helpful to define disposal regulations of CNTs. The objective in this study is to investigate the effect of solution chemistry (pH and ionic strength) and physical factors (collector grain size and flow rate) on the transport of multi-walled carbon nanotubes (MWCNTs). One-dimensional convection-dispersion model incorporated with collector efficiency for cylindrical nanoparticles was used to simulate the transport of MWCNTs in porous media. It was observed that higher pH led to increase in mobility of MWCNTs. The critical point of ionic strength for MWCNTs getting mobilized was narrowed down in the range of 2 to 5 mM. It was observed that the finer porous media could retain more nanoparticles. The decrease in pore water velocity resulted in a clear retardation, lowered the hydrodynamic force acting on the particles and led to more retention.

Titanium dioxide nanoparticles are widely used in a variety of products, such as pigments, paints, paper, plastics, cosmetics, nano-fibers, food coloring and photovoltaic cells, and the industry is growing at anexponential rate. It is believed that by 2025, 2.5 million tons of nano-TiO2 will be manufactured annually. Thus far, there has been very little research in the environmental impact of nano-TiO2. There is a need to understand the fate and transport of nanoTiO2 to mitigate their effect on human health, the ecosystems and the environment in general. The aim of this study was to investigate the impact of pH, flow rate and ionic strength on the deposition of nano-TiO2 in a saturated porous media (sand). Nano-TiO2 formed aggregates in solutions that had a pH near the point of zero charge for TiO2, which is at approximately pH 6.2 for TiO2. The formed aggregates showed very little mobility due to site blocking in the pores of the sandy medium, whereas at pH 7.5, the solutions’ concentration was more stable than at pH 6.3 and more mobile up to 10 mM. Above 10 mM, a decrease in mobility, due to reduction in repulsive energy interaction between the medium and the nanoparticles could be observed. Flow rate had also a marked effect on the deposition, i.e., the slower the flow rate, the higher on deposition, because of an increase in attachment efficiency. To verify the experimental results, a finite element solution of the reactive transport equation in one dimension was used to compare the fit between observed and simulated results. The model was run in inverse mode, to determine unknown parameter values such as dispersivity and detachment rate. In general, it was possible to obtain a good fit to theexperimental BTCs. / Nanopartiklar av titaniumdioxid används allmänt i en mängd olika produkter, såsom pigment, färger,papper, plast, kosmetika, nanofibrer, matfärgläggning, och solceller. Branschen växer explosionsartat.Man tror att år 2025 kommer 2,5 miljoner ton nano-TiO2 tillverkas årligen. Hittills har väldigt lite forskning gjorts på området nano-TiO2. Det finns ett behov av att förstå transportprocesser och vad som händer med nanoTiO2 i miljön för att bla kunna mildra effekter av dessa partiklar på människors hälsa, ekologi och miljö. Syftet med denna studie var att undersöka effekten av pH, flöde och jonstyrka (IS) på transporten av nano - TiO2 i vattenmättade porösa medier (sand). Nano - TiO2 bildade aggregat i lösningar som hade ett pH nära pH(PZC), pH(PZC) är pH-värdet vid vilket laddningen är noll, ungefär pH 6,2 för TiO2. Vid pH 6,3 visade nano partiklarna mycket liten rörlighet på grund av fysisk igentäppning i porerna av sandmediet, medan vid pH 7,5 var lösningens koncentration mer stabil och partiklarna mer mobila upp till en jonstyrka på 10 mM. Över 10 mM, observerades en minskning i rörlighet, på grund av minskad repellerande energi mellan mediet och nano partiklarna.Flödeshastighet hade också en markant inverkan på retentionen av partiklar i kolonnen, ju långsammare flöde, desto större retention, på grund av mer gynnsamma förhållande för fastläggning av partiklar till mediet. För att verifiera de experimentella resultaten och jämföra observerade och simulerade resultat användes en lösning med finita-elementmetoden av den reaktiva transportekvationen i en dimension. Inversmodellering gjordes för att ta reda på okända parametervärden såsom dispersivitet och fastläggning. Det var i allmänhet möjligt att uppnå god överensstämmelse mellan observerade ochexperimentella genombrottskurvor.

Up-to-date methods of numerical modelling of random fields were applied to investigate some features of solute transport in saturated porous media with stochastic hydraulic conductivity. The paper describes numerical experiments which were performed and presents the first results.

This work is devoted to the numerical analysis of saturated porous media, taking into account the damage phenomenon on the solid skeleton. The porous media is taken into poroelastic framework, in full-saturated condition, based on the Biot\'s Theory. A scalar damage model is assumed for this analysis. An implicit Boundary Element Method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and the elasto-damage problems. The integration over boundary elements is evaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear system is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficiency. / Este trabalho trata da análise numérica de meios porosos saturados, considerando danificação na matriz sólida. O meio poroso é admitido em regime poroelástico, em condição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregado nesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC), baseada em soluções fundamentais independentes do tempo, é desenvolvida e implementada de forma a acoplar os problemas de difusão de fluido e de elasto-dano. A integração sobre os elementos de contorno é feita através da quadratura de Gauss. Um esquema semi-analítico é aplicado sobre células triangulares para avaliar as integrais de domínio do problema. A solução do sistema não linear é obtida através de um procedimento do tipo Newton-Raphson. Apresentam-se exemplos numéricos a fim de validar a formulação implementada e demonstrar sua eficiência.

Les centrales nucléaires jouent un rôle important au niveau mondial dans la production d'électricité aujourd'hui. Dans l'histoire humaine, deux accidents tragiques ont déjà eu lieu, à Tchernobyl et Fukushima, provoquant des fuites des matières radioactives. Pour éviter ce genre d'accident dans la future, la construction en béton prend un rôle important en tant que matériau de construction de confinement qui est la dernière barrière pour isoler la matière radioactive de l'environnement. La compréhension des transferts dans le béton dans des circonstances graves, en particulier à étudier le comportement du béton sous haute température jusqu'à 200°C. Dans la première partie, un modèle de déshydratation a été appliqué dans le modèle thermo-hygro. Le modèle thermo-hygro a ensuite été mis en oeuvre pour simuler une maquette dont les résultats expérimentaux sont disponibles dans la littérature, sans tenir compte des comportements mécaniques. Enfin, des études paramétrique ont été réalisées pour étudier l'influence de certains paramètres. Le modèle à ensuite été appliqué à des structures sous vitesse de chauffage différente, et le modèle à ensuite été appliqué à des structure sous rythme de chauffage différents et celles avec des épaisseurs différentes pour comparer les profiles de température et de pression de gaz à travers de la mur. / Nuclear power plant now takes an important part in the world's electricity generation. In human history, there have already been two tragic accidents in Chernobyl and Fukushima causing severe radioactive matter leakage. To pre- vent this kind of accident from happening again, concrete structure plays an important role as material of containment building, which is the last barrier to isolate the radioactive matter from the environment. Hence, the transfer properties of concrete under severe circumstances, especially high tempera- ture, are important for this usage. This PhD thesis aims to investigate the behavior of the concrete under high temperature up to 200°C. In the first part, a dehydration model was proposed. The model consists of different dehydration sub-models for main hydrates in the cement paste. In the second part, the dehydration model was implemented in a thermo-hygral model. The thermo- hygral model was then used to simulate a mock-up for which experimental results are available in the literature, without considering the mechanical behaviors. At last, parametric studies were performed to investigate the influ- ence of some parameters, and the model was then applied to structures under different heating rates, and structures with different thicknesses to compare the temperature and gas pressure profiles across a wall.

This work is devoted to the numerical analysis of saturated porous media, taking into account the damage phenomenon on the solid skeleton. The porous media is taken into poroelastic framework, in full-saturated condition, based on the Biot\'s Theory. A scalar damage model is assumed for this analysis. An implicit Boundary Element Method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and the elasto-damage problems. The integration over boundary elements is evaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear system is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficiency. / Este trabalho trata da análise numérica de meios porosos saturados, considerando danificação na matriz sólida. O meio poroso é admitido em regime poroelástico, em condição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregado nesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC), baseada em soluções fundamentais independentes do tempo, é desenvolvida e implementada de forma a acoplar os problemas de difusão de fluido e de elasto-dano. A integração sobre os elementos de contorno é feita através da quadratura de Gauss. Um esquema semi-analítico é aplicado sobre células triangulares para avaliar as integrais de domínio do problema. A solução do sistema não linear é obtida através de um procedimento do tipo Newton-Raphson. Apresentam-se exemplos numéricos a fim de validar a formulação implementada e demonstrar sua eficiência.

Ce travail est consacré à l'analyse numérique des milieux poreux saturés, en tenant comptele phénomène d'endommagement sur le squelette solide. Le milieu poreux est pris dans lecadre poro-élastique, dans un état complètement saturé, d'après la théorie de Biot. Unmodèle scalaire d'endommagement est supposé pour cette analyse. Une formulationimplicite de la Méthode des éléments de frontière, basée sur des solutions fondamentalesindépendantes du temps, est développé et implantée numeriquement pour coupler lesproblèmes de l'écoulement de fluide et de l'elasticité endommageable. L'intégration sur deséléments de frontière est realisée en utilisant la méthode numérique de Gauss. Un schémasemi-analytique pour le cas des cellules triangulaires de domaine est suivie pour évaluer lesintégrales de domaine pertinentes. Le systéme non-linéaire est résolu par une procédure deNewton-Raphson. Des exemples numériques sont présentés, afin de valider la formulationimplantée et pour illustrer son efficacité. / This work is devoted to the numerical analysis of saturated porous media, taking into accountthe damage phenomenon on the solid skeleton. The porous media is taken into poroelasticframework, in full-saturated condition, based on the Biot’s Theory. A scalar damage model isassumed for this analysis. An implicit Boundary element Method (BEM) formulation, basedon time-independent fundamental solutions, is developed and implemented to couple thefluid flow and the elasto-damage problems. The integration over boundary elements isevaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case oftriangular domain cells is followed to carry out the relevant domain integrals. The non-linearsystem is solved by a Newton-Raphson procedure. Numerical examples are presented, inorder to validate the implemented formulation and to illustrate its efficiency. / Este trabalho trata da análise numérica de meios porosos saturados, considerandodanificação na matriz sólida. O meio poroso é admitido em regime poroelástico, emcondição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregadonesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC),baseada em soluções fundamentais independentes do tempo, é desenvolvida eimplementada de forma a acoplar os problemas de difusão de fluido e de elasto-dano. Aintegração sobre os elementos de contorno é feita através da quadratura de Gauss. Umesquema semi-analítico é aplicado sobre células triangulares para avaliar as integrais dedomínio do problema. A solução do sistema não linear é obtida através de um procedimentodo tipo Newton-Raphson. Apresentam-se exemplos numéricos a fim de validar a formulaçãoimplementada e demonstrar sua eficiência.

La protection et la remédiation des ressources en eau sont un enjeu sociétal majeur, ainsi il est nécessaire de comprendre l’évolution de solutés, tels les polluants, au sein de la zone saturée et non saturée. Dans ce but, de nombreux travaux ont été consacrés à la modélisation du transport réactif en milieux poreux. Son déroulement à l’échelle de Darcy dépend des hétérogénéités microscopiques du milieu. Les modèles de réseau de pores qui simplifient la géométrie en un ensemble de pores reliés par des liens de sections constantes, permettent de se placer à une échelle mésoscopique, faisant le lien entre l’échelle porale et l’échelle de Darcy. Sur de telles formes géométriques, l’écoulement admet un traitement analytique. En ce qui concerne le transport réactif des solutés, nous proposons une solution analytique dans les liens qui permet de calculer le débit de masse entre pores. Le modèle de transport se formule alors comme un système d’équations de Volterra de secondes espèces dont les noyaux de convolution sont des séries d’exponentielles décroissantes (hormis le premier terme qui est constant). Leurs temps de relaxation sont pilotés essentiellement par le temps de dispersion td. Dans la limite où td tend vers 0 à Péclet constant, les termes transitoires des noyaux se réduisent à un Dirac, débouchant sur un premier modèle simplifié à réponse instantanée c'est-à-dire un modèle de transport quasi-statique. Dans le cas où les volumes des pores sont suffisamment grands, les noyaux se réduisent à leur premier terme. Ces formulations du transport généralisent celles de la littérature. En particulier pour des Péclet petit ou grand on retrouve respectivement les modèles usuels en régime dispersif et convectif. Numériquement, la décroissance exponentielle des noyaux permet d’optimiser le calcul des convolutions avec une précision arbitrairement fixée, réduisant drastiquement le temps de résolution. / Protection and remediation of ground water resources are a major societal challenge. It implies to understand the evolution of solutes as pollutant in the saturated and non-saturated zones. For that purpose numerous studies have been conducted for modeling the reactive transport in a porous media. At Darcy scale, the behavior of solutes depends on microscopic heterogeneity for the media. The Pore Network Models (PNM) simplifies drastically its geometry and considers pores linked by straight throats the section of which is constant. They give a description which is in between the macroscopic and the pore descriptions. With such geometry it is possible to use a Poiseuille flow modeling the flux. With respect to the reactiontransport equation, we seek the analytical solution of the CDE in throats, which in turn allows computing the mass flux in pores. The transport solution consists of a Volterra equation system. Its convolution kernels result in a summation of time function which is decreasing exponentially with time (except the first term which still constant). The time constant is driven by the diffusion time td. As td goes to zero, keeping the Peclet number fixed, each term of the summation reduces to a Dirac. The response of the system is then instantaneous. When the volume of the pore is large enough it is possible to neglect all the term of the kernel except the constant one. In the limit where the Peclet number goes to zero, usual models are recovered. Numerically, the exponential time decreasing of the kernel allow to optimize their computational time up to an arbitrary fixed precision.