Numerical analysis and computing of free boundary problems for concrete carbonation chemical corrosion

[EN] This paper deals with the construction, analysis and computation of a numerical method to solve a moving boundary coupled nonlinear system of parabolic reaction-diffusion equations, arising in concrete carbonation problems. By means of a front-fixing transformation, the domain of the problem becomes fixed, and the position of the moving carbonation front has to be determined together with the mass concentrations of the involved chemical species. Qualitative properties like positivity and stability of the numerical solution are established. Spatial monotone behaviour of the solution is also proved. Numerical examples illustrate these results.This work has been partially supported by the Ministerio de Economia y Competitividad Spanish grant 2017-89664-P.Piqueras-García, MÁ.; Company Rossi, R.; Jódar Sánchez, LA. (2018). Numerical analysis and computing of free boundary problems for concrete carbonation chemical corrosion. Journal of Computational and Applied Mathematics. 336:297-316. https://doi.org/10.1016/j.cam.2017.12.036S29731633

Analysis of a two-scale system for gas-liquid reactions with non-linear Henry-type transfer

In this paper, we consider a coupled two-scale nonlinear reaction-diffusion system modelling gas-liquid reactions. The novel feature of the model is the nonlinear transmission condition between the microscopic and macroscopic concentrations, given by a nonlinear Henry-type transfer function. The solution is approximated by using a Galerkin method adapted to the multiscale form of the system. This approach leads to existence and uniqueness of the solution, and can also be used for numerical computations for a larger class of nonlinear multiscale problems

Multiscale reaction-diffusion systems describing concrete corrosion : modeling and analysis

This thesis deals with the modeling and multiscale analysis of reaction-diffusion systems describing concrete corrosion processes due to the aggressive chemical reactions occurring in concrete. We develop a mathematical framework that can be useful in forecasting the service life of sewer pipes. We aim at identifying reliable and easy-to-use multiscale models able to forecast the penetration of sulfuric acid into sewer pipes walls. For modeling of corrosion processes, we take into account balance equations expressing physico-chemical processes that take place in the microstructures (pores) of the partially saturated concrete. We consider two dierent modeling strategies: (1) we propose microscopic reaction-diusion systems to delineate the corrosion processes at the pore level and (2) we consider a distributed microstructure model containing information from two separated spatial scales (micro and macro). All systems of dierential equations are semi-linear, weakly coupled, and partially diusive. Since the precise microstructure of the material is far too complex to be described accurately, we consider two approximations, namely uniformly-periodic and locally-periodic array of microstructures, which are tractable by using averaging mathematical tools. We use different homogenization techniques to obtain the effective behavior of the microscopically oscillating quantities. For the formal derivation of our multiscale models, we apply the asymptotic expansion method to the microscopic reaction-diffusion systems defined in locally-periodic domains for two special choices of scaling in ¿ of the diffusion coefficients. We end up with (i) upscaled systems and (ii) distributed-microstructure systems. As far as rigorous derivations are concerned, we apply the notion of two-scale convergence to the PDE system defined in the uniformly periodic domain. To deal with the non-diffusive object, i.e. the ordinary dierential equation tracking the damage-by-reaction, we combine the two-scale convergence idea with the periodic-boundary-unfolding technique. Additionally, we use the periodic unfolding techniques to obtain corrector estimates assessing the quality of the averaging method. These estimates are convergence rates measuring the error contribution produced while approximating macroscopic solutions by microscopic ones. We derive these estimates under minimal regularity assumptions on the solutions to the microscopic and macroscopic systems, microstructure boundaries, and to the corresponding auxiliary cell problems. We prove the well-posedness of a distributed-microstructure reaction-diusion system which includes transport (diusion) and reaction effects emerging from two separated spatial scales. We perform this analysis by incorporating a variational inequality requiring minimal regularity assumptions on the initial data. We ensure basic estimates like positivity and L8-bounds on the solution to the system. Then we prove the global-in-time existence and uniqueness of a suitable class of positive and bounded solutions. To predict the position of the corrosion front penetrating the concrete, we use our distributed-microstructure model to perform simulations at macroscopic length scales while taking into account transport and reactions occurring at small length scales. Using an ad hoc logarithmic expression, we approximate numerically macroscopic pH proles dropping down with the onset of corrosion. We extract from the gypsum proles the approximate position of the corrosion front penetrating the uncorroded concrete. We illustrate numerically that as the macroscopic mass-transfer Biot number BiM -> 8, BiM naturally connects two different multiscale reaction-diusion scenarios: the solution of the distributed-microstructure system having the Henry's law acting as micro-macro transmission condition converges to the solution of the matched distributed-microstructure system

Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition

We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry's law) posed at air-liquid interfaces. We prove the rate of convergence of the two-scale Galerkin method proposed in Muntean & Neuss-Radu (2009) for approximating this system in the case when both the microstructure and macroscopic domain are two-dimensional. The main difficulty is created by the presence of a boundary nonlinear term entering the transmission condition. Besides using the particular two-scale structure of the system, the ingredients of the proof include two-scale interpolation-error estimates, an interpolation-trace inequality, and improved regularity estimates.Comment: 14 pages, table of content

A multiscale Galerkin approach for a class of nonlinear coupled reaction–diffusion systems in complex media

AbstractA Galerkin approach for a class of multiscale reaction–diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented. This type of models are obtained e.g. by upscaling of processes in chemical engineering (particularly in catalysis), biochemistry, or geochemistry. Exploiting the special structure of the models, the functions spaces used for the approximation of the solution are chosen as tensor products of spaces on the macroscopic domain and on the standard cell associated to the microstructure. Uniform estimates for the finite dimensional approximations are proven. Based on these estimates, the convergence of the approximating sequence is shown. This approach can be used as a basis for the numerical computation of the solution

Phase-Field Modeling for Self-Healing of Mineral-Based Materials

Concrete is the most widely used building material in the world. The low raw materials cost, its high compressive strength and the simplicity of the production process makes it an enormous attractive and easy to apply material for the construction and building sector. However, when applied, concrete suffers from cracks, which are inevitable and are the result of various environmental and loading impacts such as traffic load, freeze-thaw cycles, but it also depends on the construction quality. These cracks provide harmful elements such as chloride, carbon dioxide or sulphur ions a pathway, which may induce steel corrosion of reinforced concrete structures. It is a mechanism that will seriously threaten the service life of a concrete structure, while causing significant maintenance costs. Mitigating this phenomenon has led to a worldwide development on self-healing methods for crack closure. In the last few years, research efforts on self-healing methods have mainly concentrated on experimental work, where only a limited number of numerical models have been reported in literature. These models treat the boundaries, i.e. interfaces, between different the surfaces of components with a zero thickness. In fact, such interface describes the kinetics of a phase transformation from a non-equilibrium to an equilibrium state. This problem requires the diffusion equations to be solved at the interface under moving boundary conditions, which, although feasible for the evolution of simple geometries, becomes rather impossible for higher-dimensional systems and/or complicated interfaces. For a more accurate description of the above problem, this PhD study presents a novel approach for self-healing of cementitious materials by means of a phase-field (PF) method. Unlike the traditional sharp interface models, a PF method provides a convenient way to numerically deal with free moving boundaries, where the interface is implicitly expressed as a time- and space-dependent function, representing the phase state, and is defined over the entire domain. In this work, the diffusion-controlled isotropic dissolution of minerals is first investigated from a mesoscale phase transition point of view. Based on earlier formulations by Kim and co-workers [1], an expression of interface mobility under diffusion-controlled conditions is proposed. Using sodium chloride dissolution as an example, the results of their PF method are compared with that of analytical models and experiments, while extending the application of a PF method to the field of mineral dissolution. Based on this, the evolution of a carbonation front, which separates the dissolution zone from the carbonation fraction, is modelled on a thermodynamic basis, while mimicking the self-healing carbonation reaction in cementitious materials. Physical-chemical aspects are used to construct the free energy functions for incorporating dissolution and precipitation systems. Moreover, the dissolution model determines the local concentration fields of the active species in the PF. The model parameters were experimentally calibrated on a single mineral, i.e. the carbonation of calcium hydroxide. As a novel feature, the evolution of multiple interfaces is investigated and demonstrated by an experimental case of self-healing with calcium hydroxide carbonation. Good qualitative agreement was achieved between the model results and the experimental data and the evolution of the crack morphology was demonstrated. This PhD study showed the potential of a PF method as a predictive tool to estimate self-healing in cementitious materials

Numerical and Experimental Investigations on Corrosion and Self-Protection Processes in Reinforced Concrete

The chloride induced corrosion of steel in concrete is one of the biggest durability issues affecting structures worldwide. Concrete structures that are installed in marine environment and those exposed frequently to de-icing salts in the winter season, such as bridges and parking structures, are particularly susceptible to corrosion induced damage. In worst cases, the structure is unable to fulfil its entire service life and needs extensive repairs or is decommissioned quite early. Such situations can have a strong impact on society which is dependent on infrastructures for mobility and transportation of essential materials. Moreover, the economic losses are predicted in billions in the coming future and can impact the global economy. In an attempt to increase the service life of concrete structures with respect to chloride durability, Layered Double Hydroxides (LDH) are introduced as chloride ion entrapping additive in concrete. LDH encapsulates chloride ions from the environment which can extend the service life of concrete structures. It can also be tailored to deliver corrosion inhibiting ions which can mitigate the chloride induced damage in concrete. A new concrete mix with LDH was developed in this work for building long lasting infrastructure exposed to chloride ingress in submerged marine zones. Predictive modelling approaches are used to study the corrosion processes and chloride durability of concrete. Multi-ion transport model is used to predict the efficiency of LDH in concrete concerning chloride ingress. Computational results are presented which compare chloride ingress in concrete with and without LDH. Formation factor has been used in this study to determine the microstructure related properties of concrete with and without LDH. Additionally, experimental investigations are presented which report on the stability and chloride binding capacity of LDH in synthetic alkaline solutions, concrete pore solutions, mortars and also in concrete. The compatibility of LDH with cement is also presented. The work highlights that LDH is able to improve the chloride durability of concrete. Furthermore, In-situ investigations are carried out to understand the stability of LDH inside concrete

Proceedings of the International RILEM Conference Materials, Systems and Structures in Civil Engineering segment on Service Life of Cement-Based Materials and Structures

Vol. 1O volume II encontra-se disponível em: http://hdl.handle.net/1822/4390

International RILEM Conference on Materials, Systems and Structures in Civil Engineering Conference segment on Service Life of Cement-Based Materials and Structures

Vol. 2O volume I encontra-se disponível em: http://hdl.handle.net/1822/4341