Modelling and simulation of concrete carbonation with internal layers

Transport and reaction of carbon dioxide with alkaline species in concrete is modelled by a closed system of ordinary and partial differential equations. Varying porosity and varying external exposure as well as nonlinear reaction rates are taken into account. Proper nondimensionalisation is introduced to pay attention to the different characteristic time and length scales. We emphasise the effects of the size of the Thiele modulus on the penetration curves. It is shown that an internal reaction layer is formed whose properties are related to the Thiele modulus. The model is tested for accelerated and natural carbonation settings and is found reliable. A discussion of the effects of different sizes of several model parameters yields information about their relevance. Special attention is paid to the effects of moisture on the whole process. For the accelerated setting, a water-production layer is observed.

[1]  F. Camilli,et al.  A regularization of Zubov’s equation for robust domains of attraction , 2001 .

[2]  Koichi Maekawa,et al.  Theoretically Identified Strong Coupling of Carbonation Rate and Thermodynamic Moisture States in Micropores of Concrete , 2004 .

[3]  Koichi Maekawa,et al.  MODELING OF PH PROFILE IN PORE WATER BASED ON MASS TRANSPORT AND CHEMICAL EQUILIBRIUM THEORY , 2000 .

[4]  Eberhard Bänsch,et al.  Numerical simulation of a silicon floating zone with a free capillary surface , 1999 .

[5]  R. Ramlau.  MOROZOV'S DISCREPANCY PRINCIPLE FOR TIKHONOV-REGULARIZATION OF NONLINEAR OPERATORS , 2002 .

[6]  A. Muntean,et al.  Modelling and simulation of concrete carbonation : competition of several carbonation reactions , 2005 .

[7]  Michael N. Fardis,et al.  Hydration and Carbonation of Pozzolanic Cements , 1992 .

[8]  M. Böhm,et al.  On a moving reaction layer for the prediction of the service life of concrete structures , 2004 .

[9]  Heike Fassbender,et al.  Error Analysis of the Symplectic Lanczos Method for the Symplectic Eigenvalue Problem , 2000 .

[10]  Eberhard Bänsch,et al.  Finite element discretization of the Navier–Stokes equations with a free capillary surface , 2001, Numerische Mathematik.

[11]  Lothar Reichel,et al.  Discrete least squares approximation by trigonometric polynomials , 1991 .

[12]  Peter Kunkel,et al.  Symmetric collocation methods for linear differential-algebraic boundary value problems , 2002, Numerische Mathematik.

[13]  Gerd Teschke,et al.  Construction of Generalized Uncertainty Principles and Wavelets in Anisotropic Sobolev Spaces , 2005, Int. J. Wavelets Multiresolution Inf. Process..

[14]  Wolfgang Dahmen,et al.  Adaptive Wavelet Methods for Saddle Point Problems - Optimal Convergence Rates , 2002, SIAM J. Numer. Anal..

[15]  Fabian Wirth,et al.  A Linearization Principle for Robustness with Respect to Time-Varying Perturbations , 2002 .

[16]  Roberto Natalini,et al.  A Mathematical Model for the Sulphur Dioxide Aggression to Calcium Carbonate Stones: Numerical Approximation and Asymptotic Analysis , 2004, SIAM J. Appl. Math..

[17]  Fabian R. Wirth,et al.  Complex Polytope Extremality Results for Families of Matrices , 2005, SIAM J. Matrix Anal. Appl..

[18]  Ingrid Daubechies,et al.  Variational image restoration by means of wavelets: simultaneous decomposition , 2005 .

[19]  I. Daubechiesa,et al.  Variational image restoration by means of wavelets : Simultaneous decomposition , deblurring , and denoising , 2005 .

[20]  Gerd Teschke,et al.  A new method to reconstruct radar reflectivities and Doppler information , 2022 .

[21]  Volker Mehrmann,et al.  Symmetric collocation for unstructured nonlinear differential-algebraic equations of arbitrary index , 2004, Numerische Mathematik.

[22]  Michael N. Fardis,et al.  A reaction engineering approach to the problem of concrete carbonation , 1989 .

[23]  F. Wirth.  The generalized spectral radius and extremal norms , 2002 .

[24]  Peter Benner,et al.  A Hybrid Method for the Numerical Solution of Discrete-Time Algebraic Riccati Equations , 2001 .

[25]  Alexander Steffens.  Modellierung von Karbonatisierung und Chloridbindung zur numerischen Analyse der Korrosionsgefährdung der Betonbewehrung , 2000 .

[26]  Renato Vitaliani,et al.  Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part I: Theoretical formulation , 2004 .

[27]  Michael N. Fardis,et al.  FUNDAMENTAL MODELING AND EXPERIMENTAL INVESTIGATION OF CONCRETE CARBONATION , 1991 .

[28]  Rolf Clackdoyle,et al.  Accurate attenuation correction in SPECT imaging using optimization of bilinear functions and assuming an unknown spatially-varying attenuation distribution , 2000 .

[29]  Ingrid Daubechies,et al.  Wavelet-based image decomposition by variational functionals , 2004, SPIE Optics East.

[30]  D. Do.  On the validity of the shrinking core model in noncatalytic gas solid reaction , 1982 .

[31]  Alexander Steffens,et al.  Modeling carbonation for corrosion risk prediction of concrete structures , 2002 .

[32]  Eberhard Bänsch,et al.  Adaptivity in 3D image processing , 2001 .

[33]  Y. F. Houst,et al.  A Model to Predict Service Life of Concrete Structures , 1983 .

[34]  Michael Wolff,et al.  Evaluation of various phase-transition models for 100Cr6 for application in commercial FEM programmes , 2004 .

[35]  Heike Faßbender,et al.  Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems , 2001 .

[36]  R. Clackdoyle,et al.  Accurate attenuation correction in SPECT imaging using optimization of bilinear functions and assuming an unknown spatially-varying attenuation distribution , 1998, 1998 IEEE Nuclear Science Symposium Conference Record. 1998 IEEE Nuclear Science Symposium and Medical Imaging Conference (Cat. No.98CH36255).

[37]  G. Froment,et al.  Chemical Reactor Analysis and Design , 1979 .

[38]  Ronny Ramlau,et al.  On the use of fixed point iterations for the regularization of nonlinear ill-posed problems , 2005 .

[39]  Peter Benner,et al.  An Implicitly Restarted Symplectic Lanczos Method for the Symplectic Eigenvalue Problem , 2000, SIAM J. Matrix Anal. Appl..

[40]  C. Büskens,et al.  Higher Order Real-Time Approximations in Optimal Control of Multibody-Systems for Industrial Robots , 2006 .

[41]  Gabriele Steidl,et al.  Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to Analyzing Functions on Spheres , 2004 .

[42]  Peter Wust,et al.  Efficient Methods in Hyperthermia Treatment Planning , 2000 .

[43]  Michael Böhm,et al.  On a moving-boundary system modeling corrosion in sewer pipes , 1998, Appl. Math. Comput..

[44]  Gerd Teschke,et al.  Wavelet based methods for improved wind profiler signal processing , 2001 .

[45]  Jesper Arfvidsson.  Moisture Transport in Porous Media. Modelling Based on Kirchhoff Potentials , 1998 .

[46]  Francis A. DiGiano,et al.  Process Dynamics in Environmental Systems , 1996 .

[47]  Heike Faßbender,et al.  The parameterized SR algorithm for symplectic (butterfly) matrices , 2001, Math. Comput..

[48]  Ricardo H. Nochetto,et al.  A posteriori error control for the Allen–Cahn problem: circumventing Gronwall's inequality , 2004 .

[49]  Fabian R. Wirth,et al.  Robustness of Nonlinear Systems and Their Domains of Attraction , 2001 .

[50]  Stephan Dahlke,et al.  Interpolating Scaling Functions with Duals , 2004 .

[51]  Jacques-Louis Lions,et al.  Mathematical Analysis and Numerical Methods for Science and Technology: Volume 5 Evolution Problems I , 1992 .

[52]  Eberhard Bänsch,et al.  Simulation of dendritic crystal growth with thermal convection , 2000 .

[53]  Asymptotics of reaction–diffusion fronts with one static and one diffusing reactant , 1999, physics/9904008.

[54]  A. Schmidt.  h{p{MULTIRESOLUTION VISUALIZATION OF ADAPTIVE FINITE ELEMENT SIMULATIONS , 2003 .

[55]  T. Chaussadent.  Etat des lieux et reflexions sur la carbonatation du beton arme , 1999 .

[56]  Renato Vitaliani,et al.  2 — D model for carbonation and moisture/heat flow in porous materials , 1995 .

[57]  Enrique S. Quintana-Ortí,et al.  Partial stabilization of large-scale discrete-time linear control systems , 2001, Proceedings International Conference on Parallel Processing Workshops.

[58]  James W. Evans,et al.  Gas-solid reactions , 1976 .

[59]  C. Page,et al.  Effects of carbonation on pore structure and diffusional properties of hydrated cement pastes , 1997 .

[60]  M. Ishida,et al.  Comparison of kinetic and diffusional models for solid-gas reactions. , 1968 .

[61]  Enrique S. Quintana-Ortí,et al.  Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search , 2000, Parallel Comput..

[62]  Ronny Ramlau,et al.  Nonlinear inverse unbalance reconstruction in rotor dynamics , 2005 .

[63]  Rafael Mayo,et al.  Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic Linear Systems , 2002, J. Parallel Distributed Comput..

[64]  Renato Vitaliani,et al.  The carbonation of concrete and the mechanism of moisture, heat and carbon dioxide flow through porous materials , 1993 .

[65]  Enrique S. Quintana-Ortí,et al.  Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers , 2000 .

[66]  P. Maass,et al.  AN OUTLINE OF ADAPTIVE WAVELET GALERKIN METHODS FOR TIKHONOV REGULARIZATION OF INVERSE PARABOLIC PROBLEMS , 2003 .

[67]  Christof Büskens,et al.  Approximation of reachable sets by direct solution methods for optimal control problems , 2007, Optim. Methods Softw..

[68]  Peter Benner,et al.  Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices , 2002 .

[69]  Enrique S. Quintana-Ortí,et al.  NUMERICAL SOLUTION OF DISCRETE STABLE LINEAR MATRIX EQUATIONS ON MULTICOMPUTERS , 2002, Parallel Algorithms Appl..

[70]  Matthias K. Gobbert,et al.  Numerical exploration of a system of reaction–diffusion equations with internal and transient layers , 2005 .

[71]  Design of an effective numerical method for a reaction-diffusion system with internal and transient layers , 2004 .

[72]  P. Maass,et al.  Tikhonov regularization for electrical impedance tomography on unbounded domains , 2003 .

[73]  Peter Knabner,et al.  Numerik partieller differentialgleichungen : eine anwendungsorientierte Einführung , 2000 .

[74]  Peter Benner,et al.  Computational Methods for Linear-Quadratic Optimization , 1999 .

[75]  Barzin Mobasher,et al.  Modeling of damage in cement-based materials subjected to external sulfate attack. I: Formulation , 2003 .

[76]  Robert C. Weast,et al.  Handbook of chemistry and physics : a readyreference book of chemical and physical data , 1972 .

[77]  Eberhard Bänsch,et al.  Taylor-Couette system with asymmetric boundary conditions , 2000 .

[78]  Michael Böhm,et al.  A two-reaction-zones moving-interface model for predicting Ca(OH)_2-carbonation in concrete , 2003 .

[79]  L. J. Hayes,et al.  Iterative Methods for Large Linear Systems , 1989 .

[80]  Peter Benner,et al.  A NOTE ON THE NUMERICAL SOLUTION OF COMPLEX HAMILTONIAN AND SKEW-HAMILTONIAN EIGENVALUE PROBLEMS , 1999 .

[81]  Frank Stenger,et al.  A Unified Approach to the Approximate Solution of Pde , 2007 .

[82]  Ronald Stöver,et al.  Collocation methods for solving linear differential-algebraic boundary value problems , 2001, Numerische Mathematik.

[83]  Enrique S. Quintana-Ortí,et al.  Efficient numerical algorithms for balanced stochastic truncation , 2001 .

[84]  Hiroyuki Ohga,et al.  CHANGE IN MICRO-STRUCTURE OF CONCRETE DUE TO CARBONATION , 1990 .

[85]  R Grotmaack,et al.  Stabilitätsanalyse eines Moving-Boundary-Modells der beschleunigten Karbonatisierung von Portlandzementen , 2003 .

[86]  Lars Grüne,et al.  On the rate of convergence of infinite horizon discounted optimal value functions , 2000 .

[87]  A. Schmidt,et al.  A Multi-mesh Finite Element Method for 3D Phase Field Simulations , 2003 .

[88]  Michael Böhm,et al.  On a prediction model for concrete carbonation based on moving interfaces : interface concentrated reactions , 2003 .

[89]  Vladimir L. Kharitonov,et al.  Exponential estimates for time delay systems , 2004, Syst. Control. Lett..

[90]  Michael Böhm,et al.  Numerical Experiments with Self-Adaptive Finite Element Simulations in 2D for the Carbonation of Concrete , 2005 .