Abstract
Humidity field in the concrete may be found by solving the diffusion differential equation. The discussion of possible boundary conditions was done on the example of the infinite concrete cylinder, drying upon its surface. Two proposed boundary conditions lead to very similar solutions, provided that the evaporation coefficient at the surface is high enough. A comparison with the experimental results was made. Linear diffusion equation does not describe the drying process adequately. Diffusion coefficient has been suggested to be a quadratic function of the humidity, and the corresponding nonlinear equation has been solved by the numerical way.
Résumé
Le champ d'humidité dans le béton peut être défini en résolvant l'équation différentielle (1) de diffusion. On examine les conditions aux limites possibles—(3) et (4)—à l'aide de l'exemple du cylindre de béton infini, entièrement saturé au début et se desséchant en surface. Les deux types de conditions aux limites mènent à des solutions très voisines, à condition d'avoir un coefficient d'évaporation—h dans l'équation (4)—suffisament élevé. On compare avec les résultats expérimentaux. L'équation de diffusion linéaire ne décrit pas le processus de séchage de façon adéquate. On propose de considérer le coefficient de diffusion D comme une fonction quadratique de l'humidité (8). L'équation non linéaire correspondante (9) a été résolue par les différences finies (10).
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Abbreviations
- w :
-
humidity of concrete—non dimensional
- t :
-
time—dimensional or non-dimensional
- ∇2 :
-
Laplacian
- D :
-
diffusion coefficient—non-dimensional or dimensional (cm2h−1)
- x :
-
position vector
- ℬ:
-
region occupied by the body under consideration
- w o :
-
initial humidity of concrete
- w z :
-
equivalent environment humidity
- δℬ:
-
surface of the regionℬ
- n :
-
outside versor normal to σ“
- h :
-
coefficient of evaporation at the surface, non-dimensional or dimensional (cm−1)
- ϱ:
-
radial component of cylindrical coordinates—non-dimensional
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Kasperkiewicz, J. Some aspects of water diffusion process in concrete. Mat. Constr. 5, 209–214 (1972). https://doi.org/10.1007/BF02474070
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DOI: https://doi.org/10.1007/BF02474070