Journal of Applied Science and Engineering

Published by Tamkang University Press

1.30

Impact Factor

2.10

CiteScore

Wen-Hu Tsao This email address is being protected from spambots. You need JavaScript enabled to view it.1,2, Ming-Te Liang1 , Jiang-Jhy Chang3 and Ming-Yi Fang3

1Department of Civil Engineering, China University of Science and Technology, Taipei, Taiwan 115, R.O.C.
2Department of Banking and Finance, Tamkang University, Tamsui, Taiwan 215, R.O.C.
3Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan 202, R.O.C.


 

Received: September 12, 2012
Accepted: May 15, 2015
Publication Date: June 1, 2015

Download Citation: ||https://doi.org/10.6180/jase.2015.18.2.13  


ABSTRACT


The principal objective of this paper is to investigate the modelling of chloride diffusion in fly ash and slag concretes laden in chloride environments. The capacity of the concrete cementitious system to bind chloride ions has an important effect on the rate of chloride ionic transport in concrete. Four mathematical models concerning chloride binding in concrete are stated and used. The analytical solution of Fick’s second law of nonlinear (diffusivity ≠ constant) diffusion in conjunction with initial and boundary conditions is used as a predictive model. The experimental data obtained by Thomas and Bamforth [Modelling chloride diffusion in concrete: Effect of fly ash and slag. Cement and Concrete Research 1999;31:487-495] was cited as input parameters. The results at the present study show that after 30 years the predicted chloride profiles obtained by the nonlinear model may be one order of magnitude lower than that of linear (diffusivity = constant) model. The nonlinear model associated with four mathematical models related to chloride binding in concrete is not suitable to predict the transport mechanism of chloride diffusion in concrete containing fly ash and slag. However, the analytical solution of a nonlinear partial differential equation (PDE) in association with initial and boundary conditions for the concentration of Cl- in the aqueous phase [Cl-(aq)] (in kg/m3 pore solution) is proper to estimate the transport behavior of chloride diffusion in both fly ash and slag concretes. The Cl- bound in the solid phase [Cl-(s)] (kg/m3 concrete) can thus be computed algebraically. Further research in-depth is obviously needed and suggested.


Keywords: Chloride, Diffusion, Mathematical Model, Fly Ash, Slag, Pozzolan


REFERENCES


  1. [1] Everett, L. H. and Treadaway, K. W., “Deterioration due to Corrosion in Reinforced Concrete,” Information paper 12/80, Building Research Establishment, Garstion, (1980).
  2. [2] Schiessl, P., Corrosion of Steel in Concrete, RILEM Report, Chapman and Hall, Loudon (1988).
  3. [3] Arya, C., Buenfeld, N. R. and Newman, J. B., “Assessment of Simple Methods of Determining the Free Chloride Ion Content of Cement Paste,” Cement and Concrete Research, Vol. 17, No. 6, pp. 907918 (1987). doi: 10.1016/0008-8846(88)90062-2
  4. [4] Arya, C. and Newman, J. B., “An Assessment of Four Methods of Determining the Free Chloride Content of Concrete,” Materials and Structures, Vol. 23, pp. 319 330 (1990). doi: 10.1007/BF02472710
  5. [5] Birnin-Yauri, U. A. and Glasser, F. P., “Friedal’s Salt, Ca2Al(OH)6(Cl, OH)  2H2O: Its Solid Solutions and their Pole in Chloride Binding,” Cement and Concrete Research, Vol. 28, No. 12, pp.17131723 (1998). doi: 10.1016/S0008-8846(98)00162-8
  6. [6] Lambart, P., Page, C. L. and Short, N. R., “Pore Solution Chemistry of the Hydrated System Tricalcium Silicate/Sodium Chloride/Water,” Cement and Concrete Research, Vol. 15 pp. 675680 (1985). doi: 10.1016/ 0008-8846(85)90068-7
  7. [7] Rasheeduzzafar, Al-Saadoun, S. S., Al-Gahtani, A. S. and Dahhil, F. H., “Effect of Tricalcium Aluminate Content of Cement on Corrosion of Reinforcing Steel in Concrete,” Cement and Concrete Research, Vol. 20, pp. 723738 (1990). doi: 10.1016/0008-8846(90)900 06-J
  8. [8] Rasheeduzzafar, Ehtesham Hussain, S. and Al-Saadoun, S. S., “Effect of Cement Composition on Chloride Binding and Corrosion of Reinforcing Seel in Concrete,” Cement and Concrete Research, Vol. 21, pp. 777794 (1991). doi: 10.1016/0008-8846(91)90173-F
  9. [9] Rasheeduzzafer, Ehtesham Hussain, S. and Al-Saadoun, S. S., “Effect of Tricalcium Aluminate Content of Cement on Chloride Binding and Corrosion of Reinforcing Steel in Concrete,” ACI Materials Journal, Vol. 89, No. 1, pp. 312 (1992). doi: 10.14359/1239
  10. [10] Margat, P. S. and Molloy, B. T., “Chloride Binding in Concrete Containing PFA, gbs or Silica Fume under Sea Water Exposure,” Magazine of Concrete Research, Vol. 47, No. 171, pp. 129-141 (1995). doi: 10.1680/macr. 1995.47.171.129
  11. [11] Friedmann, H., Amiri, O. and Aït-Mokhtar, A., “Physical Modeling of the Electrical Double Layer Effects on Multispecies ions Transport in Cement-based Materials,” Cement and Concrete Research, Vol. 38, pp. 13941400 (2008). doi: 10.1016/j.cemconres.2008. 06.003
  12. [12] Bourbatache, K., Millet, O., Aït-Mokhtar, A. and Amiri, O., “Modeling the Chlorides Transport in Cementitious Materials By Periodic Homogenization,” Transport in Porous Media, Vol. 94, pp. 437459 (2012). doi: 10.1007/s11242-012-0013-1
  13. [13] Nilsson, L. O., Massat, M. and Tang, L., “The Effect of Non-linear Chloride Binding on the Prediction of Chloride Penetration into Concrete Structures,” in : V. M. Malhotra (Ed.), Durability of Concrete, ACI, Detroit, pp. 469486 (1994).
  14. [14] Anil Dogan, U., Bora Kunt, E., Görkem Saran, A. and Hulusi Ozkul, M., “Benchmarking Concretes with Pozzolanic Materials in Terms of Rapid Chloride Penetration Test,” ACI Materials Journal, Vol. 106, No. 3, pp. 251257 (2009). doi: 10.14359/56549
  15. [15] Bamforth, P. B., “In Situ Measurement of the Effect of Partial Portland Cement Replacement using either Fly Ash or Ground Granulated Blast-Furnace Slag on the Performance of Mass Concrete,” Proceeding of Institution of Civil Engineers, Part 2, Vol. 69, pp. 777800 (1980). doi: 10.1680/iicep.1981.1904
  16. [16] Berry, E. E., Hemmings, R. T., Zhang, M. H., Cornelius, B. J. and Golden, D. M., “Hydration in High-Volume Fly Ash Concrete Binders,” ACI Materials Journal, Vol. 91, No. 4, pp. 382389 (1994). doi: 10.14359/4054
  17. [17] Bifen, J., “Benefits of Slag and Fly Ash,” Construction and Building Materials, Vol. 10, No. 5, pp. 309314 (1996). doi: 10.1016/0950-0618(95)00014-3
  18. [18] Bilodeau, A., Sivasundaram, V., Painter, K. E. and Malhotra, V. M., “Durability of Concrete Incorporating High Volumes of Fly Ash from Sources in the U.S.,” ACI Materials Journal, Vol. 91, No. 1, pp. 312 (1994). doi: 10.14359/4411
  19. [19] Chowdhury, S. and Basu, P. C., “New Methodology to Proportion Self-Consolidating Concrete with HighVolume Fly Ash,” ACI Materials Journal, Vol. 107, No. 3, pp. 222230 (2010). doi: 10.14359/51663750
  20. [20] Dhir, R. K., Ho, N. Y. and Munday, J. G. L., “Pulverized Fuel Ash in Sturctural Precast Concrete,” Concrete, Vol. 19, No. 1, pp. 3235 (1985).
  21. [21] Dhir, R. K., Munday, J. G. L. and Ong, L. T., “Investigations of the Engineering Properties of OPC/Pulverized-Fuel Ash Concrete: Deformation Propertied,” The Structural Engineer, Vol. 64B, No. 2, pp. 3642 (1988).
  22. [22] Domone, P. L. and Soutsos, M. N., “Properties of HighStrength Concrete Mixes Containing PFA and ggbs,” Magazine of Concrete Research, Vol. 47, No. 173, pp. 355367 (1995). doi: 10.1680/macr.1997.49.180.263
  23. [23] Katyal, N. K., Sharma, J. M., Phawan, A. K., Ali, M. M. and Mohan, K., “Development of Rapid Method for the Estimation of Reactive Silica in Fly Ash,” Cement and Concrete Research, Vol. 38, pp. 104106 (2008). doi: 10.1016/j.cemconres.2007.08.020
  24. [24] Mehta, P. K. and Gjrv, O. E., “Properties of Portland Cement Concrete Containing Fly Ash and Condensed Silica-Fume,” Cement and Concrete Research, Vol. 12, pp. 587595 (1982). doi: 10.1016/0008-8846(83) 90114-X
  25. [25] Thomas, M. D. A., Osborne, G. J., Matthews, J. D. and Cripwell, J. B., “A Comparison of the Properties of OPC, PFA and ggbs Concrete in Reinforced Concrete Tank Walls of Slender Section,” Magazine of Concrete Research, Vol. 42, No. 152, pp. 127134 (1990). doi: 10.1680/macr.1990.42.152.127
  26. [26] Thomas, M. D. A., “Marine Performance of PFA Concrete,” Magazine of Concrete Research, Vol. 4., No. 150, pp. 171185 (1991). doi: 10.1680/macr.1992.44. 159.141
  27. [27] Thomas, M. D. A. and Matthews, J. D., “Performance of Fly Ash Concrete in U.K. Structures,” ACI Materials Journal, Vol. 90, No. 6, pp. 586593 (1993). doi: 10.14359/4436
  28. [28] Thomas, M. D. A. and Bamforth, P. B., “Modelling Chloride Diffusion in Concrete: Effect of Fly Ash and Slag,” Cement and Concrete Research, Vol. 29, pp. 487495 (1999). doi: 10.1016/S0008-8846(98)00192-6
  29. [29] Wang, X. Y., Lee, H. S. and Park, K. B., “Simulation of Low-Calcium Fly Ash Blended Cement Hydration,” ACI Materials Journal, Vol. 106, No. 2, pp. 167175 (2009). doi: 10.14359/56464
  30. [30] Zhang, Y., Sun, W., Li, Z. and Zhou, X., “Geopolymer Extruded Composites with Incorporated Fly Ash and Polyvinyl Alcohol Short Fiber,” ACI Materials Journal, Vol. 100, No. 1, pp. 310 (2009). doi: 10.14359/ 56310
  31. [31] De Ceukelaire, L. and Van Nieuwenburg, D., “Accelerated Carbonation of a Blast-Furnace Cement Concrete,” Cement and Concrete Research, Vol. 23, pp. 442452 (1993). doi: 10.1016/0008-8846(93)90109-M
  32. [32] Gouda, V. K., Shater, M. A. and Mikhail, R. Sh., “Hardened Portland Blast-Furnace Slag Cement Pastes II. The Corrosion Behavior of Steel Reinforcement,” Cement and Concrete Research, Vol. 5, pp. 113 (1975). doi: 10.1016/0008-8846(75)90068-X
  33. [33] Jiang, L., Lin, B. and Cai, Y., “A Model for Predicting Carbonation of High-Volume Fly Ash Concrete,” Cement and Concrete Research, Vol. 30, pp. 699702 (2000). doi: 10.1016/S0008-8846(00)00227-1
  34. [34] Macphee, D. Z. and Cao, H. T., “Theoretical Description of Impact of Blast Furnace Slag (BFS) on Steel Passivation in Concrete,” Magazine of Concrete Research, Vol. 45, No. 162, pp. 6369 (1993). doi: 10. 1680/macr.1994.46.167.151
  35. [35] Sha, W. and Pereira, G. B., “Differential Scanning Calorimetry Study of Hydrated Ground Granulated BlastFurnace Slag,” Cement and Concrete Research, Vol. 31, pp. 327329 (2001). doi: 10.1016/S0008-8846(00) 00472-5
  36. [36] Števule, L., Madej, J., Kozánková, J. and Madejová, J., “Hydration Products at the Blastfurnace Slag Aggregate-Cement Paste Interface,” Cement and Concrete Research, Vol. 24, No. 3, pp. 413423 (1994). doi: 10.1016/0008-8846(94)90128-7
  37. [37] Thomas, M. D. A., Scott, A., Bremner, T., Bilodeau, A. and Day, D., “Performance of Slag Concrete in Marine Environment,” ACI Materials Journal, Vol. 105, No. 6, pp. 628634 (2008). doi: 10.14359/20205
  38. [38] Andrade, C., “Calculation of Chloride Diffusion Coefficients in Concrete from Ionic Migration Measurements,” Cement and Concrete Research, Vol. 3, pp. 724742 (1993). doi: 10.1016/0008-8846(94)90067-1
  39. [39] Xu, A. and Chandra, S., “A Discussion of the Paper “Calculation of Chloride Diffusion Coefficients in Concrete from Ionic Migration Measurements,” by C. Andrada,” Cement and Concrete Research, Vol. 24, No. 2, pp. 375379 (1994). doi: 10.1016/S0008-8846(97) 00083-5
  40. [40] Amiri, O., Aït-Mokhtar, A. and Seigneurin, A., “A Complement to the Discussion of A. Xu, and S. Chandra about the Paper “Calculation of Chloride Coefficients Diffusion in Concrete from Ionic Migration Measurements,” by C. Andrade,” Cement and Concrete Research, Vol. 27, No. 6, pp. 951-957 (1997). doi: 10. 1016/S0008-8846(97)00082-3
  41. [41] Martín-Pérez, B., Zibara, H., Hooton, R. D. and Thomas, M. D. A., “A Study of the Effect of Chloride Binding on Service Life Predictions,” Cement and Concrete Research, Vol. 32, pp. 12151223 (2000). doi: 10.1016/S0008-8846(00)00339-2
  42. [42] Brebbia, C. A., Telles, J. C. and Wrobl, L. C., Boundary Element Techniques: Theory and Application Engineering, Springer-Verlag, New York (1984). doi: 10.1007/978-94-009-6192-0_2
  43. [43] Gebhart, B., Heat Conduction and Mass Diffusion, McGraw-Hill Inc., New York (1993). doi: 10.5860/ CHOICE.31-0358
  44. [44] Kane, J. H., Boundary Element Analysis: In Engineering Continuous Mechanism, Prentice Hall, Englewood (1994).
  45. [45] O’Neil, P. V., Advanced Engineering Mathematics, 5th Edition, Brooks/Cole-Thomson Learning Inc., CA (2003).
  46. [46] Sun, Y. M., Chang, T. P. and Liang, M. T., “Kirchhoff Transformation Analysis for Determining Time/Depth Dependent Chloride Diffusion Coefficient in Concrete,” Journal of Material Science, Vol. 43, No. 4, pp. 14291437 (2008). doi: 10.1007/s10853-007-2304-4
  47. [47] Tumidajski, P. J., Chan, G. W., Feldman, R. F. and Strathdee, G., “A Boltzmann-Matano Analysis of Chloride Diffusion,” Cement and Concrete Research, Vol. 25, No. 7, pp. 15561566 (1995). doi: 10.1016/0008- 8846(95)00149-7
  48. [48] Carslaw, H. S. and Jaeger, J. C., Conduct of Heat in Solids, Second Edition, Oxford University Press, New York (1959).
  49. [49] Boddy, A., Benta, E., Thomas, M. D. A. and Hooton, R. D., “An Overview and Sensitivity Study of a Multimechenistic Chloride Transport Model,” Cement and Concrete Research, Vol. 29, pp. 827837 (1999). doi: 10.1016/S0008-8846(99)00045-9
  50. [50] Page, C. L., Short, N. R. and El Tarras, A., “Diffusion of Chloride Ions into Hardened Cement Paste,” Cement and Concrete Research, Vol. 11, No. 3, pp. 395406 (1981). doi: 10.1016/0008-8846(81)90111-3
  51. [51] Wolfam Research, Mathematica User Manual, Version 4.0, Trade Center Drive, Champaign, IL 61820-7237, USA (1999).
  52. [52] Crank, J., The Mathematics of Diffusion, Second Edition, Oxford University Press, London (1975).
  53. [53] Papadakis, V. G., “Effect of Supplementary Cementing Materials on Concrete Resistance Against Carbonation and Chloride Ingress,” Cement and Concrete Research, Vol. 30, pp. 291299 (2000). doi: 10.1016/ S0008-8846(99)00249-5
  54. [54] Papadakis, V. G. and Tsimas, S., “Supplementary Cementing Materials in Concrete Part I: Efficiency and Design,” Cement and Concrete Research, Vol. 32, pp. 15251532 (2002). doi: 10.1016/S0008-8846(02)00 827-X
  55. [55] Lu, X., Li, C. and Zhang, H., “Relationship between the Free and Total Chloride Diffusivity in Concrete,” Cement and Concrete Research, Vol. 32, pp. 323326 (2002). doi: 10.1016/S0008-8846(02)00970-5
  56. [56] Fang, M. Y., Theoretical Modelling Chloride Diffusion in Concretes Containing Fly Ash and Slag, Master Thesis, Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan, ROC (2011).