In this paper, a two-dimensional finite difference numerical model with time varying coefficient using Alternating Direction Implicit Method (ADI) is developed to predict Chloride diffusion in concrete. This model is proved to be unconditionally stable and has higher accuracy. And a numerical example is given to show the effectiveness of this model.
| Published in | Mathematical Modelling and Applications (Volume 2, Issue 1) |
| DOI | 10.11648/j.mma.20170201.11 |
| Page(s) | 1-7 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Chloride Ion, Time Varying Coefficient, ADI Method, Stable, Convergent
| [1] | Collepardi M, Marcialis A. Turrizzani R. The kinctics of penetration of Chloride ions into the concrete. II Cemenoto(Italy), 1970, 4: 157-164. |
| [2] | Collepardi M, Marcialis A. Turrizzani R. Penetration of Chloride ions into cement pastes and concrete. 1972, 55: 534-535. |
| [3] | Yuan, Q., Shi, C. De Schutter, G. Audenaert, K. And Deng, D.. Chloride Binding of Cement-Based Materials Subjected to External Chloride Environment - A Review, Construction and Building Materials. 2009, 23 (1): 1–13. |
| [4] | M. Funanshi. Prediction corrosion-free service life of a concrete structure in a Chloride environment. ACI Materials Journal,1990, 87 (6): 581-587. |
| [5] | S. L. Amey, D. A. Johnson etc. Predicting the service of concrete marine structures. An Environmental Methodology, ACI Structural Journal.1998, 95 (2): 205-214. |
| [6] | Ali H. Al-Gadhib. Numerical simulation of Chloride diffusion in RC structures and the implications of Chloride binding capacities and concrete mix. International Journal of Civil & Environmental Engineering.2010, 10 (5): 22-35. |
| [7] | F. Hou, Y. Bai, J. Dong. Numerical Analysis of the 2-Dimensional Diffusion Models of Chloride Ions Based on the FDM with Alternating Direction Implicit Schemes. Advanced Materials Research, 2014, 1020: 92-97. |
| [8] | Zhang Wei, Dong Zhiliang, Lv Huang. Two-dimensional concrete Chloride ion diffusion model and engineering verification, Hydraulic Engineering. 2009, 6: 35-39. |
| [9] | M. Bitaraf, S. Mohammadi. Analysis of Chloride diffusion in concrete structures for prediction of initiation time of corrosion using a new meshless approach. Construction and Building Materials, 2008, 22: 546-556. |
| [10] | Lvfeng Yang, Zheng Chen etc. Numerical analysis of Chloride diffusion in concrete with time varying coefficient by boundary element method. Civil Engineering and Environmental Engineering, 2011, 33 (4): 73-79. (in Chinese). |
| [11] | Zheng Chen, Wocheng Huang etc. Two phase boundary element model of Chloride diffusion in concrete. Concrete, 2016, 2: 12-16. (in Chinese). |
| [12] | Hongfa Yu, Wei Sun, Haiyan Ma etc. Chloride diffusion in concrete under multiple factors. Building Material Science, 2002, 5 (3): 240-247. (in Chinese). |
| [13] | S. H. HAN. Influence of diffusion coefficient on Chloride ion penetration of concrete structure. Construction and Building Materials, 2007, 21: 370-378. (in Chinese). |
| [14] | E. C. Bentz. Probabilistic modeling of service life for structures subjected to Chlorides. Aci Materials Journa. 2003. 100 (5): 391-397. |
| [15] | T. Luping, J. Gulikers. On the mathematics of time-dependent apparent Chloride diffusion coefficient in concrete. Cement and Concrete Research. 2007. 37 (4): 589–595. |
| [16] | Y. P. Xi, Z. P. Bazant. Modeling Chloride penetration in saturated concrete. Journal of Materials in Civil Engineering, 1999, 11 (1): 58–65. |
| [17] | N. Damrongwiriyanupap, L. Y. Li, Y. P. Xi. Coupled Diffusion of Multi-Component Chemicals in Non-Saturated Concrete. Computers and Concrete. 2013, 11 (3): 201-222. |
| [18] | J. S. Kong, A. N. Ababneh, D. M. Frangopol, Y. P. Xi. Reliability analysis of Chloride penetration in saturated concrete. Probabilistic Engineering Mechanics. 2002, 17: 305-315. |
| [19] | Yu Bai, Ali Harajli, Yunping Xi. Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media. Journal of Applied Mathematics, 2015, Article ID 208914, 11 pages, http://dx.doi.org/10.1155/2015/208914. |
| [20] | G. M. Wang, Y. Kong, Z. H. Shui, Q. Li, J. L. Han. Experimental investigation on Chloride diffusion and binding in concrete containing metakaolin. Corrosion Engineering, Science and Technology. 2014, 49 (4): 282-286 (in Chinese). |
| [21] | Zhang Baolin, Su Xiumin. Alternating Block Explicit-Implicit Method For the Two-Dimensional Diffusion Equation. Intern. J. Computer Math.. 1991, 38: 241-255. |
| [22] | Lu. J. F. & Guan. Z. Numerical solutions for partial differential equations. Tsinghua University press. 2007. (in Chinese). |
| [23] | D. Ali, S. Mohammad. Effect of exposure temperature on Chloride-binding capacity of cementing materials. Magazine of Concrete Research. 2015, 67 (15): 821-832. |
| [24] | Y. Ren, Q. Huang, Q. Y. Liu, J. Z. Sun, X. L. Liu. Chloride ion diffusion of structural concrete under the coupled effect of bending fatigue load and Chloride. Materials Research Innovations. 2015, 19: 181-184 (in Chinese). |
| [25] | N. Ganesana1, A. Ruby, S. D. Rajb. Durability characteristics of steel fibre reinforced geopolymer concrete. Construction and Building Materials. 2015, 93: 471-476. |
APA Style
Yu Bai, Mengjie Tang, Fei Hou, Jun Dong. (2017). Numerical Analysis of Chloride Diffusion in Concrete with Time Varying Coefficient Based on the ADI Method. Mathematical Modelling and Applications, 2(1), 1-7. https://doi.org/10.11648/j.mma.20170201.11
ACS Style
Yu Bai; Mengjie Tang; Fei Hou; Jun Dong. Numerical Analysis of Chloride Diffusion in Concrete with Time Varying Coefficient Based on the ADI Method. Math. Model. Appl. 2017, 2(1), 1-7. doi: 10.11648/j.mma.20170201.11
AMA Style
Yu Bai, Mengjie Tang, Fei Hou, Jun Dong. Numerical Analysis of Chloride Diffusion in Concrete with Time Varying Coefficient Based on the ADI Method. Math Model Appl. 2017;2(1):1-7. doi: 10.11648/j.mma.20170201.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.mma.20170201.11,
author = {Yu Bai and Mengjie Tang and Fei Hou and Jun Dong},
title = {Numerical Analysis of Chloride Diffusion in Concrete with Time Varying Coefficient Based on the ADI Method},
journal = {Mathematical Modelling and Applications},
volume = {2},
number = {1},
pages = {1-7},
doi = {10.11648/j.mma.20170201.11},
url = {https://doi.org/10.11648/j.mma.20170201.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170201.11},
abstract = {In this paper, a two-dimensional finite difference numerical model with time varying coefficient using Alternating Direction Implicit Method (ADI) is developed to predict Chloride diffusion in concrete. This model is proved to be unconditionally stable and has higher accuracy. And a numerical example is given to show the effectiveness of this model.},
year = {2017}
}
TY - JOUR T1 - Numerical Analysis of Chloride Diffusion in Concrete with Time Varying Coefficient Based on the ADI Method AU - Yu Bai AU - Mengjie Tang AU - Fei Hou AU - Jun Dong Y1 - 2017/03/21 PY - 2017 N1 - https://doi.org/10.11648/j.mma.20170201.11 DO - 10.11648/j.mma.20170201.11 T2 - Mathematical Modelling and Applications JF - Mathematical Modelling and Applications JO - Mathematical Modelling and Applications SP - 1 EP - 7 PB - Science Publishing Group SN - 2575-1794 UR - https://doi.org/10.11648/j.mma.20170201.11 AB - In this paper, a two-dimensional finite difference numerical model with time varying coefficient using Alternating Direction Implicit Method (ADI) is developed to predict Chloride diffusion in concrete. This model is proved to be unconditionally stable and has higher accuracy. And a numerical example is given to show the effectiveness of this model. VL - 2 IS - 1 ER -
Email: