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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (7): 1393-1401    DOI: 10.3785/j.issn.1008-973X.2023.07.014
    
Diffusion model of multi ions in concrete based on composite theory
Zhuang TIAN(),Guan-yan XIAO,Wei-liang JIN*(),Jin XIA,Xin CHENG
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
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Abstract  

The influence of multi-ion concentration on the ionic diffusion coefficient was analyzed according to Nernst-Einstein equation and the relationship between ionic concentration and electrical conductivity. The difference of diffusion coefficient between single-ion transport and multi-ion transport was compared. The ion diffusion coefficient of concrete was obtained based on the general effective media (GEM) theory by calculating the ionic diffusion coefficient and volume fraction of cement paste, aggregate and ITZ. The influence of components on the ionic diffusion coefficient in the concrete was analyzed. A prediction model of diffusion coefficient of multi ions in the concrete based on composite theory was constructed by comprehensively considering components of concrete, multi-ion species and concentration. The calculation results and experimental data were compared. Results show that the ionic diffusion coefficient decreases with the increasing of ionic concentration. The model can predict the ionic diffusion coefficient in the concrete based on ionic species and concentration compared with the traditional diffusion coefficient model. The prediction results are more rational.

Key words： concrete      multi ions      diffusion coefficient      general effective media theory      multi-phase composite material     
Received: 20 July 2022      Published: 17 July 2023
CLC:  TU 375  
Fund:  国家自然科学基金资助项目（5217080389）
Corresponding Authors: Wei-liang JIN     E-mail: 22012037@zju.edu.cn;jinwl@zju.edu.cn
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Zhuang TIAN
Guan-yan XIAO
Wei-liang JIN
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Xin CHENG
Cite this article:

Zhuang TIAN,Guan-yan XIAO,Wei-liang JIN,Jin XIA,Xin CHENG. Diffusion model of multi ions in concrete based on composite theory. Journal of ZheJiang University (Engineering Science), 2023, 57(7): 1393-1401.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.07.014     OR     https://www.zjujournals.com/eng/Y2023/V57/I7/1393


基于复合材料理论的混凝土内多离子扩散模型

根据Nernst-Einstein方程以及离子的浓度和电导率关系，探究多离子传输时离子浓度对离子扩散系数的影响，比较单离子传输和多离子传输的离子扩散系数差异. 根据通用有效介质（GEM）理论，分别计算水泥浆、骨料和ITZ内部的离子扩散系数和体积分数，得到混凝土内部离子扩散系数，探究混凝土的构成组分对离子扩散系数的影响. 综合考虑混凝土的构成组分以及离子的种类和浓度，提出基于多相复合材料理论的混凝土内部多离子扩散预测模型. 比较计算结果与试验数据可知，离子的扩散系数随着离子浓度的增加而明显下降. 和传统的离子扩散预测模型相比，该模型可以通过混凝土内部离子的种类和浓度预测离子的扩散系数，预测结果更加合理.


关键词： 混凝土,  多离子,  扩散系数,  通用有效介质理论,  多相复合材料 
Fig.1 Comparison of predicted results of ion diffusion coefficient model in solution and experimental data
Fig.2 Variations of ionic diffusion coefficient in composite with different parameter values
Fig.3 Variations of ionic diffusion coefficient in composite with different diffusion coefficients in phases
Fig.4 Modeling flow chart of diffusion model of multi ions in concrete
Fig.5 Schematic diagram of chloride ion diffusion coefficient measurement experiment
dr/mm wr/%
4.75 0.35
2.36 8.01
1.18 23.51
0.60 27.81
0.30 28.95
0.15 8.54
剩余 2.83
Tab.1 Grading of aggregate
Fig.6 Comparison of calculated values and test values of chloride ion diffusion coefficient
方法 公式
文献[13]方法 ${D}_{\mathrm{m} }={D}_{\mathrm{h} }{\left(1-{\varphi }_{\mathrm{l} }\right)}^{3/2}$
文献[14]方法 $ {D}_{\mathrm{m}}={D}_{\mathrm{h}}+\dfrac{{\varphi }_{\mathrm{l}}}{\dfrac{1}{{D}_{\mathrm{l}}-{D}_{\mathrm{h}}}+\dfrac{1-{\varphi }_{\mathrm{l}}}{3{D}_{\mathrm{h}}}} $
文献[15]方法 $ {D}_{\mathrm{m}}={D}_{\mathrm{h}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\dfrac{1.5{\varphi }_{\mathrm{l}}}{1-{\varphi }_{\mathrm{l}}}\right) $
文献[16]方法 $ \dfrac{{D}_{\mathrm{m}}-{D}_{\mathrm{h}}}{{D}_{\mathrm{m}}+2{D}_{\mathrm{h}}}={\varphi }_{\mathrm{l}}\left(\dfrac{{D}_{\mathrm{l}}-{D}_{\mathrm{h}}}{{D}_{\mathrm{l}}+2{D}_{\mathrm{h}}}\right) $
文献[17]方法 ${D}_{\mathrm{m} }=\left\{\begin{array}{c}\dfrac{ {D}_{\mathrm{h} }{D}_{\mathrm{l} } }{\left(1-{\varphi }_{\mathrm{l} }\right){D}_{\mathrm{l} }+{\varphi }_{\mathrm{l} }{D}_{\mathrm{h} } }\\ {D}_{\mathrm{h} }\left(1-{\varphi }_{\mathrm{l} }\right)+{D}_{\mathrm{l} }{\varphi }_{\mathrm{l} }\end{array}\right.$
文献[18]方法 $ {D}_{\mathrm{c}\mathrm{o}\mathrm{n}}={D}_{\mathrm{c}\mathrm{e}\mathrm{m}}(0.11{\varphi }_{\mathrm{ITZ}}+1-{\varphi }_{\mathrm{A}})\dfrac{2}{2+{\varphi }_{\mathrm{A}}} $
文献[19]方法 $ {D}_{\mathrm{c}\mathrm{o}\mathrm{n}}={D}_{\mathrm{c}\mathrm{e}\mathrm{m}}\left(1+\dfrac{{\varphi }_{\mathrm{A}}}{\dfrac{1-{\varphi }_{\mathrm{A}}}{3}+\dfrac{1}{{2\left({D}_{\mathrm{I}}/{D}_{\mathrm{c}\mathrm{e}\mathrm{m}}\right)}^{\varepsilon }-1}}\right) $
Tab.2 Overview of diffusion coefficient model
Fig.7 Comparison of prediction result of different chloride ion diffusion coefficient models
[1]   金伟良. 腐蚀混凝土结构学 [M]. 北京: 科学出版社, 2011.
[2]   王涛, 朴香兰, 朱慎林. 高等传递过程原理 [M]. 北京: 化学工业出版社, 2005.
[3]   NOSKOV A V, LILIN S A, PARFENYUK V I Simulation of ion mass transfer processes with allowance for the concentration dependence of diffusion coefficients[J]. Russian Chemical Bulletin, 2006, 55 (4): 661- 665
doi: 10.1007/s11172-006-0309-9
[4]   孙国文, 孙伟, 张云升, 等 骨料对氯离子在水泥基复合材料中扩散系数的影响[J]. 硅酸盐学报, 2011, 39 (4): 662- 669
SUN Guo-wen, SUN Wei, ZHANG Yun-sheng, et al Influence of aggregates on the chloride ion diffusion coefficient in cement-based composite materials[J]. Journal of Chinese Ceramic Society, 2011, 39 (4): 662- 669
[5]   刘清风 基于多离子传输的混凝土细微观尺度多相数值模拟[J]. 硅酸盐学报, 2018, 46 (8): 1074- 1080
LIU Qing-feng Multi-phase modeling of concrete at meso-micro scale based on multi-species transport[J]. Journal of Chinese Ceramic Society, 2018, 46 (8): 1074- 1080
[6]   LI L, PAGE C L Finite element modeling of chloride removal from concrete by an electrochemical method[J]. Corrosion Science, 2000, 42 (12): 2145- 2165
doi: 10.1016/S0010-938X(00)00044-5
[7]   XIA J, LI L Numerical simulation of ionic transport in cement paste under the action of externally applied electric field[J]. Construction and Building Materials, 2013, 39 (Supple.I): 51- 59
[8]   THOMAS M DA, SCOTT A, BREMNER T, et al Performance of slag concrete in marine environment[J]. ACI Materials Journal, 2008, 105 (6): 628- 634
[9]   BENTZ E C, THOMAS M. Life-365 service life prediction model and computer program for predicting the service life and life-cycle cost of reinforced concrete exposed to chlorides [R]. Toronto: University of Toronto, 2012.
[10]   KHATRI R P Characteristic service life for concrete exposed to marine environments[J]. Cement and Concrete Research, 2004, 34 (5): 745- 752
doi: 10.1016/S0008-8846(03)00086-3
[11]   ERDOGDU S, KONDRATOVA I L, BREMNER T W Determination of chloride diffusion coefficient of concrete using open-circuit potential measurements[J]. Cement and Concrete Research, 2004, 34 (4): 603- 609
doi: 10.1016/j.cemconres.2003.09.024
[12]   RIDING K A, THOMAS M D, FOLLIARD K J Apparent diffusivity model for concrete containing supplementary cementitious materials[J]. ACI Materials Journal, 2013, 110 (6): 705- 714
[13]   CHUEH C C, BERTEI A, PHAROAH J G, et al Effective conductivity in random porous media with convex and non-convex porosity[J]. International Journal of Heat and Mass Transfer, 2014, 71: 183- 188
doi: 10.1016/j.ijheatmasstransfer.2013.12.041
[14]   HASHIN Z, SHTRIKMAN S A variational approach to the theory of the effective magnetic permeability of multiphase materials[J]. Journal of Applied Physics, 1962, 33 (10): 3125- 3131
doi: 10.1063/1.1728579
[15]   JEFFREY D J Conduction through a random suspension of spheres[J]. Proceedings of the Royal Society of London Series A, 1973, 335 (1602): 355- 367
[16]   MALLET P, GUERIN C A, SENTENAC A Maxwell-Garnett mixing rule in the presence of multiple scattering: derivation and accuracy[J]. Physical Review B, 2005, 72 (1): 14201- 14205
doi: 10.1103/PhysRevB.72.014201
[17]   TIEDJE E W, GUO P Modeling the influence of particulate geometry on the thermal conductivity of composites[J]. Journal of Materials Science, 2014, 49 (16): 5586- 5597
doi: 10.1007/s10853-014-8268-2
[18]   CARÉ S Influence of aggregates on chloride diffusion coefficient into mortar[J]. Cement and Concrete Research, 2003, 33 (7): 1021- 1028
doi: 10.1016/S0008-8846(03)00009-7
[19]   HASHIN Z Thin interphase/imperfect interface in conduction[J]. Journal of Applied Physics, 2001, 89 (4): 2261- 2267
doi: 10.1063/1.1337936
[20]   LU X Application of the Nernst-Einstein equation to concrete[J]. Cement and Concrete Research, 1997, 27 (2): 293- 302
doi: 10.1016/S0008-8846(96)00200-1
[21]   傅献彩. 物理化学 [M]. 5版. 北京: 科学出版社, 2005.
[22]   SNYDER K A, FENG X, KEEN B D, et al Estimating the electrical conductivity of cement paste pore solutions from OH−, K+ and Na+ concentrations [J]. Cement and Concrete Research, 2003, 33 (6): 793- 798
doi: 10.1016/S0008-8846(02)01068-2
[23]   NIELSEN J M, ADAMSON A W, COBBLE J W The self-diffusion coefficients of the ions in aqueous sodium chloride and sodium sulfate at 25 ℃[J]. Journal of the American Chemical Society, 1952, 74 (2): 446- 451
doi: 10.1021/ja01122a050
[24]   MCBAIN J W, DAWSON M The diffusion of potassium chloride in aqueous solution[J]. Proceedings of the Royal Society of London Series A, 1935, 148 (863): 32- 39
[25]   LOBO V, RIBEIRO A, VERISSIMO L Diffusion coefficients in aqueous solutions of potassium chloride at high and low concentrations[J]. Journal of Molecular Liquids, 1998, 78 (1-2): 139- 149
doi: 10.1016/S0167-7322(98)00088-9
[26]   CRC handbook of chemistry and physics [M]. 89th ed. Boca Raton: CRC Press, 2009.
[27]   MCLACHLAN D S, BLASZKIEWICZ M, NEWNHAM R E Electrical resistivity of composites[J]. Journal of the American Ceramic Society, 1990, 73 (8): 2187- 2203
doi: 10.1111/j.1151-2916.1990.tb07576.x
[28]   OH B H, JANG S Y Prediction of diffusivity of concrete based on simple analytic equations[J]. Cement Concrete Research, 2004, 34 (3): 463- 480
doi: 10.1016/j.cemconres.2003.08.026
[29]   ISICHENKO M B Percolation, statistical topography, and transport in random media[J]. Review of Modern Physics, 1992, 64 (4): 961- 1043
doi: 10.1103/RevModPhys.64.961
[30]   LUO X, QU M, SCHUBERT D W Electrical conductivity and fiber orientation of poly (methyl methacrylate)/carbon fiber composite sheets with various thickness[J]. Polymer Composites, 2020, 42 (2): 548- 558
[31]   LIN J, CHEN H Effect of particle morphologies on the percolation of particulate porous media: a study of superballs[J]. Powder Technology, 2018, 335: 388- 400
doi: 10.1016/j.powtec.2018.05.015
[32]   LI M, CHEN H, LIN J, et al Effects of the pore shape polydispersity on the percolation threshold and diffusivity of porous composites: theoretical and numerical studies[J]. Powder Technology, 2021, 386: 382- 393
doi: 10.1016/j.powtec.2021.03.055
[33]   XU W, JIA M, ZHU Z, et al n-Phase micromechanical framework for the conductivity and elastic modulus of particulate composites: design to microencapsulated phase change materials (MPCMs)-cementitious composites[J]. Materials and Design, 2018, 145: 108- 115
doi: 10.1016/j.matdes.2018.02.065
[34]   CHRISTENSEN B J, COVERDALE T, OLSON R A, et al Impedance spectroscopy of hydrating cement-based materials: measurement, interpretation, and application[J]. Journal of the American Ceramic Society, 1994, 77 (11): 2789- 2804
doi: 10.1111/j.1151-2916.1994.tb04507.x
[35]   POWERS T C. Physical properties of cement paste [C]// Proceedings of the 4th International Conference on the Chemistry of Cement. Washington, DC: Cementand Concrete Association, 1960: 577–613.
[36]   WALLER V, DELARRARD F, ROUSSEL P. Modelling the temperature rise in massive HPC structures. [C]// 4th International Symposium on Utilization of High-Strength/High-Performance Concrete. Paris: RILEM, 1996: 415-421.
[37]   GARBOCZI E J, BENTZ D P Computer simulation of the diffusivity of cement-based materials[J]. Journal of Materials Science, 1992, 27 (8): 2083- 2092
doi: 10.1007/BF01117921
[38]   BENTZ D P, GARBOCZI E J. Computer modelling of interfacial transition zone: microstructure and properties [C]// RILEM Report 20. Cachan: RILEM, 1999: 349-385.
[39]   BOURDETTE B, RINGOT E, OLLIVIER J P Modelling of the transition zone porosity[J]. Cement Concrete Research, 1995, 25 (4): 741- 751
doi: 10.1016/0008-8846(95)00064-J
[40]   JIANG J, SUN G, WANG C Numerical calculation on the porosity distribution and diffusion coefficient of interfacial transition zone in cement-based composite materials[J]. Construction and Building Materials, 2013, 39: 134- 138
doi: 10.1016/j.conbuildmat.2012.05.023
[41]   YANG C C, SU K J Approximate migration coefficient of interfacial transition zone and the effect of aggregate content on the migration coefficient of mortar[J]. Cement Concrete Research, 2002, 32 (10): 1559- 1565
doi: 10.1016/S0008-8846(02)00832-3
[42]   ZHENG J J, WONG H S, BUENFELD N R Assessing the influence of ITZ on the steady-state chloride diffusivity of concrete using a numerical model[J]. Cement Concrete Research, 2009, 39 (9): 805- 813
doi: 10.1016/j.cemconres.2009.06.002
[43]   应敬伟, 肖建庄 模型再生混凝土氯离子非线性扩散细观仿真[J]. 建筑材料学报, 2013, 16 (5): 863- 868
YING Jing-wei, XIAO Jian-zhuang Meso-level simulation of chloride nonlinear diffusion in modeled recycled aggregate concrete[J]. Journal of Building Materials, 2013, 16 (5): 863- 868
doi: 10.3969/j.issn.1007-9629.2013.05.022
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