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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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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 wordsconcrete      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:;
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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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
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