Email Alerts
RSS
Analytical model for time-dependent chloride diffusion in circular section concrete
-
摘要: 为了克服传统常扩散解析模型无法考虑氯离子扩散系数时变特性所存在的缺陷，研究建立了圆形截面混凝土中氯离子时变扩散解析模型。在极坐标系中建立了圆形截面混凝土中氯离子时变扩散的控制方程、边界条件和初始条件，然后通过引入等效扩散时间将氯离子的时变扩散方程转化为常扩散方程，进而结合贝塞尔函数和变量代换法，建立了圆形截面混凝土中氯离子时变扩散的解析模型，并与数值模型和常扩散解析模型进行对比验证。分析结果表明，该解析模型具有较高计算精度和计算效率，不仅可以克服数值模型对空间离散网格和时间步长的依赖性，而且还可以克服常扩散模型由于忽略氯离子扩散系数时变性而高估混凝土中氯离子质量分数所存在的缺陷；圆形截面混凝土中的氯离子质量分数分布介于一维和二维扩散之间，随着圆形截面半径和龄期衰减系数的增大逐渐趋近于一维扩散情况。Abstract: In order to overcome the shortcomings of the traditional analytical model of constant diffusion which can not consider the time-varying characteristics of chloride diffusion coefficient, a time-dependent analytical model for the chloride diffusion in circular cross-section concrete is developed. Firstly, the governing equation, boundary conditions and initial conditions for the time-dependent chloride diffusion in the circular cross-section concrete are established in the polar coordinate system. Then, by introducing the equivalent diffusion time, the time-dependent diffusion equation of chloride ion is transformed into the constant diffusion equation, and then an analytical model of chloride time-dependent diffusion in the circular cross-section concrete is developed by combining the Bessel function and variable substitution method. Finally, the proposed analytical model is validated by comparing with the numerical model and the constant diffusion analytical model. Analysis results show that the proposed analytical model is of high accuracy and efficiency, which not only overcomes the limitations of the traditional numerical models whose accuracy and efficiency are largely depended on the spatial discrete grids and time steps, but also overcomes the shortcomings of the constant diffusion analytical models which often overestimate the chloride ion concentration in concrete since they cannot take into account the time-dependent characteristics of the chloride diffusion coefficient. The chloride ion concentration profile in the circular cross-section concrete is between the one- and two-dimensional diffusions, which gradually tends to the one-dimensional diffusion with the increase of the circular cross-section radius and age decay coefficient.
-
Key words:
- concrete /
- circular section /
- age decay coefficient /
- chloride ion /
- time-dependent diffusion /
- analytical model
-
图 1 圆形截面混凝土构件及其氯离子暴露条件
Figure 1. Circular section concrete members and their chloride exposure conditions
图 2 解析模型和数值模型所计算的氯离子质量分数分布比较
Figure 2. Comparison between chloride concentration distribution calculated by analytical and numerical models
图 3 贝塞尔函数零点个数对解析模型计算精度的影响
Figure 3. Effects of zero numbers of zero-order Bessel functions on accuracy of analytical model
图 4 氯离子扩散系数时变性对氯离子质量分数分布的影响
Figure 4. Effects of time-dependent chloride diffusion coefficients on chloride concentration distribution
图 5 圆形截面半径对氯离子质量分数分布的影响
Figure 5. Effect of cross-section radius on chloride concentration distribution
表 1 空间离散网格和时间步长对数值模型计算精度与计算效率的影响
Table 1. Influences of spatial discrete grids and time steps on calculation accuracy and efficiency of numerical model
Δx/mm 氯离子质量分数计算值/% 计算耗时/s Δt=5.00 a Δt=1.00 a Δt=0.50 a Δt=0.10 a Δt=0.05 a Δt=5.00 a Δt=1.00 a Δt=0.50 a Δt=0.10 a Δt=0.05 a 25.0 0.880 1.008 1.039 1.074 1.080 2.64 8.77 17.05 87.75 170.28 10.0 0.827 0.969 1.002 1.041 1.047 5.88 24.38 47.67 233.33 479.36 5.0 0.819 0.964 0.997 1.036 1.043 19.06 79.90 153.12 753.75 1 519.75 2.5 0.818 0.963 0.996 1.035 1.042 61.65 270.80 546.13 2 844.46 5 392.50 
下载: 导出CSV
表 2 不同n, t和半径情况下圆形截面与一维扩散的氯离子质量分数相对误差
Table 2. Relative errors of chloride concentration between 1D diffusion and circular cross-section with different n, t and radius
% 半径/mm n=0.2 n=0.4 n=0.6 t=30 a t=50 a t=100 a t=30 a t=50 a t=100 a t=30 a t=50 a t=100 a 700 5.937 6.072 6.209 5.162 5.562 5.852 2.029 3.167 4.363 800 5.122 5.234 5.344 4.459 4.802 5.051 1.753 2.737 3.769 900 4.504 4.600 4.691 3.924 4.226 4.442 1.545 2.409 3.318 1 000 4.019 4.103 4.181 3.504 3.773 3.965 1.407 2.154 2.963 1 100 3.629 3.702 3.770 3.165 3.407 3.580 1.288 1.950 2.677
下载: 导出CSV
表 3 不同D0, Cs和半径情况下圆形截面与一维扩散的氯离子质量分数相对误差
Table 3. Relative errors of chloride concentration between 1D diffusion and circular cross-section with different D0, Cs and radius
% 半径/mm D0=2×10-12 m2/s D0=6×10-12 m2/s D0=10×10-12 m2/s Cs=2.0% Cs=3.5% Cs=5.0% Cs=2.0% Cs=3.5% Cs=5.0% Cs=2.0% Cs=3.5% Cs=5.0% 700 0.441 0.748 1.024 4.079 4.832 5.204 5.000 5.511 5.739 800 0.380 0.644 0.882 3.523 4.173 4.500 4.316 4.757 4.954 900 0.383 0.584 0.799 3.101 3.673 3.956 3.797 4.185 4.358 1 000 0.384 0.651 0.106 2.769 3.280 3.532 3.390 3.736 3.890 1 100 0.341 0.578 0.791 2.501 2.962 3.191 3.061 3.374 3.513
下载: 导出CSV
-
[1] 王胜年, 汤雁冰, 杨海成, 等.基于长期性能观测的海工混凝土结构耐久性研究的新思路[J].水运工程, 2017(10): 60-66. doi: 10.3969/j.issn.1002-4972.2017.10.012 WANG Shengnian, TANG Yanbing, YANG Haicheng, et al. New idea on durability study of marine concrete structure based on long-term property observation [J]. Port and Waterway Engineering, 2017(10): 60-66. (in Chinese) doi: 10.3969/j.issn.1002-4972.2017.10.012 [2] COLLEPARDI M. Penetration of chloride ions into cement pastes and concrete[J]. Journal of the American Ceramic Society, 1972, 55(10): 534-535. doi: 10.1111/j.1151-2916.1972.tb13424.x [3] SURYAVANSHI A K, SWAMY R N, CARDEW G E. Estimation of diffusion coefficients for chloride ion penetration into structural concrete[J]. ACI Materials Journal, 2002, 99(5): 441-449. http://cn.bing.com/academic/profile?id=8b288abef84945d571b6dc6c12ecc836&encoded=0&v=paper_preview&mkt=zh-cn [4] 窦雪梅, 余红发, 麻海燕, 等.珊瑚混凝土在海洋环境中氯离子扩散实验[J].海洋工程, 2017, 35(1): 129-135. http://d.old.wanfangdata.com.cn/Periodical/hygc201701015 DOU Xuemei, YU Hongfa, MA Haiyan, et al. Experiment on chloride diffusion coefficient of coral concrete exposed to marine environment[J]. The Ocean Engineering, 2017, 35(1): 129-135. (in Chinese) http://d.old.wanfangdata.com.cn/Periodical/hygc201701015 [5] CASTALDO P, PALAZZO B, MARINIELLO A. Effects of the axial force eccentricity on the time-variant structural reliability of aging r.c. cross-sections subjected to chloride-induced corrosion[J]. Engineering Structures, 2017, 130: 261-274. doi: 10.1016/j.engstruct.2016.10.053 [6] JUSTNES H, KIM M O, NG S, et al. Methodology of calculating required chloride diffusion coefficient for intended service life as function of concrete cover in reinforced marine structures[J]. Cement and Concrete Composites, 2016, 73: 316-323. doi: 10.1016/j.cemconcomp.2016.08.006 [7] ZHANG J Z, ZHENG Y Y, WANG J D, et al. Chloride transport in concrete under flexural loads in a tidal environment[J]. Journal of Materials in Civil Engineering, 2018, 30(11): 04018285(1-11). doi: 10.1061/(ASCE)MT.1943-5533.0002493 [8] ZHANG J Z, GUO J, LI D H, et al. The influence of admixture on chloride time-varying diffusivity and microstructure of concrete by low-field NMR[J]. Ocean Engineering, 2017, 142(9): 94-101. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0419b3cac41bbaaa1626ab7f65e08314 [9] MAAGE M, HELLAND S, POULSEN E, et al. Service life prediction of existing concrete structures exposed to marine environment[J]. ACI Materials Journal, 1996, 93(6): 602-608. http://cn.bing.com/academic/profile?id=a31434fcf350d290a3394b2c2faff25b&encoded=0&v=paper_preview&mkt=zh-cn [10] WANG Y, WU L, WANG Y, et al. Prediction model of long-term chloride diffusion into plain concrete considering the effect of the heterogeneity of materials exposed to marine tidal zone[J]. Construction and Building Materials, 2018, 159: 297-315. doi: 10.1016/j.conbuildmat.2017.10.083 [11] TANG L P, GULIKERS J. On the mathematics of time-dependent apparent chloride diffusion coefficient in concrete[J]. Cement and Concrete Research, 2007, 37(4): 589-595. doi: 10.1016/j.cemconres.2007.01.006 [12] 余红发, 孙伟, 麻海燕, 等.混凝土在多重因素作用下的氯离子扩散方程[J].建筑材料学报, 2002, 5(3): 240-247. doi: 10.3969/j.issn.1007-9629.2002.03.008 YU Hongfa, SUN Wei, MA Haiyan, et al. Diffusion equations of chloride ion in concrete under the combined action of durability factors[J]. Journal of Building Materials, 2002, 5(3): 240-247. (in Chinese) doi: 10.3969/j.issn.1007-9629.2002.03.008 [13] LIANG M T, WANG K L, LIANG C H. Service life prediction of reinforced concrete structures[J]. Cement and Concrete Research, 1999, 29(9): 1411-1418. doi: 10.1016/S0008-8846(99)00109-X [14] 杨绿峰, 胡春燕, 陈正, 等.混凝土中氯离子随机时变扩散过程和浓度分布[J].建筑材料学报, 2013, 16(2): 210-216. doi: 10.3969/j.issn.1007-9629.2013.02.005 YANG Lufeng, HU Chunyan, CHEN Zheng, et al. Stochastic and time-dependent diffusion of chloride ion in concrete and its concentration distribution[J]. Journal of Building Materials, 2013, 16(2): 210-216. (in Chinese) doi: 10.3969/j.issn.1007-9629.2013.02.005 [15] YANG L F, MA Q, YU B. Analytical solution and experimental validation for dual time-dependent chloride diffusion in concrete[J]. Construction and Building Materials, 2018, 161: 676-686. doi: 10.1016/j.conbuildmat.2017.11.176 [16] 王显利, 吴智敏, 郑建军.氯离子侵蚀圆形截面钢筋混凝土结构耐久性分析[J].东北林业大学学报, 2006, 34(2): 76-77, 108. doi: 10.3969/j.issn.1000-5382.2006.02.028 WANG Xianli, WU Zhimin, ZHENG Jianjun. Durability analysis of reinforced concrete structure with circular section under chlorine anion corrosion[J]. Journal of Northeast Forestry University, 2006, 34(2): 76-77, 108. (in Chinese) doi: 10.3969/j.issn.1000-5382.2006.02.028 [17] 唐敏康, 王霆, 何勇, 等.圆形截面下混凝土中氯离子扩散的数值模拟[J].有色金属科学与工程, 2015, 6(3): 105-110. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jxysjs201503020 TANG Minkang, WANG Ting, HE Yong, et al. Numerical simulation of chloride ions diffusion at circular cross-section concrete[J]. Nonferrous Metal Science and Engineering, 2015, 6(3): 105-110. (in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jxysjs201503020 [18] 周明, 杨绿峰, 陈正, 等.圆柱体混凝土构件中氯离子扩散的解析研究[J].水利水运工程学报, 2012(6): 38-43. doi: 10.3969/j.issn.1009-640X.2012.06.007 ZHOU Ming, YANG Lufeng, CHEN Zheng, et al. Chloride diffusion in concrete component with circular section[J]. Hydro-Science and Engineering, 2012(6): 38-43. (in Chinese) doi: 10.3969/j.issn.1009-640X.2012.06.007 [19] 杨博, 李镜培, 岳著文.氯离子在混凝土桩中扩散的解析解[J].低温建筑技术, 2013, 35(2): 79-80. doi: 10.3969/j.issn.1001-6864.2013.02.032 YANG Bo, LI Jingpei, YUE Zhuwen. Analytical solution of chloride ion diffusion in concrete piles[J]. Low Temperature Architecture Technology, 2013, 35(2): 79-80. (in Chinese) doi: 10.3969/j.issn.1001-6864.2013.02.032 [20] 杨绿峰, 李冉.混凝土中氯离子二维扩散规律的解析研究[J].水利水电科技进展, 2009, 29(3): 20-23. http://d.old.wanfangdata.com.cn/Periodical/slsdkjjz200903006 YANG Lufeng, LI Ran. Analytical study of two-dimensional diffusion of chloride ion in concrete[J]. Advances in Science and Technology of Water Resources, 2009, 29(3): 20-23. (in Chinese) http://d.old.wanfangdata.com.cn/Periodical/slsdkjjz200903006 -
点击查看大图
图(5) / 表 (3)
计量
- 文章访问数: 265
- HTML全文浏览量: 101
- PDF下载量: 12
- 被引次数: 0
