圆形截面混凝土中氯离子时变扩散解析模型

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。

Analytical model for time-dependent chloride diffusion in circular section concrete

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.