混凝土中变扩散系数的时间分数阶氯离子扩散模型研究

Research on the Time-Fractional Diffusion Model of Chloride Ion with Variable Diffusion Coefficient in Concrete

摘要: 研究氯离子在混凝土中的扩散机理可以有针对性地对混凝土进行修护，从而有效地延长混凝土的耐久性。对于氯离子在混凝土中扩散的一维问题，首先基于Caputo分数阶导数建立了变扩散系数的时间分数阶扩散模型，结合L1算法得到了数值求解该模型的有限差分格式。随后，针对一个实例，利用已有实验数据和最小二乘原理优化了模型中不同暴露时间下分数阶导数的阶数；通过数据拟合得到了时间分数阶导数的阶数与暴露时间之间的关系，进而建立了混凝土中变扩散系数的时间变分数阶的氯离子扩散模型。

Abstract: Research on the diffusion mechanism of Chloride ion in concrete can be applied to repair concrete, which can effectively prolong the durability of concrete. This paper is focusing on one-dimensional diffusion of Chloride ion in concrete. Firstly, the time-fractional diffusion model of Chloride ion with variable diffusion coefficient in concrete is established based on Caputo fractional derivative, which is solved by the finite difference scheme combining with L1 algorithm. Next, the fractional derivative parameter on different exposure time is optimized by using the existing experimental data and the least square method in the model. At last, the relationship between the optimal fractional derivative parameter and the exposure time is fitted, which results in the time variable fractional diffusion model of Chloride ion with variable diffusion coefficient in concrete.