A simplified solving method for Fickian diffusion model and its application in simulating moisture distribution in asphalt concrete

ABSTRACT

Moisture accumulated in the pavement can further access the internal asphalt concrete (AC) through the diffusion effect, causing loss of adhesion and cohesion in AC. Previous studies have contributed significantly to formulating the diffusion process, among which the Fickian diffusion model is widely used. However, solving such a model challenges researchers due to its second-ordered partial differential equation form. To address this issue, we developed an alternative approach that integrated spatial discretization and nonlinear regression to solve the Fickian diffusion model based on realistic vapour sorption profiles. The results showed that $R^2$ exceeded 0.73, and the orders of diffusion coefficient lay between ${10}^{-8}\sim {10}^{-6}$, which aligned well with existing studies. Furthermore, we used the solved Fickian diffusion model to predict moisture concentration and distribution in AC through the finite element (FE) method. The sum of squared errors (SSe) between simulation and measurement is lower than $3.62\times {10}^{-5}$ g/mm³. The simulation showed that ambient conditions and material properties influenced the moisture field evolution with diffusion time. The statistical analysis indicated that the interface was prone to accumulate moisture and generate damage. Our work provides a sequential method, including solving and applying the Fickian diffusion model, to predict moisture evolution in AC.

KEYWORDS:

• Long-term vapour exposure
• asphalt concrete
• kinetic vapour sorption
• diffusion model
• Moisture diffusing simulation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China: [grant no 52178433]; National Natural Science Foundation of China: [grant no 51878499]; Fundamental Research Funds for the Central Universities: [grant no 22120200447].