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

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) similar to 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 x 10(-5) g/mm(3). 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.