Diffusion-reaction model of stochastically mixed sulfate in cast-in-situ piles

Abstract This study investigated the diffusion-reaction of sulfate in a cast-in-situ pile after different serving times. The diffusion equation was established based on Fick’s second law, and the model was established via the method of separation of variables by considering the appropriate initial and boundary conditions. An example of the diffusion-reaction of sulfate was compared to a traditional model. Additionally, the validity and advantages of the proposed method were verified. The results of this study showed that the discrepancy of the sulfate concentration profile increases as the radius of a cast-in-situ pile decrease. Additionally, the discrepancy was found to increase over time, which indicated that the diffusion-reaction of sulfate in a cast-in-situ pile has the characteristics of time and size effect. The initial concentration, gradient and reaction rate were shown to have significant effects on the diffusion-reaction of sulfate. The variations in the sulfate concentration profile were found to be larger at locations of high concentration and surface of pile. Thus, a higher concentration of sulfate tended to produce more sulfate consumption. Conversely, a decrease in the sulfate gradient led to a decrease in sulfate consumption proportion, even in the presence of a higher concentration of sulfate. A faster kinetic rate of chemical reactions was also found to produce higher consumption rates of sulfate, and the concentration gradient decreased concurrently.