Abstract
In this paper, searching for a better chloride ions sub-diffusion system, a multi-term time-fractional derivative diffusion model is proposed for the description of the time-dependent chloride ions penetration in reinforced concrete structures exposed to chloride environments. We prove the stability and convergence of the model. We use the modified grid approximation method (MGAM) to estimate the fractional orders and chloride ions diffusion coefficients in the reinforced concrete for the multi-term time fractional diffusion system. And then to verify the efficiency and accuracy of the proposed methods in dealing with the fractional inverse problem, two numerical examples with real data are investigated. Meanwhile, we use two methods of fixed chloride ions diffusion coefficient and variable diffusion coefficient with diffusion depth to simulate chloride ions sub-diffusion system. The result shows that with the new fractional orders and parameters, our multi-term fractional order chloride ions sub-diffusion system is capable of providing numerical results that agree better with the real data than other models. On the other hand, it is also noticed from the numerical solution of the chloride ions sub-diffusion system that setting the variable diffusion coefficient with diffusion depth is more reasonable. And it is also found that chloride ions diffusion coefficients in reinforced concrete should be decreased with diffusion depth which is completely consistent with the theory. In addition, the model can be used to predict the chloride profiles with a time-dependent property. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.