A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures

By Wen Chen, Jianjun Zhang, Jinyang Zhang. 2012

126 citations recorded by the source corpus.

This study proposes a new variable-order fractional diffusion equation model to describe the coupled chloride diffusion-binding processes in reinforced concrete, in which the order of fractional derivative term is a variable function instead of a constant in the standard fractional model. The concentration influence coefficient k is introduced to capture the effect of concentration dependency on chloride transport due to the chloride binding behavior. The two parameters in the proposed model can be determined directly by a statistical analysis of measurement data. Four test cases illustrate that the proposed variable-order fractional derivative model agrees significantly better with experimental data than the most commonly used traditional model governed by the classical Fick’s second law, especially when a large concentration coefficient k is involved. That proposed model is also verified by accurately predicting chloride concentration profiles in a period of 200 days.

Subfields: Mechanics of Materials, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/245b82b3e2c4b895bedab4733237a9441cf39c69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. M. Kashani
2. N. Alexander
3. Wen Chen
4. Adam J. Crewe
5. L. Lowes
6. Yan Gu
7. Zhuojia Fu
8. Jinyang Zhang

In Modeling and Simulation

1. Yong Zhang
2. A. Chang
3. Wen Chen
4. Hongguang Sun
5. Dumitru Băleanu
6. Arran Fernandez
7. Ali H. Bhrawy
8. M. A. Zaky

In Statistics and Probability

1. Wen Chen
2. Yong Zhang

Citations in the corpus

• A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications (2019, background): “Fractional derivative model has been recognized as a powerful modeling approach in many natural and engineering fields [28, 33].”
• Phenomenological hysteretic model for corroded reinforcing bars including inelastic buckling and low-cycle fatigue degradation (2015, background): “32 models for concrete structures and diffusion equations that predict the diffusion of chloride ions in concrete and corrosion initiation time [50-52].”