Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions...

Area of Science:

• Materials Science
• Civil Engineering
• Applied Mathematics

Background:

• Chloride ion penetration in reinforced concrete structures is a critical factor in material degradation.
• Existing diffusion models may not fully capture the complex time-dependent behavior of chloride ingress.

Purpose of the Study:

• To propose and validate a multi-term time-fractional derivative diffusion model for chloride ion penetration.
• To accurately estimate fractional orders and diffusion coefficients in reinforced concrete.
• To compare model performance against real data and established methods.

Main Methods:

• Development of a multi-term time-fractional diffusion model.
• Application of the modified grid approximation method (MGAM) for parameter estimation.
• Numerical simulations using fixed and variable diffusion coefficients.
• Validation with two numerical examples using real data.

Main Results:

• The proposed multi-term fractional order model shows improved agreement with real data compared to other models.
• A variable diffusion coefficient, decreasing with depth, provides a more realistic simulation of chloride ion sub-diffusion.
• Estimated diffusion coefficients align with theoretical predictions, decreasing with diffusion depth.
• The model demonstrates capability in predicting time-dependent chloride profiles.

Conclusions:

• The multi-term time-fractional diffusion model offers a superior approach for modeling chloride ion penetration in reinforced concrete.
• Variable diffusion coefficients that decrease with depth are more physically representative.
• The model provides a valuable tool for predicting material degradation and ensuring structural integrity.