PARAMETER ESTIMATION METHODOLOGY FOR THE HALL DIFFUSION MODEL IN REINFORCED CONCRETE SAMPLES

This article presents a methodology for fitting the parameters of the chloride-ion Hall’s diffusion coefficient in re-inforced concrete samples exposed to aggressive marine environments. The methodology aims to minimize the mean square error (MSE) between experimental and simulated chloride-ion concentration profiles, based on Fick’s second law coupled with Hall’s empirical diffusion equation and appropriate initial and boundary value condi-tions (IBVP). This minimization problem is formulated as a nonlinear dynamic optimization problem (NDOP) and solved using the Levenberg-Marquardt algorithm, with constraints set on each parameter to ensure they fall within a specific range. The numerical solution of the IBVP, which is also part of the NDOP constraints, is achieved through a spatial finite element semi-discretization, combined with an explicit Runge-Kutta RK(4) scheme for temporal approximation at each time step. The estimated MSE for the fitted diffusion coefficient pa-rameters was on the order of 10^-5, and the relative error between experimental and predicted concentration values was less than 1%. The consistency and accuracy of the numerical results demonstrate that the model effectively explains the diffusion behavior of chloride ions in reinforced concrete exposed to aggressive marine conditions, with a composition like that reported by Anzola E. et al. in [6]. Furthermore, the average value of the predicted diffusion coefficient can be compared with the reference threshold value reported in the literature [4], supporting the potential of this methodology for determining the service life of this specific material con-figuration.