Stochastic modeling and calibration of chloride content profile in concrete based on limited available data

Chloride ion ingress in concrete is the main reason of concrete corrosion. In real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. Regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. In this paper after inspiration from classical physics related to diffusion and random walk concepts a stochastic partial differential equation (SPDE) of diffusion is introduced to show a more realistic modeling/calibration scheme for construction of stochastic chloride content profile in concrete. Diffusion SPDE provides a consistent quantitative way of relating uncertainty in inputs to uncertainty in outputs. Although it is possible to run sensitivity analysis to get some statistical results from deterministic models but the nature of diffusion is inherently stochastic. Brownian motion process (Wiener process) is used in SPDE to simulate the random nature of the diffusion in heterogeneous media or random fields like concrete. The proposed method can be used to calibrate/model the chloride ion profile in concrete by only some limited data for a given depth. Then the stochastic chloride ion diffusion can be simulated by langevin equation. Results of the method are compared with data from some references and all show good agreements.