Probabilistic approach to concrete durability based on combined stochastic differential equations and Monte Carlo method

Abstract Cementitious materials are often exposed to aggressive environments, which have a significant impact on their durability. Proper prediction of concrete corrosion helps to apply the right measures and technologies, to extend the service life of structures. Carbonation and cyclic freezing are recognized among the most common corrosive factors for concrete. Their progress is linked to the penetration of CO 2 and water into the concrete structure. Due to the random arrangement of aggregates and cement paste, concrete is an inhomogeneous material. Therefore, the progress of carbonation and frost-induced damage should be treated as random variables with appropriate probabilistic parameters. Experimental studies on concrete carbonation and freezing were conducted in accordance with the standards EN 12390–12 and EN 12390–9. As observed in the experiments, the progress of carbonation and frost damage of concrete could be described by zigzag, not necessarily monotonic functions. Stochastic differential equations (SDE) were employed to predict the behavior of concrete exposed to elevated CO 2 concentrations and cyclic freezing. The stochastic model consisted of a drift term, which described the general trend of concrete durability exposed to carbonation and frost cycles, as well as a diffusion term, which accounted for the stochastic features of inhomogeneous concrete microstructure. The Euler–Maruyama approximation with Milstein improvement was applied to model the realization of the stochastic changes in concrete microstructure/durability. The proposed approach predicted experimental results with high accuracy. The application of the Monte Carlo (MC) method with 100,000 SDE realizations allowed to calculate the statistical parameters of the processes, such as concrete carbonation and freezing cycles. The probabilistic parameters, such as expected values and standard deviations, calculated using the SDE_MC approach, were in good agreement with experimental results for both problems, i.e. decelerating concrete carbonation and accelerating concrete scaling.