Calculation of reinforced concrete corrosion initiation probabilities using the Rosenblueth method

Abstract

The Rosenblueth method is used to analyze stochastic parameters in a numerical model to calculate the solution for independent variables. By replacing all or a part of the independent variables with random variables, the solution becomes itself random. The Rosenblueth method simplifies this passage, while being limited to dichotomous random variables. This avoids the complex and computer intensive Monte Carlo simulation method. A specific example is developed in this article using a nonlinear transport model to simulate the chloride ion penetration into reinforced concrete and to predict the development of corrosion in the civil structure. The making into consideration of complex physical chemical process and a reconstituted climate increase considerably the simulation time, making impossible the usual use of the Monte Carlo method. The two numerical examples show that the exposure degree affects in a dominating way the apparition of structural damage.

Markov Chain-Based Stochastic Modeling of Chloride Ion Transport in Concrete Bridges

“…The surrogate Markov model is derived by defining a set of discrete states for the chloride ion concentration at the depth of the reinforcement from the concrete surface. Historical climatic data are used to model the time series for the chloride content and uncertainties associated with transport properties are addressed by performing a set of analyses for optimally selected values from the probability distribution functions of the transport and diffusion parameters using the Rosenblueth point estimation procedure (Rosenblueth, 1975;Conciatori et al, 2009;Wolofsky, 2011). The simulation is used to generate a large sample of state transitions for estimating the transition probabilities.…”

“…In the simulations, the lower value is represented by X1 and the upper value by X2. The formulas used to determine the distinct values (X1, X2) and the associated probabilities (F1, F2) are defined as follows (Rosenblueth, 1975;Conciatori et al, 2009):…”

“…The distinct values (X1, X2) and the associated probabilities (F1, F2) for a normal and log-normal distribution are shown in Table 2 (Conciatori et al, 2009).…”

“…The average values of DHR, DCL and DCAP, coefficient of variation and distinct values with their associated probabilities are shown in Table 3. The average values and coefficient of variation are determined from data bases for concrete typical at the time of construction of the bridges (Conciatori et al, 2009). Previous studies also indicate the log-normal distribution is appropriate for the distribution of the diffusion parameters as well as for the distribution for the chloride content given the duration of exposure and depth into the concrete (Wolofsky, 2011).…”

“…Several physical models are available to predict the ingress of chloride ions in concrete. The simplest models are based on the diffusion equation (Crank and Gupta, 1975), while more advanced models can account for other ion transport mechanisms, types of exposure, climatic conditions (Conciatori et al, 2009(Conciatori et al, , 2010, and chemical reactions (Samson and Marchand, 2007). Most models are developed for undamaged concrete elements; however, corrosion induced cracking of the concrete can greatly accelerate the deterioration process once corrosion has progressed (Jefremczuk, 2005).…”