PSI - Issue 63

Petr Konečný et al. / Procedia Structural Integrity 63 (2024) 21 – 26

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2.2. Finite Element Analysis In the present study, an in-house Finite Element Analysis (FEA) code (Konecny & Lehner, 2017) utilizes three node finite elements, a methodology commonly applied in various contexts such as (Kone č ný et al., 2019). The computational model features a depth of 0.2 meters and a width of 0.01 meters, effectively modeling a one dimensional problem. The triangular elements are systematically arranged in a regular rectangular grid with dimensions of 10 by 10 millimeters. Transient analysis, crucial for capturing time-dependent behaviors, incorporates an adaptive time-stepping mechanism. This mechanism adjusts a time step automatically based on the size of the finite elements and a diffusion coefficient, ensuring accurate and efficient simulation of chloride ingress over time. Previous validation efforts have shown that the FEA model’s results align well with those obtained from analytical model given in Eq. (Tang & Nilsson, 1996) even though it does not account for delayed exposure to chlorides. Moreover, it was validated even with 2D analytical model. See eg. (Lehner & Kone č ný, 2019) This validation provides a robust foundation for extending the model to include time-delayed chloride application. Consequently, it is reasonable to assume that the modified model, which incorporates a time delay in chloride exposure, will produce reliable and accurate results. This approach is particularly relevant for simulating real-world scenarios where chloride exposure does not occur immediately but rather after a certain period, as often seen in surface-treated or aging concrete structures. 2.3. Time to onset of corrosion The time t i to onset of corrosion (initiation time) as introduced by (Tuutti, 1982) is obtained by finding a time related to exceeding of chloride threshold C th by chloride concentration C (t) as described by Eq. (5): (5) 3. Testing example The study investigates the diffusion coefficients and aging factors of concrete based on laboratory measurements of resistivity. Specifically, an ordinary Portland cement (OPC) mixture with normal diffusion properties and a high performance concrete (HPC) mixture with very low diffusion properties were analyzed. The input parameters, including the material descriptions, are adopted from previous work (Kone č ný et al., 2019) to provide reference numerical results. These parameters include C s = 1.8 (% by mass of cementitious material), C th = 0.18 (% by mass of cementitious material), x = 0.05 (m), t ’ 0 = 28 (days). The effect of delayed exposure with variable t ’ ex in range 1 to 5 (years) is evaluated and complemented with reference solution where immediate exposure to chlorides is considered and therefore t ’ ex = 0 (years). The diffusion and aging coefficients for the concrete mixtures are derived from resistivity measurements and applied consistently in this study (see Table 1). Diffusion coefficients for the concrete mixtures are based on (Ghosh & Tran, 2015) and applied also in (Kone č ný et al., 2019). OPC concrete refers to mixture ID 100TII-V mixture and HPC concrete to mixture ID 50TII-V/40G120S/10M. These classifications ensure a comparative analysis of concrete performance under varying diffusion and aging conditions. The OPC mixture exhibits standard diffusion properties, making it a suitable baseline for comparison. In contrast, the HPC mixture demonstrates significantly reduced diffusion rates due to its enhanced durability and prolonged maturation, highlighting the impact of material composition on chloride ingress resistance. 4. Results The onset of corrosion times computed using the mentioned analytical formulas and the Finite Element Method (FEM) model (Konecny & Lehner, 2017) are presented in Table 1 with and without consideration of the effect of five