PSI - Issue 84

Simone Celati et al. / Procedia Structural Integrity 84 (2026) 127–134

128

Structural reliability updating procedures have previously been investigated for reinforced concrete structures (e.g., Straub 2011, Jacinto, Neves et al. 2015, Faroz, Pujari et al. 2016, Chen 2017, Fan, Ang et al. 2017, Kouta and Bucher 2019, Kim and Song 2021, Geyer, Papaioannou et al. 2023). However, when it comes to chloride ingress measurements specifically, the literature remains sparse. Few studies (see, for instance, Liljefors and Köhler 2023) have focused on the explicit updating of reliability estimates using such data, and even fewer have addressed the challenge of preserving the temporal consistency of chloride transport processes during the updating procedure. Given the high costs and long term implications of maintenance decisions in reinforced concrete infrastructure, a more rigorous approach to reliability quantification, grounded in measurement data, is of importance. This paper aims to address this gap by developing a probabilistic framework for the structural reliability assessment of reinforced concrete, updated over time using chloride ingress measurements. The remainder of this paper is structured as follows. In Section 2, a structural reliability modelling framework for reinforced concrete structures is presented, building on previous work by the authors (Björnsson, Thöns et al. 2024, Celati, Natali et al. 2024, Thöns, Björnsson et al. 2024). Section 3 introduces a reliability updating procedure that incorporates chloride ingress measurements while preserving the temporal characteristics of chloride transport. Section 4 presents a case study that demonstrates the proposed approach and illustrates how intermediate chloride measurements influence the evolving reliability of the structure. Finally, Section 5 discusses the broader implications of the findings for integrity management and provides an outlook toward a more systematic and data-driven approach to maintaining reinforced concrete infrastructure. 2. Reinforcement corrosion reliability analysis The service life quantification in relation to reinforcement corrosion relies on modelling the sectional capacity, acting effect, and the corrosion process. The limit state function ( ) for an element section can be modelled as ( ) = ( ) − ≤ 0 , where is the capacity of the section, is the annual maximum acting effect, and ̅ is the year of evaluation. The capacity is considered to reduce over time because of the corrosion process, as presented in the following section. The yearly probability of failure can be evaluated as: ( ( ̅)) = ( ( ̅) = ( ̅) − ≤ 0) . 2.1. Corrosion prior modelling In general, corrosion can become active in a marine environment when the concentration of chlorides at the rebar level exceeds a critical threshold, and the pH of the concrete surrounding the rebars drops below approximately 9, or in the case of significantly high chloride concentrations, regardless of the pH of the surrounding concrete. These conditions apply to sound, i.e., uncracked concrete (Lindvall 2003, Melchers and Li 2006, Melchers and Li 2009, Melchers 2018). The increase in chloride concentration in concrete is generally attributed to the diffusion of chloride ions from the concrete surface, as widely discussed in the literature (e.g., Guo, Chen et al. 2016, Dias-da-Costa, Neves et al. 2019, Kim and Song 2021, Björnsson, Thöns et al. 2024, Celati, Natali et al. 2024, Celati, Natali et al. 2025). On the other hand, the alkalinity and pH reduction may be attributed to the carbonation process of concrete. For submerged elements, carbonation is inhibited, and corrosion is considered activated only at very high chloride concentrations. Therefore, the time needed for severe and continuous corrosion to activate (Melchers 2018) is evaluated based solely on the chloride diffusion process. Specifically, corrosion is assumed to occur at a higher critical chloride concentration threshold than for elements exposed to air (Lindvall 2003). In the following, the models employed to estimate the time needed for chlorides to reach the steel surface are provided. The concentration of chloride ions inside the concrete ( ( , ) ) can be modelled in space and time employing Fick’s second law (fib 2015) while the time to initiation of corrosion due to chlorides ( ℎ ) can be defined as the time needed for ( , ) to reach the critical chloride threshold ( ) at the cover depth . ℎ can be calculated as follows: ℎ = ℎ ∙ [ 4 1 ,0 0 ( erf −Δx −1 (1− , Δ ) ) 2 ] 1− 1 (1) where is the environmental variable, ,0 is the chloride diffusion coefficient [mm 2 /year], is the environmental transfer parameter equal to 1, and is the ageing coefficient. Eq. (1) is derived considering the ageing