# Chloride ingress in de-icing salt-exposed bridge: Numerical modeling and field investigations

Samaneh Khani, David Conciatori, Luc Chouinard, Benoit Fournier, Mohammad Khaleghi Esfahani, Abdoul S Bah, Xuande Chen

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Samaneh Khani, David Conciatori, Luc Chouinard, Benoit Fournier, Mohammad Khaleghi Esfahani, et al.. Chloride ingress in de-icing salt-exposed bridge: Numerical modeling and field investigations. Case Studies in Construction Materials, 2025, 23, pp.e05003. 10.1016/j.cscm.2025.e05003. hal-05531767

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# Chloride ingress in de-icing salt-exposed bridge: Numerical modeling and field investigations

Samaneh Khani<sup>a</sup>, David Conciatori<sup>a,c,*</sup>, Luc Chouinard<sup>b</sup>, Benoit Fournier<sup>a</sup>, Mohammad Khaleghi Esfahani<sup>a</sup>, Abdoul S. Bah<sup>a</sup>, Xuande Chen<sup>a,d</sup>

## ARTICLE INFO

Keywords:

De-icing salt

Chloride penetration

Durability

Field exposure

Concrete repair

## ABSTRACT

This research focuses on assessing the durability of various components of an onshore section of the Original Champlain Bridge in Montreal, specifically in relation to chloride ingress from de-icing salting operations. Chloride penetration in both the original and repaired concrete are both numerically modelled and measured. The transport characteristics of repaired and original parts of the concrete were determined using non-destructive air permeability tests and used in the TransChlor® to predict chloride ingress into the air-exposed repaired sections and underlying unrepaired sections over the service life of the bridge. By selecting appropriate boundary conditions, and historical climatic data, the predicted chloride profiles are shown to be a close match to core sample data from both the repaired and unrepaired sections of structural elements. This research proposes a blind a-priori prediction method for analyzing and predicting chloride ingress in ageing concrete structures as opposed to a-posteriori predictions made by matching chloride profiles obtained from cores, which is a common practice in the literature. Furthermore, it was clearly demonstrated that cathodic protection is effective in preventing chloride ingress into concrete. However, the ability to predict chloride ingress in the presence of cathodic protection was identified as a gap in current chloride ingress models such as TransChlor®, and an objective for future research.

## 1. Introduction

Reinforced concrete structures, such as bridges, are susceptible to deterioration caused by chloride-induced corrosion of the reinforcing steel. This is a major durability issue, especially for structures exposed to de-icing salts or marine environments. Chloride ions can penetrate the concrete cover and once they reach a critical concentration at the depth of the reinforcing steel, they initiate corrosion by breaking down the passive oxide film that protects the steel [1]. Accurately predicting the time to corrosion initiation is crucial for estimating the remaining service life and planning maintenance and rehabilitation activities for these structures [2,3]. Numerous short- and medium-span highway bridges in Canada and the northern United States have been severely impacted by corrosion-induced deterioration stemming from the use of de-icing salts on roads during winter seasons. Many of these bridges,

<footnote><sup>a</sup> Department of Civil Engineering and Water Engineering, Université Laval, Canada</footnote>

<footnote><sup>b</sup> Department of Civil Engineering, McGill University, Canada</footnote>

<footnote><sup>c</sup> Laboratory ICube CNRS UMR 7357, Department of Civil Engineering, INSA Strasbourg, France</footnote>

<footnote><sup>d</sup> Université du Québec à Rimouski, Département Génie Civil, Rimouski, Canada</footnote>

<footnote>* Corresponding author at: Department of Civil Engineering and Water Engineering, Université Laval, Canada.</footnote>

<footnote>E-mail address: david.conciatori@insa-strasbourg.fr (D. Conciatori).</footnote>
constructed in the 1950s, 1960s, and 1970s, are now deemed structurally deficient and lacking in functionality [4]. This situation arises from a combination of factors, including aging infrastructure, increased traffic volumes and loads, ongoing deterioration, changing environmental conditions, and more stringent design codes for bridges implemented in recent years [5]. To address this issue, it is crucial to accurately assess the current condition of these structures and predict their future performance. This allows limited maintenance and rehabilitation funds to be optimized by prioritizing efforts that minimize the risk of failure and reduce overall lifecycle costs. By properly evaluating bridge condition and performance projections, infrastructure managers can strategically invest resources into upkeep and repairs that can effectively extend the service life of deteriorating bridges. However, most existing models for predicting chloride ingress and corrosion initiation time rely on input parameters like surface chloride concentration, chloride diffusion coefficient, chloride threshold level, and corrosion rates [6]. Field monitoring data has revealed that these parameters can vary significantly over time and space due to factors like concrete mixture, curing, environmental conditions, etc. [7,8]. Using constant values from literature or short-term tests can lead to inaccurate service life predictions that do not match the actual deterioration observed in structures exposed to chlorides over longer periods [5,6]. Moreover, Song et al. [9] investigated the impact of time-independent and time-dependent surface chloride ion concentration models on chloride ingress and the effectiveness of concrete repairs over time. This research has underscored the importance of integrating long-term field monitoring data to update and improve the accuracy of chloride ingress and corrosion initiation models [5]. Continuously updating site-specific data into these models can help account for the spatiotemporal variations in the governing parameters and provide more reliable estimates of remaining service life. Moreover, models should be robust, credible, and based on physical/chemical principles, which should also be validated with long-term observations on the performance of reinforced concrete structures in service.

Several studies [8,10] have evaluated the performance of different models to predict chloride ingress into concrete structures exposed to de-icing salts in road environments. The Bonaduz field experiment in Switzerland compared models such as Mejlbro-Poulsen [11], ClinConc [12], Cerema, Double-Multi [13,14], and HETEK Convection [15], revealing significant scatter in 100-year chloride penetration predictions due to differences in assumed surface chloride concentrations and driving forces. Another study by Tang [10] validated the ERFC, ClinConc, and DuraCrete models against long-term Swedish field data from highway specimens and bridges. While ClinConc showed reasonable performance, no model could precisely predict chloride ingress, with ERFC over-estimating, DuraCrete underestimating for some concretes, and ClinConc deviating at certain ages. The studies [8,10] highlighted the challenges in accurately modeling real-world cyclic exposures, defining appropriate input parameters such as surface chlorides, and capturing the complexity of chloride transport mechanisms in de-icing salt environments.

The premature failure of repaired concrete structures is also a major global issue despite advancements in materials and methods, leading to costly and repetitive repairs. Chloride diffusion in repaired concrete involves both ongoing ingress from the surface and redistribution of chlorides within the original substrate. Accurate service life prediction models are crucial for selecting compatible repair materials and techniques to reduce economic losses from premature failures. However, modeling degradation in repaired concrete is complex due to factors like pre-repair damage, repair quality, and the performance of the composite repair-substrate system [4]. Lack of validated predictive models hinders proper repair strategy selection and contributes to inadequate performance in maintenance operations [16]. Therefore, advanced stochastic models that account for time-dependent chloride transport, chloride binding, repair quality, and exposure conditions are needed [17]. Under severe winter conditions, in marine environments, or in the presence of chloride (such as in water tanks, swimming pools, water treatment facilities, etc.), robust service life modeling would enable more reliable durability assessments and optimized maintenance planning for chloride-exposed repaired concrete structure worldwide.

This research aims to assess the durability of some structural elements of the Original Champlain Bridge in Montreal by examining chloride ingress under de-icing conditions, using exposure models specifically developed in the context of this study [18]. Chloride penetration in both original and repaired concrete is measured, and transport characteristics are determined from non-destructive air permeability tests, following methods previously employed for another bridge in Montreal [19]. The TransChlor® model, combined with a developed climate model, is used to predict chloride ingress over the bridge's service life. A key novelty of this study lies in reconstructing both the exposure model and the salt concentration evolution on the concrete surface, rather than relying solely on the conventional a-posteriori fitting of existing chloride profiles from core samples [20]. Traditional approaches typically calibrate models using observed chloride profiles, which can bias the predictive capability, and limit the generalizability of the model. By explicitly

<figure><img src="image_2.png" /><figcaption>Fig. 1. Original Champlain Bridge across the St. Lawrence River.</figcaption></figure>
modelling surface chloride concentrations and their evolution under realistic de-icing scenarios, this study introduces a forward-predictive approach that enhances the accuracy and applicability of long-term chloride ingress predictions, even without exhaustive field core sampling. Additionally, the effectiveness of cathodic protection in preventing chloride ingress is evaluated, and a gap in the TransChlor® model's predictive capabilities in the presence of cathodic protection is identified, highlighting the need for further study.

## 2. Case study: description of the bridge and sampled structural elements

The Original Champlain Bridge was a critical transportation link across the St. Lawrence River, connecting the island of Montreal to the South Shore region. Inaugurated in 1962, it was designed with six lanes to accommodate high traffic volumes, with around 150,000 vehicles crossing each day at speeds up to 60 mph (100 km/h), making it one of the busiest bridges in Canada (Fig. 1). However, the bridge's design did not adequately account for the long-term effects of using de-icing salt and lacked proper drainage systems. While salt was not applied in the early years, its use began shortly after opening. The original design failed to incorporate measures to prevent corrosion of the reinforced concrete and steel components from salt exposure.

A particularly problematic section of the bridge (Section 5) starts at Île des Sœurs up to the main steel superstructure of the bridge. This section consists of 40 prestressed concrete spans (girder and deck construction). Numerous substructure components such as pier caps, stems, and foundations showed severe deterioration after 48 years - spalling, cracking, concrete degradation, and erosion [21]. In previous research [22], the presence of ASR gel was documented in core samples extracted from the crosshead beams. Petrographic examination confirmed the presence of reactive aggregate particles and gel deposits consistent with ASR-induced distress. The lack of a drainage system from the outset was a major culprit behind the damage on girders since water and chlorides could easily infiltrate due to the absence of waterproofing at deck joints. This enabled salt and moisture penetration into critical elements like the edge beams containing the main prestressing cables. In November 2013, the Original Champlain Bridge faced the risk of collapse. In an emergency, a 75-ton "super-beam" was installed on the structure. The bridge was subsequently deconstructed in 2018. Therefore, the external and internal girders, top of the pile and the crosshead beam from Section 5 which spanned over land, were sampled for this research (Fig. 2).

The degradation patterns were systematically investigated through condition surveys starting in the 1980s [23], which identified extensive cracking, spalling, honeycombing, and chloride contamination, especially in piers and prestressed girders. Underwater inspections also revealed cracking in submerged pier segments and extensive surface erosion.

To address these issues, a multi-decade rehabilitation program was implemented. A new drainage system was installed in 1995, and polymer-modified asphalt provided some waterproofing when sections were repaved in 2000 and 2010. Between 1990 and 1996, repairs to piers included epoxy injection of cracks and resurfacing spalled areas with underwater grouts [23]. In 2004, exposed surfaces of crosshead beams and piers were repaired with a layer of 200 mm of concrete after removing 25 mm of the original concrete, which was removed to reach the surface of the reinforcement. The longitudinal post-tensioned girders received shotcrete repairs around 15 mm thick using cementitious mortar between 2013 and 2018. To protect prestressing tendons in severely deteriorated girders, external post-tensioning was installed using greased, sheathed tendons, and cathodic protection systems were tested and implemented on selected spans starting in the early 1990s. A sacrificial anode cathodic protection system was installed on the studied girder. Hence, the concrete components have been classified into three types: repaired crosshead beams and piers, old crosshead beams and piers, and longitudinal beams (girders).

## 3. Experimental investigation

### 3.1. Chloride profiles

Chloride profiling was made on core specimens extracted from the following structural elements shown in Fig. 2b:

* the exterior (D7–36.1) and interior (D7–37.1) beam sections.

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Original Champlain Bridge in Montreal, view of the bridge in Section 5 (a), showing the studied structural components (girders, crosshead beam, pier) (b).</figcaption></figure>
* The exterior (D7–39.1 and 39.2) and interior (D6–35.1, 35.2) sections of crosshead beam.

* The top of pier section (D7–38.2).

To obtain the chloride profile, powder samples were collected from various layers of the specimens located beneath the exposed surface. The depth of each layer was measured with the precision of 1 mm through dry extraction using a diamond blade. Chlorides were extracted from the powder using a nitric acid (HNO₃) solution with a purity level of 69 % ± 1 % principally based on AASHTO T260 [24]. Subsequently, the chloride concentration in each layer was determined by titration using a silver nitrate (AgNO₃) solution with Mettler Toledo T50 titrator [25].

The general trend observed in all profiles is that the chloride front gradually penetrates to deeper parts of the specimen, but with lower concentrations. The peak value is observed close to the surface and the profile extends gradually to larger depths as a function of the level of exposure of the concrete element. The location of core samples extracted from the studied crosshead beam is depicted in Fig. 3. Chloride profiles of eight cores were obtained from blocks D7–39.1 and D7–39.2 in two directions, as well as from blocks D6–35.1 and D6–35.2 in one direction. The chloride profile of samples from the exterior sections D7–39.1 and D7–39.2 is shown in Fig. 4a, while that from the blocks D6–35.1 and D6–35.2 is depicted in Fig. 4b. It is important to mention that the chloride profiling was performed in the surface layer of the blocks, which is characterized by a 200mm-thick layer of repair concrete. Analyzing the ingress of chlorides into old concrete is further investigated. As expected, the results indicate that the chloride content level and penetration depth decrease moving from the edge toward the middle of the sections. The concrete at the edge is more susceptible to chloride ingress. In some cases, chlorides penetrated down to 50 mm over the 14 years of exposure from 2004 to 2018 (repaired concrete). Some literature [26] suggests that the increase in chloride levels in concrete depth can be explained by the impact of wetting-drying cycles on the pore solution. This phenomenon is observed in the chloride profile of E'1 and E'2 in Fig. 4a. It is interesting to note that significant chloride levels are measured down to a depth of 50 mm in the case of E1 and E'2 (Fig. 4a), corresponding to the utmost portions of the crosshead beam (D7–39.1 and 39.2), while detected chloride levels are obtained down to a depth of only 25 mm in the case of the interior portions of the crosshead beam (Fig. 4b; D6–35.1 and 35.2).

Fig. 5 shows the location of the cores extracted from the top of the pier (block D7–38.2) and the results indicate a very small amount of chloride penetrated the concrete for these sections. The results of cores P1 and P2 (Fig. 5a) are somewhat similar to the chloride profile obtained from the specimens M3 and M4 of the interior block D6–35.2 of the crosshead beam (Fig. 4b). It is evident that the chloride content in the cover concrete of the repaired sections (approximately 70 mm) (Fig. 4 & Fig. 5) almost did not exceed the chloride threshold value (0.05 % by concrete mass).

The chloride profiles from the crosshead beam and top of the pier presented so far were from the exposed surface to the depth of the repaired concrete. To evaluate the chloride content in the vicinity of the border between old and repaired concrete (transition zone), measurements were done for six of the cores identified earlier. The results indicate that the chloride content around the interface of the repaired and old concrete is extremely high. The chloride value around the border is indeed much higher than the chloride threshold for reinforced concrete established at 0.05 % by concrete mass. The presence of corrosion products verifies this finding by Fig. 6. Evidence of chloride diffusing back into the repaired concrete from the old concrete is shown in Fig. 7. Moreover, it is evident that chloride entered the old concrete down to more than 200 mm.

As mentioned earlier, chloride measurements were also carried out on the interior beam Sections D7–37–1. It was found that only the first layer near the surface (5 mm) had a very low level of chloride at 0.02 % by weight of concrete. Since there was only one data point, there is no chloride profile to show. This indicates that the internal beam was not exposed to chlorides as much as other sections. On the other hand, the exterior beam (D7–36.1) (Fig. 8a) had the highest chloride concentration level with the deepest penetration compared to other sections, with noticeable chloride concentrations being measured down to a depth of about 45 mm. Note that the shotcrete repair thickness was 15 mm, and beneath the shotcrete layer, approximately 68 mm was reported as the concrete cover.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Positions of the core samples extracted from Crosshead Beam. Core specimens extracted from blocks D7–39.1 (E1 and E2), D6–35.1 (M1 & M2) and D6–35.2 (M3 & M4) (a). Core specimens extracted from block D7–39.2 (E'1 and E'2) (b).</figcaption></figure>
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Chloride profile of cores extracted from (a) Edge (blocks D7–39.1 and 39.2), and (b) Middle of the crosshead beam (blocks D6–35.1 and 35.2), red line: threshold value of 0.05 %.</figcaption></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 5. Top of the pier (block D7–38.2) (a) Positions of extracted core samples, and (b) Chloride profile.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6. Trace of corrosion product in the transition zone.</figcaption></figure>

## 3.2. Concrete cover characterization

The ability of ions to move through concrete is directly linked to the permeability of the material [27]. To determine the air permeability and resistivity of the concrete cover on various components of the bridge, measurements were taken (Fig. 9). These measurements are highly sensitive to the amount of water present in the concrete pores. The presence of water reduces both air permeability and resistivity of the concrete.

In the case of dry concrete, the air permeability $k_T$ of the concrete cover measured using the TorrentVR permeability device (Fig. 9a) demonstrates good agreement with laboratory methods. The quality class for the cover concrete is established based on $k_T$ values (Table 1). To address the impact of humidity, the primary factor affecting permeability, additional measurements include the electrical resistivity of the concrete. The electrical resistivity $\rho$ of the concrete was measured with the WennerVR device (Fig. 9b). The quality class, determined by both $k_T$ and $\rho$, corresponds to the classification obtained through the nomogram (Fig. 10).

Following non-destructive testing conducted in situ, measurements were taken for longitudinal beams (girders) (Fig. 10a), repaired concrete of crosshead beams and piers (Fig. 10b), and old concrete of crosshead beams and piers (Fig. 10c). To evaluate the measured values, the concrete quality of longitudinal beams (Fig. 10a) was categorized as medium permeability (3) and permeable (4) concrete.
<figure><img src="image_11.png" /><figcaption>Fig. 7. Chloride profile in cores from crosshead beams and top of the pier at the old and repaired concrete border.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. Locations of the core samples extracted from exterior beam sections D7-36.1 (a), and Chloride profile of cores from the exterior beam section (b).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 9. Measurement of the air permeability (a), and resistivity (b) of concrete cover.</figcaption></figure>
<table><caption>**Table 1**
Concrete quality (1–5) according to the air permeability [28].</caption><thead><tr><td>Quality of the concrete cover</td><td>Index</td><td>k<sub>T</sub> (10<sup>-16</sup> m<sup>2</sup>)</td></tr></thead><tbody><tr><td>Highly permeable</td><td>5</td><td>&gt; 10</td></tr><tr><td>permeable</td><td>4</td><td>1.0–10</td></tr><tr><td>Medium permeability</td><td>3</td><td>0.1–1</td></tr><tr><td>Low permeability</td><td>2</td><td>0.01–0.1</td></tr><tr><td>Very low permeability</td><td>1</td><td>&lt; 0.01</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Air permeability and resistivity (a) for longitudinal beams (girder), for repaired crosshead beams and Piers (b), for old concrete of crosshead beams and piers.</figcaption></figure>

For the repaired crosshead beams and piers (Fig. 10b), the concrete varied extensively from low permeability (2) to relatively high permeability (4), with most data points concentrated in the low-permeable range (2). For the old concrete of crosshead beams and piers (Fig. 10c), only 4 measurements were taken since the uneven surface did not allow for more reliable values; according to these values, its concrete was categorized as permeable (4). The measurement of the air permeability coefficient ($k_T$) not only helps in assessing concrete durability but also aids in determining the transport properties of concrete. These transport properties would be used as input parameters for deterioration models [19,29,30].

## 4. Chloride transport prediction over exposure time

The 1D-TransChlor® predictive chloride transport model considers chloride movement by diffusion and advection by water. The current limitations of the 1D-model mean that particular care must be taken when selecting cores on the structure (at the center of structural elements) to ensure a negligible 2D or even 3D effect.

### 4.1. Chloride transport in repaired and original concrete

The transport model incorporates (i) one chemical reaction: reversible chloride ion adsorption by cement paste and (ii) several physical phenomena as explained in the following. Diffusion, described by a simplified Fick's law, involves molecules or ions moving from high to low concentrations in the interstitial fluid. Capillarity suction [27] drives liquid water movement, modeled by kinetic equations, which are then adapted to simulate chloride ion movement. The TransChlor® model accounts for thermal diffusivity, water transport and chloride ion transport. Further details on the model can be found in the referenced articles [27,31–34].

For chloride penetration in concrete after repair, there is an interaction between two primary sources of chloride ions: the chloride concentration in the surrounding environment and the residual chloride ions present in the remaining original concrete. Additionally,

<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Chloride profile of original concrete before repair (a), immediately after repair (b), after repair in time t (c).</figcaption></figure>
the redistribution of chloride ions from the aged concrete to the newly applied repair material due to difference in chloride diffusion coefficient, further complicates the process [9].

Prior to repair, the chloride concentration at the concrete surface acts as the main source of chloride ions, with the initial chloride content assumed to be zero throughout the concrete, and the diffusion coefficient corresponding to the original concrete (Fig. 11a). Immediately after the repair, the chloride-contaminated concrete cover is removed to a specific depth, and a cement-based repair material is applied as a new layer (Fig. 11b). At this stage, only the repaired concrete is exposed to the surface chloride concentration.

The transport mechanism of chloride penetration in the repaired material is modeled in TransChlor® model, where the boundary condition is the flux of chlorides crossing the concrete surface. However, the initial conditions in repaired concrete and original concrete will differ. Furthermore, after the repair, there is a redistribution of chloride ions from the aged concrete to the new repair material (Fig. 11c). Immediately following repair, the initial chloride content will be zero in the new repair concrete layer. However, the remaining original aged concrete section retains residual chloride ions from prior exposure. Subsequently, three principal processes govern chloride transport. Firstly, the residual chlorides redistribute within the aged concrete layer itself. Secondly, these residual chlorides diffuse across the transition zone, penetrating the initial chloride-free repair layer which offers low initial resistance. Thirdly, the overall chloride distribution results from a combination of external chloride ingress from the exposed surface and internal redistribution of residual chlorides. TransChlor® software, are employed to simulate this two-layer concrete system, accounting for the distinct initial chloride conditions in each area following repair to accurately predict the long-term chloride profiles.

## 4.2. Input parameters

The input parameters in TransChlor® model includes a reconstituted exposure, i.e., the climate and salt loading conditions as a boundary condition, and transport properties of each specific concrete, constituting the concrete permeability through thermal property, vapor diffusion coefficient, water capillarity coefficients, chloride diffusion coefficient and CO₂ diffusion coefficient. After the input files were completed, the simulations were launched, and chloride ion profiles were obtained.

### 4.2.1. Boundary conditions

Hourly measurements of climatic factors such as temperature, humidity, and precipitation were obtained from weather station data located at the Montréal-Pierre Elliott Trudeau International Airport from 1962 to 2018 (Fig. 12). During winter months, the application of de-icing salt on road surfaces represented the environmental action being implemented. Evaluating the impact of this action necessitated information on the temporal evolution of the de-icing salt, specifically the precise timing of its application, the quantity dispersed on the road surface, and the rate of salt dissolution, which is influenced by prevailing weather conditions. The deployment of

<figure><img src="image_16.png" /><figcaption>Fig. 12. Hourly climate data.</figcaption></figure>
de-icing trucks was governed by a diverse set of criteria [35]. However, records from internal report of PJCCI indicate that approximately 9650 g/m² of salt was annually applied on the road corresponding to a salt application of 24 g/m² per spreading [36]. Therefore, the estimated number of salt truck spreading operations per year is approximately 402. Based on the assumptions of the climate model in TransChlor® (Fig. 13), the interval between truck passages (t<sub>interval</sub>) and the temperature threshold (T<sub>lim</sub>) that triggers truck salt spreading operations was estimated as 8 h and 0.2°C respectively.

Given the timing of each salting operation (Fig. 13), the evolution of the salt concentration on the road surface is determined using a two-stage multiple linear regression model proposed in [18] and summarized here in Eqs. (1–3). The evolution of salt concentration over the service life of the bridge, as predicted by the proposed model, is shown in Fig. 14a during a snow event (from 12/01/2000–12/03/2000), where dashed red vertical lines correspond to the timing of salt spreading operations.

The first stage predicts time (t<sub>1</sub>) in Eq.(1) and salt concentration function (c<sub>s1</sub>(t)) in Eq.(2) using air temperature (T<sub>a</sub>), the product of relative humidity with air temperature delta (RT), and initial salt concentration (C<sub>0</sub>) remaining on the street from the previous salt spread on the road. Since the predicted t<sub>1</sub> may not be a discrete time point, the first stage's salt concentration (c<sub>s1</sub>(t)) might not precisely reach 0.36 (Fig. 14b).

$$t_1 = \frac{2 (57.15T_a + 213.4RT)}{(100 + C_0)} \qquad (1)$$

$$c_{s1}(t) = \frac{(100 - C_0)}{t_1} t + C_0 \qquad (2)$$

The second stage begins at 0.36 and decreases salt concentration using a time-series model with recursive forecasting. Input variables include wind speed (V<sub>w</sub>), air temperature (T<sub>a</sub>), precipitation depth (h<sub>s</sub>), and the previous time step's salt concentration. The model predominantly relies on the preceding time step's salt concentration as its most significant predictor, effectively capturing the dynamic salt concentration evolution on roads.

$$c_{s2}(t) = -0.187T_a + 0.097V_w - 0.198\Delta T_a + 0.017h_s + 0.88c_{s2}(t-1) \qquad (3)$$

After determining the salt concentration on the road over time, the boundary condition for the concrete structure, used as an input parameter for the TransChlor® model, can be established. The novelty of this article lies in reconstructing the exposure model and salt concentration evolution on the exposed surface, using this approach to assess whether a more accurate prediction of chloride ingress in concrete can be achieved, regardless of the actual chloride penetration observed during the concrete's service life. Although Trans-Chlor® considers three different types of exposure — direct, splash, and mist exposure [31] — in the studied structure, cores were extracted only from the mist exposure area. The boundary conditions used include air temperature, relative humidity, and chloride concentration data, as explained above.

### 4.2.2. Transport parameters

TransChlor® allows for the propagation of uncertainties on concrete transport properties to chloride concentrations as a function of depth and time. The input parameters to the probabilistic model are the mean and standard deviation of the diffusion parameters, which have been shown to be lognormally distributed, the propagation of uncertainties is done using the Rosenbluth point estimation technique [37]. The four main probabilistic variables considered are the diffusion of water (D<sub>h</sub>), the capillary suction of water (D<sub>cap</sub>) and the diffusion of chloride ions (D<sub>Cl</sub>).

The transport properties of concrete are derived from field measurements of air permeability (k<sub>T</sub>) on the various concrete elements (Fig. 10), which is assumed to follow a lognormal distribution based on goodness-of-fit analysis (Fig. 15).

Next, Monte Carlo simulations (n = 3000) of k<sub>T</sub> values were obtained from the fitted lognormal distributions and substituted in Eq. (4) to obtain corresponding values of the chloride diffusion coefficient (D<sub>Cl</sub>), which is also lognormally distributed [31]. The average λ

<figure><img src="image_17.png" /><figcaption>Fig. 13. Flowchart modeling the timing of salt truck passages during the winter period, adapted from TransChlor®.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 14. Temporal salt (NaCl) evolution concentration on road from December 1, 2000, 12 a.m. to December 3, 2000, 12 a.m. (dashed line: salt truck passage, A value of 0.36 corresponds to a concentration of 357 g NaCl per liter of H₂O). (a), Schematic model of evolution of residual salt concentration after salt application (b).</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 15. Cumulative distribution function of permeability, for longitudinal beams (girder)(a), repaired crosshead beams and Piers (b), old concrete of crosshead beams and Piers (c).</figcaption></figure>

and standard deviation ξ of lnD<sub>CI</sub> estimated from the experimental data Fig. 15, are presented in Eq. (4) and Eq. (5), respectively.

$$ \lambda_{\ln D_{CI}} = 2.3886 + 0.333966 \cdot \ln k_T \quad (4) $$

$$ \xi_{\ln D_{CI}} = 0.51 \cdot \sqrt{1 + \frac{1}{171} + \frac{(\ln k_T - 2.6313)^2}{697.25}} \quad (5) $$

Given chloride diffusion, the values for the remaining transport parameters (D<sub>h</sub> and D<sub>cap</sub>) are next calculated using Eq. (6) and Eq. (7) respectively. These both equations are empirical equation deriving from laboratory test on different receipts of concrete with a
range of w/c of 0.42–0.73 [19,34].

$$Dh = 256.41 * \ln\left(\frac{0.1266 * \ln\left(\frac{Dcl}{0.0943}\right)}{0.3245}\right) \qquad (6)$$

$$Dcap = -0.0155 * \left(0.1266 * \ln\left(\frac{Dcl}{0.0943}\right)\right)^2 + 0.0204 * \left(0.1266 * \ln\left(\frac{Dcl}{0.0943}\right)\right) - 0.00526 \qquad (7)$$

Monte Carlo simulation is used to propagate uncertainties with multiple input parameters into the transport equations [33,37]. To summarize, to obtain the chloride diffusion coefficient D<sub>Cl</sub>, both the variability of D<sub>Cl</sub> from Fig. 16 or Eqs. (4–5) and the variability of k<sub>T</sub> are considered jointly using the Monte Carlo method. For the other parameters w/c, D<sub>h</sub>, and D<sub>cap</sub>, the propagation of uncertainty is also performed using Monte Carlo with Eqs. (6–7). The simulated output distributions for the transport parameters are summarized in Tables 2–4 with the lognormal distribution identified as the best fit. The Eq. (8) transforms the sodium chloride conditions on the pavement C<sub>si</sub> (C<sub>s1</sub> and C<sub>s2</sub>), expressed as the mass ratio of sodium chloride and water, into the chloride concentration in the concrete Cl, expressed as the mass ratio of chloride and concrete.

$$Cl = \frac{C_{si} * w_{sat} * M_{Cl}}{100 * \rho_{concrete} * M_{NaCl}} \qquad (8)$$

where w<sub>sat</sub> is the water content in concrete (kg/m<sup>3</sup>), M<sub>Cl</sub>/M<sub>NaCl</sub> molar mass ratio of chloride and sodium chloride (mol/L) with values of 35 and 57 respectively, and ρ<sub>concrete</sub> volumic density of concrete (kg/m<sup>3</sup>).

After obtaining the means and standard deviations of the input variables to TransChlor®, the Rosenbluth two-point estimation approach is used to estimate the mean and variance of the chloride content probability distribution as a function of time and depth [34, 37]. Given that exposure of the concrete elements is only relative to spray, the elements were never in direct contact with liquid water (e.g., splashing or direct exposures). Therefore, capillary suction is not considered as a water transport process, leaving only two input parameters (D<sub>Cl</sub> and D<sub>h</sub>) to be modelled probabilistically. The Rosenbluth technique uses just two points to represent each input distribution (Table 5). The point estimators of X (X<sub>1</sub> and X<sub>2</sub>) and their associated weights (P<sub>1</sub> and P<sub>2</sub>) are defined in [30].

# 5. Results and discussion

## 5.1. Simulation results using the modified TransChlor® model

Adopting the input data from § 4.2 into the TransChlor® model, chloride ion profiles, were obtained using the Rosenbluth probabilistic method. The curves represent 95 % confidence interval (CI) from four simulated permutations. The data points show that the measured chloride concentrations from bridge samples, indicating that the observations are within the expected range of uncertainties. Fig. 17a compares the 95 % confidence intervals (CI) for the repaired concrete on piers and crosshead beams over 14 years after repair (2004–2018). The range of chloride content in the concrete of crosshead beams and piers at the end of exposure time (2018), all the entire service life of the bridge (56 years), is depicted to a depth of 500 mm in Fig. 17b. As illustrated in Fig. 7, the repair section extends to a depth of 200 mm, while depths beyond 200 mm represent the original concrete beneath the repair. The variability among different samples can be related to the different severity of exposure, which decreases from the edge of the crosshead beam (E) to its middle (M) and piers (P). The dash line indicating the 95 % confidence interval shows the expected range of chloride content across the depth, providing a measure of uncertainty related to the transportation parameters of the concrete.

## 5.2. Analysis of chloride penetration patterns and repair effectiveness

The variation of the level of exposure among each section of the bridge components has not been considered; however, most data points fall within the confidential interval, indicating that the model is accurate when based on air permeability measurements conducted on each structural element (Fig. 17). Regarding the aged structure, high values of k<sub>T</sub> were associated with the evolution of microcracks during its service life rather than the intrinsic pore structure of the concrete [39]. Therefore, the high chloride content in the first 10 mm of concrete (Fig. 17a) might be related to the microcracks, while the pores were tight enough to prevent chloride penetration at greater depths. However, the high value of k<sub>T</sub> in the simulation causes more penetration of chloride. This explanation might also explain why the green points (transition zone) are above the expected range in the Fig. 17b. Although the model captures average trends in transport processes, the confidence interval envelope is too narrow, indicating that the variability of transport parameters is underestimated. This result is mainly attributed to variable exposure conditions of the various elements, which should be investigated in future research.

Results of Fig. 18 corresponds to the concrete layer beneath the shotcrete repairs (15 mm) of the longitudinal girders after 56 years of service life. The mean value of simulations is compared with the measurements of 3 core samples. Deviations of observed values outside the simulated ranges correlate with the presence of cathodic protection systems. Since TransChlor® cannot model the effects of cathodic protection, results may not align with the actual state of protected girder elements. The model simulates an unprotected chloride ingress scenario. The next version of TransChlor® will consider chloride diffusion under an electric field [40]. The basic
<figure><img src="image_20.png" /><figcaption>Fig. 16. Relationship between the coefficient of chloride-diffusion D<sub>cl</sub> and k<sub>T</sub> [38].</figcaption></figure>

**Table 2**

<table><caption>Transport parameters of repaired concrete (crosshead beams and pires).</caption><thead><tr><th>Transport Parameters</th><th>μ</th><th>σ</th><th>Distribution</th></tr></thead><tbody><tr><td>k<sub>T</sub> (10<sup>-16</sup> m<sup>2</sup>)</td><td>0.28</td><td>0.89</td><td>Lognormal</td></tr><tr><td>w/c (%)</td><td>0.49</td><td>0.08</td><td>Lognormal</td></tr><tr><td>D<sub>cl</sub> (10<sup>-6</sup> mm<sup>2</sup>/s)</td><td>5.95</td><td>5.12</td><td>Lognormal</td></tr><tr><td>D<sub>h</sub> (10<sup>-6</sup> mm<sup>2</sup>/s)</td><td>100.91</td><td>45.63</td><td>Lognormal</td></tr><tr><td>D<sub>cap</sub> (10<sup>-4</sup> mm/s)</td><td>8.95</td><td>4.58</td><td>Lognormal</td></tr><tr><td>w<sub>sat</sub> (kg/m<sup>3</sup>)</td><td>141</td><td>-</td><td>Deterministic</td></tr><tr><td>ρ (kg/m<sup>3</sup>)</td><td>1740</td><td>-</td><td>Deterministic</td></tr></tbody></table>

**Table 3**

<table><caption>Transport parameters of concrete (girder).</caption><thead><tr><th>Transport Parameters</th><th>μ</th><th>σ</th><th>Distribution</th></tr></thead><tbody><tr><td>k<sub>T</sub> (10<sup>-16</sup> m<sup>2</sup>)</td><td>0.96</td><td>0.96</td><td>Lognormal</td></tr><tr><td>w/c (%)</td><td>0.58</td><td>0.07</td><td>Lognormal</td></tr><tr><td>D<sub>cl</sub> (10<sup>-6</sup> mm<sup>2</sup>/s)</td><td>11.51</td><td>7.51</td><td>Lognormal</td></tr><tr><td>D<sub>h</sub> (10<sup>-6</sup> mm<sup>2</sup>/s)</td><td>149.43</td><td>32.28</td><td>Lognormal</td></tr><tr><td>D<sub>cap</sub> (10<sup>-4</sup> mm/s)</td><td>12.85</td><td>2.05</td><td>Lognormal</td></tr><tr><td>w<sub>sat</sub> (kg/m<sup>3</sup>)</td><td>175</td><td>-</td><td>Deterministic</td></tr><tr><td>ρ (kg/m<sup>3</sup>)</td><td>1654</td><td>-</td><td>Deterministic</td></tr></tbody></table>

**Table 4**

<table><caption>Transport parameters of old concrete (crosshead beams and pires).</caption><thead><tr><th>Transport Parameters</th><th>μ</th><th>σ</th><th>Distribution</th></tr></thead><tbody><tr><td>k<sub>T</sub> (10<sup>-16</sup> m<sup>2</sup>)</td><td>8.62</td><td>1.21</td><td>Lognormal</td></tr><tr><td>w/c (%)</td><td>0.69</td><td>0.06</td><td>Lognormal</td></tr><tr><td>D<sub>cl</sub> (10<sup>-6</sup> mm<sup>2</sup>/s)</td><td>25.49</td><td>14.28</td><td>Lognormal</td></tr><tr><td>D<sub>h</sub> (10<sup>-6</sup> mm<sup>2</sup>/s)</td><td>192.67</td><td>25.25</td><td>Lognormal</td></tr><tr><td>D<sub>cap</sub> (10<sup>-4</sup> mm/s)</td><td>13.65</td><td>1.18</td><td>Lognormal</td></tr><tr><td>w<sub>sat</sub> (kg/m<sup>3</sup>)</td><td>149</td><td>-</td><td>Deterministic</td></tr><tr><td>ρ (kg/m<sup>3</sup>)</td><td>1805</td><td>-</td><td>Deterministic</td></tr></tbody></table>

**Table 5**

<table><caption>Weights and points estimation for Rosenbluth technique.</caption><thead><tr><th rowspan="2">Transport properties<br>Parameter coefficient</th><th colspan="4">D<sub>cl</sub> (mm<sup>2</sup>/s)</th><th colspan="4">D<sub>h</sub> (mm<sup>2</sup>/s)</th></tr><tr><th>X<sub>1</sub></th><th>X<sub>2</sub></th><th>P<sub>1</sub></th><th>P<sub>2</sub></th><th>X<sub>1</sub></th><th>X<sub>2</sub></th><th>P<sub>1</sub></th><th>P<sub>2</sub></th></tr></thead><tbody><tr><td>Crosshead beam and pile (Repair)</td><td>2.14E-06</td><td>9.49E-06</td><td>0.67</td><td>0.32</td><td>59.73E-06</td><td>14.15E-05</td><td>0.61</td><td>0.39</td></tr><tr><td>Crosshead beam and pile (Old)</td><td>13.18E-06</td><td>37.49E-06</td><td>0.62</td><td>0.37</td><td>16.76E-05</td><td>21.76E-05</td><td>0.53</td><td>0.46</td></tr><tr><td>Girder</td><td>5.31E-06</td><td>17.48E-06</td><td>0.64</td><td>0.35</td><td>11.79E-05</td><td>18.08E-05</td><td>0.62</td><td>0.37</td></tr></tbody></table>
<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>Fig. 17. Comparison of samples with chloride ion distribution curves; for the pier and cross head beam (repair + old) over 56 years of service using Probabilistic Analysis (a), for repair piers and cross head beam using probabilistic analysis over 14 years after repair (b).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 18. Comparison of samples with average chloride ion distribution curve for girders, the layer under shotcrete using probabilistic analysis after 56 years of service.</figcaption></figure>

principles of cathodic protection are by connecting the metal to be protected with another more easily corroded metal to act as the anode (zinc, aluminium and magnesium). The most active metal (which also is the less noble) becomes the anode to the others and sacrifices itself by corroding (giving up metal) to protect the cathode. Due to the potential difference between the anodic (less noble) and the cathodic area (steel), positively charged metal ions leave the anode surface, while electrons leave the surface at the cathode. In same times, it establishes an electrical field between anode-cathode slowing down the ingress of chloride.

At the transition zone of crosshead beams and piers, at a depth of 25 mm, the chloride content increased rapidly because this position was closer to the concrete surface. Immediately after repair, the entire cover layer of chloride-contaminated concrete was removed through demolition. As a result (Fig. 19), the chloride level at the 25 mm depth decreased quickly after the repair but did not

<figure><img src="image_24.png" /><figcaption>Fig. 19. Time-dependent chloride content at the transition zone (x = 25 mm, old concrete of cross head beam and piers) before and after repair in 2004 vs. measured value.</figcaption></figure>
reach zero; it reduced to the level of residual salt at that depth. Normally, chloride levels are expected to increase over time. However, in our study, the repair layer was approximately 200 mm thick. Therefore, the 25 mm depth in the old concrete was no longer near the exposed surface, and only residual salts diffused deeper and redistributed into the repair layer. This explains why the chloride content decreased slowly at this depth for the rest of the bridge's service life. As depicted in Fig. 19, this repair strategy was not effective in preventing the risk of corrosion initiation because the chloride concentration exceeded the critical value of 0.05 wt% in concrete before the repair. In addition, the measured chloride content at the end of exposure in 2018 showed excellent agreement with model predictions, with most measurements falling within the 95 % confidence interval (black dashed line), validating the model's predictive capabilities.

## 6. Conclusions

This research investigated the long-term durability of structural components from the Original Champlain Bridge in Montreal, focusing on chloride infiltration caused by decades of exposure to de-icing salts. Through core sampling of both original and repaired concrete sections after over 50 years of service, the study revealed that accurate prediction of chloride ingress depends critically on understanding two key factors: the concrete's exposure conditions and its transport properties. Building on our previous research [18] that developed a methodology to track surface salt concentration evolution, this investigation implements this model in a real-world context using the Original Champlain Bridge as a case study. The application of this previously developed approach to an actual bridge structure demonstrates how understanding exposure pattern and surface concentration dynamics can improve chloride ingress predictions beyond traditional measurement methods.

The following conclusions can be drawn based on the experimental and modelling results:

* Chloride levels varied significantly between exterior and interior portions of the repaired crosshead beam, with deeper penetration observed in exterior sections exposed to greater environmental chlorides.

* Extremely high residual chloride content was observed at the interface between original and repaired concrete, posing an ongoing corrosion initiation risk despite repairs.

* Evidence indicated chlorides migrating from the original concrete back into the new repair layers over time.

* Interior beam sections had lower surface chloride levels compared to exterior sections, a result of reduced chloride exposure for internal elements.

* Implementing site-specific historical climate data and de-icing salt application rates enabled accurate simulation of time-varying salt concentrations and applicator truck deployment timing.

* TransChlor® effectively predicted chloride ingress in both repaired and unrepaired concrete by incorporating site-specific boundary conditions, validated transport properties, and long-term exposures.

* Model predictions showed good alignment with observed chloride levels in repaired crosshead beams, piers over the 56-year analysis period.

* The implemented shotcrete repair was highly porous, leading to rapid chloride penetration.

* Deviations in girders with cathodic protection highlight the need to enhance TransChlor® to model such supplemental protection systems.

* Advancements are needed in chloride exposure assessment using a probabilistic approach in TransChlor®, considering key environmental factors such as wind, traffic patterns, etc.

## CRediT authorship contribution statement

**Samaneh Khani:** Writing – review & editing, Writing – original draft, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **David Conciatori:** Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization. **Luc Chouinard:** Writing – review & editing, Validation, Supervision, Methodology. **Xuande Chen:** Formal analysis. **Benoit Fournier:** Writing – review & editing, Project administration. **Mohammad Khaleghi Esfahani:** Formal analysis. **Bah Abdoul Salam:** Formal analysis.

## Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: David Conciatori reports financial support and equipment, drugs, or supplies were provided by The Jacques Cartier and Champlain Bridges Incorporated. no addition relationships or activity If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors gratefully acknowledge the Canada Foundation for Innovation (John R. Evans Leaders Fund), les Fonds de recherche du Québec – Nature et Technologies for their financial support and the Research Center on Concrete Infrastructures (CRIB). This research and development project would not have been possible without the contribution and collaboration of The Jacques Cartier and Champlain Bridges Incorporated.
# Data availability

Data will be made available on request.

# References

[1] C. Alonso, C. Andrade, M. Castellote, P. Castro, Chloride threshold values to depassivate reinforcing bars embedded in a standardized OPC mortar, Cem. Concr. Res. 30 (2000) 1047-1055.

[2] K.A.T. Vu, M.G. Stewart, Structural reliability of concrete bridges including improved chloride-induced corrosion models, Struct. Saf. 22 (2000) 313-333.

[3] A. Petcherdchoo, Probability-based sensitivity of service life of chloride-attacked concrete structures with multiple cover concrete repairs, Adv. Civ. Eng. 2018 (2018) 1-17, https://doi.org/10.1155/2018/4525646.

[4] W. Zewdu, Taffesea, E. Sistonenb, Service life prediction of repaired structures using concrete recasting method: state-of-the-art, Procedia Eng. 57 (2013) 1138-1144, https://doi.org/10.1016/j.proeng.2013.04.143.

[5] D. Cusson, L. Daigle, Z. Lounis, Improving Performance Prediction of Corroding Concrete Bridges with Field Monitoring, (2010). https://doi.org/10.1201/b10552-18.

[6] M.K. Kassir, M. Ghosn, Chloride-induced corrosion of reinforced concrete bridge decks, Cem. Concr. Res. 32 (2002) 139-143, https://doi.org/10.1016/S0008-8846(01)00644-5.

[7] L. Tang, D. Boubitsas, P. Utgenannt, Z. Abbas, Chloride Ingress and Reinforcement Corrosion - After 20 Years' Field Exposure in A Highway Environment, 2018. (http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-37572) (Accessed 25 March 2023).

[8] E. Koenders, K. Imamoto, A. Soive, Benchmarking Chloride Ingress Models on Real-life Case Studies—Marine Submerged and Road Sprayed Concrete Structures: State-of-the-Art Report of the RILEM TC 270-CIM, Springer Nature, 2022.

[9] H.-W. Song, H.-B. Shim, A. Petcherdchoo, S.-K. Park, Service life prediction of repaired concrete structures under chloride environment using finite difference method, Cem. Concr. Compos 31 (2009) 120-127, https://doi.org/10.1016/j.cemconcomp.2008.11.002.

[10] L. Tang, A. Lindvall, Validation of models for prediction of chloride ingress in concrete exposed in de-icing salt road environment, Int. J. Struct. Eng. 4 (2013) 86-99.

[11] E. Poulsen, L. Mejlbro. Diffusion of Chloride in Concrete: Theory and Application, first ed., CRC Press, 2010.

[12] L. Tang, L.-O. Nilsson, P.A.M. Basheer, Resistance of concrete to chloride ingress: testing and modelling, CRC Press, 2011.

[13] Q. Liu, J. Yang, J. Xia, D. Easterbrook, L. Li, X.-Y. Lu, A numerical study on chloride migration in cracked concrete using multi-component ionic transport models, Comput. Mater. Sci. 99 (2015) 396-416, https://doi.org/10.1016/j.commatsci.2015.01.013.

[14] L. Mao, Z. Hu, J. Xia, G. Feng, I. Azim, J. Yang, Q. Liu, Multi-phase modelling of electrochemical rehabilitation for ASR and chloride affected concrete composites, Compos. Struct. 207 (2019) 176-189, https://doi.org/10.1016/j.comstruct.2018.09.063.

[15] L.-O. Nilsson, A Numerical Model for Combined Diffusion and Convection of Chloride in Non-saturated Concrete, in: 2000.

[16] A. Pelle, B. Briseghellà, G. Fiorentino, G.F. Giaccu, D. Lavorato, G. Quaranta, A. Rasulo, C. Nuti, Repair of reinforced concrete bridge columns subjected to chloride-induced corrosion with ultra-high performance fiber reinforced concrete, Struct. Concr. 24 (2023) 332-344, https://doi.org/10.1002/suco.202200555.

[17] A. Pelle, B. Briseghellà, A.V. Bergami, G. Fiorentino, G.F. Giaccu, D. Lavorato, G. Quaranta, A. Rasulo, C. Nuti, Time-dependent cyclic behavior of reinforced concrete bridge columns under chlorides-induced corrosion and rebars buckling, Struct. Concr. 23 (2022) 81-103, https://doi.org/10.1002/suco.202100257.

[18] S. Khani, D. Conciatori, L. Chouinard, Modeling the Time-Dependent Variation of Road Salt Concentrations Using Analytical and Machine-Learning Approaches to Advance Service Life Predictions for Concrete Structures, Transp. Res. Rec. J. Transp. Res. Board (2024) 03611981241284616, https://doi.org/10.1177/03611981241284616.

[19] A.S. Bah, T. Sanchez, Y. Zhang, K. Sasai, D. Conciatori, L. Chouinard, G.J. Power, N. Zufferey, Assessing the condition state of a concrete bridge combining visual inspection and nonlinear deterioration model, Struct. Infrastructure. Eng. 20 (2022) 149-164, https://doi.org/10.1080/15732479.2022.2081987.

[20] J. Marchand, E. Samson, Predicting the service-life of concrete structures—limitations of simplified models, Cem. Concr. Compos. 31 (2009) 515-521.

[21] W. Victor Anderson, The Future Of the Champlain Bridge, Delcan corporation, 2011.

[22] M. Khaleghi-Esfahani, B. Fournier, B. Bissonnette, P.-L. Fecteau, D. Conciatori, S. Khani, Diagnostic and prognostic assessments on a 50 year-old bridge subjected to severe environmental and in-service conditions, in: L.F.M. Sanchez, C. Trottier (Eds.), in: Proceedings of the Seventeenth Int. Conf. Alkali-Aggreg. React. Concr, Springer Nature Switzerland Cham, 2024, pp. 597-605, https://doi.org/10.1007/978-3-031-59419-9 6.9.

[23] G.P. Carlin, M.S. Mirza, M. Gaudreault, Rehabilitation measures for Champlain Bridge, Montreal, Canada, Can. J. Civ. Eng. 23 (1996) 1326-1340.

[24] AASHTO T 260 (SMT Chloride Ion in Concrete) | PDF, Scribd (n.d.). (https://www.scribd.com/document/354830229/AASHTO-T-260-SMT-Chloride-Ion-in-Concrete) (Accessed 21 December 2023). 2023.

[25] ASTM C1152.C1152M - Acid-Soluble Chloride in mortar and Concrete, ASTM International, 2012.

[26] K. Hong, R.D. Hooton, Effects of cyclic chloride exposure on penetration of concrete cover, Cem. Concr. Res. 29 (1999) 1379-1386.

[27] D. Conciatori, H. Sadouki, E. Brühwiler, Capillary suction and diffusion model for chloride ingress into concrete, Cem. Concr. Res. 38 (2008) 1401-1408.

[28] Torrent, Proceq, TORRENT Permeability Tester - Mode d'emploi, Proceq SA, Zürich, (1997).

[29] D. Conciatori, E. Grégoire, É. Samson, J. Marchand, L. Chouinard, Statistical analysis of concrete transport properties, Mater. Struct. 47 (2014) 89-103.

[30] R. Wolofsky, L. Chouinard, D. Conciatori, J. Bastien, Updating of chloride ingress models using core data measurements, International Journal of Reliability and Safety (IJRS), Vol. 9, No. 4, p. 291-310, Int. J. Reliab. Saf. 9 (2015) 291-310.

[31] D. Conciatori, E. Brühwiler, C. Linden, Numerical simulation of the probability of corrosion initiation of RC elements made of reinforcing steel with improved corrosion performance, Struct. Infrastructure. Eng. 0 (2018) 1-9.

[32] D. Conciatori, F. Laferrière, E. Brühwiler, Comprehensive modeling of chloride ion and water ingress into concrete considering thermal and carbonation state for real climate, Cem. Concr. Res. 40 (2010) 109-118.

[33] D. Conciatori, Effet du microclimat sur l'initiation de la corrosion des aciers d'armature dans les ouvrages en béton armé, Thèse de doctorat, École Polytechnique Fédérale de Lausanne, 2006. (http://infoscience.epfl.ch/record/56049).

[34] D. Conciatori, E. Brühwiler, R. Gysler, Brine absorption in concrete at low temperature: experimental investigation and modeling, J. Mater. Civ. Eng. 23 (2010) 846-851.

[35] S. Khani, D. Conciatori, L. Chouinard, Modeling the Time-Dependent Variation of Road Salt Concentrations Using Analytical and Machine Learning Approaches to Advance Service Life Predictions of Concrete Structures, Transp. Res. Rec. J. Transp. Res. Board (2024).

[36] Les Ponts Jacques Cartier et Champlain Incorporée, PJCCI, (n.d.). (https://jacquescartierchamplain.ca/) (Accessed 7 July 2024) 2024.

[37] D. Conciatori, E. Grégoire, E. Samson, J. Marchand, L. Chouinard, Sensitivity of chloride ingress modelling in concrete to input parameter variability, Mater. Struct. 48 (2015) 3023-3036.

[38] Roberto J. Torrent, Rui D. Neves, Kei-ichi Imamoto. Concrete Permeability and Durability Performance: From Theory to Field Applications | Request PDF, first ed., CRC Press/Taylor & Francis, 2022. (https://www.researchgate.net/publication/356179508_Concrete_Permeability_and_Durability_Performance_From_Theory_to_FieldApplications?_cf_chl_rtk_tk=t34YDA.hgyDx9bxHhJdjojKpNEk7p.EQGjqtI9c1O0c-1716462315-0.0.1.1-1855), accessed May 23, 2024.

[39] G. Frenzer, F. Jacobs, R.J. Torrent, In situ durability characteristics of new and old concrete structures, J. Adv. Concr. Technol. 19 (2021) 53-66.

[40] X. Chen, D. Conciatori, T. Sanchez, L. Sorelli, B. Selma, C. Mohamed, Numerical modeling of multi-ionic transport with/without electrical field applied in sound and microcracked ordinary and ultra-high-performance fiber-reinforced concrete, Arch. Civ. Mech. Eng. 23 (2023) 232, https://doi.org/10.1007/s43452-023-00765-w.