Study of the environment factor from Fick’s and electrical resistivity models by simulation of chloride diffusivity prediction

Abstract

The penetration of chlorides in concrete is the main reason for the beginning of corrosion in reinforced concrete structures exposed to a marine environment, reducing their service life. This article proposes correlations between the surface chloride content (C_s) of Fick’s model and the ambient factor (k_Cl) of a resistivity model. Literature data for three types of cement were used to simulate chloride diffusivity: (1) CEM I 52.5 R; (2) CEM II/A-P 42.5 R (with 6%–20% of pozzolans); and (3) CEM type II (with 12% of pozzolans and 8% of silica fume). Concretes containing these cements were analyzed for different environmental conditions: atmosphere zone, seawater immersion, and tidal/splash zones. The surface chloride contents were determined by a combination of Fick’s and resistivity models. In this article, it was noticed that the estimated C_s value varies with the exposure class from 0.484% to 0.644% (total chloride concentration by weight of cement). An equation has been proposed to correlate C_s with the ambient factor k_Cl of the resistivity model.

Keywords

chloride marine environment model resistivity surface concentration

Introduction

Chloride penetration in concrete

Reinforcement corrosion is the degradation process that has the most impact on the durability of reinforced concrete structures. The natural conditions of high alkalinity in concrete normally protect the reinforcement from corrosion reactions. However, some agents may induce corrosion even in an alkaline environment, such as chloride, which destroys the passivation layer in the reinforcement–concrete interface.

Chloride-induced corrosion is an important subject studied in the literature. Balestra et al. (2019a) studied the reinforcement corrosion risk of marine concrete structures evaluated through electrical resistivity. Farzad et al. (2019) studied the effect of moisture on macrocell current and evaluated the suitability of ultra-high performance concrete as a repair material. Rossi et al. (2020) evaluated the effect of defects at the steel–concrete interface for chloride-induced pitting corrosion using the X-ray computed tomography. Thus, the effects of different variables on corrosion kinetics have been studied over the years.

Modeling the chloride penetration in concrete is a recurrent subject in researches (Andrade et al., 2013; Mazer et al., 2018; Petcherdchoo, 2013). Especially in the last 30 years, these models progressed considerably in terms of the complexity of the input variables and the number of factors taken into consideration (Meira et al., 2014; Torres-Luque et al., 2014). Some chloride penetration models are presented below.

Saetta et al. (1993) used a numerical procedure based on the finite element method to model the chloride ingress in concrete (equation (1))

\begin{matrix} D_{c 2} = D_{c 1} \cdot {\exp [\frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})]} \\ \cdot {ζ + (1 - ζ) \cdot {(\frac{28}{t_{e}})}^{0.5}} \cdot {{[1 + \frac{{(1 - RH)}^{4}}{{(1 - R H_{c})}^{4}}]}^{- 1}} \end{matrix}

(1)

where D_c₁ and D_c₂ (cm²/s) are the reference and adjusted chloride diffusion coefficients, respectively; T₁ is the reference temperature (296 K) and T₂ (K) is the current temperature; E_a is the activation energy of diffusion (kJ/mol), which is related to the water/cement ratio of the concrete; R is the universal gas constant (8.314 J/mol K); ζ measures how much the diffusivity decreases with time and varies from 0 to 1; t_e (days) is the actual time of exposure to chloride; RH_c is the relative humidity at which D_c₁ drops halfway between its maximum and minimum values; and RH is the current relative humidity considered (%).

Bastidas-Arteaga et al. (2010) used a stochastic approach to determine the influence of weather and global warming in chloride ingress into concrete. Mazer et al. (2018) proposed a mathematical model to estimate the chloride diffusion coefficient using fuzzy logic, considering parameters of the concrete including water/cement ratio, compressive strength, and concrete curing temperature. Wang et al. (2019a) proposed a semi-empirical prediction model of chloride-induced corrosion for application in uncracked reinforced concrete.

Balestra et al. (2019b) recently presented the modified Holliday equation in order to model chloride profiles (equation (2)) of field naturally degraded structures that present a sharp peak of maximum concentration, contemplating the convection and diffusion zones

C_{(x, t)} = \frac{1}{R_{1} \cdot [1 + \frac{{(x - R_{3})}^{2}}{(D \cdot t)}]}

(2)

where C_(x,t) is the chloride concentration (% by weight of concrete); $1 / R_{1}$ is the maximum chloride concentration at the peak (% by weight of concrete); D is the apparent diffusion coefficient (cm²/s); R₃ is the peak position from the concrete surface (cm); x is the depth from the concrete surface (cm); and t is the time (s).

Several other models can be found in the literature to predict chloride penetration. However, the application of most of these models presents difficulties mainly due to the following three factors: (1) boundary conditions that reproduce the reality of chloride penetration; (2) variables that change with the exposure time and the location; and (3) equations too complex to be applied under practice conditions.

Despite the difficulties discussed, service life models are extremely useful for the durability design of concrete structures. These models provide the opportunity to pre-arrange a maintenance program and, therefore, to guarantee the minimum service life specified in standards (above 50 or 100 years). Another benefit is the possibility of considering the local environmental variables acting on different parts of the structure in a microclimate concept.

Electrical resistivity model

Electrical resistivity indicates the amount and connection of pores in the concrete and can be used as a parameter to model the transport of different agents in this material (Medeiros-Junior et al., 2019). The resistivity and diffusivity relation can be established according to Einstein’s law (equation (3)), which relates to the movement of electric charges and the conductivity of the medium (Andrade, 1993). Factor A in equation (3) is dependent on the external ionic concentration. In the case of chloride ions, Andrade (2004) named A as k_Cl (cm³·Ω/year)

D_{ef} = \frac{A}{ρ_{ef}}

(3)

where D_ef is the effective diffusion coefficient (cm²/year), which is also known as the steady-state diffusion coefficient; and ρ_ef is the effective resistivity at 28 days on saturated conditions (Ω·cm).

Andrade (2004) proposed a chloride diffusivity model based on concrete electrical resistivity. The reaction factor (r_Cl) is the factor responsible for transforming the D_ef (steady state) diffusion coefficient into the D_ap (non-steady state) diffusion coefficient. D_ef considers only the ionic transport while D_ap also takes into account the binding of chlorides with cement matrix. According to Castellote and Andrade (2006), the ratio between D_ef and D_ap (=r_Cl) addresses the binding ability of the cement matrix. This reaction or binding factor is responsible for taking into account the delay in chloride penetration due to chloride binding and depends mainly on the cement composition. Thus, by definition, r_Cl is equal to D_ef/D_ap (Andrade 2004, 2014). D_ef and D_ap parameters can be obtained through a multi-regime test (UNE 83987, 2014) and then applied to equation (4) to determine r_Cl. Porosity (ε, % by volume) multiplied by D_ap is used in order to homogenize the units in which D_ef and D_ap are expressed

r_{Cl} = \frac{D_{ef}}{D_{ap} \cdot ε}

(4)

Dividing both sides of equation (3) by r_Cl factor, the apparent diffusion coefficient (in non-steady state) is determined using equation (5) (Andrade, 2004). Therefore, when the first-half part of equation (5) is divided by r_Cl, D_ef becomes D_ap. The concepts of effective and apparent for electrical resistivity are similar to concepts for the diffusion coefficient mentioned before. The r_Cl factor represents the number of times the effective resistivity is apparently increased when the chloride combination is considered (Andrade, 2004; Andrade et al., 2014). That is, as part of the initially free chloride will become chemically bonded with the cementitious matrix, the resistivity of the concrete tends to increase because less free chloride will be available to interfere with the electrical conductivity. Therefore, the apparent resistivity (ρ_ap = ρ_ef·r_Cl) was proposed by Andrade (2004), which takes into account the slower chloride advance

\frac{D_{ef}}{r_{Cl}} = \frac{k_{Cl}}{ρ_{ef} \cdot r_{Cl}} ∴ D_{ap} = \frac{k_{Cl}}{ρ_{ap}}

(5)

where D_ap is the diffusion coefficient in non-steady state (cm²/year); r_Cl is the chloride reaction factor; ρ_ap is the concrete apparent resistivity (Ω·cm); and k_Cl is the ambient factor (cm³·Ω/year).

Finally, using the well-known “square root law” (equation (6)), the corrosion initiation period (t_i) is estimated by equation (7) (Andrade, 2004), considering the moment of depassivation of the reinforcement as a threshold condition

t = \frac{x^{2}}{D_{ap}}

(6)

t_{i} = \frac{x^{2} \cdot ρ_{t} \cdot r_{Cl}}{k_{Cl}}

(7)

where t_i is the corrosion initiation period (years); x is the penetration depth of the chloride threshold concentration, which is equal to concrete cover (cm) when t_i is considered; and ρ_t is the resistivity corrected over time.

In addition, the concrete age factor (q) should be used in equation (7) to consider that the concrete electrical resistivity increases over time, as shown in equation (8) (Andrade, 2004). ρ_t is the effective resistivity corrected over time due to the effect of concrete aging. Over time, concrete tends to increase electrical resistivity due to the evolution of cement hydration reactions and the consequent pore refinement (Mendes et al., 2018). Thus, the effect of increased resistivity over time due to concrete aging is taken into account in the Andrade (2004) model for chloride penetration by the factor q.

ρ_{t} = ρ_{ef} \cdot {(\frac{t}{t_{o}})}^{q}

(8)

where t is the time considered for application of the age factor; t₀ is the age of first resistivity measurement, which is 28 days; and q is the age factor of resistivity.

Andrade and D’Andrea (2010) calculated k_Cl values to different exposure classes defined by the European Standard EN 206-1 (2007). These k_Cl values were proposed based on rough estimations of experimental results of real structures exposed for a long period to the aggressive attack of chloride ions.

According to Andrade and D’Andrea (2010), the environment factor (k_Cl) is equal to 5000, 10,000, 17,000, and 25,000 cm³·Ω/year to the exposure classes XS1a, XS1b, XS2, and XS3, respectively. These classes are classified as follows (EN 206-1, 2007):

XS1: parts of structures in contact with marine aerosol, but without direct contact with seawater. It represents cases of structures in the coastal zone or close to the coastal zone. This class can be subdivided according to the distance to the shoreline as XS1a (distance > 500 m) and XS1b (distance < 500 m).

XS2: parts of marine structures subjected to permanent seawater immersion.

XS3: parts of marine structures located in tidal or splash zones.

Due to the difficulty of finding concrete structures with all variables required and available for a complete durability study, the number of samples analyzed to estimate the environmental coefficient for this model was relatively scarce. Therefore, it is assumed that the results are close to the desired conditions, although probably different from the overall average value (Andrade and D’Andrea, 2010).

Model based on Fick’s law

The chloride diffusion model (equation (9)) based on Fick’s second law (Collepardi et al., 1972; Crank, 1975) is well known and applied in the studies of the service life of the reinforced concrete structure (Medeiros-Junior et al., 2015; Wang et al., 2014)

C_{x} = C_{s} \cdot [1 - \erf \frac{x}{2 \sqrt{D_{ap (t)} \cdot t}}]

(9)

where C_x is the chloride concentration (%) at depth x and time t; C_s is the surface chloride content (%); x is the depth (cm); D_ap_(t) is the apparent diffusion coefficient in time (cm²/s); t is the exposure time (s); and erf is the mathematical error function.

According to Mangat and Molloy (1994) and Maage et al. (1996), a mathematical model expressed by a power function (equation (10)) may estimate the effect of concrete maturity on diffusion

D_{ap (1)} = D_{ap (0)} \cdot {(\frac{t_{1}}{t_{0}})}^{- n}

(10)

where t₁ is the maturity age of the concrete—a time considered for application of the maturity factor; and t₀ is a reference time for the first diffusion coefficient measurements generally assumed to be 28 days. The effect of diffusion coefficient reduction over time is represented by n in equation (10). According to Andrade et al. (2011), n can be related to the age factor q from the resistivity model using equation (11)

q = 0.8 \cdot n

(11)

Discussion concerning resistivity and Fick’s models

Some similarities can be identified by observing the resistivity (equation (7)) and Fick’s (equation (9)) models, since both equations model the chloride transport in concrete. Table 1 shows some similarities of each variable used in these models.

Table 1.

The similarity between variables from resistivity and Fick’s models.

	Fick(equation (9))	Resistivity (equation (7))
Depth of chloride penetration	x	x
Exposure time to chloride	t	t
Penetration rate	D_ap _(t)	ρ_ap = (ρ·r_Cl)
Age factor	n	q
Environment factor	C_s	k_Cl

According to Table 1, the environment factor (k_Cl) from the resistivity model is equivalent to the C_s on Fick’s model. Considering the time needed for the depassivation of the reinforcement, C_x is considered as the threshold chloride concentration (C_thr) at the depth equal to the concrete cover (x = x_c), and t is the service life of concrete structures (t = t_i).

Thus, the aim of this article is to verify which C_s of Fick’s model is equivalent to several environment factors (k_Cl) from the resistivity model for different cement types by numerical simulation based on data already available in the literature. This relationship was identified for each of the exposure classes proposed in the EN 206-1 (2007) standard for chloride attack (XS1a, XS1b, XS2, and XS3). Experimental data obtained from the literature were used for simulations of chloride diffusivity and for studying the correlations between both environmental factors (C_s and k_Cl).

The advantages and significance of this study are to stimulate the use of durability models in predicting chloride penetration. The lack of defined variables for different types of environment and materials inhibits the use of these mathematical equations. Therefore, although good models for predicting chloride diffusivity exist, their practical application is hampered by the lack of data. This article attempts to narrow this gap by defining an equation to obtain environment factor data of Fick’s model from the resistivity model and vice versa.

In practice, determining the concentration of chlorides on the concrete surface (C_s) is time-consuming and expensive. However, this variable is essential for the model based on Fick’s second law (equation (9)). Even though some sensors (Meira et al., 2010) can be used for this determination, the application in real structures is still rare. Due to this difficulty, sometimes the concentration of chlorides in the first millimeters is assumed as being C_s. Some studies have also determined C_s by fitting the profiles of chlorides on Fick’s law (Medeiros-Junior et al., 2015; Wang et al., 2014). However, this practice has been questioned in the literature, because it results in an extrapolation of C_s and ignores the peak of chlorides (Andrade et al., 1997; Ann et al., 2009; Balestra et al., 2019b). The main reason for this article is trying to relate C_s with k_Cl values that were previously determined for different marine environments. This methodology highlights the importance of this study for the advancement of concrete durability studies in the marine environment.

In addition, electrical resistivity is a non-destructive technique that allows the continuous evaluation of processes occurring in a concrete structure by characterizing the electrical resistance inside the material. Electrical resistivity has the advantage of characterizing the corrosion kinetics, and it has also been used as a parameter for concrete design (Mendes et al., 2018). Therefore, this article defines environmental factor values for some common types of marine environments (exposure classes: XS1a, XS1b, XS2, and XS3) through an easily applied equation that allows the conversion of environmental factors from two different models.

Methods

The chloride reaction factor (r_Cl), age factor (q), resistivity at 28 days (ρ_ef), and apparent diffusion coefficient at 28 days (D_ap) for three usual types of cement were taken from previous researches (Andrade et al. (2014); Andrade (2014)). Three different cement types were selected for this study: CEM I 52.5 R and CEM II/A-P 42.5 R (Portland-composite cement with 6%–20% of pozzolans (PN)), according to the EN 206-1 (2007) standard, and CEM type II moderate sulfate resistance cement with 12% of PN and 8% of silica fume (SF). Andrade et al. (2014) used seven test specimens for CEM I 52.5 R, three test specimens for CEM II/A-P 42.5 R, and four test specimens for CEM type II with 12% PN + 8% SF. The amount of cement (kg/m³) ranges from 300 to 450, and the water/cement ratio ranges from 0.28 to 0.60. The details regarding material specifications can be found in Andrade et al. (2014).

According to the data available in Andrade et al. (2014), the chloride reaction factor (r_Cl) ranges from 0.7 to 2.6 (CEM I 52.5 R), 3.5 to 6.2 (CEM II/A-P 42.5 R), and 2.5 to 3.7 (CEM type II with 12% PN + 8% SF). The resistivity at 28 days (ρ_ef) ranges from 6591 to 12,742 Ω·cm (CEM I 52.5 R), 4533 to 5072 Ω·cm (CEM II/A-P 42.5 R), and 20,365 to 45,299 Ω·cm (CEM type II with 12% PN + 8% SF). The apparent diffusion coefficient at 28 days (D_ap) ranges from 6.24 to 43.38 × 10⁻⁸ cm²/s (CEM I 52.5 R), 3.85 to 11.5 × 10⁻⁸ cm²/s (CEM II/A-P 42.5 R), and 2.62 to 4.93 × 10⁻⁸ cm²/s (CEM type II with 12% PN + 8% SF). The age factor (q) is 0.22 for CEM I 52.5 R and 0.37 (recommended value for up to 20% PN) for CEM II/A-P 42.5 R and CEM type II with 12% PN + 8% SF.

Since CEM II has additions (PN and/or SF) in its composition, this explains the lower diffusion coefficient of CEM II when compared to CEM I, due to the pore refinement caused by these additions. The reaction factor is higher due to the presence of aluminates, which chemically fix a greater amount of chlorides in the cementitious matrix. The age factor for CEM II is also higher since the pozzolanic reactions are slower and progressive (Andrade, 2014; Medeiros-Junior and Lima, 2016).

In this article, these cement types were analyzed under different environmental conditions of chloride attack: XS1a, XS1b, XS2, and XS3, proposed by the EN 206-1 (2007) standard. The k_Cl values used for each class were suggested by Andrade and D’Andrea (2010), which are already discussed in the introduction of this article.

The first age for the measure of resistivity and apparent diffusion coefficient (t₀, from equations (8) and (10)) was 28 days. The exposure period (t₁, from equations (8) and (10)) considered was 91 days due to the time needed for the cement hydration, since at this age, over 80% of the cement is already hydrated (Taylor, 1997). The chloride threshold concentration assumed was 0.4% by weight of cement, considering total chloride concentration. The breakdown of the passivating film and subsequent corrosion process begins when a certain concentration of chloride ions reaches the reinforcement surface. The threshold value is highly relevant in chloride penetration studies in concrete structures and can be expressed in different ways. Some common examples are the percentage by weight of cement or concrete or from the Cl⁻/OH ratio of the solution present in the pores of the cementitious matrix. In a comprehensive literature review of the critical chloride ion content, Angst et al. (2009) commented that due to the existence of several factors involved (reinforcement characteristics, cement type, water/cement ratio, and temperature), the establishment of a single critical content for application in all real conditions is not reasonable. However, the value of 0.4% by weight of cement is one of the most used values in the literature (Meira et al., 2014; Mohammed and Hamada, 2006; Pacheco and Polder, 2016; Wang et al., 2019b; Wu et al., 2019). Although considered conservative, this value is adopted by standards in some countries—such as Brazil, Portugal, and England—in order to meet most exposure situations of a reinforced concrete structure to chlorides.

The combination of the models (resistivity and Fick) results in equation (12), which was used to determine C_s for each selected condition. Equation (12) comes from the substitution of t from equation (7) in equation (9). The concrete cover (x_c) does not interfere in the analyses since this value is present in the numerator and the denominator of equation (12). A constant (=31,536,000) must be used in equation (12) to transform time t₁ from years to seconds. The rearranged equation is presented in equation (13)

\frac{C_{thr}}{C_{s}} = [1 - \erf \frac{x_{c}}{2 \sqrt{D_{apt (0)} \cdot {(\frac{t_{1}}{t_{0}})}^{- \frac{q}{0.8}} \cdot \frac{x_{c}^{2} \cdot ρ_{ef} \cdot {(\frac{t}{t_{o}})}^{q} \cdot r_{Cl}}{k_{Cl}} \cdot 31, 536, 000 (s / years)}}]

(12)

C_{s} = \frac{C_{thr}}{[1 - \erf \frac{1}{11, 231.38 \sqrt{D_{apt (1)} \cdot {(3.25)}^{- \frac{q}{0.8}} \cdot \frac{ρ_{ef} \cdot {(3.25)}^{q} \cdot r_{Cl}}{k_{Cl}}}}]}

(13)

Results and discussion

Figures 1 to 4 show the surface chloride content (C_s) for the exposure classes XS1a, XS1b, XS2, and XS3, respectively. These values are based on a threshold concentration, considering the total chloride concentration in concrete (C_thr = 0.4% by weight of cement).

Figure 1.

Surface chloride contents to XS1a.

Figure 2.

Surface chloride contents to XS1b.

Figure 3.

Surface chloride contents to XS2.

Figure 4.

Surface chloride contents to XS3.

According to Figures 1 to 4, C_s did not present great variations between the types of cement. The standard deviations ranged from 0.023 to 0.085. This indicates that the surface concentration of chlorides is a measure that depends more on the exposure environment—the proximity of the coast, temperature, wind, and relative humidity—than on the cement type. The coefficients of variation ranged from 4.79% to 13.17%. Figure 5 shows the mean value of C_s for each exposure environment.

Figure 5.

Mean surface chloride contents for each exposure environment.

According to Figure 5, C_s grows with the aggressiveness of chlorides of the environment. This behavior seems reasonable since the surface chloride content tends to be reduced once the concrete structure is further away from the coast. The C_s value of marine structures located in tidal or splash zones is 33.2% higher when compared to that of structures at 500 m from the shoreline. Meira et al. (2006, 2007) observed this behavior by monitoring the chloride concentration through equipment called “wet candle.”

The results of Figure 5 were statistically analyzed, in order to verify if the differences are due to the effective changes in the control variables. The one-way analysis of variance (ANOVA) method was applied, with a significance level of 5%, followed by a multiple-variance analysis to verify the differences between the exposure classes. Tables 2 and 3 present the results of the statistical analysis.

Table 2.

One-way ANOVA.

Variation source	SQ	FD	AS	F	p	F_critical	Significant
Between groups	0.202	3	0.067	21.18	4.2E−09	2.78	Yes
Withinthe groups	0.166	52	0.003
Total	0.368	55

ANOVA: analysis of variance; SQ: sum of squares; FD: freedom degree; AS: average squares.

Table 3.

Multiple-variance analysis.

Analysis	F > F_critical	Significant
XS1a × XS1b	Yes	Yes
XS1a × XS2	Yes	Yes
XS1a × XS3	Yes	Yes
XS1b × XS2	Yes	Yes
XS1b × XS3	Yes	Yes
XS2 × XS3	Yes	Yes

According to Tables 2 and 3, all classes generated concentrations that are statistically different from each other. According to Figure 5, C_s varies with the exposure class from 0.484% to 0.644%. These results seem reasonable, according to the data of surface chloride content measured and estimated in the field by other studies in the literature. Table 4 shows several surface chloride concentrations found in the literature. According to Table 4, there is no consensus on the C_s value on previous studies related to chloride ingress in concrete. Different authors have found C_s ranging from 0.4% to more than 4.0%, either through chloride profile fitting or laboratory experiments. However, in general, some tendencies can be noticed: the results are higher for tidal > spray zone > atmosphere. Furthermore, C_s grows with time, with the water/cement ratio, and with the proximity to the seashore. As shown in Table 4, the following studies found C_s from 0.4% to 0.7% by weight of cement: Mustafa and Yusof (1994), Costa and Appleton (1999), Yoon (2007), Meira et al. (2010), O’Connor and Kenshel (2013), Safehian and Ramezanianpour (2013), Valipour et al. (2013), and Kim et al. (2016). These values are very close to the results in Figure 5, confirming and validating the results obtained in this article.

Table 4.

Surface chloride concentration found in the literature.

C_s (% binder)	Time (months)	Exposure	Concrete mix		References
			Binder	W/B
1.50–3.10	288	Structure (tidal/splash)	OPC	0.5	Liam et al. (1992)
0.20–2.43	360	Structure (atmosphere)	OPC	Unknown	Morinaga (1992)
1.2	3	Specimens (aerated—30 m seashoreand 5 m above sea level)	OPC	0.5	Mustafa and Yusof(1994)
0.88	3	Specimens (aerated—30 m seashore and15 m above sea level)
0.69	3	Specimens (aerated—400 m seashore and5 m above sea level)
0.57	3	Specimens (aerated—away from seashore)
1.95	6	Specimens (aerated—30 m seashore and5 m above sea level)
1.63	6	Specimens (aerated—30 m seashore and 15 m above sea level)
1.44	6	Specimens (aerated—400 m seashore and5 m above sea level)
1.071	6	Specimens (aerated—away from seashore)
2.58	9	Specimens (aerated—30 m seashore and 5 m above sea level)
2.45	9	Specimens (aerated—30 m seashore and15 m above sea level)
2.2	9	Specimens (aerated—400 m seashore and5 m above sea level)
1.82	9	Specimens (aerated—away from seashore)
3.53	12	Specimens (aerated—30 m seashore and5 m above sea level)
3.33	12	Specimens (aerated—30 m seashore and 15 m above sea level)
3.08	12	Specimens (aerated—400 m seashore and5 m above sea level)
2.2	12	Specimens (aerated—away from seashore)
3.8	15	Structure (submerged)	OPC	0.4	Kim et al (2016)
1.27–2.19	15	Structure (tidal)
0.62	15	Structure (splash)
1.72	3	Specimens (tidal)	OPC	0.4	Moradllo et al (2012)
1.17–1.90	Specimens(laboratory—ponding)		OPC	0.35–0.65	Chiang and Yang (2007)
1.4–2.2			20% FA	0.35–0.65
1.5–2.2			40% SLAG	0.35–0.65
1.5–2.2			9% FA + 21%SLAG	0.35–0.65
0.70	6	Structure (spray zone)	OPC	0.3–0.5	Costa and Appleton(1999)
1.02	9		OPC	0.3–0.6
0.88	12		OPC	0.3–0.7
0.97	15		OPC	0.3–0.8
1.39	18		OPC	0.3–0.9
1.35	24		OPC	0.3–0.10
1.72	30		OPC	0.3–0.11
1.58	36		OPC	0.3–0.12
0.85	6	Structure (tidal zone)	OPC	0.3–0.13
0.93	9		OPC	0.3–0.14
1.40	12		OPC	0.3–0.15
1.32	15		OPC	0.3–0.16
1.40	18		OPC	0.3–0.17
1.78	24		OPC	0.3–0.18
1.63	30		OPC	0.3–0.19
1.94	36		OPC	0.3–0.20
0.70	24	Structure (atmosphere)	OPC	0.3–0.21
0.74	30		OPC	0.3–0.22
0.84	36		OPC	0.3–0.23
4.2	1	Specimens (laboratory—partial submerged)	OPC	0.3	Elahi et al. (2010)
2.6	1	Specimens (laboratory—partial submersion)	OPC	0.38	Liu et al. (2011)
1.5	3	Specimens (laboratory—ponding)	OPC	0.5	McPolin et al. (2005)
2.4	3		30% PFA	0.5
2.8	3		50% SLAG	0.5
3	3		10% MK	0.5
0.35	46	Specimens (aerated—10 m away from seashore)	OPC	0.5	Meira et al. (2010)
0.15	46	Specimens (aerated—100 m away from seashore)	OPC	0.5
0.05	46	Specimens (aerated—200 m away from seashore)	OPC	0.5
0.48	46	Specimens (aerated—10 m away from seashore)	OPC	0.57
0.45	46	Specimens (aerated—10 m away from seashore)	OPC	0.65
1.2–2.73	324	Structure (tidal/splash)—Pier 1	Unknown	Unknown	O’Connor and Kenshel (2013)
0.78–1.84	324	Structure (tidal/splash)—Pier 2	Unknown	Unknown
0.78–2.93	324	Structure (tidal/splash)—Pier 3	Unknown	Unknown
0.33–0.51	324	Structure (tidal/splash)—Pier 4	Unknown	Unknown
0.48	60	Structure (atmosphere)	OPC + 7% SF	0.38	Safehian and Ramezanianpour(2013)
1.9	60	Structure (splash)	OPC + 7% SF	0.38
2.4	60	Structure (tidal)	OPC + 7% SF	0.38
2.7	3	Structure (submerged)	OPC + 35% SLAG + 20% FA + 3% SF	0.35	Song et al. (2009)
4.48	12	Specimens (tidal)	OPC	0.35	Valipour et al. (2013)
3.91	12		OPC	0.4
4.6	12		OPC	0.45
4.71	12		OPC	0.5
4.8	12		20% SF	0.4
4.74	12		20% MK	0.4
1.61	12	Specimens (splash)	OPC	0.35
2	12		OPC	0.4
2.2	12		OPC	0.45
1.75	12		OPC	0.5
4	12		20% SF	0.4
3.74	12		20% MK	0.4
0.69	12	Specimens (soils)	OPC	0.35
1.15	12		OPC	0.4
1.1	12		OPC	0.45
1.4	12		OPC	0.5
1.3	12		20% SF	0.4
1.75	12		20% MK	0.4
0.51	12	Specimens (atmosphere)	OPC	0.35
0.51	12		OPC	0.4
0.57	12		OPC	0.45
0.52	12		OPC	0.5
1.03	12		20% SF	0.4
0.69	12		20% MK	0.4
1.26	3	Specimens (laboratory—ponding)	OPC	0.35	Yang and Wang (2004)
1.62	3			0.45
2.13	3			0.55
2.83	3			0.65
1.51	3		20% FA	0.35
1.90	3			0.45
2.25	3			0.55
2.65	3			0.65
1.37	3		20% SF	0.35
1.68	3			0.45
1.94	3			0.55
2.29	3			0.65
0.67	12	Specimens (laboratory—submerged)	OPC	0.45	Yoon (2007)
0.94	12			0.5
1.1	12			0.55
0.8	12	Specimens (laboratory—wet and dry cycles—tidal)		0.45
1.06	12			0.5
1.23	12			0.55

W/B: water/cement ratio; OPC: ordinary portland cement; FA: fly ash; SLAG: blast furnace slag; PFA: pulverised fuel ash; MK: metakaolin; SF: silica fume.

An explanation for the variation of C_s found in Table 4 is the chloride threshold concentration (C_thr). The C_thr assumed in this article was 0.4%; however, there is also no consensus in the literature about the limit chloride concentration to initiate the corrosion process. Values from 0.2% up to 1.5% have already been documented and summarized by Meira et al. (2014). Figure 6 shows an example for a class XS1a of how C_s depends on the C_thr parameter.

Figure 6.

C_s and C_thr relationship for XS1a.

Another relevant consideration is the variation of C_s in time. However, according to Ann et al. (2009), the time-dependent characteristic of the surface chloride content has been rarely considered in chloride ingress. Therefore, the values proposed by this article refer to the final concentration of C_s, after their stabilization in time. For further study on this topic, Petcherdchoo (2013) showed a literature review on how to consider the increasing of C_s in time. Figure 7 shows the relationship found between C_s of Fick’s model and k_Cl of resistivity model.

Figure 7.

C_s and k_Cl relationship according to the conditions used in this study.

The proposed correlations in Figure 7 show a high R² (0.98). This equation allows determining the surface chloride content in the concrete as a function of the exposure classes (k_Cl) of the concrete resistivity model and vice versa. These proposed correlations are based on the application of calculation models conducted in this article and require validation in real concrete structures for safe use in service life models.

Conclusion

This article proposes correlations between the surface chloride content (C_s) of Fick’s model and the ambient factor (k_Cl) of a resistivity model. All environmental classes have shown C_s values that are statistically different from each other. C_s did not show great variations between the types of cement. This indicates that the surface concentration of chlorides is highly dependent on the exposure environment. C_s grows with the aggressiveness of chlorides of the environment since the surface chloride content tends to increase when the concrete structure is closer to seawater. The estimated C_s values vary with the exposure class from 0.484% to 0.644% (by weight of cement). These values are very close to some results found in the literature. Although surface concentration may be time-dependent, the values proposed by this article refer to the C_s after their stabilization in time. An equation has been proposed to correlate C_s with the ambient factor k_Cl of the resistivity model. The results contribute to facilitating the application of both models for the conditions used in this article. An experimental validation would be essential to reinforce the values obtained in this article and the limits of application of the proposed equation. Therefore, although probably different from the overall average value, the results are assumed to be close to some real conditions.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Ronaldo A Medeiros-Junior

Diogo H Bem

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