1 Introduction

Concrete cover is the least distance between the surface of the embedded reinforcement and the exposed surface. It plays a crucial function as the first shielding, protecting the inner part of a concrete structure and the embedded steel reinforcement [1,2,3]. Nonetheless, it is the most permeable part of the structure because of its higher porosity than that of the concrete's internal part. The movement of gases, liquids, and ions through this layer occurs during the service life of concrete structures and can cause the deterioration of reinforced concrete structures [4,5,6]. Thus, an appropriate assessment of the transport properties of the concrete cover is crucial for controlling the longevity and durability of concrete structures [7,8,9].

Depending on the process' driving force and the transported matter type, transport qualities can be characterized as diffusion, absorption, or permeation [2, 8]. Among these, air-permeability, a reliable characteristic representing permeation, is closely related to the pore structure of concrete [2, 8, 10] and can be measured via destructive and non-destructive test methods [11,12,13]. Pertaining to the non-destructive aspect, several permeability assessment methods have been proposed and validated [14,15,16,17,18]. Among these methods, a double vacuum cell test, Torrent’s air-permeability test, was proposed to determine the coefficient of permeability kT and the affected depth [15]. The application of the method was preliminarily verified via comparison with the Cembureau method [19, 20].

Indeed, the Torrent air-permeability test has been extensively applied as a non-destructive method for quality control of concrete on site without damaging its structures [15, 21]. Numerous studies have employed the kT measured by the Torrent method, as a robust durability indicator to discuss and verify other indices or other concrete durability characteristics [21,22,23]. Moreover, it has been considered a durability design factor for the residual service life of reinforced structures affected by carbonation and chloride ingress [5, 24].

On the other hand, the measured air-permeability values strongly depend on the drying condition (i.e., the surface moisture content, m) of the measured concrete, as observed via the increment in kT of around three orders of magnitude from near saturation to oven-drying at 105 °C [7, 25,26,27]. For instance, Parrott investigated the correlation between moisture conditioning and transport properties at the surface of concrete test specimen [7]. Based on the experimental results, he found that air-permeability was sensitive to changes in the moisture content of the concrete, especially at relative humidity (RH) > 60%. The corresponding sample preconditions were recommended as a countermeasure to prevent the effect of the surface moisture content. Jacobs studied changes in the gas permeability of partially saturated concrete [26] and demonstrated a linear correlation between the gas permeability and water content in concrete pores using a logarithmic function. Romer monitored the influence of surface moisture content on kT values in controlled environmental conditions for a period of up to one year [27]. They found that the absolute values of kT depend on the concrete age and its surface moisture conditions. The reduction in the kT value owing to the elevated water saturation of concrete can underestimate the intrinsic permeability. As a result, changes in the degree of saturation of the pore system were reflected in variations in surface moisture content and variable blockage of gas flow through the pore system. In addition, it was found that moisture remaining in the pores or low-permeability concrete can evaporate into the test cell at very low vacuum pressures, artificially raising its pressure [28].

To address the above problems, several studies have focused on attempts to compensate for the effect of moisture on kT, or on methods used to assess kT at moisture equilibrium [29,30,31,32,33]. In early attempts to compensate for the effect of moisture on kT, two different techniques were investigated: James H2O meter (that failed) and the Wenner method [29]. A solution was proposed to compensate for the influence of moisture using a combination of kT and electrical resistivity measurements (by the Wenner method), which failed owing to difficulties in measuring the electrical resistivity on-site [34] and to the strong effect of the binder type on that property. Another solution requested a waiting time, such as 3–4 weeks after the completion of curing or 2–5 days after the last exposure to moisture, to withstand the high moisture influence (e.g., rain, sea spray) [35, 36]. Furthermore, incorporating in-situ and laboratory-based permeability testing techniques was suggested as part of an integrated strategy [37]. This strategy aimed to reduce the influence of moisture on in situ permeability measurements. The test results indicated that the controlled moisture content did not significantly affect the kT value in the context of the overall classification. However, no specific equation was provided to complement the effect of moisture content on the kT value. Based on experimental data, Misak et al. [30] proposed an equation to assess the impact of moisture content h (measured by KAKASO capacitive humidity meter) on the kT values:

$$kT={kT}_{0}\times {e}^{-\alpha .h}$$
(1)

where \({kT}_{0}\) and \(\alpha\) are compensation factors for the kT value measured at moisture h. Based on 153 test results, the proposed values of \({kT}_{0}\) and \(\alpha\) were 5.25 × 10–16 m2 and 0.862, respectively. In Switzerland, a study conducted at the Empa laboratory proved the suitability of a device to assess the surface moisture m of concrete based on changes in electrical impedance [27]. Recently, a comprehensive study was conducted on the relationship between m and kT for drying concretes [38]. Based on a large database from five different independent sources and a robust analysis process, a novel practical approach was proposed to compensate for the effect of moisture content m on kT. The proposed approach uses the kT5 value, which corresponds to a moisture content of 5.0%, as a reference index. The obtained results indicate a promising application of Torrent air-permeability for the flexible assessment of air-permeability at various surface moisture conditions.

In fact, assessing concrete carbonation resistance through Torrent air-permeability has been attended to due to their close correlations and the advantages of the Torrent test as an in-situ non-destructive method [23, 39, 40]. However, thus far, assessing concrete carbonation resistance through Torrent air-permeability considering the effect of surface moisture content has not been investigated, although a potential approach utilizing the application of the kT5 concept was proposed, as mentioned above.

Taking into account the literature results summarized above, the objective of the present study is to establish a unified approach for kT measurement at any moisture state to assess and predict the concrete carbonation resistance based on extensive experimental data in a laboratory. To realize this, the Torrent air-permeability was applied to various specimen qualities to collect the kT values at the ages of 1, 3, 6, 12, and 18 months (hereafter called kTm at the surface moisture content m). The correlations between kT5 calculated from these kTm values and the corresponding carbonation rates collected on the specimens were established and discussed to validate the usability of kT5 as an excellent index for predicting carbonation resistance.

2 Experimental program

2.1 Test variables

To analyze the changes of air-permeability and carbonation rate for different concrete qualities, 25 concrete specimens were prepared with three types of cement, nine water-to-binder ratios (W/B), and five curing conditions, as indicated in Table 1. Here, 20 of the 25 specimens were collected from four earlier works [23, 31, 40, 41]. Details on the specimens, such as the materials, mix compositions and curing procedures, can be found in the earlier publications. To widen the scope of this investigation to include other concrete qualities, five more specimens were cast using the same materials as for the prior specimens: OPC concretes with greater W/B (65% and 75%) and HPC concrete with a W/B of 41%. After curing, the air-permeability kTm and the surface moisture m were measured at five different ages and the carbonation depth at 6, 12, and 18 m, as described below.

Table 1 Mix compositions, fresh concrete properties, and curing of concrete specimens [23, 31, 40, 41]
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2.2 Materials and mix proportions

Three types of cement were used in the concrete mixes: ordinary Portland cement (OPC), blast-furnace slag-type B cement (BBC), and high early strength Portland cement (HPC) according to JIS R 5210 [42] and JIS R 5211 [43]. Fine (S) and coarse (G) aggregates of crushed porphyry were used. Expansive agents of the ettringite type were used. To meet the required workability and improve the performance of fresh concrete even under cold weather conditions, chemical agents were utilized, including superplasticizers (SF500U and type-I VP700) and AE water-reducing agents (EX60 and SV10L) (AD). To mix the cement components, tap water was used. The 13 mix compositions and fresh concrete properties are listed in Table 1.

2.3 Specimen preparation

Thirteen concrete mixes were investigated to monitor m, kTm, and carbonation depth. A manufacturer produced ready-mixed concretes for mixes HPC41 and BBC53E. The remaining concrete mixtures were prepared in the laboratory with the use of a pan-type mixer. Prior to casting, the slump (or slump flow), and air content of fresh concrete were measured. The prismatic specimens were then cast, as shown in Fig. 1. The dimensions of the six large prismatic specimens (mixes HPC41 and BBC53E) were 600 × 900 × 600 mm (see Fig. 1a). Those of the two small prismatic specimens (mixes OPC65 and OPC75) were 400 × 100 × 100 mm (see Fig. 1c), and those of the 17 medium prismatic specimens (for the remaining mixes) were 800 × 300 × 200 mm (see Fig. 1b).

Fig. 1
figure 1

Overview of prismatic specimens (mm): a 600 × 900 × 600 specimens, b 800 × 300 × 200 specimens, and c 400 × 100 × 100 specimens

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The specimens were kept in the moulds for the periods indicated in Table 1 (i.e., 1, 3, 5, 7, and 28 days) to create 25 different concrete qualities, protecting the exposed surface from evaporation and stored in a room at ~ 20.7 °C. Then, specimens were demoulded and exposed to air as follows. The six large prismatic specimens (Fig. 1a) and the two small prismatic specimens (Fig. 1c) were exposed without sealing, whereas the 17 medium prismatic specimens were sealed using aluminium foil with two 800 × 300 mm surfaces left exposed (Fig. 1b). The two small prismatic specimens were stored in a controlled room at 20 °C /60% RH, whilst the other specimens were stored in a normal room at 21.2 °C /62.1% RH on average. Carbon dioxide concentration was around 0.04%, as recorded by the ZG106 CO2 monitor. Four test locations were selected on each measurement surface, avoiding large bubbles and visible cracks to limit their effects on the results.

2.4 Test methods

At each measurement age, the tests (surface moisture content, air permeability, and carbonation) were directly conducted on the given surfaces, i.e., vertical surfaces of the large, medium, and small specimens with the dimensions of 900 × 600 mm, 800 × 300 mm, and 400 × 100 mm, respectively.

2.4.1 Surface moisture measurement

The moisture content of the specimens m was monitored throughout the experiment. An impedance-based CMEXpert II Concrete Encounter Moisture Meter (Tramex, Ireland) was employed in compliance with the American Society for Testing and Materials (ASTM) standard F2659 [44]. The device works by sending a low-frequency signal through parallel co-planar electrodes into the concrete. Its suitability for monitoring changes in the surface moisture content of concrete specimens has been verified in previous investigations, despite the fact that it offers indirect readings [32, 38, 45]. The specimens were measured at the ages of 1, 3, 6, 12, and 18 months later. The arithmetic means of the surface moisture content values measured on four test locations are reported.

2.4.2 Air-permeability measurements

The kTm was assessed by utilizing a Torrent tester, PermeaTORR AC (Active cell) in accordance with the Swiss standard SN 505 262/1:2013 [15, 20]. The tester uses a double chamber cell to create a unidirectional airflow toward the central chamber so that kTm can be calculated using a suitable model [15, 46]. After the surface moisture measurement, the Torrent tests were conducted at 1, 3, 6, 12, and 18 months. The geometric mean of the values obtained at four test locations was utilized to compute the kTm values.

2.4.3 Carbonation depth measurements

After the surface moisture and air permeability measurements, five cores (30 mm, length 50 mm) were drilled at 12 and 18 months for the large and medium specimens and split. The small prismatic specimens were split at 6 and 12 months. Detailed measured carbonation depths of the specimens are provided in Appendix 1. The carbonation depth was measured by spraying the split surface with 1% phenolphthalein indicator solution. The averages of five and ten measured points of the split surfaces were calculated to evaluate the concrete carbonation progress (the carbonation rate was computed as the carbonation depth divided by the square root of the exposure time, averaging the values obtained at both ages).

3 Results and discussion

3.1 Assessing concrete carbonation resistance via kT m index

Correlations between the carbonation rate and kTm—the latter measured at the ages of 1, 3, 6, 12, and 18 months- are presented in Fig. 2 (dashed lines). Regardless of the cement type, for each measurement age, the plots indicate a single correlation between carbonation rate and kTm, for the 25 concrete specimens, which agrees with and expands the findings of previous studies [22, 47, 48]. The resulting high coefficients of determination (R2 ≥ 0.797) validated the regressions obtained by fitting power lines. However, the results indicated that the correlation is dependent on the age at which kTm was measured and the resulting moisture conditions. As shown in Fig. 2, the coefficient of determination gradually increases with the age of the kTm (from 0.797 to 0.916). A single estimated red line covering all data with high correlation could not be obtained (R2 = 0.753). It means that kTm can be proposed as a promising durability index for predicting the carbonation progress of different concrete types, when the measurement age could be selected, in particular, when later measurement age was selected.

Fig. 2
figure 2

Correlation between kTm and carbonation rate at the ages of 1, 3, 6, 12, and 18 months

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Figure 3 shows the significant changes in kTm with surface moisture m for the 25 concrete specimens investigated. A monotonic increase in kTm for lower m (drier concrete) can be observed for each mix. In other words, the moisture conditions of the specimens (i.e., the surface moisture content of the specimens) play a vital role in obtaining representative measurements of the air-permeability coefficient. Even though the short-age correlations in Fig. 2 are acceptable [20, 40], later age measurements of kTm yield better coefficients of determination. In particular, the kTm values at 18 months are considered highly representative measurements for predicting the carbonation progress.

Fig. 3
figure 3

Correlation between kTm and m

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Nevertheless, a sufficient drying stage strongly depends on the surrounding conditions during the exposure period for in situ measurements. Even under laboratory conditions, a late-age measurement (e.g., at 18 months) requires a prolonged waiting time for representative measurements, which is not practical. Thus, concrete structures' changing surface moisture content is the main barrier preventing the above approach for assessing concrete carbonation resistance through kTm. To address this issue and provide a flexible approach for predicting the concrete carbonation resistance, a new approach utilizing kT5 was presented in the next section.

3.2 Predicting concrete carbonation resistance based on the kT 5 index

This section proposes a flexible and practical approach for predicting the concrete carbonation resistance using the kT5 index. Herein, kT5 is the air-permeability value corresponding to a moisture m = 5.0% [38], computed as,

$${kT}_{5}={F}_{5}\times {kT}_{m}$$
(2)

where \({F}_{5}\) is a compensation factor for the value of kTm measured at moisture m, and is computed as follows,

$$F_{5} = e^{{1.45 \left( {m - 5.0} \right)}} \quad {\text{valid}}\;{\text{for}}\;1.0\% \; \le m \le 6.0\%$$
(3)

Equations (2) and (3) were derived from the analysis of the variation of kT with m during the drying of 50 concrete mixes which originated from five different sources [38]. Ideally, for a particular concrete and m ranging between 1 to 6%, the kT5 value is expected to compensate the effect of m on kTm and remain unchanged [38]. To clarify this idea, in this study, the kT5 values at 1, 3, 6, 12, and 18 months were calculated based on Eqs. (2) and (3), and correlations with the carbonation rate were established. Figure 4 shows the correlations between the carbonation rate and kT5 calculated from kTm and m at the ages of 1, 3, 6, 12, and 18 months. Two aspects are worth mentioning in Fig. 4. First, for each measurement age, especially for early measurement ages from 1 to 6 months, the scatter of the kT5 values is smaller compared with that of the kTm values shown in Fig. 3. This supports the use of the former as a valid indicator of the air-permeability of the mix. Second, regardless of the measurement age, a single line (solid red line) giving unique correlations with high coefficients of determination (R2 = 0.856) can be established between the carbonation rate and kT5 for all concretes. This means that the results in Fig. 4 indicate the differences between the regression dashed lines (carbonation rate and kT5) obtained for each testing age, and the overall red solid line, are insignificant. Additionally, the values for three binders follow reasonably well the general trend and, therefore, are not differentiated.

Fig. 4
figure 4

Correlation between carbonation rate and kT5 calculated from kTm and m

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To find out the most appropriate measurement procedure for accessing carbonation resistance utilizing the kT5 index, correlations between carbonation rate and kT5 calculated from different accumulated ages were established and discussed. In detail, correlations between carbonation rate and kT5 calculated from double and triple measurements were then established, as presented in Figs. 5a and b, respectively. The procedure to calculate kT5 from single, double, triple, and accumulated measurement ages was presented in Appendix 2. The result indicates that the strongest correlation was found in the case of kT5 calculated at all accumulated ages rather than other measurement cases. The obtained R2 value of 0.914 for all accumulated ages (1 + 3 + 6 + 12 + 18 months) was higher than those from single (Fig. 4), double (Fig. 5a), and triple (Fig. 5b) measurements. Outcomes suggested that the adopted approach was the most appropriate for accessing carbonation resistance under a standard environmental condition (~ 20 °C and ~ 60%RH). Based on the found correlation, concrete carbonation resistance can be assessed by utilizing the kT5 index, as shown in Eq. (4).

$${K}_{c}= 4.27{{ kT}}_{5}^{0.77}$$
(4)

where Kc denotes carbonation rate, (mm/\(\sqrt{month}\)), obtained from concrete specimens with OPC, BBC, or HPC around 20 °C /60%RH /0.04%CO2, kT5 is the air-permeability value, (10–16 m2), corresponding to a moisture m = 5.0%, and is calculated from kTm and m via Eqs. (2) and (3).

Fig. 5
figure 5

Correlations between carbonation rate and kT5 calculated from: a double and b triple measurements and all measurements at the five ages

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For a detailed comparison of kTm and kT5 for predicting concrete carbonation resistance, their accuracies were further evaluated using additional analytical indices: mean, standard deviation (SDs), and coefficient of variation (CoV) of the ratio of the predicted carbonation rate to the measured carbonation rate (see Table. 2). Here, the carbonation rates were predicted by using kTm in the equation for all the data (\({K}_{c}= 1.16{{ kT}}_{{m}}^{0.29}\)) in Fig. 2 or kT5 in Eq. (4). As expected, the mean, SDs, and CoV indices were improved significantly from 1.076, 0.427, and 39.7% for kTm to 1.028, 0.230, and 22.3% for kT5, respectively. The results verified the higher accuracy of the kT5 index for predicting concrete carbonation resistance. Furthermore, the results indicated that variations in the analytical indices using kT5 predicted from multiple measurement times (geomean) were slightly reduced compared to those from a single measurement. These imply that the measured coefficient of air-permeability, kTm, can be used to obtain the moisture-compensated air-permeability indicator, kT5, for accurately predicting the carbonation resistance of concrete. They also indicate that multiple measurements can further improve accuracy.

Table 2 Ratio of predicted to measured carbonation rates for different kT indicators
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On the basis of the obtained results, a novel approach for predicting concrete carbonation resistance using kT5 as an indicator can be formulated as described below.

The proposed procedure used to predict the carbonation rate consists of the following steps:

  1. 1.

    Define concrete lots following, for instance, the recommendations of [20].

  2. 2.

    Measure the kTm values and the surface moisture m on at least six random test locations of each lot, at an age that ranged from 1 and 18 months, preferably between 1 and 6 months. Multiple measurements can be conducted at two or more different ages for improved prediction.

  3. 3.

    For each single age measurement, kT5 value is calculated from the geometric mean of kTm and average moisture m, calculated from single measurement age, applying Eqs. (2) and (3). For multiple measurements, kT5 value is calculated from the geometric mean value of kT5 at several measurement ages, as presented in Appendix 2.

  4. 4.

    Calculate the predicted carbonation rate Kc by applying Eq. (4).

4 Conclusions

This study presented and validated the application of the Torrent method to measure the coefficient of air-permeability kTm, coupled with the parallel measurement of the surface moisture m for the assessment of the concrete carbonation resistance. Both non-destructive tests were applied on 25 concretes of various qualities, which were produced by using different cement types, W/B ratios, and curing periods to collect kTm and m values measured at the ages of 1, 3, 6, 12, and 18 months. At ages of 12 ± 6 months, the carbonation depth was measured, from which the carbonation rate of each mix could be computed based on the assumption of a “square-root law” of the carbonation process. The measured values of kTm increased whilst those of m decreased with age owing to the continuous exposure to a relatively dry environment. For each mix and age of test, a kT5 value –corresponding to a reference moisture content of 5.0%– was computed, which compensated for the effect of m on kTm. Strong correlations were found between the calculated kT5 and the corresponding carbonation rates. These correlations indicated the usability of kT5 as a good indicator for predicting the carbonation resistance of various concrete qualities, for which a simple procedure was proposed.

This study's findings contributed to the establishment of a simple and practical method for predicting carbonation resistance from the moisture-compensated index, kT5. In practice, the proposed Eq. (4) can be employed flexibly as a promising solution for predicting carbonation resistance of concrete structures produced by OPC, BBC, or HPC under a drying process at a standard condition (i.e., around at temperature/RH of 20 °C /60%). Given the limitation of this study, the approach is valid with three cement types at the standard condition. Thus, further investigations should be conducted with other binders, such as fly ash or limestone filler cement, to clarify the extended application of the proposed approach in the broader range. In addition, the effect of moisture state on carbonation progress under various environmental conditions will be another research topic in the future.