2.1. Reference Methods

2.1.1. Direct or TEM

This procedure, which involves the use of two flat steel electrodes positioned in parallel at the ends of the concrete specimen to be assessed (as specified in the standard UNE-EN 12390-19 [16] and ASTM C1876 [46]), is illustrated in Figure 1(a). Resistivity is calculated (equation (1)) by measuring the alternating current-based electrical resistance (R_E) between the two electrodes and applying the cell factor k = S/L, where S is the cross-sectional area of the concrete specimen assessed (in cm²) and L is the interelectrode spacing (in cm). The specifications laid down in the respective standards are seldom applied. Rather, researchers prefer to use the most suitable setup for the purpose of their work, as is the case in the present study (Figure 2(a)). The literature describes a number of types of embedded and surface electrodes (stainless steel or copper plates, meshes or gauzes) [33].

As described in a previous paper [47], measurements prove to be reliable when the electrode area (S_E) is greater than or equal to S. That is not the case in real structures, where S_E < S, which would imply the need for prior calibration for different S/ S_E relationships. Therefore, this method is normally applied to standardised cylindrical/prismatic specimens or cores taken from existing structures devoid of reinforcement, thus ensuring S_E = S. In other words, onsite application of this technique is attendant upon destructive coring.

2.2. CSA

The method analysed in the present study, CSA, entails the use of a readily implemented embedded sensor consisting in just two electrodes: (i) a WE comprising a carbon steel element with a composition nearly the same as in the rebars; and (ii) a counter electrode (CE) consisting in the rebar itself in the area to be assessed in the respective structure. By incorporating a reference electrode into this setup, the corrosion rate can also be determined either by applying any of the more common techniques (such as LPR [42, 43]) or a novel technique that deploys potentiostatic pulses, described in detail in earlier papers [39, 44, 60, 61], so the description of the method in this section partly reproduces their wording. The sensor operating principle is illustrated in Figure 3, where a typical sensor configuration is shown as an example, that is a section of rebar acting as the WE and the rebars in the area of the structure involved surrounding the WE acting as CEs (CE = CE1 + CE2 + CE3 + CE4).

For a better understanding, a case study on the determination of the k cell factor for the CSA method is presented in Appendix A.

R_E−PSV measurement should be adopted in cases where the CSA is used with INESSCOM technology, for as the corrosion rate measurement is also based on the PSV technique, that option rules out any need to add further components to the electronic system. With the R_E−AC measurement, the CSA method can be adapted to any sensor system with a measuring cell similar to the one shown in Figure 3(a).

3.1. Concrete Specimens

Specimens were prepared with two types of concrete with similar water/cement ratios (0.56–0.57) but different types of cement to cover a sufficiently wide range of resistivity values. Concrete-1, prepared with blended limestone cement (CEM-II/B-L), was deployed to cover the low to medium resistivity range, while Concrete-2, prepared with slag-bearing blended cement (CEM-III/C), was used to cover the high resistivity range. Siliceous aggregates were used. The detailed composition of concrete mix designs is given in Table 2.

The specimen types prepared for the measuring methods described in Section 2 are illustrated in Figures 2 and 4. Prismatic 10 × 10 × 50 cm³ specimens were used for the methods TEM, FEM and RDM (Figures 2(a), 2(b), 2(c)), a 7.5 cm diameter, 15 cm high cylindrical specimen for the CCM (Figure 2(d)) and a 50 × 50 × 10 cm³ slab for the method to be validated, CSA (Figure 4). Three specimens were prepared with Concrete-1 and three with Concrete-2 for each method, with the exception of the method CSA, for which a single slab was manufactured with each concrete. The specimens so prepared were stored in a climatic chamber at 20 ± 2°C and 100% relative humidity for 24 h, after which they were demoulded and subjected to the different exposure conditions detailed in Section 3.2.

For the TEM, two square (8 × 8 cm²) stainless steel plates 6 mm thick were embedded in parallel and spaced at L = 40 cm (Figure 2(a)), a setup used previously by other authors [34, 63]. Here, S = 10 × 10 cm² = 100 cm², that is, the cross-section of the sample. In the FEM, the specimens were fitted with four 5.8 mm diameter, 2 cm long smooth stainless-steel bars embedded in the concrete and spaced at a = 3.5 cm (Figure 2(b)). In the RDM, an 8 mm diameter, 45 cm long corrugated stainless-steel bar was embedded at 5 cm from a 2 mm thick stainless-steel ring with an outer diameter of 2.45 cm and an inner diameter of 0.8 cm (Figure 2(c)). A pseudo-reference electrode made from a 1 mm diameter titanium wire activated with mixed-metal oxide (Ti-MMO) was positioned in the centre of the ring. In the CCM, the WE, an 8 mm diameter corrugated carbon steel bar embedded in the centre of the specimen, had a total S_WE of 25.13 cm², in as much as 10 cm of its length was exposed to the concrete. A stainless-steel mesh (0.14 mm wire diameter and 0.495 mm aperture) served as the CE, which was wrapped around the WE at a spacing of L = 2.1 cm (Figure 2(d)).

The slab used in the method CSA was fitted with two embedded rebars set at right angles and spaced at 5 cm from the respective sides of the specimen (Figure 4). The two rebars acted as separate and electrically insulated electrodes (CE1 and CE2) that could be interconnected via external wires to act jointly (CE=CE1 + CE2). As in both CE1 and CE2, the length exposed to the concrete came to 40 cm, S_CE1 = S_CE2 = 100.53 cm². The five WEs installed were prepared with a section of rebar with the same composition as the CE, here exposed to the concrete along a length of 4.5 cm, whereby S_WE = 11.31 cm². The concrete cover at the top and bottom of the slab was 4.1 cm thick, in both the CEs and the WEs. A type K thermocouple was cast at 5 cm from the exposed concrete surface of the slab to record the inner temperature of the concrete in an area of the slab where it would not interfere with the other measurements.

In the CSA, the WEs were installed strategically to ensure different spacing from CE1 (WE-CE1 = d₁) and CE2 (WE-CE2 = d₂). Specifically, d₁ = 5.5, 12.5, 19.5, 26.5 and 33.5 cm; and d₂ = 5, 13.5, 22, 30.5 and 39 cm. The aim was to validate the CSA over a very wide range of WE-CE distances, while also envisaging the three most representative WE-CE setups: parallel (cell WE-CE1), perpendicular (cell WE-CE2) and both parallel and perpendicular (cell WE-CE1+CE2) (Figure 4). In the third case, equations (3), (5)–(7) would have to be applied as described in Section 2.2 to determine the sensor’s equivalent working area (S_EQ), a parameter required to find the cell factor k (equation (2)). The findings for the cell WE-CE1+CE2 are given in Table 3. Where CE1 or CE2 were used separately (cells WE-C1 and WE-CE2), the S_EQ would be found by applying equation (3) directly, giving an S_EQ = 10.17 cm².

All the 8 mm diameter corrugated carbon steel rebars embedded in the specimens were sealed at both ends with epoxy resin and set inside a polymeric tube to delimit the exposed area and protect the electrical connection to the copper wire installed at one of the ends. An epoxy resin-coated copper wire was also installed in all the other embedded steel electrodes (plates, meshes and discs) for the measurement.

3.2. Measuring Procedure

Resistivity measurements were taken in these stages as described in Section 2.1. In stages 1 and 2, readings were generally recorded twice a week. In stage 3, they were taken in the last half-hour of each 12 h interval at a constant temperature, on the assumption that by that time the inner temperature in the concrete had reached the steady state. In stage 3, the temperatures were deemed to be as recorded from the thermocouple embedded in the concrete slabs (Figure 4) using a Fluke 87V multi-metre.

In the methods TEM, CCM and CSA, the interelectrode electrical resistance (R_E) needed to find resistivity (equation (1)) was determined on a Keysight Technologies U1733C handheld alternating current LCR metre operating with a sinusoidal wave of 1.05 V amplitude and 1 kHz frequency applied for 15 s. In the RDM, R_E was found with an interrupted current galvanostatic pulse described elsewhere [18, 64], applying a pulse between 1 μA and 200 μA, depending on the concrete resistance, and 50 milliseconds in duration. In the method CSA, the potentiostatic pulse procedure proposed in Figure 3(b) was applied as an innovative alternative to determine R_E.

In the FEM, R_E was obtained from the current and voltage recorded at the outer and inner electrodes (Figure 2(b)), respectively, when an excitation 24 V sinusoidal signal at 1 kHz was applied for 15 s to the outer electrodes from the authors’ self-made power source that used a Vemer VN313300 TMD 15/24 transformer. Current was recorded on Fluke 87 V and voltage on RS PRO IDM73-IV multi-metres. This methodology, implemented with the four-electrode system illustrated in Figure 2(b), was calibrated prior to embedment against a Proceq Resipod commercial instrument on prismatic specimens with the same geometry and composition as the ones described in Section 3.1. The widest deviation recorded for any single measurement was 9%, while the mean was < 4%, results consistent with those reported in the literature [62].

In the case of TEM, FEM, RDM and CCM methods, the corresponding cell factors described in Section 2.1 have been considered. In the case of the CSA, the measurement and analysis procedure has been carried out according to Section 2.2.

Polarisation resistance (R_P) was found from the slope on the linear region of the polarization curve resulting from applying a linear potential scan from open circuit potential (OCP) −0.02 V to OCP +0.02 V at a scan rate of 0.010 V/minute according to [66]. The OCP corresponds to the potential difference of WE1 with respect to the CE. The OCP used was the value found once the OCP stabilised (∂V/∂t ≤ 0.03 mV/s). The LPR technique was applied using a two-electrode cell configuration, where WE1 of the slab was used as the WE, and Rebar 1 (CE1) and Rebar 2 (CE2) were used together as the CE (Figure 4). As demonstrated in a previous study [42], this type of two-electrode cell provides reliable results when the CE area (S_CE) is approximately 20 times greater than the WE area (S_WE). This condition is closely met by the cell used in this study for the i_CORR measurement, where S_WE1 = 11.31 cm² and S_CE1+CE2 = 201.06 cm², resulting in S_CE1+CE2/S_WE1 = 17.8.

The galvanostatic and potentiostatic techniques used to obtain the R_E in the RDM and CSA methods, respectively, as well as the potentiodynamic technique applied to measure the R_P used to determine the i_CORR, were carried out using a Metrohm Autolab PGSTAT100 instrument, and the Nova 1.11 software was used for signal processing.

4.1. Potentiostatic Method for Determining Electrical Resistance

The reliability of the PSV method is discussed under this heading. Illustrated in Figure 3(b), PSV was deployed in the CSA to determine the concrete electrical resistance (R_E) value to be entered in equation (1) to find resistivity. Figure 5 compares the PSV-determined R_E (R_E−PSV) to the values found with the alternating current technique (R_E−AC) between each WE and CE (CE1 + CE2) in the measuring cell depicted in Figure 4 across the entire study period (stages 1, 2 and 3). As can be seen, Concrete-2 shows notably higher values than Concrete-1, which could be related to differences in porosity as a consequence of the type of cement used (Table 2). It is known that blast furnace slag cements, such as Portland cement type III used in Concrete-2, lead to the formation of denser microstructure within the cement paste matrix and therefore to a lower porosity [67], compared to the use of limestone cements [68], as is the case of Portland cement type II used in Concrete-1. In any case, the main objective of this section is to compare the two R_E measurement techniques. As shown in Figure 5, the findings for the two approaches were found to be very closely and linearly correlated (R² = 0.9958) when the two types of concrete (Concrete-1 and Concrete-2) were taken together, with no perceptible differences between the concretes in terms of the pattern observed in the linear correlation. A glance at the slope of the regression line shows that PSV yielded values about 0.6% higher than the alternating current technique. Given that practically negligible difference, the PSV technique was deemed to be wholly reliable for determining R_E in the CSA.

4.2. Reliability of Cell Factor Values

The reliability of the CSA cell factor k as defined in equation (2), needed to convert R_E into resistivity with equation (1), is studied under this heading. As discussed in detail in Section 2.3.1, the k value depends on certain measuring cell-related variables, including the spacing between the WE and CE, along with the equivalent working area of the sensor (S_EQ).

The measuring set up used in the slab depicted in Figure 4 was designed to provide a sufficiently wide range of WE-CE distances in three representative WE-CE setups (Table 3): parallel (WE-CE1), perpendicular (WE-CE2) and joint (WE-CE1 + CE2). The k values for the five WEs (with different WE-CE spacing) in the three cell types (WE-CE1, WE-CE2 and WE-CE1 + CE2) are listed in Table 4.

Figure 6 graphs the mean coefficient of variation (CoV) for the study period as a whole (stages 1, 2 and 3) when the aforementioned k values were applied to the R_E readings in the respective cells (Table 4). Each of the mean CoV values in Figure 6 was obtained as $$, where n is the number of measurements made over the three stages; in this case, n = 66, and CoV_i is the CoV obtained in each of these measurements for the five WEs (with different WE-CE spacing) in each cell type (WE-CE1, WE-CE2 and WE-CE1 + CE2), as well as considering as a whole the measurements with all cells (All). The CoVs for k·R_E, that is, resistivity (ρ), were observed to be lower than for R_E. As shown in Figure 7, which graphs the findings for one of the measurements, the R_E reading was linearly related and directly proportional to the WE-CE distance. That geometric relationship declined to negligibility, as intended, when the k factor was applied to resistivity calculations (ρ = k·R_E). That explains the lower CoV found for the ρ measurements in the cells (Figure 6).

Further analysis of Figure 6 revealed that when all the measurements were obtained for all the cells studied (All), the CoV was 23.3% for R_E and 14.6% for k·R_E in Concrete-1 and 18.3% for R_E and 8.1% for k·R_E in Concrete-2. The inference is that measurements varied less widely in the higher resistivity concrete (Concrete-2). Although the CoVs obtained in the cells were similar within each concrete type, k·R_E was observed to vary less in the parallel setup (WE-CE1), while the widest variation was found for the joint parallel and perpendicular setup (WE-CE1+CE2). In the latter case, in as much as cell type WE-CE1+CE2 entailed using a CE with more than one rebar, the sensor equivalent area (S_EQ) had to be found from a series of parameters related to the WE-CE distance (Table 3). That greater number of variables in resistivity calculations would explain the wider variation observed in WE-CE1+CE2 cell measurements.

As a rule, ρ exhibited narrower variability in all the cells (≈8%–18%) than R_E (≈16%–27%), confirming the normalisation capacity of the CSA cell factor k defined in equation (2). Since the measurements have been performed with different cells simulating the most typical in situ implementation configurations of the method, the variability found for resistivity could be reasonable.

4.3. Resistivity Comparison

The discussion in Sections 4.1 and 4.2 affords proof of the validity of the two main factors involved in CSA resistivity measurement, namely potentiostatic pulse-determined R_E and cell factor k. On those grounds, the CSA can be reliably compared to the reference procedures.

The correlation between ρ as computed with the CSA and the same parameter found with the reference methods across the entire study period is graphed in Figure 8(a). The regression analysis parameters obtained are given in Table 5. The entire set of measurements (stages 1, 2 and 3) are included in the analysis, covering a broad spectrum of resistivity values, that is, for the CSA values, between ≈5 and 2200 Ω·m, with the measurements of Concrete-1 lying between ≈5 and 150 Ω·m and those of Concrete-2 between ≈150 and 2200 Ω·m.

While the CSA measurements were closely and linearly related to all the references (R² = 0.9835–0.9965), the deviation found (as per the regression slope) exhibited significant differences. The RDM measurements were visibly the closest to the CSA values, with a mere 2.86% upward deviation in the latter. One meaningful similarity between the two procedures was the use of pulse-based techniques, potentiostatic in the CSA and galvanostatic in the RDM. In other words, both methods are based on direct current techniques that analyse the short-term transitory response in the steel-concrete system.

The deviation between the FEM resistivity measurements and the values found with the reference method for determining bulk resistivity, TEM (Figure 8(b)), [33, 46, 49], came to 147% and 62% in the case of considering k_{FEM_S−INF} or k_{FEM_FINIT} in the FEM, respectively. These figures are in line with the findings reported for these two techniques by other authors, such as Morris et al. [51], who observed a correction factor of 2.63 (163%); Gudimettla et al. [69] observed 1.91 (91%), and Ghosh et al. [49] observed ≈2.00–3.33 (≈100–233%). Such deviation might be the outcome of the known fact that the FEM measures surface resistivity [13, 48]. The deviation observed here in the FEM-CSA regression was as expected, for the CSA may be deemed to provide a measurement close to bulk resistivity in as much as it is taken with electrodes embedded in the specimen. Specifically, the CSA resistivity values were 20% lower than those recorded by the TEM. Compared to the CCM, the CSA tended to overestimate resistivity by 79%.

The inference to be drawn from the foregoing is the existence of considerable deviations among the resistivity measurements delivered by the reference methods themselves, depending on whether and to what extent such measurements address the two types of resistivity attributed to concrete. That in turn was the outcome of the type of study at issue: (i) bulk resistivity for laboratory studies of the properties of the cementitious matrix; or (ii) surface resistivity for onsite assessment of the reinforcement cover and therefore of corrosion risk. The CSA method proposed exhibited a close resemblance to the RDM, the reference procedure for onsite inspection of reinforcement cover resistivity. Although the FEM is also used in onsite measurements, the resistivity values found exhibited a substantial upward deviation relative to the CSA, especially if an appropriate geometric factor for finite elements is not used in the FEM. The TEM is the method of choice for laboratory studies, geared to studying the concrete matrix, although the CCM, for which no undue differences with the CSA were observed here, is also used in that context.

Despite the above discussion, it is worth noting the possibility that the deviations between methods could partially be affected by differences in the specimen size used for their implementation (Figure 2). This factor is known to influence the adsorption properties of the concrete samples [70, 71], so there might have been some differences in the internal moisture content of the samples (especially during Stages 2 and 3) and therefore some deviation in the resistivity by the different methods. A slight increase in the dispersion of values can be observed, starting at approximately 200 Ω·m, particularly in the FEM-TEM regression (Figure 8). This trend may be attributed to the greater dispersion of the electric field resulting from the lower conductivity of the medium [47], which would, to some extent, amplify the differences between methods, as has also been observed in the results reported by other authors [72].

Even so, the differences observed between methods may be deemed admissible, given the breadth of the resistivity ranges associated with corrosion risk of steel in concrete and the absence of any single criterion on the upper and lower values in each range [73]. For that reason, in practice, resistivity is assessed in conjunction with other parameters such as E_CORR and/or V_CORR, analysing its pattern over time for a more reliable assessment of the condition of concrete reinforcement. In this regard, it should be noted that a correlation between resistivity and these parameters, especially V_CORR, is only to be expected under reinforcement depassivation conditions [12]. These conditions were not present in this study. Although resistivity values below 100 Ω m—associated with a high corrosion risk according to the criterion in Table 1—were reached in the case of Concrete-1, corrosion activation of the reinforcement is not expected due to the absence of a depassivating agent (chloride ions and/or carbonation of concrete). This can be verified in Table 6, which presents the V_CORR values (expressed as current density, i_CORR, in μA/cm²) for WE1 of the slabs (Figure 4), along with the resistivity values obtained using the CSA method under the various humidity and temperature conditions considered in stage 3. The values shown in Table 6 are the averages of two determinations performed for each temperature, except for 5°C and 45ºC, where only one determination was conducted, and for 25°C, where three determinations were performed. In all cases, the i_CORR is clearly below the depassivation threshold of 0.1 μA/cm² established by the UNE 112072 standard [74] and the RILEM recommendation [75], including the most unfavourable case of Concrete-1 at 100% RH_ENV​ and a test temperature of 45°C, where, despite a resistivity of 17.8 Ω·m, indicating a high corrosion risk, the i_CORR obtained was 0.087 μA/cm².

4.4. Temperature Calibration

Resistivity is affected by different factors that are difficult to control in situ, such as temperature, humidity or the penetration of aggressive agents into the porous network. Among them, temperature is the reference parameter when establishing resistivity calibrations and normalisations [76–79], as it is an easily measurable parameter. The impact of temperature on CSA-measured resistivity was studied in stage 3 to define a temperature correction factor that might enhance the precision of the method, especially in the case of laboratory studies on material properties.

The resistivity measurements found with the method CSA at environmental exposure relative humidity (RH_ENV) of 47% or 100% are plotted against temperature in Figure 9, where resistivity is shown to decline exponentially with rising temperature. Whereas in Concrete-1, the ρ versus T relationship was affected by RH_ENV, with rises in relative humidity inducing declines in the ρ values (Figure 9(a)), and in Concrete-2, the ρ versus T curve was not significantly modified by RH_ENV (Figure 9(b)). The explanation would lie in the lower capillary porosity in Concrete-2 than in Concrete-1, which follows from the discussion provided in Section 4.1 about the R_E results shown in Figure 5. Therefore, the moisture content in the Concrete-1 pore structure, and therefore its resistivity, would be more susceptible to changes in environmental RH. Least squares-fitting of the experimental ρ versus T curves (Figure 9(a)) for Concrete-1 yielded the exponential functions shown in equation (10) (47% RH_ENV) and (11) (100% RH_ENV). The analogous expressions calculated for Concrete-2 (Figure 9(b)) are given as equations (12) and (13).

The correlation pattern differed slightly in Concretes-1 and -2, although no significant differences were observed between the values for 47% and 100% RH_ENV within a given concrete type. Hence, the three exponential models are envisaged in Figure 10: model 1 for Concrete-1, model 2 for Concrete-2 and model 3 for Concrete 1 + 2 measurements. The parameters found by least squares-fitting of the experimental ρ_T/ ρ₂₀ versus T curve (Figure 10(a)) as per the general expression given in equation (14) are listed in Table 8. While the correlation found was high in all three models, the lowest R² value found, as expected, was for model 3 (0.9368), where the dataset comprised all the measurements.

Figure 10(b) compares the ρ_T/ρ₂₀ versus T curves for models 1, 2 and 3 to the curves reported in the DuraCrete project [79] and the ones calculated by Liu and Presuel-Moreno [76] for specimens with ρ₂₁ = 50 Ω·m and 2000 Ω·m, determined from activation energy (J/mol). That parameter was found by applying one of two equations depending on the mix properties: for concretes containing ≥ 20% fly ash and > 50% slag (equation (4) in [76]) and for materials bearing < 20% fly ash and ≤ 50% slag (equation (5) in [76]). The curves obtained by Liu and Presuel-Moreno for the two calculation procedures proposed did not appear to deliver any significant differences for a given specimen. Models built for concretes with approximately the same resistivities yielded very similar results. In other words, model 1, which used Concrete-1 with a ρ₂₀ of 34.1 Ω·m to 45.8 Ω·m (Table 7), yielded curves closely resembling Liu et al.’s for a specimen with ρ₂₁ = 50 Ω·m, whereas the curve resulting from model 2, using Concrete-2 with ρ₂₀ = 749.9 Ω m to 786.3 Ω·m (Table 7), was similar to the Liu et al. curves for a specimen with ρ₂₁ = 2000 Ω·m. As model 3 was derived from measurements for both Concrete-1 and Concrete-2, the results followed an intermediate pattern. Two trends can be distinguished in the DuraCrete model. At temperatures > 20°C, the DuraCrete ρ_T / ρ₂₀ values were similar to the results for low resistivity concretes (model 1 and Liu et al. ρ₂₁ = 50 Ω m specimens), whereas at temperatures < 20°C, the DuraCrete ρ_T / ρ₂₀ values came close to the findings for high resistivity concretes (model 2 and Liu and Presuel-Moreno ρ₂₁ = 2000 Ω m specimens). The findings discussed in this paragraph confirm the reliability of the ρ_T / ρ₂₀ values used in the models (1, 2 and 3) built in this study.

The three aforementioned equations are proposed to calculate CSA-measured resistivity normalised to 20°C (ρ₂₀). The measured and normalised resistivity values found with equations (15)–(17) are compared in Figure 11. The most consistent normalisation was found for each concrete by applying the model built with the measurements taken with that material, as expected and as confirmed by the comparison of the CoVs graphed in Figure 12. The CoV for Concrete-1, at 33.3% (47% RH_ENV) and 34.2% (100% RH_ENV) prior to normalisation, declined to 5.3% and 3.6% after applying model 1. In Concrete-2, the CoV of 58.1% (47% RH_ENV) and 52.8% (100% RH_ENV) for non-normalised measurements dipped to 4.0% and 4.8% in model 2. Model 3 brought the CoV down to 10.1% and 13.7% for Concrete-1 and 13.3% and 11.9% for Concrete-2. As expected, model 3 normalised less effectively than models 1 and 2. Nonetheless, the error committed (CoV ≈ 10%–14%) in estimating the respective value would be admissible, given the wide range of resistivity values associated with the corrosion risk and the absence of a clear consensus on the upper and lower thresholds for each range [11, 12]. The lesser reliability of model 3 would in any event be offset by its applicability to any reinforced concrete member regardless of mix composition and the environmental exposure RH conditions to which it may be exposed.

It should be noted that the normalisation capability of the proposed models has been evaluated here by applying them on the values used for their construction. Consequently, further work is needed to address more comprehensive validations.

4.5. Proposal for Estimating Resistivity

The study discussed in this paper aimed to validate the proposal for measuring resistivity with the CSA method, both for monitoring existing structures in the field and characterising materials in the laboratory.

Further to the proof provided in Section 4.2, applying the k factor lowered the CoV associated with the use of different electrode setups in the CSA sensor from ≈16% to 26% for R_E to ≈ 8%–18% for R_E ·k. To avoid unnecessary complexity in S_EQ calculations, the WE should be set as close as possible to one of the rebars (the CE) at a sufficient distance D to ensure that the concrete fully covers the electrodes but, as previously stated in [44], at least six times that distance away from all the other rebars in the member. Wherever possible, the WE should be positioned parallel to the rebar acting as the CE, for i.e. the arrangement for which the CoV was observed to be lowest. In cases where the reinforcement arrangement prevents these conditions from being met when installing the sensor (e.g., in densely reinforced structures), all bars located at a distance from the WE ≤ 6⋅D will be considered in S_CE determination (equation (6)), where D is the shortest distance between the WE and the closest CE bar. If two or more CE bars are at the same distance from the WE, they will be considered as a single bar (CE-i), whose area (S_CE−i in equation (6)) is the sum of the areas of these bars.

In order to implement the proposed correction of the temperature effect, it is sufficient to incorporate a thermocouple to the CSA measurement cell, which is really simple and inexpensive. In fact, temperature recording is a common practice in structural health monitoring [29], thus facilitating the interpretation of the other monitored parameters. Of particular interest are material property studies that generally compare the performance of different concretes or dosages under standard conditions; being able to normalise resistivity measurements to the value at a temperature of 20°C using the factor proposed (equations (21) and (22)) constitutes a considerable advantage.