Evaluation of Methods to Correct the Effect of Temperature on Electrical Conductivity of Mortar

Nondestructive methods to obtain the electrical conductivity (σ) or resistivity (ρ) of concrete are gaining popularity for durability evaluation. However, these methods are susceptible to the effects of curing and conditioning, primarily temperature and degree of saturation. Before σ of concrete at varied temperatures can be used for durability assessment, appropriate corrections must be made to account for the effect of temperature (T). In this study, two existing and one new temperature correction methods were evaluated for 12 mortar mixtures varying in water-to-cementitious material ratio (w/cm) and the content and types of supplementary cementitious materials (SCM). Mortar specimens instrumented with embedded sensors were cured in sealed conditions for 11–13 months. After this period, the sealed specimens were subjected to stepwise temperature change in 5–50°C range while σ was recorded using the embedded sensors. Linear, bilinear, and Arrhenius temperature correction (LTC, BLTC, and ATC, respectively) were fitted to the obtained σ-Tdatasets and were evaluated for fitness. LTC provided an acceptable fit to the σ-T data (R> 0.81) but was found the most suitable in 5–30°C temperature range. BLTC was defined as a combination of two distinct LTC below and above the reference temperature at 23°C and had a better fit to the data (R > 0.96). Lastly, ATC showed the best fit among the tested methods (R > 0.98) and was found applicable for the full tested temperature range. Comparison of correction coefficients among the mixtures indicated that increase in w/cm results in less sensitivity of σ to temperature. Mixtures with SCM generally exhibit higher temperature sensitivity compared to the corresponding plain mixture. Since the variations in correction coefficients were not substantial (less 18% variation among 10 of 12 mixtures), a single value of activation energy of conduction (Ec) at 32 kJ/mol was identified as the general recommendation for all the tested mixtures.


Introduction
In recent years, nondestructive techniques for indirect assessment of concrete transport properties and durability by measuring electrical conductivity (σ) or resistivity (ρ) have gained popularity [1].
e measurements are taken by several available methods based on uniaxial or bulk resistivity, surface resistivity, electrical impedance spectroscopy, and noncontact resistivity measurements based on the transformer principle [1][2][3][4][5].Additionally, embedded sensors for real-time ρ monitoring were evaluated in past studies [6][7][8].Since electrical current in the concrete is primarily conducted through the pore solution in the pore system, electrical measurements can be used to indirectly evaluate pore system and transport properties of concrete [5,6,9,10].Relatively high ρ (low σ) is a characteristic of concrete with dense microstructure, low porosity, and poorly interconnected pores.
is type of microstructure hinders the ingress of water and ions that typically leads to durability-related distresses.In several research studies, σ or ρ were utilized to evaluate chloride diffusivity or permeability, which is a key input for service life predictions of reinforced concrete structures exposed to chlorides [7,[11][12][13].Due to simplicity, rapid nature, and nondestructive nature of the data collection, as well as availability of commercial apparatus, electrical methods are becoming more common in concrete durability evaluation [14,15].
Despite the convenience of these methods, data interpretation still requires more research as multiple factors, such as mixture design, temperature, and degree of saturation, have combined influences on the results [1,16].e synergistic effect of these factors should be taken into consideration when interpreting σ or ρ data in cementitious systems.e focus of this study is the effect of temperature and evaluation of existing correction methods.
Changes in temperature (T) induce changes in the ionic mobility, pore solution concentration, and ion-to-ion and ion-to-solids interactions in the pore solution, which result in changes in the overall conductivity of the concrete [14].Since accurate assessment of these effects is complex and difficult, the effect of temperature on σ is typically evaluated empirically.
e simplest type of σ-T dependency investigated in the literature is linear, typically defined through linear temperature correction (LTC) [8,[17][18][19]: where T ref is the reference temperature in °C, typically defined in a value in the 21-25 °C range, ρ ref and σ ref are the resistivity and conductivity at T ref , T c is the conditioning temperature in °C, and α is a linear correction coefficient (%/ °C).e recommended values of α range from 3 to 5% per 1 °C temperature increase [17][18][19].However, LTC was found effective only in a small temperature range (±5 °C of the reference temperature) [20].
In addition to LTC, the Arrhenius form equation was used in the literature for temperature correction (hereafter: ATC) [3,8,16,17,20,21]: where R is the universal gas constant (8.314J/molK) and E c is the activation energy of conduction in kJ/mol.Higher values of correction coefficients (α and E c for LTC and ATC, respectively) indicate higher temperature sensitivity of the mixture [17].Typical values of E c from the literature range from 12.54 to 42.47 kJ/mol and primarily depend on the degree of saturation, with sealed specimens presenting higher E c compared to the saturated ones [3,8,16,17,20,21].
Spragg et al. compared temperature correction of ρ for saturated concrete specimens measured by the uniaxial versus the surface resistivity method and found that surface resistivity method yields E c that are 7 to 15% higher than that by the uniaxial method [16].e identified difference in E c was attributed to the effects of leaching occurring on the surface of the specimen detected by surface resistivity meter [16].Weiss et al. evaluated the LTC and ATC methods for 13 concrete mixtures varying in water-to-cementitious materials ratio (w/cm) and binder type (Portland cement, binary, and ternary mixtures) for 5 < T c < 30 °C by uniaxial resistivity method [17].Saturated specimens were found to be less sensitive to temperature (smaller values of α and E c ) compared to their sealed counterparts, and both LTC and ATC were found satisfactory.However, due to higher temperature sensitivity of the sealed specimens, ATC was recommended as the reliable temperature correction method [17].
As reviewed above, the effectiveness of various temperature correction methods was evaluated in only one study.e suitability of current methods at higher temperatures (30-50 °C) which is representative of in-service conditions in hot climate areas is yet to be evaluated.Further, the effect of mixture parameters and SCMs on temperature sensitivity of mixes requires more investigation.e effectiveness of the correction methods for data collection methods other than uniaxial resistivity method deserves further research.Currently, the electrical characterization methods are mostly limited to laboratory conditions, whereas the appropriate durability characterization would require real-time in situ durability assessment.
is can be achieved by the use of embedded electrical sensors; however, appropriate corrections for environmental conditions have to be applied.So, this study puts forward a framework for temperature corrections of sensorbased σ, which is a necessary step for in situ durability evaluation.
In this study, sensor-based σ data are used from a variety of mortar mixtures over a wide temperature range from 5 to 50 °C to investigate the effectiveness of both the LTC and ATC methods.Temperature sensitivity of mixes containing varied w/cm and contents of ground granulated blast furnace slag (GGBFS), class F fly ash, and silica fume is investigated.Recommended values for the correction parameters of each method are developed based on the tested mixtures.

Materials and Mixtures.
e experimental matrix included 12 mortar mixture designs with proportioning listed in Table 1.Implemented aggregate was river sand with specific gravity 2.51 and fineness modulus 3.06.A reference mixture (control) was prepared with ordinary type I/II Portland cement, w/cm of 0.45, and aggregate-to-binder ratio of 1.95.e remaining 11 test mixtures had the same aggregate-to-binder ratio as the control but varied in water content and cementitious materials as follows: (i) W mixtures with varied w/cm at 0.35, 0.40, and 0.50 (ii) GGBFS mixtures with partial cement replacement by GGBFS at 20 and 40 percent by mass (GGBFS_20, GGBFS_40) (iii) Fly_ash mixtures with partial cement replacement by class F fly ash at 20, 40, and 60 percent by mass (Fly_ash_20, Fly_ash_40, Fly_ash_60) (iv) S_fume mixtures with partial cement replacement by class silica fume at 5, 10, and 15 percent by mass (S_fume_5, S_fume_10, S_fume_15) Chemical composition of cementitious materials used in the study is provided in Table 2. 1 were prepared following ASTM C305 [22].One Φ100 by 200 mm cylindrical specimen per mixture 2

Specimen Casting and Instrumentation. Mortar mixtures specified in Table
Advances in Civil Engineering was cast and kept in sealed conditions in a plastic mold for electrical conductivity measurements.Electrical conductivity was measured using one embedded time-domain re ectometry (TDR) sensor, Type 5TE from Meter Group [23].e 5TE sensor was used to measure T and electrical conductivity (σ) of the mortar.e sensor applies an electrical current to and measures the resistivity of the medium between the sensor probes.is type of sensor is currently used in soil applications for the assessment of soil salinity and water content.e authors demonstrated the application of the sensors in cement-based materials in earlier publications [6,7].In this study, one 5TE sensor was vertically embedded at middepth location of each cylinder specimen during casting.All sensors were connected to a CR1000 datalogger from Campbell Scienti c, and the sensor data were recorded in 5-minute intervals.Specimens were covered at the top with double plastic bags during the rst 24 hours.After this initial period, while the specimens were kept in their molds, the plastic bags were removed, and the tops were sealed using adhesive aluminum tape.Specimens were kept in the sealed condition in the laboratory with controlled ambient temperature at 21 °C for 11-13 months.

Temperature Regimes.
e specimens were placed in a temperature-controlled chamber and were subjected to stepwise temperature change, T c 's: 5, 10, 15, 23, 30, 40, and 50 °C.Each T c was kept constant for approximately ve days until the sensor-based measurements of T and σ exhibited minimal uctuations (standard deviation of T < 0.1 °C and standard deviation of σ < 0.005 dS/m).
e temperature regime based on the sensor in mix W0.35 is provided in Figure 1 as an example.

E ect of Temperature on Electrical Conductivity of Mix
Groups. Figure 2 presents the changes in σ as a function of T for all the tested mixtures.Each data point is the average of all of σ and T data during one T c step.As seen in Figure 2, σ increases as temperature is increased for all the tested mixtures.is trend is expected, since the increase in T is associated with increased mobility of ions in the pore solution, resulting in higher conductivity [14].At T c > 23 °C, σ increases at a faster rate with the same incremental increase in temperature (exponential T-σ trend.)erefore, T c 23 °C is used as the reference temperature in the following sections.
e e ect of mixture parameters can be identi ed based on the di erence in the values of σ among the di erent mixtures in Figure 2(a); mixtures with lower w/cm exhibit  lower values of σ, as an e ect of lower amount of pore solution in the pore system, as well as less connected (more tortuous) capillary pores [6,24,25].In Figures 2(b)-2(d), the use of SCM results in overall lower values of σ compared to the plain mixture and the more use of SCM results in lower values of conductivity.e trend is due to the products of SCM late pozzolanic reaction, which lls the capillary pores, making the pore system discontinuous and less conductive [6,26,27].At T c < 23 °C, σ data of GGBFS_40, Fly_ash_40, and Fly_ash_60 approach near-zero values.Since the accuracy of 5TE sensors is 0.01 dS/m, the absolute values of σ may not be reliable for these sensors.

Linear Temperature Correction (LTC)
. Linear temperature correction (equation 1) was applied to the experimental T-σ data shown in Figure 3. e e ective conductivity at T c 23 °C is marked as σ ref .
Figure 3 presents the σ/σ ref ratio at various T c based on the experimental data and the tted LTC for all the mixtures.e calibrated values of coe cient α were determined using the Solver function in Microsoft Excel, such that the sum of the squared di erences between the measured and corrected σ/σ ref is minimized.Table 3 shows the calibrated α values and high coe cients of determination (R 2 > 0.81) for the tted lines.However, for several mixtures, LTC results in negative σ values for T c 5 °C, which bears no physical meaning and should be assumed as zero.Also, the values of α obtained in this study are higher than those for concrete reported by Weiss et al., ranging from 1.87-3.37%/°C [17].e temperature range in [17] was 5-30 °C, compared to 5-50 °C in this study.e higher T c , results in a steeper exponential σ-T correlation, therefore LTC produces suboptimal t to the data.e

New Bilinear Temperature Correction (BLTC).
Based on the results in Figure 3, the rate of change in σ with T c is di erent above and below the reference temperature.erefore, a bilinear temperature correction (BLTC) model is proposed here, with two individual temperature coe cients (α 1 and α 2 ) for the ranges below and above T ref : Values of α 1 and α 2 for each mixture were determined using the Microsoft Excel Solver functions as described in Section 3.2.
e calibrated coe cients α 1 and α 2 , with the corresponding R 2 values for BLTC are listed in Table 4. e experimental data and the new model are plotted versus T c in Figure 4.As seen in Table 4, the new model provides a better t to the data compared  surpass the 1.87-3.37%/°C range due to higher T c used in this study [17].With a better t to the data, the new BLTC model presents a promising alternative to LTC for a wide range of temperature.

Arrhenius Temperature Correction (ATC).
Temperature correction based on E c , de ned earlier in equation 2 as ATC, was applied to the experimental σ-T data.Optimal values of E c for each mixture are provided in Table 5 with the corresponding R 2 .Figure 5 presents the experimental σ/σ ref data and the tted ATC model for all mixtures.As seen in Table 5, ATC provides a better t to the data compared to the LTC and BLTC methods (R 2 > 0.98).e   values of E c fall in the 23.4 to 42.47 kJ/mol range, which is reported for sealed concrete in the literature [3,8,17].

E ect of Mixture Design on Temperature
Sensitivity.e temperature sensitivity of σ measurements for each mixture can be inferred from the values of the correction coe cients (α and E c ), listed previously in Tables 3-5.Based on the obtained results, higher w/cm decreases the sensitivity of σ of the mix to temperature.is trend is consistent with ndings of Weiss et al., who reported lower temperature sensitivity of specimens at higher degree of saturation [17].It is possible that the diluted pore solution of mixtures with higher w/cm exhibits less increase in ionic mobility at elevated temperatures.Mixtures with SCM generally exhibit higher sensitivity to temperature correction compared to the control mix; the only exceptions are S_fume_5 and S_fume_10.It is likely that the di erences in temperature    6. e calibrated value of E c is 32 kJ/mol, and the t is satisfactory (R 2 0.97).

Conclusions
An experimental study was conducted with the primary objective to evaluate existing temperature correction methods for electrical conductivity (σ) of concrete.Twelve mortar mixtures were kept in stepwise temperature change in 5-50 °C range.ree methods of linear, bilinear, and Arrhenius temperature correction (LTC, BLTC, and ATC) were evaluated.Results revealed that LTC gives acceptable t to the experimental data only for the temperatures up to 30 °C.Bilinear temperature correction, with di erent coe cients below and above the reference temperature of 23 °C, presented a favorable alternative to linear correction.Lastly, ATC provided the best t among all methods over the full temperature range.Comparison of di erent mixtures indicated that increase in water-to-cementitious ratio yields lower temperature sensitivity.e implementation of supplementary cementitious materials generally increased the responsiveness of σ to the temperature change.As the values of temperature correction coe cients did not vary substantially among the tested mixtures, a single E c at 32 kJ/mol is recommended for all tested mixtures.Future research will include a wider range of mixture designs and evaluation of the established corrections for di erent electrical methods, such as axial and surface resistivity meters.

Figure 1 :
Figure 1: Stepwise temperature regime during the experiment obtained from the sensor at midlocation of mix W0.35.

Figure 3 :
Figure 3: Experimental and modeled σ/σ ref at various T c based on LTC (equation 1) for all mixtures.Vertical dashed line marks T ref 23 °C.

Figure 4 :
Figure 4: Experimental and modeled σ/σ ref at various T c 's based on bilinear temperature correction (equation 3) for all mixtures.Vertical dashed line corresponds to T ref 23 °C.

Figure 5 :
Figure 5: Experimental and modeled σ/σ ref at various T c based on ATC (equation 2) for all mixtures.Vertical dashed line corresponds to T ref 23 °C.

Figure 6 :
Figure 6: A single ATC for all tested mixtures based on E a,cond .

Table 1 :
Mortar constituents and their proportioning for the mixtures used in the study.

Table 2 :
Chemical composition of the cement and SCM based on manufacturer's mill cert.
* Fineness of y ash was 26.6 percent of retained on 45 μm (no.325) standard sieve.Blaine neness was not available.

Table 3 :
Calibrated values of coe cient α in LTC (equation 1) for all tested mixtures and values of R 2 .
2 are higher than the α 1 values, indicating higher temperature sensitivity when T c > T ref .Calibrated values of α 1 are within the range identi ed by Weiss et al.; however, values of α 2

Table 5 :
Optimized values of E c for all tested mixtures and the coe cient of determination (R 2 ). to the di erences in pore solution alkalinity and chemical composition.It is also noteworthy that Fly_ash_60 and GGBFS_40 have the highest values of E c due to low σ at T c 5 °C.e value of σ at this low temperature is close to the sensor's limit of sensitivity so if the two mixtures are removed from the data, the values of E c are within a relatively narrow range for all mixtures (maximum di erence among E c values is 18%).It is therefore bene cial to determine a single average value of E c for all mixtures as shown in Figure