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

1. Introduction

In recent years, nondestructive techniques for indirect assessment of concrete transport properties and durability by measuring electrical conductivity ([sigma]) or resistivity ([rho]) have gained popularity [1]. The 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 [1-5]. Additionally, embedded sensors for real-time [rho] monitoring were evaluated in past studies [6-8]. 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 [rho] (low [sigma]) is a characteristic of concrete with dense microstructure, low porosity, and poorly interconnected pores. This type of microstructure hinders the ingress of water and ions that typically leads to durability-related distresses. In several research studies, [sigma] or [rho] were utilized to evaluate chloride diffusivity or permeability, which is a key input for service life predictions of reinforced concrete structures exposed to chlorides [7,11-13]. 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]. The synergistic effect of these factors should be taken into consideration when interpreting [sigma] or [rho] data in cementitious systems. The 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 a is typically evaluated empirically. The simplest type of [sigma]-T dependency investigated in the literature is linear, typically defined through linear temperature correction (LTC) [8,17-19]:

[sigma]/[[sigma].sub.ref] = [[rho].sub.ref]/[rho] = ([T.sub.c] - [T.sub.ref])[alpha]/100 + 1, (1)

where [T.sub.ref] is the reference temperature in [degrees]C, typically defined in a value in the 21-25[degrees]C range, [[rho].sub.ref] and [[sigma].sub.ref] are the resistivity and conductivity at [T.sub.ref], [T.sub.c] is the conditioning temperature in [degrees]C, and a is a linear correction coefficient (%/[degrees]C). The recommended values of a range from 3 to 5% per 1[degrees]C temperature increase [17-19]. However, LTC was found effective only in a small temperature range ([+ or -]5[degrees]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]:

[sigma]/[[sigma].sub.ref] = [[rho].sub.ref]/[rho] = exp [-[E.sub.c]/R (1/[T.sub.c] + 273 + 1/[T.sub.ref] + 273)], (2)

where R is the universal gas constant (8.314 J/molK) and [E.sub.c] is the activation energy of conduction in kJ/mol. Higher values of correction coefficients ([alpha] and [E.sub.c] for LTC and ATC, respectively) indicate higher temperature sensitivity of the mixture [17]. Typical values of [E.sub.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.sub.c] compared to the saturated ones [3, 8, 16, 17, 20, 21].

Spragg et al. compared temperature correction of [rho] for saturated concrete specimens measured by the uniaxial versus the surface resistivity method and found that surface resistivity method yields [E.sub.c] that are 7 to 15% higher than that by the uniaxial method [16]. The identified difference in [E.sub.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.sub.c] < 30[degrees]C by uniaxial resistivity method [17]. Saturated specimens were found to be less sensitive to temperature (smaller values of a and [E.sub.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. The suitability of current methods at higher temperatures (30-50[degrees]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. The 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. This 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 sensor-based [sigma], which is a necessary step for in situ durability evaluation.

In this study, sensor-based [sigma] data are used from a variety of mortar mixtures over a wide temperature range from 5 to 50[degrees]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.

2. Description of Experiment

2.1. Materials and Mixtures. The 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. The 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.

2.2. Specimen Casting and Instrumentation. Mortar mixtures specified in Table 1 were prepared following ASTM C305 [22]. One [PHI]100 by 200 mm cylindrical specimen per mixture was cast and kept in sealed conditions in a plastic mold for electrical conductivity measurements. Electrical conductivity was measured using one embedded time-domain reflectometry (TDR) sensor, Type 5TE from Meter Group [23]. The 5TE sensor was used to measure T and electrical conductivity ([sigma]) of the mortar. The sensor applies an electrical current to and measures the resistivity of the medium between the sensor probes. This type of sensor is currently used in soil applications for the assessment of soil salinity and water content. The 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 Scientific, and the sensor data were recorded in 5-minute intervals. Specimens were covered at the top with double plastic bags during the first 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[degrees]C for 11-13 months.

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

3. Results and Data Analysis

3.1. Effect of Temperature on Electrical Conductivity of Mix Groups. Figure 2 presents the changes in [sigma] as a function of T for all the tested mixtures. Each data point is the average of all of a and T data during one [T.sub.c] step. As seen in Figure 2, [sigma] increases as temperature is increased for all the tested mixtures. This 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.sub.c] > 23[degrees]C, a increases at a faster rate with the same incremental increase in temperature (exponential T-[sigma] trend.) Therefore, [T.sub.c] = 23[degrees]C is used as the reference temperature in the following sections.

The effect of mixture parameters can be identified based on the difference in the values of [sigma] among the different mixtures in Figure 2(a); mixtures with lower w/cm exhibit lower values of [sigma], as an effect 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 [sigma] compared to the plain mixture and the more use of SCM results in lower values of conductivity. The trend is due to the products of SCM late pozzolanic reaction, which fills the capillary pores, making the pore system discontinuous and less conductive [6, 26, 27]. At [T.sub.c] < 23[degrees]C, [sigma] 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 [sigma] may not be reliable for these sensors.

3.2. Linear Temperature Correction (LTC). Linear temperature correction (equation 1) was applied to the experimental T-[sigma] data shown in Figure 3. The effective conductivity at [T.sub.c] = 23[degrees]C is marked as [[sigma].sub.ref]. Figure 3 presents the [sigma]/[[sigma].sub.ref] ratio at various [T.sub.c] based on the experimental data and the fitted LTC for all the mixtures. The calibrated values of coefficient [alpha] were determined using the Solver function in Microsoft Excel, such that the sum of the squared differences between the measured and corrected [sigma]/[[sigma].sub.ref] is minimized. Table 3 shows the calibrated [alpha] values and high coefficients of determination ([R.sup.2] > 0.81) for the fitted lines. However, for several mixtures, LTC results in negative [sigma] values for [T.sub.c] = 5[degrees]C, which bears no physical meaning and should be assumed as zero. Also, the values of [alpha] obtained in this study are higher than those for concrete reported by Weiss et al., ranging from 1.87-3.37%/[degrees]C [17]. The temperature range in [17] was 5-30[degrees]C, compared to 5-50[degrees]C in this study. The higher [T.sub.c], results in a steeper exponential [sigma]-T correlation, therefore LTC produces suboptimal fit to the data. The temperature range of 5-30[degrees]C seems to be the optimum range for the LTC model. To address this limitation, different temperature corrections are evaluated in Sections 3.3. and 3.4.

3.3. New Bilinear Temperature Correction (BLTC). Based on the results in Figure 3, the rate of change in [sigma] with [T.sub.c] is different above and below the reference temperature. Therefore, a bilinear temperature correction (BLTC) model is proposed here, with two individual temperature coefficients ([[alpha].sub.1] and [[alpha].sub.2]) for the ranges below and above [T.sub.ref]:

[mathematical expression not reproducible]. (3)

Values of [[alpha].sub.1] and [[alpha].sub.2] for each mixture were determined using the Microsoft Excel Solver functions as described in Section 3.2. The calibrated coefficients [[alpha].sub.1] and [[alpha].sub.2], with the corresponding [R.sup.2] values for BLTC are listed in Table 4. The experimental data and the new model are plotted versus [T.sub.c] in Figure 4. As seen in Table 4, the new model provides a better fit to the data compared to the LTC (Table 3) ([R.sup.2] > 0.96.) The fitted values for the coefficients [[alpha].sub.2] are higher than the [[alpha].sub.1] values, indicating higher temperature sensitivity when [T.sub.c] > [T.sub.ref]. Calibrated values of [[alpha].sub.1] are within the range identified by Weiss et al.; however, values of [[alpha].sub.2] surpass the 1.87-3.37%/[degrees]C range due to higher [T.sub.c] used in this study [17]. With a better fit to the data, the new BLTC model presents a promising alternative to LTC for a wide range of temperature.

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

3.5. Effect of Mixture Design on Temperature Sensitivity. The temperature sensitivity of [sigma] measurements for each mixture can be inferred from the values of the correction coefficients ([alpha] and [E.sub.c]), listed previously in Tables 3-5. Based on the obtained results, higher w/cm decreases the sensitivity of [sigma] of the mix to temperature. This trend is consistent with findings 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 differences in temperature sensitivity are due to the differences in pore solution alkalinity and chemical composition. It is also noteworthy that Fly_ash_60 and GGBFS_40 have the highest values of [E.sub.c] due to low [sigma] at [T.sub.c] = 5[degrees]C. The value of [sigma] 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.sub.c] are within a relatively narrow range for all mixtures (maximum difference among [E.sub.c] values is 18%). It is therefore beneficial to determine a single average value of [E.sub.c] for all mixtures as shown in Figure 6. The calibrated value of [E.sub.c] is 32 kJ/mol, and the fit is satisfactory ([R.sup.2] = 0.97).

4. Conclusions

An experimental study was conducted with the primary objective to evaluate existing temperature correction methods for electrical conductivity ([sigma]) of concrete. Twelve mortar mixtures were kept in stepwise temperature change in 5-50[degrees]C range. Three methods of linear, bilinear, and Arrhenius temperature correction (LTC, BLTC, and ATC) were evaluated. Results revealed that LTC gives acceptable fit to the experimental data only for the temperatures up to 30[degrees]C. Bilinear temperature correction, with different coefficients below and above the reference temperature of 23[degrees]C, presented a favorable alternative to linear correction. Lastly, ATC provided the best fit among all methods over the full temperature range. Comparison of different mixtures indicated that increase in water-to-cementitious ratio yields lower temperature sensitivity. The implementation of supplementary cementitious materials generally increased the responsiveness of [sigma] to the temperature change. As the values of temperature correction coefficients did not vary substantially among the tested mixtures, a single [E.sub.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 different electrical methods, such as axial and surface resistivity meters.

Data Availability

The temperature-conductivity data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that there are no conflicts of interest.


Funding was provided by Portland Cement Association fellowship award. The authors acknowledge Meter Group for providing the instrumentation and technical support for this study. Premix Pullman is acknowledged for aggregate donation. Thanks to Ash Grove Cement Company for supplying cement, Lafarge for fly ash and slag, and BASF for silica fume.


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Milena Rangelov (1) and Somayeh Nassiri [ID] (2)

(1) Postdoctoral Fellow, Washington State University, 2001 East Grimes Way, PACCAR, Pullman, WA 99164-5815, USA

(2) Assistant Professor, Washington State University, 2001 East Grimes Way, 248 PACCAR, Pullman, WA 99164-5815, USA

Correspondence should be addressed to Somayeh Nassiri;

Received 26 September 2018; Accepted 22 November 2018; Published 13 December 2018

Academic Editor: Xu Yang

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

Caption: Figure 2: Changes in [sigma] with T for mixes varying in (a) w/cm, (b) GGBFS, (c) fly ash, and (d) silica fume.

Caption: Figure 3: Experimental and modeled [sigma]/[[sigma].sub.ref] at various [T.sub.c] based on LTC (equation 1) for all mixtures. Vertical dashed line marks [T.sub.ref] = 23[degrees]C.

Caption: Figure 4: Experimental and modeled [sigma]/[[sigma].sub.ref] at various [T.sub.c]'s based on bilinear temperature correction (equation 3) for all mixtures. Vertical dashed line corresponds to [T.sub.ref] = 23[degrees]C.

Caption: Figure 5: Experimental and modeled [sigma]/[[sigma].sub.ref] at various [T.sub.c] based on ATC (equation 2) for all mixtures. Vertical dashed line corresponds to [T.sub.ref] = 23[degrees]C.

Caption: Figure 6: A single ATC for all tested mixtures based on [E.sub.a,cond].
Table 1: Mortar constituents and their proportioning for the mixtures
used in the study.

                            Constituent content (kg/[m.sup.3])

Mixture group     Fine      type I/II   Class F   GGBFS   Silica    w/
                aggregate   Portland    fly ash            fume     cm

Control          1,291.0      662.8        0        0       0      0.45
W Mixes               W0.35, W0.40, and W0.50 with w/cm = 0.35, 0.40,
                                      and 0.50
GGBFS mixes               GGBFS_20 and 40 with GGBFS % = 20 and 40;
                                        w/cm = 0.45
Fly_ash mixes         Fly_ash_20, 40, 60 with fly ash % = 20, 40, and
                                        60; w/cm = 0.45
S_fume mixes           S_fume_5, 10, 15 with silica fume % = 5, 10,
                                     and 15; w/cm = 0.45

Table 2: Chemical composition of the cement and SCM based on
manufacturer's mill cert.
                         Type I/II   Class F
Chemical compound (%)     cement     fly ash   GGBFS   Silica fume

Si[O.sub.2]                21.3       56.50    32.00      92.86
[Al.sub.2][O.sub.3]        3.20       23.70    12.90   Not listed
[Fe.sub.2][O.sub.3]        2.90       3.60     0.50    Not listed
S[O.sub.3]                 3.10       0.20     3.70       0.33
CaO                        64.30      9.20     41.2    Not listed
MgO                        2.10       1.00     5.70    Not listed
[Na.sub.2]O                0.26       0.29     0.21       0.20
[K.sub.2]O                 0.42       0.22     0.41       0.70
Loss on ignition           1.35       0.62     1.40       3.33
Blaine fineness             391       NA *      480      21,910
Specific gravity           3.10       2.05     2.87       2.26

* Fineness of fly ash was 26.6 percent of retained on 45 [micro]m (no.
325) standard sieve. Blaine fineness was not available.

Table 3: Calibrated values of coefficient a in LTC (equation 1) for
all tested mixtures and values of [R.sup.2].

Mix. ID                    W0.35        W0.40        W0.45

[alpha] [%/[degrees]C]      6.06         6.15         5.35
[R.sup.2]                   0.85         0.87         0.89

Mix. ID                  Fly_ash_20   Fly_ash_40   Fly_ash_60

[alpha] [%/[degrees]C]      6.28         5.97         7.83
[R.sup.2]                   0.81         0.91         0.83

Mix. ID                    W0.50       GGBFS_20     GGBFS_40

[alpha] [%/[degrees]C]      5.16         5.72         6.29
[R.sup.2]                   0.88         0.85         0.90

Mix. ID                   S_fume_5    S_fume_10    S_fume_15

[alpha] [%/[degrees]C]      4.77         4.93         5.63
[R.sup.2]                   0.87         0.87         0.83

Table 4: Calibrated values [[sigma].sub.1] and [[sigma].sub.2] BLTC
(equation 3) for all tested mixtures and [R.sup.2] values.

Mix. ID              W0.35        W0.40        W0.45        W0.50

[[alpha].sub.1]       2.84         3.06         2.92         2.72
[[alpha].sub.2]       7.41         7.39         6.36         6.21
[R.sup.2]             0.97         0.98         0.98         0.98

Mix. ID            Fly_ash_20   Fly_ash_20   Fly_ash_60    S_fume_5

[[alpha].sub.1]       2.35         3.77         3.44         2.44
[[alpha].sub.2]       7.92         6.89         9.69         5.75
[R.sup.2]             0.98         0.97         0.97         0.98

Mix. ID             GGBFS_20     GGBFS_40

[[alpha].sub.1]       2.64         2.22
[[alpha].sub.2]       7.02         8.01
[R.sup.2]             0.98         0.97

Mix. ID            S_fume_10    S_fume_15

[[alpha].sub.1]       2.50         2.51
[[alpha].sub.2]       5.95         6.95
[R.sup.2]             0.98         0.96

Table 5: Optimized values of [E.sub.c] for all tested mixtures and the
coefficient of determination ([R.sup.2]).

Mix. ID                W0.35        W0.40        W0.45        W0.50

[E.sub.c] (kJ/mol)     33.40        33.17        30.26        29.80
[R.sup.2]               0.99         1.00         1.00         1.00

Mix. ID              Fly_ash_20   Fly_ash_40   Fly_ash_60    S_fume_5

[E.sub.c] (kJ/mol)     34.49        32.05        39.34        28.15
[R.sup.2]               0.99         0.99         0.99         0.99

Mix. ID               GGBFS_20     GGBFS_40

[E.sub.c] (kJ/mol)     32.18        35.26
[R.sup.2]               0.99         0.98

Mix. ID              S_fume_10    S_fume_15

[E.sub.c] (kJ/mol)     28.86        32.13
[R.sup.2]               0.99         0.98
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Title Annotation:Research Article
Author:Rangelov, Milena; Nassiri, Somayeh
Publication:Advances in Civil Engineering
Date:Jan 1, 2018
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