Conductivity/activation energy relationships for cement-based materials undergoing cyclic thermal excursions

The concrete mixes used within the experimental programme are presented in Table 1. The cementitious materials comprised Portland cement (PC) clinker, CEM I 52.5N to EN197-1 [21]; CEM I cement blended with ground granulated blast-furnace slag (GGBS) to EN15167-1 [22]; and CEM I cement blended with a low-lime fly ash (FA) to EN450-1 [23]. The oxide analysis of the PC, FA and GGBS is presented in Table 2. Crushed granite aggregate, both coarse and fine, was used throughout together with a mid-range water reducer/plasticiser (SikaPlast 15RM) conforming to EN934-2 [24]. The PC and SCM’s were combined at the concrete mixer. The mixes in Table 1 are such that, when considered in terms of binder content, binder composition and strength class would satisfy the requirements specified in BS 8500-1 [25] to resist environmental exposure classes XF (exposure to freezing and thawing) for an intended working life of ‘both at least 50 years and at least 100 years’. However, when the water-binder (w/b) ratio is considered, only those concretes with w/b = 0.35 would satisfy all compositional requirements to resist XF exposure class. (Note: the binder is the mass of PC plus SCM, if present).

Samples were cast as 15 × 15 × 15 cm cubes with a total of three samples cast for each mix on Table 1 together with six, 10 × 10 × 10 cm cubes for compressive strength testing. Samples were submerged in a curing tank (20 ± 2 °C) until required; 28 and 180-day compressive strengths are presented in Table 1 and denoted, respectively, F ₂₈ and F ₁₈₀.

A pair of electrodes was positioned centrally within each 15 cm cube at the time of casting which ensured intimate contact between the electrodes and the surrounding concrete. Each electrode comprised a 0.2 cm diameter stainless steel rod (approximately 10 cm in length); the rod was sleeved with heat shrink insulation to expose a 1.5 cm tip with the centre-to-centre spacing between the electrodes being 2.5 cm; this spacing was adopted with due consideration being given to the maximum aggregate size, minimizing thermal gradients between the electrodes and reducing the influence of boundary effects at the cube surfaces (e.g. possible moisture loss). A thermistor was attached to one of the electrodes to allow the temperature to be recorded in the vicinity of electrical measurements. This is shown schematically in Fig. 1a. The electrical resistance of the concrete between the electrode pair was obtained employing a two-point technique using signal amplitude of 350 mV at a frequency of 1 kHz. This frequency was optimised from a priori experiments using multi-frequency measurements (impedance spectroscopy) to ensure electrode polarization effects were reduced to a minimum [26]. Specimens were contained in an environmental chamber with cabling from the cubes ducted out through a small porthole in the side of the chamber and connected to a multiplexing unit to log electrical resistance and temperature. Measurements were recorded every 5 min over the entire test period.

Electrical measurements are presented as conductivity (denoted, σ in Siemens/cm, S/cm). The bulk conductivity, σ, of a prismatic sample of length L (cm) and cross-sectional area A (cm²), is given by,where R is the measured resistance (in ohms). As the electrical field between the tips of the electrode pair embedded within a cube is non-uniform, the electrode array required calibration so that the measured resistance could be converted to conductivity. The geometrical parameter L/A in Eq. (1) was evaluated by obtaining the conductivity of the concrete specimens from a 4-point measurement technique using an Agilent 4263B LCR metre at a frequency of 1 kHz. In this method, the embedded electrodes within the 15 cm cubes served as the voltage (sensing) electrodes with externally applied stainless steel plates serving as the current (source) electrodes (see Fig. 1b). The concrete conductivity was obtained using the method presented in [27]. The slope of the plot of concrete conductivity obtained from the 4-point method against conductance (1/R in Siemens, S) measured across the electrode pair using the two-point method, obtains the calibration factor for the electrode pair. The data for all the concrete mixes on Table 1 are presented in Fig. 2a with the calibration factor being 0.223 cm⁻¹; x and y error bars represent one standard deviation and in those cases where the error bar appears missing, the data markers are larger than the error bar. This procedure was undertaken at 20 °C and prior to subjecting the cubes to temperature cycling. The measured resistance, R (in ohm, Ω) across the electrode pair was then converted to conductivity, σ (in S/cm), through the relationship,

On removal from the curing tank at approximately 12 months, the samples were surface dried and then tightly wrapped with several layers of cling film with all edges firmly sealed with duct tape. At this age, the change in conductivity due to hydration is reduced to a minimum [28]; furthermore, it is only at such longer time scales that the influence of the FA and GGBS on pore structure becomes evident. The cubes were placed in an environmental chamber at an initial temperature of 20 °C and taken through the following temperature regime:

Published rates for cooling (−) and heating (+) vary considerably ranging from ±1.2; +4.1/−3.3; ±10; ±11; ±15 °C/h [5, 6, 29‐31] to more rapid rates of ±24 °C/h [20] and ±88 °C/h [32] and ultra-rapid rates of ±120 °C/h [16] and ±230 °C/h [20]. The regime adopted was thus taken to represent a compromise.

For illustrative purposes, Fig. 2b presents the chamber temperature and the temperature recorded at the centre of a concrete cube (PC mix with w/b = 0.65). The results show that there is a thermal lag of approximately 1.5 h which increases marginally at the upper and lower temperature extremes. The mass of the concrete cubes was monitored over the duration of the testing programme and was found to decrease by ~0.05 %/cycle (by mass of specimen) indicating some moisture loss from the surface of the samples.

Figure 3a displays the Arrhenius response for the PC concrete mix (w/b = 0.35) presented over the entire temperature range (+70 to −30 °C) for the 7th and 28th cooling/heating cycles, with the direction of cooling/heating indicated. Regarding Fig. 3a, a linear relationship dominates the response for temperatures >~0 °C with the cooling and heating portions of the cycle being virtually coincident over an individual thermal cycle. This implies that the conduction process is reversible within this region. It is known that electrical conduction through saturated concrete occurs via ions in the continuous (percolated) aqueous phase between the electrodes [28]; since linearity exists over this portion of the thermal cycle, it implies that electrolytic conduction through the saturated pore network prevails within this region. It is also apparent from Fig. 3a that the conductivity of the concrete gradually decreases as the number of thermal cycles increases and results in a progressive downward displacement of the Arrhenius plot. This could, in part, be attributed to microstructural changes resulting from further hydration (being a thermally activated process [33, 34]); thermally induced changes in the existing hydration products which can occur above about 60 °C due to increased polymerization of the C–S–H gel phase [35] and possible shrinkage microcracking.

Considering the low-temperature end (<~0 °C) of a particular cycle as displayed in Fig. 3a, a change in gradient in the response is detected. The temperature at which this occurs depends on whether the sample is on the cooling (freezing) or heating (thawing) part of the thermal cycle. This has the effect of introducing hysteresis into the electrical conduction process in this region. Consider, for example, the cooling portion of the curve on the 7th cycle presented in Fig. 3a, where a change in gradient is detected at approximately −8.7 °C. The slope of the response over most of the temperature range (i.e. +70 → −8.7 °C) obtains an activation energy of, approximately, 22.6 kJ mol⁻¹; over the remainder of the cooling cycle (i.e. −8.7 → −30 °C) the activation energy is evaluated as 54.3 kJ mol⁻¹. It could be inferred that the freezing point of the pore water within the pore network occurs at approximately −8.7 °C. Freezing results in a decrease in the volume of conductive pore fluid which, in turn, decreases the conductivity at a faster rate than the effect of decreasing temperature alone. As ice forms within the pore network, ionic concentrations within the unfrozen pore water must gradually increase; this would, in turn, increase its conductivity. It is evident, however, that the conductivity of the concrete decreases by more than an order of magnitude over the freezing portion of the cycle so it can be inferred that the decrease in conductivity due to the formation of ice in the pore network dominates over any increase in conductivity of the pore water due to increasing ionic concentration which would tend to increase the conductivity of the concrete.

Figure 3a also indicates that the conductivity increases monotonically during the thawing portion of the thermal cycle with a change in gradient occurring at approximately −2.9 °C. The activation energy over the range −30 → −2.9 °C is 46.0 kJ mol⁻¹; at temperatures >−2.9 °C, the heating curve ‘joins’ the cooling curve and has the same activation energy to the cooling curve viz. 22.6 kJ mol⁻¹. The conductivity data in Fig. 3a also show that ice thaws at a higher temperature within the pore network than it forms; −2.9 °C in the case of the former and −8.7 °C for the latter. The hysteresis in conductivity could be explained by ‘ink-bottle’ effects whereby the pore network is regarded as comprising capillary cavities connected via finer capillary pore necks. During freezing, the phase transition in the pore network will be controlled by the radius of the constriction or pore neck as ice cannot intrude into larger capillary cavities until freezing is initiated in the pore neck whereas during thawing, ice in the pore neck will melt first.

Consider the freezing portion of the Arrhenius plot presented in Fig. 3b; if the decrease in conductivity was purely due to the decrease in temperature of the pore water without ice formation, then the Arrhenius plot would tend to follow the dashed line with an activation energy of 22.6 kJ mol⁻¹. In this Figure, σ _T represents the conductivity of the concrete at a given temperature, T, assuming no ice formed within the pore network and σ _T ,_ice represents the as-measured conductivity with ice formation. If, as a first approximation, it can be assumed that the conductivity of the concrete is proportional to the fractional volume of unfrozen pore water then the volumetric ratio of frozen pore water (commonly called the ice saturation ratio, S _c [3]) within the pore network could be estimated by the expression,

At a given temperature, the data in Fig. 3b indicate that the conductivity of the concrete is lower on the thawing portion of the cycle than it is on the freezing portion. Hence, from Eq. (4) above, more ice remains within the pore system on thawing than on freezing.

As the concrete undergoes thermal cycling, further changes in the Arrhenius plot are evident on the cooling, the temperature at which the gradient change, noted above, takes place decreases. On the 28th cycle, the gradient change on the cooling curve occurs at approximately −15.4 °C giving respective values over the temperature range +70 → −15.4 °C of 24.5 kJ mol⁻¹, and 53.0 kJ mol⁻¹ over the range −15.4 → −30 °C. Whilst the activation energy over the respective parts of the freezing curves presented in Fig. 3a remains relatively constant with thermal cycling, the freezing point depression of the pore fluid decreases from −8.7 °C on the 7th cycle to −15.4 °C on the 28th cycle. Considering the thawing portion of each cycle presented in Fig. 3a, the gradient change on the 28th cycle occurs at −2.9 °C remaining unchanged from the 7th cycle. The activation energy evaluated over the temperature range −30 → −2.9 °C on the 28th cycle is 41.3 kJ mol⁻¹ indicating a decrease with thermal cycling. The activation energy for conduction on the heating/cooling portions of each cycle over the temperature range +70 to −30 °C is summarised in Tables 3 and 4 for the PC concretes.

The Arrhenius format of presentation allows evaluation of both the undercooling where thawing occurs (denoted ΔT _t) and undercooling where freezing occurs (denoted ΔT _f). The ratio ΔT _t/ΔT _f is called the shape factor, λ, and is dependent on the radius of curvature of the ice–water meniscus during freezing and thawing [9, 36]. The shape factor provides information on the pore geometry but only if the freezing and thawing events occur in the same pore. A value λ = 1 is expected for spherical pores i.e. freezing and thawing occur at the same temperature whereas a value of λ = 0.5 occurs when ice melts in cylindrical pores [13, 34]. The shape factor will also be affected by the connectivity of the pores and generally falls in the range 0 < λ ≤ 1 [9]. Table 4 presents the shape parameter, λ, for the PC mix presented in Fig. 3 where it has been assumed that freezing/thawing of the bulk liquid occurs at 0 °C. It should be noted that ions in the pore water would reduce its freezing point below 0 °C. Considering the ionic concentration in the pore water (primarily Na⁺, K⁺, OH⁻), it is estimated that the freezing point would lie between 0 and −1 °C [37, 38]. For the purposes of this current study, a value of 0 °C is assumed. In all cases, λ < 0.5 indicating a more complex pore structure than a simple spherical or cylindrical pore model can explain and other shapes may be required to explain this discrepancy (e.g. ‘ink-bottle’ effects noted above).

Regarding the undercooling during freezing/thawing, the Gibbs–Thompson equation allows the phase transition temperature of liquids in pores to be calculated, viz,where, T _f,t is the phase transition temperature and the subscripts f and t refer to freezing or thawing, respectively (in Kelvin); T ₀ is the normal melting point of ice and assumed to be 273.15 K (0 °C), hence ΔT _f,t = T _f,t ; η is the heat of fusion of ice per unit mass; ρ is the density of water; γ is the ice/water interfacial tension at temperature T; dA/dV is the curvature of the solid–liquid interface which is 1/r for a cylindrical interface and 2/r for a spherical interface and r is the radius of the curvature. ΔT _f,t represents the depression or undercooling of the freezing/thawing point below the normal freezing/thawing point of ice. Based on the assumption that the ice–water interface adopts a spherical shape during freezing, the following expression for cement pastes has been presented to estimate the pore-neck radius, r _pn (in nm, see Fig. 4 adapted from [39]), from the measured undercooling in freezing, ΔT _f [9, 13, 14],

On the assumption that on thawing, ice melts from a cylindrical pore wall, the pore-cavity radius, r _pc (in nm, see Fig. 4) can be estimated from the undercooling in thawing, ΔT _t [13, 14],

Equations (6) and (7) also assume that an unfrozen layer of water of thickness 0.8 nm lines the pore walls [9, 13]. Using the data obtained for the PC concrete (w/b = 0.35) above, Table 4 presents the values for the radius of the pore neck and pore cavity evaluated from Eqs. (6) and (7). It must be stressed that these values represent, at best, an estimate as they must be considered with the inherent assumptions in Eqs. (6) and (7) and that the freezing point of bulk pore water is taken to be 0 °C.

Figure 5 presents the results for the PC concrete with w/b = 0.65 during the 7th and 28th cooling/heating cycles. Similar trends and features are observed, with the Arrhenius plot dominated by a linear response with the heating and cooling portions of the response being, as before, coincident, highlighting the reversible nature of the electrical conduction processes. Based on the linear portion of the response over the temperature range +70 ↔ ~0 °C in Fig. 5, the activation energy on the 7th and 28th cooling/heating cycles, respectively, is presented in Table 2. Increasing the water-binder ratio not only results in an increase in conductivity of the concrete, but also there is a corresponding decrease in activation energy for conduction processes although, as with the PC concrete with w/b = 0.35, the activation energy increases only marginally with thermal cycling. The undercooling on the freezing and thawing portions of each cycle estimated from Fig. 5 are summarised in Table 4, together with the pore radii based on Eqs. (6) and (7) above. The activation energy estimated from these plots over the range T _f → −30 °C for freezing, and −30 °C → T _t for thawing, is also presented in Table 4.

Figure 6 presents the Arrhenius plot for both the PC/GGBS concrete (Fig. 6a) and the PC/FA concrete (Fig. 6b) with w/b = 0.35. In terms of absolute values, the conductivity of the PC/FA concrete is almost an order of magnitude lower than the PC/GGBS concrete and would result from a more disconnected and tortuous pore network. As with the PC concretes, there is an overall downward displacement of the Arrhenius plot with continued thermal cycling regime. The decrease in conductivity with thermal cycling is significantly less in the SCM concretes as compared to the PC concrete. As noted above, the changes could be due, in part, to heat treatment effects on the already formed products of hydration and if the SCM concretes have less change, it may indicate that the hydration products are more stable. It is interesting to note that there are no discernible hysteresis effects or abrupt changes in slope at the low-temperature end of the plot with the cooling/heating curves displaying a linear response. Furthermore, the heating and cooling responses indicate that the electrical conduction process is reversible over the entire temperature range. The activation energy for these concrete mixes is presented in Table 3. Figure 6 would suggest that the pore sizes within the concrete are such that the freezing point of the pore water has been reduced to less than −30 °C and, from Eq. (6) above, this would imply a pore-neck radius <~3 nm. Consider, again, Fig. 4 which presents a schematic of the pore system; for ice to propagate from, say, left to right across the diagram, water must freeze in the pore neck before ice will form within the adjacent pore cavity. As ice formation will be controlled by the pore-neck size, these concretes must have a finer pore entry size than the equivalent PC concrete in Fig. 3 which displays hysteresis.

The activation energy over the thermal cycling regime for the PC/GGBS and PC/FA concretes (w/b = 0.35) is presented in Table 3. When compared to the PC concrete, the higher activation energy and lower conductivity for these concretes would reflect further refinement to the microstructure. Figure 7 presents the Arrhenius response for the PC/GGBS concrete (w/b = 0.65). Based on the portion of the response over the temperature range +70 ⟷ ~0 °C, the activation energy for each heating/cooling cycle is summarised in Table 3. It is observed that the activation energy on heating is lower than on cooling and indicates hysteresis effects now exist in this temperature range with the concrete being more conductive on heating than on cooling. The difference between the conductivity value obtained on the heating portion and the cooling portion of the cycle (at the same temperature) increases with thermal cycling. This is further discussed below. Unlike the PC/GGBS concrete with w/b = 0.35, Fig. 7 indicates that hysteresis effects are now present at the low-temperature end of the curves. This feature would be associated with microstructural differences in the pore network and the pore sizes are such that water can now freeze within them. Table 4 summarizes the activation energy and pore radii based using on the freezing and thawing point depression evaluated from Fig. 7. Again, it must be noted, Eqs. (6) and (7) have been developed on the assumptions that, upon cooling, the ice/water interface is assumed to be hemispherical, and on thawing, the interface is assumed to be cylindrical.

Figure 8 presents the Arrhenius plots for the fly ash concrete (w/b = 0.65). The activation energy is summarised in Table 4 for both the freezing and thawing portions of the response, together with the undercooling in freezing/thawing and estimated pore radii. The data presented in Table 4 indicate that the PC/GGBS and PC/FA concrete (w/b = 0.65) has a pore structure comprising large pore cavities linked by fine pore necks. The pore-neck size will have a controlling influence on ice formation and propagation and would account for the fly ash concrete having a much reduced conductivity in comparison to the PC and PC/GGBS concretes. As with the PC concretes, at temperatures <~0 °C, the conductivity of the PC/GGBS concrete and PC/FA (w/b = 0.65) is greater on the cooling portion of the response than the thawing portion indicating that more ice remains within the pore structure on thawing.

Closer examination of Figs. 7 and 8 shows that hysteresis effects are observed over virtually the entire heating/cooling temperature cycle i.e. +70 ⟷ −30 °C, particularly in the case of the PC/FA concrete. This exemplified in Fig. 9 which presents the response on the 28th cooling/heating cycle for both the PC/GGBS (Fig. 9a) and PC/FA (Fig. 9b) for w/b = 0.65. These Figures indicate that the conductivity on the heating portion of the cycle is greater than on the cooling. In addition, the difference between these two portions of the response increases with thermal cycling and represents a behaviour which does not manifest itself in the other concretes. The emergence of more noticeable hysteresis effects could possibly be attributed to internal microcracking due to the heating and cooling regime as visual examination of the external surfaces of the specimens did not show any signs of damage. In addition to potential damage caused by ice formation on freezing, expansion of pore water on heating will cause the pore pressure in small pores to temporarily increase until internal diffusion equilibrates the pressure [40] and could result in another source of damage. The degree of damage will thus be related to the rate of heating and pore size distribution as the thermal expansion of water is confined pore spaces is greater than that of bulk water [41]. More work is continuing on this aspect although it is interesting to note that a similar hysteresis effect was observed in a more limited study on cement mortar prisms undergoing ultra-rapid heating/cooling cycles [20].

With reference to Table 1, the compressive strength of the concretes increases with time due to continuing hydration and pozzolanic reaction. It is also evident from Table 1 that at longer time scales the difference in strength between the PC, PC/GGBS and PC/FA concrete mixes (at a given w/b ratio) reduces. As the strength of concrete is strongly correlated with its porosity [42‐45], this would indicate that the concretes attain a similar overall porosity. It has been observed that although concretes containing SCM’s are not of lower total porosity than PC concretes, they produce a more tortuous and disconnected capillary pore network [46, 47]. Table 3 presents the conductivity of the concrete mixes (denoted σ ₂₀), obtained prior to the start of the thermal cycling. It is apparent that the conductivity values for the different mixes in Table 1 can vary by a factor of between three and four (at a given w/b ratio). In addition, low conductivity correlates with high activation energy and vice versa although, as with strength, the variation in activation energy between mixes is not as marked as their respective conductivity value.

As noted in section “PC concretes” above, electrical conduction through concrete will be primarily via the continuous, interstitial aqueous phase between the electrodes, hence conductivity will be dependent upon the continuous porosity which will, in turn, be related the pore tortuosity and pore constriction. These features, ultimately, determine properties such as the diffusivity and permeability of the concrete which are of importance in relation to concrete durability and performance [1]. A conductivity measurement may thus be more discriminating than strength in identifying durable concrete mixes and the methodology could be developed as a durability test method.