Conductivity vs. Total Charge Correlations

Since there have been previous attempts to correlate specimen conductivity to the total charge passed, it will be useful to study this behavior using the data from this experiment. Figure 8 contains a plot of the measured conductivities σ_IS as a function of the total charge passed Q_T for the data in this experiment. When considering all the data for a given specimen length, the relationship is not linear over the entire range of Q _T values. The experiment of Zhao et al. [40] correlated total charge to specimen resistance, but only for specimens passing less than 4500 coulombs. Based upon the data shown in Fig. 8, one would expect a reasonable correlation between total charge passed and specimen conductivity for specimens passing fewer than 4500 coulombs. However, extrapolating a linear correlation for fewer than 4500 coulombs to specimens passing as much as 10,000 coulombs could prove to be erroneous.

Figure 8: Comparison between measured conductivity and predicted conductivity based upon the equation by Berke and Hicks [19].

The dashed curve in Fig. 8 represents the empirical prediction of Berke and Hicks (BH) [19] that was developed from correlations between measurements of total charge and conductivity measurements using a lollipop apparatus shown schematically in Fig. 9. The apparatus consists of a 9.5 mm diameter reinforcing bar embedded along the axis of a 76 mm diameter, 152 mm long concrete cylinder, with the reinforcing bar positioned 38 mm from the far end of the cylinder. The top 25 mm of the rod penetrating the cylinder is coated with epoxy. Since the BH equation was developed using 50 mm specimens, it should not be expected to predict the response of 100 mm specimens. Also, the equation was developed using data with few values of Q_T greater than 4000 Coulombs. for our experiment, the BH equation is a reasonably good predictor of the 50 mm data for Q_T less than 4000, but is a poor predictor for values of Q _T greater than 4000. This is to be expected, given the parameter space over which the equation was developed. However, there are two features worthy of note. Use of the equation for samples passing greater than 4000 Coulombs would introduce large errors. Also, the estimate is consistently greater than the conductivity values measured here. This artifact may be due to the longitudinal component of the current originating from the end of the reinforcement bar used in the Berke and Hicks experiment. This additional current would cause an overestimate of the specimen conductivity, as is demonstrated in Fig. 9.

Figure 9: Schematic cross section of lollipop apparatus used elsewhere [16, 18, 19] to measure specimen conductivity. Dimensions shown are in units of millimeters.