The findings of this study are reported in this section. By comparing experimental data to empirical data from Eq. 2, it was established that the new equation is more appropriate for FRC. All the fibers studied in this study showed excellent agreement between their experimental findings and those predicted by the equation. COV for each kind of fiber is also determined.
Influence of Fiber Volume Fraction and w/c Ratio on Electrical Resistivity of FRC
Fig. 1 depicts the ER vs w/c and Vf for all the FRC’s tested in this study. Fig. 1A–D displays ER (kΩ * cm) versus Vf (0.5–1.0% vol.) for NFRC, PFRC, SFRC, and GFRC, respectively, at the ages of 1, 3, 7, and 28 days. Fig. 1E–H displays ER versus w/c ratio (0.4–0.5) for NFRC, PFRC, SFRC, and GFRC, respectively, at the ages of 1, 3, 7, and 28 days. Fig. 1A shows adding Nylon fibers to concrete gives rise to ER up to the threshold limit of this investigation (1.0% vol.) at all ages because nylon fibers are non-conductive and absorb water. Therefore, high fiber volume fractions of nylon fiber reduce the water-to-cement ratio resulting in higher ER.
Fig. 1B shows that the ER of PFRC reduces when fibers are added up to the threshold limit of this investigation at all ages despite being a non-conductive fiber because polypropylene fibers have the lowest specific gravity. Therefore, more strands of polypropylene fibers were added to the mix than any other fiber type. Having so many strands of polypropylene fibers reduced concrete workability, reduced concrete homogeneity, increased void content, and decreased electrical resistivity (Tapkın, 2008; Wang et al., 2021). Fig. 1C depicts that the ER of SFRC decreases with adding fibers up to the threshold limit of this investigation at all ages which is a result of steel fibers being conductive and rigid. Therefore, the rigid non-conductive fibers caused fiber balling which reduced the workability of concrete, increased void content, and decreased the electrical resistivity. Fig. 1D reveals that the ER of GFRC remains almost constant with the addition of fibers up to the threshold limit of this investigation because glass fibers are non-conductive but reduced the workability of concrete. Therefore, adding high fiber volume fractions of non-conductive glass fibers increased electrical resistivity but adding high amounts of fibers caused fiber balling which reduced the workability of concrete and electrical resistivity. Fig. 1D–H depicts that the ER of all types of FRC in this investigation decreases with the increases in w/c because as the water content increases the cement content decreases and having a lower cement content results in lower electrical resistivity. Finally, due to the hydration process, the electrical resistivity of all test samples increased with age, disregarding Vf and w/c ratio.
Influence of Fiber Volume Fraction and w/c Ratio on Elastic Modulus of FRC
Fig. 2 depicts Ed versus w/c and Vf ratio for all kinds of FRC investigated in this study. The dynamic modulus was influenced by the properties of the fiber incorporated. This could be due to the increased porosity of concrete because of fiber incorporation (Banyhussan et al., 2019). Steel fibers had the best flexural and tensile strength followed by glass, polypropylene, and nylon fibers, respectively. Therefore, SFRC had the highest dynamic modulus followed by GFRC, PFRC, and NFRC, respectively, as shown in Fig. 2A–D at all ages. The impact of the w/c on the dynamic modulus of FRC is demonstrated in Fig. 2E–H. It is observed that despite fiber type or age, the dynamic modulus of FRC decreases with the decrease in w/c ratio because there is less cement in the mix. Again, lower elastic modulus has no effect on flexural and tensile strength of fibers because it is only useful in bridging micro-cracks (Banyhussan et al., 2019).
For GFRC with a w/c ratio of 0.4, values for the elastic modulus fluctuated at the early age. However, the variation in all other fiber types remained consistent during early age for concrete containing polypropylene, nylon, and steel, regardless of fiber volume fraction or water-to-cement ratio. The formation of micro-annuli around the FRC results in higher electrical modulus early in the curing process, which persists as curing progresses into the later stages due to the hydration reaction of cement paste (Appah & Reichetseder, 2001; Danjuschewskij & Ghofrani, 1991).
Relationship Between Electrical Resistivity and Elastic Modulus for PFRC
Fig. 3 depicts the relationship between PFRC’s dynamic modulus (Ed) and electrical resistivity (ER) at 3 and 7 days. The predicted ER was computed using the proposed Eq. 2 and adjustment coefficients for PFRC.
All the data points from mixes containing polypropylene fibers (M7–M11) were used to establish a good correlation between PFRC’s measured Ed and measured ER while considering Vf between 0.5 and 1.0% and w/c between 40 and 50%. The 3-day measured Ed and ER of PFRC range from 25 to 27 GPa and 3.3–6.2 kΩ * cm, respectively. The 7-day measured Ed and ER of PFRC range from 29 to 31 GPa and 4.5–8.6 kΩ * cm, respectively.
The COV was established to explain the discrepancy between Ed’s observed and anticipated values. At 45 degrees, the measured and projected values are perfectly correlated, allowing the Keynesian Cross or the 45-degree line to be used to determine the equilibrium value (Blinder, 2008). The data points above and below this 45-degree line show conservative and non-conservative deviations, respectively (Yuan, 2015). Fig. 4 contains three scatter plots comparing PFRC’s measured Ed (x-axis) to its predicted Ed (y-axis) in GPa at the ages of 3, 7, and 28 days. The calculated COV’s were lower at 3 and 7 days of age.
Relationship Between Electrical Resistivity and Elastic Modulus for NFRC
Fig. 5 depicts NFRC’s dynamic modulus (Ed) versus electrical resistivity (ER). The measured data points belong to all mixes containing nylon fibers (M2–M6) and the predicted data points were obtained using the adjustment coefficients for NFRC.
The 3-day measured Ed and ER of NFRC range from 23 to 29 GPa and 3.9–5.3 kΩ * cm, respectively. The 7-day measured Ed and ER of NFRC range from 25 to 31 GPa and 5.0–7.0 kΩ * cm, respectively.
NFRC’s measured Ed to its predicted Ed is presented in Fig. 6. The COV’s at 3 and 7 days show that the proposed Eq. 2 works correctly at these ages.
Relationship Between Electrical Resistivity and Elastic Modulus for SFRC
Fig. 7 shows SFRC’s dynamic modulus (Ed) versus electrical resistivity (ER). The measured data points are achieved from all mixes containing steel fibers (M12–M16) and the predicted data points were obtained using the adjustment coefficients for SFRC.
The 3-day measured Ed and ER of SFRC range from 31.5 to 33.1 GPa and 3.7–5.4 kΩ * cm, respectively. The 7-day measured Ed and ER of SFRC range from 33.5 to 37.0 GPa and 4.8–7.3 kΩ * cm, respectively.
SFRC’s measured Ed to predicted Ed is depicted in Fig. 8. The axis, units, ages, and significance of the 45-degree dotted line are consistent with those in Fig. 3. The COV is low between the ages of 3 and 7 days which indicates that the proposed equation is valid for early age SFRC.
Relationship Between Electrical Resistivity and Elastic Modulus for GFRC
Fig. 9 presents GFRC’s dynamic modulus (Ed) to its electrical resistivity (ER). However, the measured data points belong to all mixes containing glass fibers (M17–M21) and the predicted data points were obtained using the adjustment coefficients for GFRC.
The 3-day measured Ed and ER of GFRC range from 24.7 to 27.4 GPa and 2.8–4.1 kΩ * cm, respectively. The 7-day measured Ed and ER of GFRC range from 28.6 to 31.5 GPa and 4.3–5.8 kΩ * cm, respectively.
Fig. 10 compares GFRC’s measured Ed to its predicted Ed. Since the COV’s at ages 3 and 7 were low, the proposed equation is correct in its early stages.