# Dielectric Characterization of Chinese Standard Concrete for Compressive Strength Evaluation
## 5 Conclusions  
This paper presents the dielectric characterization of GB concrete, using three permittivity models. Namely, the first-order exponential model, the Debye model, and the Jonscher model were used to characterize the measured dielectric constants. The five common types of GB concrete, C30, C35, C40, C45, and C50, were fabricated in accordance with the Chinese standard JGJ55-2011, whereas their measured compressive strengths were analyzed against the water-to-cement ratio. The purpose of this study was to develop an innovative model for the correlation between the compressive strength and the dielectric constant of the standard GB concrete. The ultimate goal was to establish a model of dielectric constants for future SHM of concrete structures. The following remarkable findings can be drawn within the scope of this study:  
Figure 8: Compressive strength versus dielectric constant of GB concrete, (**a**) at various frequencies; (**b**) at 2.45 GHz with both the standard deviations from measurement.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(f\) (GHz) & \(r\) & \(A\) & \(R^{2}\) & \(SSE\) \\ \hline
0.50 & 1.943 & 25.99 & 0.9996 & 0.5606 \\
2.45 & 1.988 & 26.07 & 0.9996 & 0.5970 \\
5.0 & 1.997 & 26.12 & 0.9985 & 0.5931 \\
10 & 2.010 & 26.49 & 0.9997 & 0.4922 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Regression coefficients (with 95% confidence bounds) and goodness-of-fits for Equation (12).  
1. The measured dielectric constant of 28-day concrete is best regressed and predicted by using the [PERSON] model, rather than the other selected models, whereas the first-order exponential model and Debye model have a similar and equivalent performance.
2. The modeled dielectric constant of 28-day concrete decreases with increasing \(w/c\). The nonlinear variation can be described by using a double power-law function.
3. The compressive strength of 28-day concrete increases with an increasing average dielectric constant in a power-law function. This correlation model shows that the compressive strength of concrete will decrease, due to the reduction of the dielectric constant of concrete structures. For instance, cracks occurring inside the concrete structure.
4. The presented results will be very useful for the future design of concrete-embedded antennas [43; 44] and wireless power transfer to embedded sensors [45]. Nevertheless, further investigation into the imaginary part of complex permittivity, namely the loss factor of concrete, which has a different initial water content, is one of the immediate research works.  
The research is supported by the National Natural Science Foundation of China (Project No. 51678322 and 51650110509), and the Taishan Scholar Priority Discipline Talent Group program, funded by the Shan Dong Province.  
[PERSON], [PERSON] and [PERSON] initiated and designed the methodology; [PERSON] and [PERSON] performed the experiments; [PERSON] and [PERSON] analyzed the measurement data; [PERSON] and [PERSON] contributed reagents/materials/analysis tools; [PERSON], [PERSON] and [PERSON] drafted the paper; [PERSON] and [PERSON] revised the manuscript.  
The authors declare no conflict of interest.