# Detecting Reinforced Concrete Rebars Using Ground Penetrating Radars
## 6 Conclusions  
This study focused on determining the rebar depth and size in reinforced concrete structures using Ground Penetrating Radar (GPR) data. The approach involved developing a theoretical equation for the two-wave travel time, based on the assumptions of positive peak reflection corresponding to the negative peaks of the transmitting wave and the shortest two-wave travel path. A biquadratic equation was adopted to approximate the rebar reflection curve obtained from the radargram, facilitating the determination of the peak coordinates of the hyperbola, which represent rebar spacing and depth. The rebar size was then determined by matching the theoretical equation with the rebar reflection curve. The study concluded the following:  
* Time zero can be accurately determined based on the negative peak of the transmitted signal in the air.
* The thickness of the concrete slab was a reliable indicator for determining the electromagnetic wave.
* The biquadratic equation proved to be an efficient method for fitting hyperbolas and estimating both the horizontal location and depth of the rebar.  
Figure 13: R\({}^{2}\) for specimen S2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Adjacent Rebar** & **Calculated Spacing (mm)** & **Difference (\%)** \\ \hline \#3–\#4 & 127 & 0.0 \\ \hline \#4–\#5 & 122 & 3.9 \\ \hline \#5–\#6 & 127 & 0.0 \\ \hline \#6–\#7 & 135 & 6.3 \\ \hline \#7–\#8 & 123 & 3.1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Rebar spacing for specimen S2.  
* The rebar size was successfully estimated with high accuracy using the proposed theoretical equation, provided the reflected hyperbola remained unaffected by adjacent embedded objects.
* The overlapping zone of the rebar reflections may not occur if the minimum spacing of the rebar is approximately 150 mm for rebars #3 to #8.  
Compared with existing methods in the literature, the proposed method efficiently processes signals and accurately and reliably determines rebar information.  
Conceptualization, W.Z.; Methodology, W.Z. and H.N. ([PERSON]); Software, H.N. ([PERSON]); Validation, W.Z., H.N. ([PERSON]) and H.N. ([PERSON]); Formal analysis, W.Z., H.N. ([PERSON]) and H.N. ([PERSON]); Investigation, W.Z.; Resources, W.Z.; Data curation, W.Z., H.N. ([PERSON]) and H.N. ([PERSON]); Writing--original draft, H.N. ([PERSON]); Writing--review & editing, W.Z. and H.N. ([PERSON]); Supervision, W.Z.; Project administration, W.Z.; Funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript.  
Not applicable.  
The data presented in this study are available on request from the corresponding author (due to restrictions from the funding agency).  
The authors wish to express their appreciation for the financial support provided by the West Virginia Department of Transportation (WVDOT) for the research project titled \"Corrosion Research to Maintain and Sustain Infrastructure in West Virginia.\" It is important to note that the findings, conclusions, or recommendations expressed in this study are those of the authors and do not necessarily reflect the viewpoints of the WVDOT. The author would like to extend sincere gratitude and appreciation to [PERSON], [PERSON], and [PERSON] for their assistance during the experimental and analytical tasks of this research project.  
The authors declare no conflict of interest.