# Detecting Reinforced Concrete Rebars Using Ground Penetrating Radars
## 5 Results and Discussion  
The radargram shown in Figure 8 visually represents the GPR scan conducted on slabs S1-1, S1-2, and S1-3. It reveals the presence of three rebars (#3, #5, and #7) through hyperbolic reflections. Figure 9 depicts the positive peaks of rebar reflections and theoretical hyperbolic curves for all rebars. Figure 10 showcases the R-squared values of the best-fitting curves corresponding to rebar diameter, ranging from zero with increments of 0.1 mm. Figure 8: Radargram of slab specimens S1-1, S1-2, and S1-3. (**a**) Radargram of Specim S1-1. (**b**) Radargram of Specim S1-2. (**c**) Radargram of Specim S1-3. Figure 7: Biquadratic approximation. Figure 9: Hyperbolas and best fit curves for rebars of slab specimens S1-1, S1-2 and S1-3. (**a**) Hyperbolas and best fit curves for rebars of Specim S1-1. (**b**) Hyperbolas and best fit curves for rebars of Specim S1-2. (**c**) Hyperbolas and best fit curves for rebars of Specim S1-3. Figure 10: R\({}^{2}\) for slab specimens S1-1, S1-2, and S1-3. **(a)** S1-1. **(b)** S1-2. **(c)** S1-3. The wave velocity of 133 mm/ns is determined from the reflection of the bottom of the 89 mm thick slab. With this known wave velocity, the depths of the rebars can be calculated by utilizing Equation (5). Subsequently, the rebar diameter is estimated by identifying the diameter corresponding to the maximum R-squared values in Figure 10. This analysis provides valuable insights into the composition and characteristics of the slabs, aiding in further understanding and decision-making  
The comparison of the rebar depth and diameter is detailed in Table 2. After examining the comparison of rebar diameters, the variations are typically under 10 percent. However, accurately estimating the #5 rebars in S1-1 and S1-3 slabs proves to be challenging due to the asymmetrical signal reflections, deviating from the typical hyperbolic pattern. This deviation is supported by evidence in Figures 8a,c and 8a,c. The reflections of the #5 rebars on the left side are notably impacted by adjacent surface void reflections, which affect the clarity of the #5 rebar's reflections. Despite this, the predicted rebar depth using the proposed approach closely aligns with the designed depths with high accuracy, typically less than 8 percent. The proposed method's reliability is demonstrated by comparing the determined spacing with the designed rebar spacing, as detailed in Table 3. The rebar spacings closely match the designed spacing, with minimal deviations of less than 6 percent. The variations in the calculated spacings point to actual spacings primarily influenced by uncontrolled factors, such as assembly and construction errors. These results strongly affirm the efficiency and reliability of the proposed method, especially when utilizing the biquadratic equation to determine the peak coordinates of the hyperbola. The radargram and hyperbolas of the rebars for the S2 slab specimen, subjected to a rigorous analysis, can be seen in Figures 11 and 12, respectively. It is evident that the hyperbolas partially overlap due to the small spacings between them. To address the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Slab**} & **Rebar No./Diameter** & **Designed Depth** & **Calculated** & **Diameter/Depth** \\  & **(mm)** & **(mm)** & **Diameter/Depth** & **Differences (\%)** \\ \hline \multirow{3}{*}{S1-1} & \#3/9.525 & 50.8 & 10/48 & 5.0/5.5 \\ \cline{2-5}  & \#5/15.875 & 50.8 & (-)/47 & (-)/7.5 \\ \cline{2-5}  & \#7/22.225 & 50.8 & 22.2/48 & 0.1/5.5 \\ \hline \multirow{3}{*}{S1-2} & \#3/9.525 & 50.8 & 10.4/49 & 9.2/3.5 \\ \cline{2-5}  & \#5/15.875 & 50.8 & 16/48 & 0.8/5.5 \\ \cline{2-5}  & \#7/22.225 & 50.8 & 22.2/49 & 0.1/3.5 \\ \hline \multirow{3}{*}{S1-3} & \#3/9.525 & 50.8 & 8.6/47 & 9.7/7.5 \\ \cline{2-5}  & \#5/15.875 & 50.8 & (-)/48 & (-)/5.5 \\ \cline{1-1} \cline{2-5}  & \#7/22.225 & 50.8 & 23.8/47 & 7.1/7.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rebar diameters and depths for S1-1, S1-2, and S1-3 slabs.