## 3 Results and Analysis
### Formulas  
The characteristic bond load and the average characteristic bond strength of specimens are shown in Table 5. The formulas for the average bond stress of the four factors were established by statistical regression analysis. They can be expressed as follows. \[\overline{\tau}_{s}=(\frac{-0.686C_{\text{ss}}}{d}+\frac{0.020L_{e}}{d}+2.506 \rho_{sv}+0.067)f_{t} \tag{15}\]  
\[\overline{\tau}_{u}=(\frac{-0.335C_{\text{ss}}}{d}+\frac{0.015L_{e}}{d}+0.718 \rho_{sv}+0.683)f_{t} \tag{16}\]  
\[\overline{\tau}_{r}=(\frac{-0.493C_{\text{ss}}}{d}+\frac{0.006L_{e}}{d}-0.842 \rho_{sv}+0.590)f_{t} \tag{17}\]  
where \(\overline{\tau}_{s}\) is average initial bond strength; \(\overline{\tau}_{u}\) is average ultimate bond strength; \(\overline{\tau}_{r}\) is average residual bond strength. In order to verify the reliability of the formulas, the comparison was performed between the calculation of the formulas and the experiment data from this test, as well as using data from [PERSON] et al. [35], [PERSON] et al. [24], and [PERSON] et al. [36]. The results are shown in Table 6.  
Table 6 indicates that the average ultimate bond strength and the average residual bond strength fit well, but the fitting result of the average initial bond strength has a certain error. One of the reasons for this error is the different values of initial load between the man-made and instrument methods. In addition, Equation (2) by [PERSON] et al. [34] for the tensile strength of RAC was used in this study, but the rest of the articles adopted ordinary concrete formulas. The tensile strength of RAC under the same compressive strength is higher than in this paper. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Initial Bond Strength**} & \multicolumn{3}{c}{**Limit Bond Strength**} & \multicolumn{3}{c}{**Residual Bond Strength**} & \multirow{2}{*}{**Calculated/Tested**} & \multicolumn{3}{c}{**Calculated/Tested**} \\ \cline{3-11}  & & **Calculated** & **Tested** & **Calculated** & **Tested** & **Calculated** & **Tested** & **Calculated** & **Tested** \\ \hline \multirow{4}{*}{Article} & SRRC-1 & 0.630 & 0.633 & 0.996 & 1.320 & 1.426 & 0.926 & 0.827 & 0.827 & 1.000 \\  & SRRC-2 & 0.600 & 0.710 & 0.845 & 1.344 & 1.629 & 0.825 & 0.892 & 0.972 & 0.918 \\  & SRRC-3 & 0.833 & 0.520 & 1.602 & 1.475 & 1.202 & 1.228 & 0.993 & 0.702 & 1.416 \\  & SRRC-4 & 0.497 & 1.288 & 0.386 & 1.311 & 1.684 & 0.779 & 0.751 & 0.977 & 0.769 \\  & SRRC-5 & 0.829 & 0.724 & 1.144 & 1.736 & 1.717 & 1.011 & 1.087 & 1.219 & 0.892 \\  & SRRC-6 & 0.507 & 0.617 & 0.822 & 1.063 & 1.268 & 0.838 & 0.665 & 0.732 & 0.909 \\  & SRRC-7 & 0.848 & 0.972 & 0.872 & 1.382 & 1.457 & 0.949 & 0.900 & 0.847 & 1.062 \\  & SRRC-8 & 1.065 & 1.140 & 0.934 & 1.444 & 1.472 & 0.981 & 0.973 & 1.097 & 0.887 \\  & SRRC-9 & 0.731 & 0.602 & 1.213 & 1.442 & 1.448 & 0.996 & 0.853 & 0.755 & 1.129 \\ \hline [PERSON] et al. & SRRAC-11 & 1.438 & 1.670 & 0.861 & 1.719 & 1.963 & 0.876 & 1.258 & 1.404 & 0.896 \\ [PERSON] et al. & SRAC-5 & 1.318 & 0.930 & 1.417 & 1.821 & 1.510 & 1.206 & 1.238 & 0.990 & 1.251 \\ \hline \multirow{2}{*}{[PERSON] et al.} & SRRC-34 & 0.860 & 0.501 & 1.717 & 1.213 & 0.905 & 1.340 & 0.801 & 0.412 & 1.944 \\  & SRRC-35 & 0.807 & 0.349 & 2.311 & 1.125 & 1.139 & 0.988 & 0.798 & 0.629 & 1.269 \\ \cline{1-1}  & SRRC-36 & 0.379 & 0.492 & 0.770 & 1.000 & 1.038 & 0.964 & 0.573 & 0.637 & 0.899 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of characteristic bond strength. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**No.