## 3 Results and Discussion
### The Constitutive Model of Bond-Slip between RBFC and Rebar  
Nowadays, there are many types of bond-slip constitutive models between rebar and concrete, which can be mathematically classified into segmented function and polynomial models. Since the polynomial models rely on large amounts of experimental data that can only be fitted by unique expressions, the training process requires a lot of computational power. In addition, the trends of the center pull-out tests of each stage are obvious where there are linear and non-linear sections. Therefore, the semi-empirical and semi-theoretical segmented function model can be used. Based on the discussion of the causes of the three damage forms in Section 3.1, the main damage form is pull-out damage. Therefore, this paper mainly focuses on fitting the constitutive model for the pull-out damage form of RBFC with rebar. Due to the lack of a complete bond-slip curve for rebar pull-off damage and the insufficient number of specimens for splitting damage, the parameters have a high degree of dispersion; therefore, these two damage forms are not fit. Based on the modification of the model proposed by [PERSON] [1], as shown in Figure 13, points A-D are the inflection points for each segment. \(\tau\) is the bond stress (MPa); \(s\) represents the slip at the free end (mm); \(a\) signifies the test parameter; \(\tau_{u}\) is the bond stress (MPa); \(\tau_{0}\) is the initial bond stress (MPa); \(\tau_{g}\) is the bond stress at the inflection point (MPa); \(\tau_{c}\) is the residual stress (MPa); \(s_{0}\) is the slip corresponding to the initial bond stress (mm); \(s_{g}\) represents the slip corresponding to the bond stress at the inflection point (mm); \(s_{u}\) represents the slip corresponding to the bond  
Figure 13: Bond stress–displacement relationship diagram. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & **Pearson’s Correlation Coefficients** & & & \\ \hline Value & 0.8–1.0 & 0.6–0.8 & 0.4–0.6 & 0.2–0.4 & 0–0.2 \\ Correlation & extremely strong & strong & moderate & weak & extremely weak \\ \hline \end{tabular}
\end{table} 
Table 8: Classification criteria of relevance. stress (mm)); and \(s_{c}\) represents the slip corresponding to the turning point between the descending section and the residual section (mm). From Figure 13, it can be seen that the proposed bond stress-displacement model has four important characteristic points, which divide the whole model into five stages. The first stage is the micro-slip section (OA section), in which the chemical bond between the rebar and the concrete, as well as some of the friction forces, provide the bond stress. The main feature of this stage is the rapid increase in the bond stress (\(\tau\)) with the increase in the displacement (\(s\)). The displacement (\(s_{0}\)) is small at this time, and its value is between 0.05 and 0.2 mm. Its graph is an almost vertical line from the origin. The second stage is the rising section (AB section). In this stage, the concrete in front of the rib starts to be gradually extruded. The friction and mechanical occlusion forces mainly provide the bond stress at this time. Its main characteristic is that as the load increases, the free-end slip value increases significantly and approaches a straight line, which is close to the elastic state. The third stage is the slipping section (BC section), in which the concrete in front of the rib is gradually crushed in an elastic-plastic state as the load increases. The main characteristic is that the stress increases with the displacement of the free end and the growth rate slows down until it does not increase. The fourth stage is the descending section (CD section), in which the concrete in front of the rib is rapidly crushed, and is mainly characterized by a rapid decrease in the bond stresses to a stabilized value.