## 4 Conclusions  
In this paper, based on the results of center pull-out tests, the different damage forms and the causes of the damage in the center pull-out tests were summarized. The effects of rebar diameter, bonding length, and concrete type on the average bond strength of reinforced concrete were analyzed, and the extent of their influence was evaluated. The mechanisms of influence of three factors on bond strength were investigated. A constitutive model of bond-slip between RBFC and rebar was developed based on a semi-empirical and semi-theoretical model. The main conclusions are as follows:  
1. The damage forms of the two tests were summarized based on the bonding mechanism between the rebar and the RBFC. For the center pull-out test, the damage forms were rebar pull-off damage and bond anchorage damage. The bond anchorage damage included pull-out damage and splitting damage.
2. Based on the test results, the bond stress-slip curve was summarized, and a mathematical model was constructed. It was divided into a micro-slip section, a rising section, a slipping section, a descending section, and a residual section.  
Figure 15: Comparisons of experimental and analog values of bond stress–slip curves: **(a)** 60-12-RBFC, **(b)** 60-14-RBFC, **(c)** 60-16-RBFC, **(d)** 80-12-RBFC, **(e)** 80-14-RBFC, **(f)** 80-16-RBFC, **(g)** 100-12-RBFC, **(h)** 100-14-RBFC, and **(i)** 100-16-RBFC.  
3. The incorporation of rubber granules reduced the compressive strength and the bond strength of the concrete, which had a negative effect. However, the addition of small amounts of rubber granules did not significantly reduce the bonding properties. The incorporation of moderate amounts of basalt fibers had a positive effect on the bond strength.
4. In the center pull-out tests, the bond stresses in specimens with the same rebar diameter for RBFC decreased by 13.91-16.72% for every 20 mm increase in bonding length in the range from 60 to 100 mm. The ultimate bond strength (\(\tau_{u}\)) decreased by 3.96-5.94% for every 2 mm increase in rebar diameter for the same bonding length in the 12 to 16 mm diameter range.
5. The segmented bond-slip constitutive relationship between RBFC and rebar based on the center pull-out test program was developed using a semi-empirical and semi-theoretical model as the theoretical basis.  
Conceptualization, L.T.; formal analysis, Y.G., L.T. and T.J.; investigation, Y.G. and T.J.; data curation, Q.Z., T.J. and L.S.; writing--original draft preparation, Y.G., L.S. and T.J.; writing--review and editing, Y.G., S.L., L.S. and W.J.; project administration, L.T., W.J., S.L. and Q.Z.; funding acquisition, Y.G., W.J., Q.Z., L.T. and S.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Technological Developing Scheme Program of Jilin Province (Award Number: 20230402048 GH), the Transportation Technology Program of Jilin Province of China (Award Numbers: 2021-1-1 and 2022-1-8), the Key Project of Department of Transportation of Heilongjiang Province of China (Award Numbers: 2022-1 and 2022-2), the Science and Technology Research and Planning Project of Jilin Education Department (Award Number: JJKH20211113 KJ), and the Graduate Innovation Fund of Jilin University (Award Number: 2023 CX053).  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to privacy.  
We would like to acknowledge the following people from Jilin University. Thank you to [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] for technical support related to the testing procedure and data processing.  
Authors [PERSON], [PERSON], [PERSON] and [PERSON] were employed by the company China Railway Tunnel Group Road & Bridge Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.