## 1 Introduction  
With the acceleration of industrialization and urbanization, the construction industry has developed rapidly, and the accompanying construction waste has increased dramatically. Due to the large cost of traditional landfill methods and serious environmental pollution, reusing the construction waste resources is imperative [1; 2]. As a product of the recycling construction waste, recycled aggregate concrete (RAC) has its own advantages in terms of economy and protection for the environment. RAC is prepared by mixing recycled aggregate [3; 4; 5; 6] with a certain proportion and grading, and partially or completely replacing natural aggregates (mainly coarse aggregates). The recycled aggregates are obtained by crushing, cleaning, and classifying the waste concrete.  
In recent years, various scholars have conducted investigations on the properties of RAC [7; 8; 9; 10; 11; 12; 13]. It was found that RAC with an optimized mix ratio has better mechanical properties compared with ordinary concrete [14; 15]. RAC has low weight, which is beneficial for reducing the weight of structure and improving the seismic performance of RAC members. Therefore, the combined application of RAC and section steel in construction engineering not only reduces the overall weight of a structure, but also solves the problem of poor bearing capacity and rigidity of the structure.  
Previous investigations [16; 17; 18; 19; 20; 21; 22; 23] indicated that the bond slip behavior between section steel and RAC is an important factor affecting the structural performance, and the numerical simulation method of bond slip is an important theoretical basis of engineering extension and structural calculation analysis. [PERSON] et al. [24] carried out push-out tests on twenty-two specimens of RAC with different replacement rates, and analyzed the effects of the replacement rate, the cover thickness, the bonding site, the hooping ratio, and the particle diameter of the aggregate on the bond strength. However, a mathematical model of the constitutive relationship for bond slip was not proposed. [PERSON] et al. [25] studied the bond slip performance of section steel and RAC under different replacement rates and carried out a push-out test on thirty-six specimens. The constitutive relationship of bond strength under the position function was obtained, and the relationship between replacement rate and average characteristic bond strength was also acquired. [PERSON] et al. [26] established a numerical model for the bond slip analysis of concrete-filled steel tubular columns, considering the bond slip effect at two nodes. [PERSON] et al. [27] established a new bond slip model for fiber-reinforced concrete, characterized by the fact that the model was based on anchored carbon fiber rebar and fiber-reinforced concrete.  
In general, the research studies on the bond slip and numerical simulation between section steel and RAC are incomplete, especially for section steel and RAC with a full replacement ratio. Further study is important for determining the theoretical and engineering relationships between section steel and RAC.  
In this study, the impact factors of bond slip strength between section steel and RAC with a full replacement ratio and the constitutive relationship of bond slip were studied. Moreover, reliable numerical simulation was provided to solve engineering challenges and to be used by other researchers and engineers.