## 4 Numerical Simulation of the Adhesive-Rebar Interface  
### Establishment of FE Model  
For this study, ABAQUS had a good adaptability for the simulation of the pull-out and bond failure analysis of the rebar planting system, and its concrete damaged plasticity model and spring element met the requirements for the simulation of test conditions. Therefore, the finite element model of the rebar planting specimen was established by ABAQUS (ver. 2020). software. The stress system of a rebar planting specimen can be simply summarized as three kinds of materials and two kinds of interfaces (rebar, concrete substrate, adhesive-, rebar interface, adhesive-concrete interface). In the establishment of the finite element model, the C3D8R element was selected to simulate the rebar and concrete substrate, and the Spring2 element was selected to simulate the bond-slip behavior of the adhesive-rebar interface. Previous studies have shown that the bond stress at the adhesive-rebar interface is the main factor controlling the failure of the specimen after reaching a certain depth of rebar [28]. At the same time, according to the failure mode in the above pull-out test, there was no specimen with a failure of adhesive-concrete interface. Therefore, in the  
Figure 9: Axial strain–load curve of steel bars: (**a**) specimen of 8 mm steel bar (10d); (**b**) specimen of 8 mm steel bar (15d); (**c**) specimen of 8 mm steel bar (20d). establishment of the finite element model, it was assumed that there was no slip at the interface between rebar and concrete, so as to focus on the bond-slip behavior of the interface between the rebar and planting adhesive. The double broken line model and CDP model were used for the rebar and concrete substrate, respectively. The constitutive relationship of rebar and concrete substrate were determined according to the corresponding material property test results and Appendix C, the Chinese standard [37]. The adhesive-rebar interface was simulated by the Spring2 element, and the F-U relationship of the spring was determined based on the test results. Bond-Slip Constitutive Relationship of the Adhesive-Rebar Interface under Medium and Low Cycle Fatigue Loads  
According to the test and the existing research literature [38; 39], the characteristics of the load-slip curve of the rebar planting specimen can be summarized. It can be seen that the average bond stress and the corresponding bond-slip constitutive model at each stage included three stages. In the time history of the pull-out test, it is divided into an elastic bond stage, elastic-plastic slip stage and failure decline stage. The elastic slip stage is an oblique straight line passing through the origin at the initial stage of the drawing load of the rebar planting specimen. The load of the specimen and the slip show a linear positive correlation. The slope of the curve is the bonding stiffness of the elastic bonding stage, and the relative slip increase in this stage was small. The elastic-plastic slip stage appears after the elastic bonding stage, and its curve form can be approximated as a quadratic parabola with an opening downward. In the definition domain of this section of the curve, the function value still maintains a monotonous increase, but the slope of the curve gradually decreases to zero. At this time, it is the end of the curve in the elastic-plastic slip stage. The position of this point corresponds to the ultimate drawing bearing capacity of the rebar specimen, and the function value reaches the maximum value of the whole curve. The failure descent curve is defined as an oblique straight line with a negative slope, which appears after the elastic-plastic slip stage. As shown in Figure 10, the characteristic points of the constitutive relationship include: average ultimate bond stress \(\tau_{u}\), elastic stage ultimate bond stress \(\tau_{e}\), residual bond strength \(\tau_{r}\), ultimate load slip displacement \(S_{u}\), elastic stage ultimate slip displacement \(S_{e}\), residual slip displacement \(S_{r}\).