## 4 Effects of Different Mode Bond-Slip Fracture
### Investigation of Different Bond-Slip Failure Modes Based on FEA  
#### 4.3.1 Pull-Out Failure Mode  
Pull-out failure is one of the most common forms of bond failure in reinforced concrete (RC) structures, primarily caused by the reduction in bond strength due to concrete damage. When the reinforcements sustain tension, spiral-shaped micro-cracks will form around the ribbed bars, eventually leading to full penetration along the longitudinal direction of the reinforcements and being pulled out [35]. In practical RC cyclic loading tests, it is challenging to determine the root cause of foundation cracks. To address this issue, the research first employs a pull-out bond-slip model for analysis, with the numerical model illustrated in Figure 25 and parameters of model is refer to Table 2. According to the CEB-FIP guidelines, the research obtains the maximum bond stress \(\tau_{max}=3.47\) MPa based on the average concrete strength of 27.6 MPa obtained from the compression tests of the concrete material used and considering the average strain at the yield of the reinforcements and the influence of stirrups. After the bond failure of the reinforced concrete, the residual bond strength \(\tau_{f}=0.4\cdot\tau_{max}=1.388\) MPa. Figure 24: CEB-FIP 2010 Bond-Slip Model. (**a**) Bond-slip unloading/reloading Model. (**b**) Bond Stress-Slip-Strain 3D Model. Upon applying the aforementioned bond model, the analytical results for both specimens are shown in Figure 26. For the Case-1 specimen, although the maximum and minimum load capacities are slightly different compared with the experimental results, the stable load capacity is maintained up to 3.5% Drift, which is the same as the experiment. Furthermore, the load capacity degradation starting at 4.0% Drift is also replicated. During the loading and unloading processes, the changes in stiffness are well represented compared to the hysteresis curve which does not consider the bond-slip shown in Figure 20a. The pinching phenomenon in the hysteresis curve of the RC column is also accurately reproduced, enabling a more precise evaluation of the energy absorption capacity of the RC column during an earthquake. As shown in Figure 26b, the analytical results of the Case-2 specimen are generally similar to those of the previous chapter, where the reinforcement and concrete are assumed to be perfect bonding. However, the reproducibility of the maximum and minimum load capacity has increased compared to the results in the previous chapter. Although the pinching phenomenon of the hysteresis curve is not well reproduced, the stiffness of the RC column during the initial unloading and reloading is essentially consistent with the experimental results. On the other hand, when using the pull-out bond-slip model, as shown in Figure 27, the strain history of the reinforcement on both sides of the bottom of the Case-2 specimen. \begin{table}
\begin{tabular}{c c c c c} \hline \(s_{1}\) & \(s_{2}\) & \(s_{3}\) & \(\tau_{max}\) & \(\tau_{f}\) \\ \hline
1 mm & 2 mm & 4 mm & 3.47 Mpa & 1.38 Mpa \\ \hline \(s_{1}\): Slip when reaching maximum bond strength. \(s_{2}\): Slip at the start of bond strength drop. \(s_{3}\): Slip when reaching minimum bond strength. & & \\ \end{tabular}
\end{table} 
Table 2: Parameters of Pull-Out Model. Figure 26: Examples of Force–Displacement Responses for Pull-Out slip model. Figure 25: CEB-FIP pull-out model. The analysis results of the reinforcement strain on both sides are much smaller in both the tension and compression domains compared to Figure 22, which is consistent with the experimental results shown in Figure 8c. However, the strains of the north and south reinforcements are basically symmetric, and the asymmetry of damage to the reinforcements on both sides, as observed in the experiment, is not reproduced. The analysis overestimates the influence of the contact area between the reinforcement and the concrete on the bond strength and neglects the insufficient bonding between the small diameter reinforcement ribs and the concrete.