## 4 Effects of Different Mode Bond-Slip Fracture
### Investigation of Different Bond-Slip Failure Modes Based on FEA
#### 4.3.2 Splitting Failure Mode  
In the experiments, the diameter and arrangement density of the longitudinal reinforcement in RC columns is closely related to the bond performance between the reinforcement and concrete. The high diameter of the longitudinal reinforcement, the smaller the frictional force per unit length on the surface of the reinforcements, and is more prone to pull-out failure. When the diameter of the longitudinal reinforcement is smaller, the frictional force per unit length on the surface of the reinforcements is more significant, resulting in higher bond strength and a higher likelihood of splitting failure [36]. Furthermore, when the arrangement of the longitudinal reinforcement is too dense, the stress concentration within the concrete structure is more pronounced, which also contributes to the higher probability of splitting failure [37]. Therefore, we assume that the failure mode of the Case-2 specimen, with densely arranged small-diameter reinforcement, is splitting failure (splitting failure typically results in transverse cracks through the entire concrete structure, which is consistent with the experimental observations in Figure 9). Figure 28 shows the splitting bond failure model used in this analysis with the same maximum bond strength as in the previous section. In the CEB model, the most significant difference with splitting is the absence of a maximum bond stress maintenance interval (S1-S2) compared to the pull-out model. Upon reaching the maximum bond strength, plastic failure occurs immediately, and the bond strength drops directly to the minimum value. Figure 27: Damage to Axial Reinforcements at Base of Columns by Analysis for Pull-Out slip model (Case-2). (**a**) South Side. (**b**) North Side. The hysteresis curve obtained from the analysis of Case-2 using the splitting bond model is shown in Figure 29 and parameters of model is refer to Table 3. Although the horizontal load capacity at each Drift is smaller than the experimental results after 1.0% Drift, the maximum load capacity is accurately reproduced. On the positive side, the degradation trend of load-bearing performance after reaching the maximum horizontal force is also replicated. The pinching behavior during unloading and reloading is not sufficiently reproduced. However, generally capturing the history of the bending deformation behavior observed in the experiments shows the replication of the stiffness degradation during unloading and reloading. Moreover, the history of horizontal load and longitudinal reinforcement strain are shown in Figure 30. While the north-side longitudinal reinforcement exhibits elastic deformation, the south-side longitudinal reinforcement shows permanent strain on the tensile side after plasticization. In the experiment, as shown in Figure 8, the damage was concentrated on the north-side longitudinal reinforcement rather than the south side. Apart from the reversed damage situations between the north and south sides, the experimental results are accurately reproduced. Figure 28: CEB-FIP Splitting model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(s_{1}\) & \(s_{2}\) & \(s_{3}\) & \(\tau_{max}\) & \(\tau_{f}\) \\ \hline
1 mm & 1 mm & 3 mm & 3.47 Mpa & 1.38 Mpa \\ \hline \hline \end{tabular} \(s_{1}\): 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{table} 
Table 3: Parameters of Splitting Model. Figure 29: Examples of Force–Displacement Responses for Pull-Out slip model. Regarding the rotational deformation of the Case-2 RC column, the comparison between the experimental and analytical results is shown in Figure 31. Although the analytical results do not exhibit a sudden drastic rotational deformation at a certain moment, the maximum value in the positive direction reaches 3.1%, while the negative direction only reaches \(-\)2.4%, as shown in Figure 31b. Similar to the experiment, the tendency to shift in one direction is well reproduced.