# Mechanical Analysis of Ground Sleeve
## 4 Comparison between Grouted Splice Connectors and Grouted Sleeve Lapping Connectors
### Failure Mode  
As shown in Table 2, the failure modes of the specimens of the grouted splice connectors and the grouted sleeve lapping connectors with the same bar anchorage length of 100 mm were the grout-sleeve slip and the bar-grout slip, respectively. The different structural forms of the bars resulted in these different failure modes. It is well-known that the bond for deformed bars comprises three components: chemical adhesion, friction, and mechanical interlock between the concrete and the bar [41; 42]. The sleeve of the grouted splice connector has a smooth inner pipe-wall and there is no mechanical interlock between the grout and the sleeve. Thus, the bond force between the grout and the sleeve consists of the chemical adhesion force (\(P_{\text{ad}}\)) and the friction force (\(P_{\text{f}}\)). In light of the load-displacement curves of the grouted splice connectors (as shown in Figure 9c), we define the first load peak value as the rupture load (\(P_{s}^{r}\)), and the second load peak value as the ultimate friction force (\(P_{s}^{f}\)). Then, Equations (1) and (2) can be written as:  
\[P_{s}^{r}=P_{\text{g}}^{u}+P_{ad}^{max} \tag{1}\]  
\[P_{s}^{f}=P_{f}^{max} \tag{2}\]  
where \(P_{g}^{u}\) denotes the ultimate tensile force of the grout at the middle cross section, \(P_{ad}^{max}\) denotes the ultimate chemical adhesion force between the separated grout and the sleeve, and \(P_{f}^{max}\) denotes the ultimate friction force between the separated grout and the sleeve. The values of \(P_{ad}^{max}\) and \(P_{f}^{max}\) for the three specimens are shown in Table 3.  
By establishing a force equilibrium at the middle of the grout and assuming a uniform tensile stress distribution for the grout at the cross section (Figure 13), it follows that:  
\[P-P_{\text{g}}=P_{\text{b}} \tag{3}\]  
where \(P\) is the load, \(P_{\text{g}}\) is the resultant tensile stress of the grout, and \(P_{\text{b}}\) is the resultant bond stress between the grout and the sleeve, which equals the chemical adhesion force (\(P_{\text{ad}}\)) before the grout slips, and it is equivalent to the friction force (\(P_{f}\)) after the grout slips. Figure 12: Load transferred from one bar to the other directly in the grouted sleeve lapping connector. Bar tensile fracture is the ideal failure mode for a connector. To guarantee that the grouted splice connector fails by the bar tensile fracture, the bond force between the grout and the sleeve (\(P_{b}\)) must be larger than \(P_{s}^{u}-P_{g}^{u}\), where \(P_{s}^{u}\) is the ultimate tensile capacity of the bar and can be calculated by Equation (4). \(P_{g}^{u}\) is the ultimate tensile force of the grout at the middle cross section and can be calculated by Equation (5) below. \[P_{s}^{u}=\frac{1}{4}\pi d^{2}f_{b}^{u} \tag{4}\]  
\[P_{g}^{u}=\frac{1}{4}\pi d_{i}^{2}f_{g}^{u} \tag{5}\]  
where \(d\) is the bar diameter, \(f_{b}^{u}\) is the ultimate tensile strength of the bar, \(d_{i}\) is the inner diameter of the sleeve, and \(f_{g}^{u}\) is the ultimate tensile strength of the grout. By substituting the values of \(d\), \(d_{i}\), \(f_{b}^{u}\), and \(f_{g}^{u}\) into Equations (4) and (5), the values of \(P_{s}^{u}\) and \(P_{g}^{u}\) can be obtained. Thus, the minimum value of \(P_{b}\) can be computed as 130.15 kN. This result means that the bond force between the half grout and the sleeve needed to be larger than 130.15 kN to ensure that the grouted splice connector failed by the bar rupture. However, as shown in Table 3, the maximum of the chemical adhesion force (\(P_{ad}^{max}\)) and the friction force (\(P_{f}^{max}\)) did not meet the requirement. Thus, certain construction measures, such as setting shear keys in the sleeve internal wall, are necessary to generate the mechanical interlock force and increase the bond force between the grout and sleeve in a grouted splice connector. No grout-sleeve slip failure could occur in the grouted sleeve lapping connector. The two lapped main bars that passed through the entire sleeve were subjected to forces in the opposite directions.