# Effects of Grout Compactness on the Tensile Behavior of Ground Splice Sleeve Connectors
## 3 Tensile Bearing Capacity of Grounded Splice Sleeve
### The Bond-Slip Model for Rebar-Grout  
Based on the aforementioned tests and related references [3; 4; 5; 6; 7; 8; 9; 18; 19], the force transfer path of grouted splice sleeve is ascertained as follows: force\(\rightarrow\)one side of rebar\(\rightarrow\)grouting material\(\rightarrow\)sleeve\(\rightarrow\)grout\(\rightarrow\)the other side of rebar. The constraint effect of the sleeve restricts the splitting of the grouting material, significantly improves the bonding strength of the rebar-grout, and greatly shortens the anchorage length of the spliced rebar. In order to derive the bond-slip model of rebar-grout material, the following assumptions are made:  
1. The constraint stress \(u_{n}\) of the sleeve acting on the grout material is evenly distributed;
2. The constraint stress \(u_{n}\) can be calculated and quantified by the transverse strain of sleeve, \(\epsilon_{t,sl}\);
3. The bonding stress of rebar-grout \(u_{b}\) is uniformly distributed in the range of the anchorage length of rebar;
4. The bonding force of the sleeve acting on the grout equals the bonding force of the grout acting on the rebar;
5. Derivation is based on a fully compact connector; the derived formula is used in the compact and incompact connectors. Moreover, an incompact connector is considered as a compact connector with a lower bearing capacity. Figure 16 shows the relationship between the transversely tensile force of spliced sleeve \(T_{t,sl}\) and the constraint stress of sleeve acting on grout material \(u_{n}\). The transverse tensile stress of sleeve \(f_{t,sl}\) is a function of sleeve strain \(\epsilon_{t,sl}\) and sleeve elastic modulus \(E_{sl}\), and the sleeve strain \(\epsilon_{t,sl}\) can be obtained from Figures 14 and 15. \(f_{t,sl}\) is expressed as:  
\[f_{t,sl}=\epsilon_{t,sl}E_{sl} \tag{4}\]  
where \(f_{t,sl}\) is controlled by the longitudinal section area of sleeve. The grout incompactness will decrease the bonding area between the grout and the sleeve. This will reduce the bearing capacity, and then decreasing the transversely tensile force of spliced sleeve \(T_{t,sl}\). When the incompact connector is considered as a compact connector with a lower bearing capacity based on the fifth assumption, the value of \(T_{t,sl}\) will  
Figure 16: Stress diagram of the isolated body for the grouted splice sleeve. (**a**) Sleeve-grout. (**b**) Grout. (**c**) Sleeve. be overestimated if the reduction of the bonding area is ignored. Because the bonding force of sleeve acting on grout material is equal to the bonding force of grout material acting on rebar. Thus, the reduction of the bonding area can be translated to the decrease of the anchorage length of the rebar. \(T_{t,sl}\) is expressed as:  
\[f_{t,sl}=\frac{T_{t,sl}}{t_{sl}l_{c}} \tag{5}\]  
\[l_{c}=Cl_{b} \tag{6}\]  
where \(t_{sl}\) is the sleeve wall thickness, \(l_{b}\) is the anchorage length of rebar, and \(C\) is the incomapctness coefficient; its value can be taken as 1.0, 0.9, and 0.7 when the grout compactness is 100%, 90%, 70%, respectively. \[T_{t,sl}=\epsilon_{t,sl}Cl_{b}t_{sl}E_{sl} \tag{7}\]  
According to the static equilibrium, we have the following equation (shown in Figure 16a):  
\[2T_{t,sl}=u_{n}d_{sl}l_{b} \tag{8}\]  
where \(d_{sl}\) is the internal diameter of the sleeve. Substitute Equation (7) into Equation (8), and the constraint stress \(u_{n}\) is obtained as:  
\[u_{n}=\frac{2C\epsilon_{t,sl}t_{sl}E_{sl}}{d_{sl}} \tag{9}\]  
The bonding force of sleeve acting on grout material \(F_{n}\) is the product of the confining stress of sleeve acting on grout material \(u_{n}\) and the inner surface area of sleeve \(A_{c,sl}\):  
\[F_{n}=u_{n}A_{c,sl} \tag{10}\]  
where \(A_{c,sl}=\pi d_{sl}l_{b}\).