## 4 Design Methodology of Composite-Anchor Uplift Piles
### Ultimate Bearing Capacity with Composite Anchor Interface Failure  
When evaluating the uplift pile's bearing capacity, it is imperative to account for potential frictional resistance failures at multiple interfaces, including those between the steel strand and cement grout, the interface between the cement grout and the inner wall of  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Soil Type** & \(\lambda_{ip}\) \\ \hline sand & 0.50–0.70 \\ clay, silt & 0.70–0.80 \\ \hline \hline \end{tabular} Note: If the length–diameter ratio is less than 20 or post-grouting technology is used, the value of pull-out coefficient can be appropriately increased.  
\end{table}
Table 5: Suggested values of pull-out coefficient \(\lambda_{ip}\).  
the steel pipe, and the interface between the outer wall of the steel pipe and the concrete of the pile body. The bearing capacity must strictly adhere to the following criteria:  
\[N_{k}\leq\frac{Q_{ck}}{2} \tag{7}\]  
where \(Q_{ck}\) denotes the minimum frictional resistance at the interfaces within the pile. As there are three distinct interfaces, specifically the steel strand-grouting body interface, the grouting body-steel pipe interface, and the steel pipe-pile concrete interface, the frictional resistance for the three interfaces can be calculated, respectively, as follows.  
(1) Friction resistance at the steel strand-cement grout interface:  
\[Q_{ck1}=n\pi d_{1}l_{1}\tau_{1} \tag{8}\]  
where \(n\) is quantity of composite-anchor cables in the pile and \(d_{1}\) is equivalent diameter of the steel strands. When using a single steel strand as reinforcement, take the single steel strand's diameter; when using multiple steel strands as reinforcement, take the equivalent diameter. The equivalent diameter can be determined in accordance with the requirements in Section 7.1.2 of \"Code for Design of Concrete Structures\", where \(\tau_{1}\) is the ultimate bond strength between the steel strand and the grout, determined experimentally or following the recommended values in the specifications, typically ranging from 2.0 to 3.0 MPa. A higher value is selected when the grout has higher strength and good construction quality, and a lower value is chosen otherwise. Here, \(l_{1}\) is the bond length of steel strands within the grout.  
(2) Friction resistance at the grout-steel pipe interface:  
\[Q_{ck2}=n\pi d_{2}l_{2}\tau_{2} \tag{9}\]  
where \(n\) is quantity of composite-anchor cables in the pile; \(d_{2}\) is inner diameter of high-strength steel pipe; and \(\tau_{2}\) is the ultimate bond strength between the cement grout and the inner wall of the steel pipe, which should be determined experimentally or following the recommended values in the specifications, typically ranging from 2.0 to 3.0 MPa. A higher value is selected when the grout has higher strength and good construction quality, and a lower value is chosen otherwise. Here, \(l_{2}\) is the bonding length between the cement grout and the inner wall of the steel pipe.  
(3) Friction resistance at the steel pipe outer wall-pile concrete interface:  
\[Q_{ck3}=n\pi d_{3}l_{3}\tau_{3} \tag{10}\]  
where \(n\) is quantity of composite-anchor cables in the pile; \(d_{3}\) is outer diameter of the high-strength steel pipe; and \(\tau_{2}\) is the ultimate bond strength between the outer wall of the steel pipe and the concrete of the pile shaft, which should be determined experimentally or following the recommended value in the specifications, typically ranging from 2.0 to 3.0 MPa. A higher value is selected when the grout has higher strength and good construction quality, and a lower value is chosen otherwise. Here, \(l_{3}\) is the bond length between the steel pipe's outer wall and the pile concrete.  
(4) The cumulative frictional resistance within the pile is determined as follows:  
\[Q_{ck}\leq\min(Q_{ck1},Q_{ck2},Q_{ck3}) \tag{11}\]