## 4 Example Verification and Engineering Application
### Engineering Application  
The residential foundation pit project at 2017 NJY-11 block in Dongyong Town, Guangzhou, China, employs prestressed anchor cables to support the foundation pit wall. The anchor holes, with a diameter of 150 mm, are designed to accommodate 5 \(\times\) 7\(\phi\)5 steel strand anchor cables featuring a Young's modulus of 195 GPa. An anchorage acceptance test for the anchor cables was conducted to assess their performance under the design load, serving as a basis for project acceptance. The experiment primarily comprised an experimental loading device, a force and displacement measuring device, and a data acquisition and processing system. The loading device utilizes a pressure plate reaction device, with the pull-out load provided by a QFZ1000-20 model hydraulic jack. The force and displacement measuring device includes a pressure gauge of model L26091517 and a displacement sensor of model BL100-V-1000. The data acquisition and processing system displays the pull-out load and displacement data of the pulling end of the anchor on the computer. The sections of the A, B, and C anchor cables embedded in the ground had lengths of 42 m, 40 m, and 42 m, respectively. The anchor cable passed through the ground from top to bottom, traversing through silt, a layer of loose and slightly dense silt, and strongly weathered argillous sandstone. The experiment was conducted in accordance with the Technical Specification for Ground Anchors (CECS22:2005) [27], utilizing graded loading and unloading. The maximum experimental load applied was 1.2 times the design value of the anchor. The cyclic loading experiments followed the sequence outlined in Table 1. Displacements under the load were recorded over ten cycles, and the next level of load was applied when the difference between ten consecutive measurements did not exceed 0.01 mm. The maximum experimental loads were 780 kN, 660 kN, and 720 kN, respectively. Table 2 and Figure 9 depict the outcomes of the experiments, illustrating the pull-out load and displacement at the anchor head. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Experimental Load** & **0.3 \(\boldsymbol{N_{\text{max}}}\)****a** & **0.5 \(\boldsymbol{N_{\text{max}}}\)****a** & **0.7 \(\boldsymbol{N_{\text{max}}}\)****a** & **0.8 \(\boldsymbol{N_{\text{max}}}\)****a** & **0.9 \(\boldsymbol{N_{\text{max}}}\)****a** & **1.0 \(\boldsymbol{N_{\text{max}}}\)****a** & **0.3 \(\boldsymbol{N_{\text{max}}}\)****a** \\ \hline Duration (min) & 10 & 10 & 10 & 10 & 10 & \textgreater{}10 & 5 \\ \hline \end{tabular}  
* \(N_{\text{max}}\) is the maximum experimental load of the anchor.  
\end{table} 
Table 1: Load grade and duration of acceptance test of anchors. Figure 9: Axial force along the anchorage segments. Taking cable A as an example for engineering application calculation, Figure 10 reveals significant changes in the slope of the load-displacement curve when the pull-out load (\(P\)) is at 234 kN and 546 kN. Accordingly:  
When \(P<234\) kN, the anchoring section of the anchor is in the elastic stage. For 234 kN \(\leq P<546\) kN, the anchoring section enters the plastic stage. When \(P\geq 546\) kN, the anchoring section enters the debonding stage. Here, the elastic limit load (\(P_{ik}\)) is 234 kN, and the plastic limit load (\(P_{sk}\)) is 546 kN. By substituting \(P_{ik}=234\) kN, \(P_{sk}=546\) kN, \(S_{1}=6.79\) mm, and \(S_{2}=20.07\) mm into Equations (12)-(14), (17)-(19), (22), and (23), the mechanical parameters of the anchorage interface are obtained: \(\tau_{1}=191\) kPa, \(\tau_{2}=44.5\) kPa. Further, bringing the limit length of the debonding part (\(L_{ik}\)) = 37.68 m into Equation (24) yields \(P_{\text{umax}}=1065.8\) kN. Considering the design load (\(P\)) for the axial pull of the anchor in this project as 650 kN, the safety factor (\(F_{s}=P_{\text{umax}}/P\)) for anchor cable A is calculated as 1.64. This meets the specified anchorage safety factor requirement of 1.6 according to the specification [27].