## 5 Results and Discussion  
### Load-Displacement Responses  
Table 8 lists the displacements measured by the displacement sensors installed on the test shafts in advance. Hence, the load versus displacement curves for the four shafts are plotted in Figure 5 from the static load test data. Figure 5 shows the upper and lower shaft segment displacements during the bi-directional static tests. It can be observed from Figure 5 that the load-displacement curves of the upper and lower shaft segments of TS1 and TS2 have similar trends. Additionally, an inflection point can be found in the curve of the load-displacement of the lower segment of TS1. Nevertheless, the curve of the load-displacement of the upper segment of TS1 and the two curves of TS2 are all in the stage of elastic change. As mentioned above, the test process of test shaft TS2 was stopped due to the loading value reached the limit range of the load cell. Therefore, the ultimate bearing capacity of the test shaft TS2 was not obtained in this test. It can also be observed from Figure 5 that the required displacements to mobilize the shaft resistance can be significantly reduced by post-grouting craftwork. This result that the performance of the shaft can be effectively improved by grouting technique is further strongly demonstrated.  
Meanwhile, the load-displacement curves for shafts TS3 and TS4 can be found in Figure 5. As shown in Figure 5, the types of \(Q\)-\(s\) curves of test shafts TS3 and TS4 are both slowly-varying, and there is no obvious proportional limit, so the ultimate bearing capacity cannot be determined. However, with the same soils along the shaft, the bearing characteristics of the test shaft TS3 are obviously weaker than that of the shaft TS4. In the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Shaft No.**} & \multicolumn{2}{c}{**Maximum Load (MN)**} & \multicolumn{2}{c}{**Maximum Displacement (mm)**} & \multicolumn{2}{c}{**Maximum Rebound (mm)**} & \multicolumn{2}{c}{**Rebound Rate (\%)**} \\ \cline{2-9}  & **Upward** & **Downward** & **Upward** & **Downward** & **Upward** & **Downward** & **Upward** & **Downward** \\ \hline TS1 & 9.0 & 9.0 & 28.73 & 60.97 & 17.76 & 30.03 & 61.82 & 49.25 \\ TS2 & 12.0 & 12.0 & 9.27 & 4.01 & 4.61 & 1.44 & 50.27 & 64.09 \\ TS3 & 12.6 & & 12.74 & & 5.68 & & 44.58 \\ TS4 & 12.6 & & 8.16 & & 2.94 & & 36.03 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Loads and displacements of the test shafts.  
Figure 5: Load versus displacement curves of the test shafts. (**a**) TS1 vs. TS2. (**b**) TS3 vs. TS4.  
initial stage of loading, the soil at the tip of the test shaft TS3 was not completely reinforced by the cement slurry. Conversely, with the increase of soil compression, the shaft tip and the soil were in full contact, and the curve begins to show the characteristics of slow-varying. From the change trend of the curve, it can be concluded that the index of shaft tip grouting has a significant influence on the performance of the test shaft. Furthermore, it can be proved that the improvement effect of the bearing performance of the test shafts by ground improvement and increasing the shaft tip area due to the formation of the grout bulb is significantly influenced by the amount of shaft tip grouting.  
The results of the bi-direction static tests were converted into the equivalent unit shaft head resistance-displacement curves for the top-down load-test method [25], as shown in Figure 6. The initial shaft head stiffnesses of the aforementioned shafts are further obtained and presented in Figure 6, i.e., \(k_{1}\), \(k_{2}\), \(k_{3}\) and \(k_{4}\), respectively. Then, it can be found from Figure 6 that the order of \(k_{4}>k_{2}>k_{3}>k_{1}\). The order indicates that the stiffness of shaft top can be significantly enhanced by the combined tip-and-side post grouting craftwork. In addition, the fact that tip grouting has a significant effect on the bearing and load transfer characteristics of the test shafts can be further clarified by the order of \(k_{4}>k_{2}>k_{3}\).