## 4 Results  
### Q-S Curve Analysis  
The loading forces and pile head displacements of the model tests and numerical models are recorded, resulting in the experimental Q-S curve for different pile models, as shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Name**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Effective Modulus**} & \multicolumn{1}{c}{**Stiffness Ratio**} & \multicolumn{1}{c}{**Friction**} \\  & & **E/MPa** & & **Sctiffness Ratio** & **Coefficient** \\  & & & & **f** \\ \hline Soil-soil & Ball-Ball & 100 & 1.5 & 0.4 \\ Soil-isolated stone & Ball-Ball & 50 & 1.5 & 0.3 \\ Soil-pile & Ball-Ball & 50 & 1.5 & 0.5 \\ Pile-isolated stone & Ball-Ball & 500 & 1.5 & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PFC3D linear contact parameters. Figure 5: FLAC3D-PFC3D coupled numerical calculation model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & \multirow{2}{*}{**Constitutive Model**} & \multirow{2}{*}{**Weight Density**} & \multicolumn{1}{c}{**Elastic Modulus**} & \multirow{2}{*}{**Poisson’s Ratio**} & \multirow{2}{*}{**Cohesion**} & \multirow{2}{*}{**Friction Angle**} \\  & & \(\gamma\) & **E** & - & **c** & \(\varphi\) \\  & & **kN/m3** & **GPa** & **-** & **kPa** & \(\circ\) \\ \hline The core pile & Elasticity & 27 & 70 & 0.33 & - & - \\ The outer concrete & Elasticity & 12 & 2 & 0.38 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: FLAC3D model parameters. Figure 6 shows that the trends and slope variations of the Q-S curve obtained from the simulation calculations are generally consistent with those obtained from model tests. The Q-S curve of the planted pile exhibits a steep increase with a noticeable inflection point (The points highlighted in red in Figure 6). Before the inflection point appears, the pile head displacement increases slowly with increasing load, but after the inflection point, the displacement of the pile head experiences a sudden change, causing the pile body to rapidly pull out as it reaches its ultimate state; the load at the inflection point can be considered the ultimate pullout load. The load at the inflection point for the planted pile without an isolated stone is 12.8 N, with a corresponding displacement of 2 mm, whereas for the planted pile with an isolated stone, the load at the inflection point is 38.4 N, with a corresponding displacement of 3.5 mm. The Q-S curve for the planted pile with an isolated stone at the base is less steep compared to that without the stone; under the same load of 12.8 N, the pullout displacement of the planted pile with an isolated stone is very small, while the planted pile without the stone has already reached the ultimate pullout displacement of 2 mm. When the pullout displacements are equal, the planted pile with the isolated stone at the bottom bears a greater pullout load. This may be attributed to the presence of the isolated stone, which increases the cross-sectional area, enhancing the vertical support provided by the overlying soil, thus allowing the planted pile foundation to support a larger pullout load. To facilitate the comparative analysis between tests, the scale on the right side of the chart is nondimensionalized using the core pile diameter D (10 mm), while the scale on the top axis of the chart is nondimensionalized based on the ultimate pullout bearing capacity of the planted pile (12.8 N). The ultimate loads and pile head displacements for the planted piles with and without isolated stones are shown in Table 4. It is evident that the ultimate pullout bearing capacity of the pile with an isolated stone at the base (38.4 N) is approximately three times that of the pile without an isolated stone (12.8 N). The corresponding pile head displacement (3.5 mm) is about 1.75 times greater than that of the planted pile without the isolated stone (2 mm).