## 6 Finite Element Simulation by PLAXIS 2D
### Simulation Results  
Figure 5a-c are the vertical stress distribution of the nodular joints, the cemented soil and the soil around. It can be seen from Figure 5a that, for the upper section (0\(\sim\)49 m), the axial force of pile and cemented soil are not in the same order of magnitude, which can also be seen from Figure 6a,b. Therefore, in this area, the cemented soil mainly plays the role of transferring load [9; 10; 11]. When approaching the joints (49\(\sim\)64 m), the slope of curve in Figure 6a shows that the decrease speed of pile axial force gets faster. Relevantly in Figure 6b, the axial force of cemented soil has a sudden increase not only at depth of 49 m, but also 61 m, where the expanded cemented soil is. So the nodular joints have contribution to the collaboration work of pile and cemented soil. Under the load at pile head, the axial force of pile tip is 1339 kN, the axial force of expanded soil at the pile tip is 1227 kN. The expanded cemented soil bears about 47.8% of composite pile tip resistance. It indicates that the expanded cemented soil at pile tip plays the role of bearing pile tip resistance.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interface** & \begin{tabular}{c} **Core Pile and** \\ **Cemented Soil** \\ \end{tabular} & \
\begin{tabular}{c} **Cemented Soil and Soil** \\ \end{tabular} &
\begin{tabular}{c} **Pile and Soil** \\ \end{tabular} \\ \hline Interface modes & From cemented soil & From soil & From soil \\ \hline \(R_{inter,1}\) & 1.0 & 1.0 & 1.0 \\ \(R_{inter,2}\) & 0.8 & 0.8 & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Three pairs of interfaces and reduction coefficient \(R_{inter}\).  
Figure 5: Vertical stress distribution cloud diagrams: (**a**) part of nodular joints, (**b**) cement soil around the joints, and (**c**) soil around the joints.  
Figure 7a,b is the plastic point distribution on the interface between cemented soil and soil under the failure mode. From Figure 7a, the distribution of failure point has a difference between soil layers due to different shear resistance. Figure 7b shows that, the failure points not only appear on the interfaces, but also develop upwards from the pile tip. It corresponds to Figure 6b. This is because the expanded cemented soil tip exposes to a large tip load. Therefore, to ensure the collaborative work of pile tip and expanded cemented soil, it is necessary and economical to strengthen the cemented soil in this specific area considering the bearing capacity of the soil layer at the pile tip.  
The load-displacement simulation curves of piles in the cases of \(R_{inter,1}\) and \(R_{inter,2}\) are shown in Figure 8. The load is set to be 2000 kN for each stage in the initial loading stage, and 1000 kN for each stage in the later stage. The load corresponding to the starting point of obviously steep drop is the ultimate bearing capacity. It can be seen from the curve that when the strength reduction of interface is not taken into consideration, \(Q_{ua}\) = 16,100 kN.  
Figure 6: Axial force\(-\)Depth curves of (**a**) piles, and (**b**) cemented soil.  
Figure 7: Plastic point distribution diagrams among (**a**) pile shaft, and (**b**) pile tip.  
When the strength reduction of interface is taken into consideration, \(Q_{ub}\) = 12,800 kN. The simulation result without considering the strength reduction are closer to the field test result. Therefore, it is confirmed that the SDRN pile method can improve the friction resistance of the interfaces. In addition, Table 5 indicates that the finite element model and the calculation method in this paper are feasible for SDRN pile.