## 4 Discussion
### Influence of Lateral Clearance between the Front Row Piles and Tunneling  
The influence of lateral clearance (C\({}_{1}\)) between the front row piles and tunneling is a key factor for tunnel-pile group interaction. However, the variation in the group effect before and after tunneling and load redistribution among group piles have not been thoroughly investigated. To consider the close tunnel-pile group lateral distance, Cases 4, 5 and 6 with tunnels excavated below the pile tip (C\({}_{2}\) = \(-\)0.25 L) and lateral distances of 0, 1.5 and 2 times the tunnel radius are selected, and the predicted pile settlements are first given in Figure 10.  
Figure 10: Influence of lateral distance on pile group settlement.  
Figure 9: Influence of pile spacing on group effect variation.  
Figure 10 shows that with the tunnel center approaching the center of the pile group, the piles are subjected to increasing soil settlements, resulting in increasing tunneling-induced pile settlement. For cases with the same tunnel excavation depth, a tunnel excavated directly below the pile group can lead to the largest additional settlement.  
Tunneling-induced axial forces for Cases 3 to 6 are given in Figure 11, and the influence of C\({}_{1}\) can be explored by considering the axial force distribution before tunneling for the pile group with 2.5 d pile spacing as the baseline. It can be observed that the pile head load is not significantly redistributed for the three cases, and the influence of lateral distance on pile head load redistribution is not monotonic. However, the maximum axial force along the pile shaft increases with decreasing lateral distance, meaning that the tunnel excavated directly below the pile group is also the most unfavorable working condition from the perspective of load redistribution.  
The variation in the group effect is also examined for the three cases and shown in Figure 12. For Case 4 with almost identical loading conditions for the group piles, the Z multipliers for all the group piles decrease after tunneling. However, for Cases 5 and 6, the Z multipliers for the rear row piles increase after tunneling, while those for the rear row piles decrease, but the group effect should also be considered in pile group analysis due to the Z multipliers larger than 1.0.  
Figure 11: Influence of lateral distance on axial force distributions: tunneling-induced axial force on the (**a**) front row and (**b**) rear row piles.  
Figure 12: Influence of lateral distance on group effect variation.  
Pile settlements before and after tunneling are shown in Figure 13, and it can be indicated that with the same lateral distance between the front-row piles and the tunnel center, the tunneling-induced pile head settlement is almost the same. However, load redistribution among group piles is shown to be largely affected by the vertical distance between the pile tip and the tunnel center. Figure 14 shows that with increasing tunnel excavation depth, the discrepancy in the pile head significantly decreases from 60% of the pile head load before tunneling to less than 5%. The front-row piles are subjected to a larger pile head load when the tunnel is excavated above the pile tip, while they withstand a smaller load with excavation below the pile tip.  
Variations in the group effect with different vertical distances are shown in Figure 15. The Z multipliers for the front row piles can be observed to decrease with deeper excavation, and the group effect for the rear row piles shows opposite changing patterns. For the three cases, the difference in the Z multipliers is minimal when the excavation depth is at the level of the pile tip due to the most likely loading condition in this case. From the perspective of the group effect, the most unfavorable condition may occur with tunneling above the pile tip.