## 4 Discussion  
Stiff clay with a shear strength changing from 50 kPa to 75 kPa and dry sand were adopted in the above centrifuge model tests, and both can be classified as favourable soil conditions. In addition, the pile-tunnel interaction can be affected by both the vertical and lateral clearances according to available studies, but mostly from the perspective of load redistribution and pile group settlement during tunneling. [9; 10; 23].  
Thus, variations in the group effect during tunnel excavation with varying tunnel-pile relative position and pile spacing are investigated by the proposed model by considering the following working conditions, as shown in Table 2. The influence of the tunnel-pile relative position is analyzed by varying the lateral distance C\({}_{1}\) between the tunnel center and the front pile and the vertical distance between the tunnel center and the pile tip, represented by C\({}_{2}\) (see Figure 6), where a positive C\({}_{1}\) and C\({}_{2}\) indicate that the tunnel is excavated on the left side of the front pile and above the pile tip (tunnel drawn as a dashed line). Relatively soft soils are included to consider unfavorable tunnel excavation conditions, and a uniform shear strength along the pile shaft is taken as 40 kPa in the following analyzes. The pile group dimensions and material parameters are kept the same as those in Section 3, except that the influence of pile spacing in pile-tunneling interaction is also investigated with changing pile spacing. Considering the relatively soft soil condition, the total load of the vertically loaded fixed-head pile group is determined to be 4.0 MN based on analysis of a single pile, with a safety factor of 2.0.  
Figure 5: Tunneling-induced axial force distributions on the (**a**) front-row and (**b**) rear-row piles.  
Figure 6: Relative position between the tunnel and the pile group.  
Figure 8 shows that with increasing pile spacing, pile settlement is significantly decreased due to the group effect both before and after tunneling. In addition, with the settlements before tunneling taken as the baseline, the tunneling-induced settlement also decreases with larger spacing, ranging from 0.0308 m for Case 1 to 0.0232 m for Case 3, which can be attributed to the stronger support provided by the rear-row pile subjected to smaller tunneling-induced soil settlements. However, discrepancy in the pile head axial force can also be induced with larger pile spacing, ranging from 30% of the maximum axial force before tunneling for Case 1 to 40% for Case 3, indicating increasing load redistribution with larger spacing and, in turn, nonnegligible shear force in the pile cap.  
The variation in the group effect before and after tunneling is also investigated for Cases 1, 2 and 3, and the group effect in the vertical direction, manifested by the Z multipliers larger than 1.0, also decreases with increasing pile spacing. However, group piles are shown to behave differently due to unsymmetrical loading conditions after tunneling. The Z-multipliers for the front row piles increase after tunneling, while those for the rear row piles decrease, but the Z multipliers for the rear row piles are still larger than 1.0, meaning that the group effect cannot be neglected in the analysis of the pile group response. In addition, the discrepancy between the front row and rear row piles is also shown to decrease with increasing pile spacing.