## 3 Results and Discussion
### Analysis of the Effect of Different Pile Spacing  
The effect of variations in pile spacing under different pile/soil load ratios on the FOS and maximum settlement of the composite roadbed is shown in Figure 5.  
According to Figure 5, the FOS for a pile spacing of 2.0 m is the largest when the pile/soil load ratio is constant, and it continuously decreases as the pile spacing increases. Similarly, when the pile spacing is constant, a higher pile/earth load ratio results in a larger FOS. For pile spacings increasing from 2.0 to 2.4 m, the FOS for pile/soil load ratios of 5:5, 6:4, and 7:3 decreases only slightly, while the FOS for a pile/soil load ratio of 8:2 decreases by 5.6%. When the pile spacing increases from 2.4 to 4.2 m, the reduction rates in the FOS for pile/soil load ratios of 5:5, 6:4, 7:3, and 8:2 are 25.8%, 29.0%, 22.2%, and 27.2%, respectively. At a pile spacing of 4.2 m, the FOS for all pile/soil load ratios is less than 1.4. The FOS for a pile/soil load ratio of 5:5 is greater than 1.4 only for pile spacings of 2.0 m and 2.4 m, while for pile/soil load ratios of 6:4, 7:3, and 8:2, a pile spacing of up to 3.0 m is required for a FOS greater than 1.4. The effective pile spacings corresponding to pile/soil load ratios of 5:5, 6:4, 7:3, and 8:2 are 2.51 m, 3.15 m, 3.62 m, and 3.75 m, respectively. This indicates that different pile/soil load ratios necessitate different pile spacings for the same pile length. The FOS is below 1.4 for pile spacings below the effective pile spacing, and the effective pile spacing varies significantly for pile/soil load ratios of 5:5, 6:4, 7:3, and 8:2, increasing with the increase in the pile/soil load ratio. For the same pile spacing, the FOS increases with the increase in the pile/soil load ratio, and the change in the FOS after  
Figure 5: Effect of pile spacing variation on PHC pipe pile composite roadbeds under different pile/soil load ratios. (**a**) Patterns of change in the factor of safety; (**b**) patterns of change in maximum settlement. increasing the pile spacing from 2.4 m for pile/soil load ratios of 7:3 and 8:2 is essentially the same. In the case of pile/soil load ratios of 7:3 and 8:2, the change in pile spacing between 2.0 and 4.2 m has a minimal impact on roadbed settlement. The pattern of change remains consistent, with the settlement of the composite roadbed increasing by 31.27% and 31.66%, respectively, when the spacing is increased from 2.0 to 4.2 m. However, when the pile/soil load ratios are 5:5 and 6:4, the pile spacing significantly affects the roadbed settlement, resulting in an increase of 49.01% and 62.80%, respectively, when the spacing is increased from 2.0 to 4.2 m. Irrespective of the variation in pile spacing within the range of 2.0 to 4.2 m, the settlement of the roadbed decreases as the pile/soil load ratio increases. Only when the pile/soil load ratio is 7:3 or higher, and the pile spacing is 4.2 m, can the roadbed settlement reach a smaller value. Conversely, in the case of pile/soil load ratios of 5:5 and 6:4, the settlement of the roadbed generally increases with the increase in pile spacing. The increase in pile spacing results in a sparser pile layout, leading to a decrease in the rate of area displacement of piles. This directly weakens the horizontal stiffness of the composite roadbed. With the same pile-to-soil load ratio, increasing the pile spacing reduces the number of piles. As a result, when the total load of the piles remains constant, each pile bears a relatively larger load. This decreases the number of piles supporting the upper load per unit area while increasing the load area between piles without changing the overall load. Consequently, the pile-to-soil stress ratio of the composite roadbed gradually increases with the increase in pile spacing. This is because, with a smaller pile spacing, each pile bears a relatively smaller upper load, allowing the bearing capacity of pipe piles to be fully utilized.