## 3 Results and Discussion
### Analysis of the Effect of Different Pile Lengths  
In slope stability analyses, the strength discount theory is applied [27; 28]. According to GBT 50783-2012 Technical Specification for Composite Foundations [29], a safety coefficient of 1.4 was used as the control standard for stability requirements. Figure 4 illustrates the impact of varying pile lengths and pile/soil load ratios on the FOS of the composite roadbed with PHC piles at the maximum settlement. Based on the findings presented in Figure 4, it can be observed that the FOS shows an increasing trend as the pile length increases at a constant pile/soil load ratio. Specifically, when the pile/soil load ratio is 5.5, increasing the pile length from 12 to 18 m results in a 34.39% increase in the FOS. However, when the pile length is further increased from 18 to 28 m, the FOS only increases by 4.6%. On the other hand, for pile/soil load ratios of 6:4, 7:3, or 8:2, the FOS exhibits a linear increase with the pile length from 12 to 22 m. After reaching 24 m, the rate of increase slows down. In the case of a pile/soil load ratio of 5:5, the FOS remains below 1.4 regardless of the variation in pile length from 12 to 28 m. Similarly, for pile/soil load ratios of 6:4, 7:3, and 8:2, the effective pile lengths show minimal differences, typically around 19m. Piles with lengths exceeding 20 m have a FOS greater than 1.4, while those with lengths below the effective length have an FOS smaller than 1.4. Moreover, for a given pile length, the FOS increases linearly with the increase in the pile/soil load from 12 to 22 m. Additionally, the FOS increases with the increase in the pile/soil load ratio, albeit at a decreasing rate. The difference in the FOS between pile/soil load ratios of 7:3 and 8:2 is minimal. When the pile length is 12 m, the composite roadbed becomes visible through the sliding surface, indicating a relatively low strength in the silt layer. However, as the pile length increases to a certain point, no connected sliding surface is formed. This highlights the importance of setting a reasonable pile length, as it effectively limits the development of the plastic zone and prevents the occurrence of thorough plastic damage within the soil body. When the pile length was increased from 12 to 20 m, the maximum settlement of the composite roadbed decreased by 67.4%, 64.3%, 75.2%, and 88.2% under the pile/soil load ratios of 5:5, 6:4, 7:3, and 8:2, respectively. Furthermore, the settlement gradually stabilized after reaching 20 m. In other words, regardless of how much the pile length increases beyond 20 m, the impact on the composite roadbed's settlement becomes smaller when the pile/soil load ratio exceeds 6:4. A comparison between two cases--one with the pile not penetrating the soft soil layer (pile length of 12 m) and the other with the pile penetrating the soft soil layer (pile lengths of 18 m, 20 m)--reveals that the settlement of  
Figure 4: Effect of pile length 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. the PHC pipe pile when passing through the soft soil layer and with the pile end placed in the better soil layer is significantly smaller than that of the pile not penetrating the soft soil layer. However, after the pile penetrates the soft soil layer and reaches a depth of 20 m, the impact of further increasing the pile length on reducing the settlement diminishes. When the pile length is short, the influence range of the pile body is limited to the surrounding soil, which limits its strengthening depth. However, as the pile length increases, the soil around the pile becomes more compacted, resulting in an increase in the strengthening depth of the pile. Additionally, the increase in pile length allows the pile and soil to share the load transmitted by the superstructure, effectively increasing the bearing capacity of the foundation.