## 3 Simulation Results and Sensitivity Analysis
### Influences of Hoop Stiffness on the Von-Mises Stress of the Pipe  
The pipe-soil interaction and the ability of the pipe to resist the external force mainly depend on the hoop stiffness of the flexible pipe; therefore, the hoop stiffness of the pipe has a profound influence on the mechanical deformation of the pipe [61]. In the investigation of Von-Mises stress response of the pipe to the hoop stiffness, the values of the hoop stiffness of the 600 mm diameter pipe were varied between 4, 8, and 10 kPa, and the traffic load was 0.7 MPa and 60 km/h.  
The hoop stiffness had a negligible impact on the Von-Mises stress of the pipe when the backfill was compacted according to the standard (Figure 16). This might be because an increase in hoop stiffness led to a weakening of the pipe-soil interaction and an increase in earth pressure above the crown. However, at the same time, the ability of the pipe to resist deformation was improved, and the Von-Mises stress of the pipe was almost unchanged. For clear description, the Von-Mises stress curves of pipes with different hoop stiffness were simplified into one and expressed as \"Standard\".  
Figure 16: The Von-Mises stresses of different hoop stiffnesses of pipe under traffic load when the backfill compactness is standard: (**a**) the crown; (**b**) the springline; (**c**) the invert.  
Figure 15: The invert Von-Mises stress of different diameter pipes under traffic load: (**a**) change in L1 compaction degree; (**b**) change in L2 compaction degree; (**c**) change in L3 compaction degree.  
The crown Von-Mises stress responses of pipes with different hoop stiffness to the compactness of L1 and L2 barely differed, but the response was proportional to the hoop stiffness when the L3 compactness decreased (Figure 17). The springline Von-Mises stress also had low sensitivity to the hoop stiffness, even in the case of loose backfill (Figure 18). When L2 was loose, the springline stress of the pipe with low hoop stiffness was slightly lower than that of the pipe with high hoop stiffness. At the invert, the influence of the Von-Mises stress on the hoop stiffness was evident. The worse the backfill was compacted, the greater the difference in the invert stress of the pipe for different hoop stiffness. When the compaction degree of L1 or L2 decreased, the invert stress was inversely proportional to the hoop stiffness (Figure 19a,b); when the compaction degree of L3 decreased, the invert stress was proportional to the hoop stiffness (Figure 19c). Under the same compaction conditions, the Von-Mises stresses of pipes with different hoop stiffness were not different, so the responses of these pipes to traffic loads were also very close. From these results, it could be concluded that, compared with the diameter, the hoop stiffness had a limited influence on the Von-Mises stress of the pipe.  
Figure 17: The crown Von-Mises stresses of pipes of different hoop stiffness under traffic load: (**a**) change in L1 compaction degree; (**b**) change in L2 compaction degree; (**c**) change in L3 compaction degree.  
Figure 18: The springline Von-Mises stresses of pipes of different hoop stiffness under traffic load: (**a**) change in L1 compaction degree; (**b**) change in L2 compaction degree; (**c**) change in L3 compaction degree.