## 3 Simulation Results and Sensitivity Analysis  
### General  
The most common failure mode of buried flexible pipes is a ductile failure because the pipes creep after being subjected to a long-term stable load [50]. The von-Mises criterion states that when the equivalent stress of a certain stress state reaches a certain value related to the stress state, the material yields, and the Von-Mises stress is this equivalent stress. Von-Mises stress can be expressed by the stress component, as shown in Equation (8). Previous studies have focused on the circumferential stress and changes in the diameter of the flexible pipe to indicate the deformation of the pipe [9; 16; 23; 51]. Compared with the real stress, the von-Mises stress comprehensively considers the deformation of materials in multiple directions, and the assessment of the ductile failure of pipes is more accurate; thus, it is reasonable to take the Von-Mises stress as a parameter that indicates the deformation of the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Backfill Condition \({}^{*}\)**} & \multicolumn{5}{c}{**Elastic modulus (MPa)**} \\ \cline{2-6}  & **Lay 01** & **Lay 02** & **Lay 03** & **Lay 04** & **Lay 05** & **Lay 06** \\ \hline
**Standard** & 5 & 7 & 7 & 3 & 5 & 5 \\
**L1-loose** & 1 & 7 & 7 & 3 & 5 & 5 \\
**L1-85\%** & 3 & 7 & 7 & 3 & 5 & 5 \\
**L2-loose** & 5 & 1 & 7 & 3 & 5 & 5 \\
**L2-85\%** & 5 & 3 & 7 & 3 & 5 & 5 \\
**L3-loose** & 5 & 7 & 1 & 3 & 5 & 5 \\
**L3-85\%** & 5 & 7 & 3 & 3 & 5 & 5 \\ \hline \hline \end{tabular}  
* In the numerical simulation, the magnitude and speed of traffic load, the hoop stiffness and diameter of the pipe are changed respectively under each backfill condition, as shown in Table 7.  
\end{table} 
Table 6: Simulation backfill compaction conditions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Backfill Material**} & \multicolumn{5}{c}{**Elastic Modulus E (MPa)**} \\ \cline{2-5}  & **Lay 01** & **Lay 02** & **Lay 03** & **Lay 04** & **Lay 05** & **Lay 06** \\ \hline
**Standard** & 5 & 7 & 7 & 3 & 5 & 5 \\
**L1-loose** & 1 & 7 & 7 & 3 & 5 & 5 \\
**L1-85\%** & 3 & 7 & 7 & 3 & 5 & 5 \\
**L2-loose** & 5 & 1 & 7 & 3 & 5 & 5 \\
**L2-85\%** & 5 & 3 & 7 & 3 & 5 & 5 \\
**L3-loose** & 5 & 7 & 1 & 3 & 5 & 5 \\
**L3-85\%** & 5 & 7 & 3 & 3 & 5 & 5 \\ \hline \hline \end{tabular}  
* In the numerical simulation, the magnitude and speed of traffic load, the hoop stiffness and diameter of the pipe are changed respectively under each backfill condition, as shown in Table 7.  
\end{table} 
Table 7: Simulation traffic load and pipe physical variables. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Backfill Material**} & \multicolumn{3}{c}{**Elastic Modulus E (MPa)**} \\ \cline{2-5}  & **Lay 01** & **Lay 02** & **Lay 03** & **Lay 04** & **Lay 05** & **Lay 06** \\ \hline
**Standard** & 5 & 7 & 7 & 3 & 5 & 5 \\
**L1-loose** & 1 & 7 & 7 & 3 & 5 & 5 \\
**L1-85\%** & 3 & 7 & 7 & 3 & 5 & 5 \\
**L2-loose** & 5 & 1 & 7 & 3 & 5 & 5 \\
**L2-85\%** & 5 & 3 & 7 & 3 & 5 & 5 \\
**L3-loose** & 5 & 7 & 1 & 3 & 5 & 5 \\
**L3-85\%** & 5 & 7 & 3 & 3 & 5 & 5 \\ \hline \hline \end{tabular}  
* In the numerical simulation, the magnitude and speed of traffic load, the hoop stiffness and diameter of the pipe are changed respectively under each backfill condition, as shown in Table 7.  
\end{table} 
Table 5: Relationship between the compaction degree and the elastic modulus of the backfill. pipe [52; 53; 54]. When the corrugated pipe is simplified as a straight-walled pipe, the circumferential and axial stress distribution of a particular section of the corrugated pipe cannot be obtained, so the Von-Mises stress is more suitable than the real stress to define the deformation of the pipe. In the tests described in the following subsections, the Von-Mises stress was calculated and output by ABAQUS, which could be used to predict the dangerous location at which the pipe is most likely to generate a ductile failure under the combined action of loose backfill and traffic loads.