## 4 Results and Discussion  
### Effect of Corrosion Depth on the Mechanical Characteristic of Pipeline  
In this section, corrosion width is 60\({}^{\circ}\), cover depth is 1.0 m, traffic load is 1.0 MPa, and corrosion is located at the crown. Different corrosion depths were simulated by chiseling out different thicknesses of the interior pipe wall. Corrosion depths of 0%, 30%, and 60% were used to investigate the effect of corrosion depth on the mechanical properties of the pipeline. [PERSON] et al. [31] inspected an 1800 km sewer network and found that 26.7% of concrete pipe defects were related to joint displacements or openings. Therefore, we examined the mechanical properties of the pipe joint for different corrosion depths. Circumferential strains (the distribution of strain around the pipe circumference) on the inside and outside of the P2 bell and P3 spigot walls for different corrosion depths were calculated and the result was compared with the values obtained from the experiment (Figures 10 and 11 ). In the figure, SIM represents the model data and TEST represents the experimental data. Figure 10: Circumferential strain curves of (**a**) outside (**b**) inside of the pipe bell wall at different corrosion depths. Figures 10 and 11 show that the model values and distributions of circumferential strains are consistent with the experimental results. The relative error is \(<\)25% at the crown, the invert, and the springline, but the relative error at the 45-225\({}^{\circ}\) and 135-315\({}^{\circ}\) diameter regions of the pipe is relatively large, in the range 25%-40%. The reasons for this difference are that the 45-225\({}^{\circ}\) and 135-315\({}^{\circ}\) diameter regions of the pipe are less stressed than other locations, the observed values at these positions are small, and the sensitivity to error is greater. Thus, the relative error at the 45-225\({}^{\circ}\) and 135-315\({}^{\circ}\) diameter regions of the pipe is correspondingly greater. The relative error was calculated using Equation (3):  
\[\delta\text{=}\Delta\text{/}L\times\text{100\%} \tag{3}\]  
where \(\delta\) is the relative error, \(\Delta\) is the difference between the numerical model results and the experimental data, and \(L\) is the experimental data. It can be seen from Figures 10 and 11 that circumferential strain on the inside and outside of the pipe wall increases as corrosion depth increases. The inside of the buried corroded pipe wall is in tension at the crown (315-45\({}^{\circ}\)) and the invert (135-225\({}^{\circ}\)) and is in compression at the springline (45-135\({}^{\circ}\), 225-315\({}^{\circ}\)), but for the outside pipe wall, the opposite is true. A comparison of Figures 10 and 11 shows that maximum circumferential strain of the pipe bell is much greater than that of pipe spigot. This is because the bell, which is convex, is more constrained by the soil than other parts of the pipe, but the spigot, which is inserted inside the bell, is not directly in contact with the soil and so the stress of the spigot is mainly transmitted through the gasket. Thus, the bell is more vulnerable to damage than the spigot. Comparing Figure 10a with Figure 10b, it can be seen that maximum circumferential strain of the inside of the pipe wall (at the crown) is much greater than that of the outside (at the springline), and the increase in the circumferential strain of the inside of the wall due to corrosion is much greater than that of the outside. This result indicates that the corroded area on the inside of the pipe wall is most susceptible to tensile damage, and the effect of corrosion depth on the inside is more significant than on the outside of the pipe wall. Pipes are prone to crack under long-term operation, affecting the normal operation of the pipeline. To explore the relationship between the risk of the pipe cracking and corrosion depth, corrosion depths of 10%, 20%, 40%, and 50% were calculated.