## 4 Results and Discussion
### Effect of Corrosion Width on the Mechanical Characteristic of Pipeline  
In this section, corrosion depth is 30%, traffic load is 1.0 MPa, and cover depth is 1.0 m. Different corrosion widths were set by altering the angle subtended by the arc of the corrosion width at the springline. Corrosion width values of \(10^{\circ},60^{\circ}\), and \(120^{\circ}\)were used in calculations to investigate the effect of corrosion width on the mechanical properties of the pipeline. As in Section 4.1, the circumferential path of P2 bell and P3 spigot were selected. The circumferential strain of the outside and inside of the pipe bell and pipe spigot walls for different corrosion widths are shown in Figures 13 and 14.  
Figure 12: Relationships between the maximum principal stress and corrosion depth.  
Figure 13: Circumferential strain curves of (**a**) inside and (**b**) outside of the pipe bell wall at different corrosion widths.  
Figures 13 and 14 show that the simulation results of the circumferential strains are consistent with the experimental results in distribution trends and values. Figures 13a and 14a show that circumferential strain on the inside changes abruptly in the corroded area at the crown and the value at which this change occurs decreases as corrosion width increases. This is mainly because when corrosion width is small, severe stress is concentrated at the corroded area of the pipe, which leads to a sharp increase in the maximum principal stress. As corrosion width increases, stress dissipates and the maximum principal stress in the area of corrosion correspondingly decreases. At some point, as corrosion width reaches a particular level, stress is not concentrated at any location and the effect of corrosion width on the maximum principal stress becomes extremely weak. Figures 13b and 14b show that circumferential strain on the outside of the pipe wall is almost coincident for different corrosion widths, which indicates that corrosion width has little effect on the outside of the pipe wall.  
Because stress at the crown is very high when corrosion width is small and low when corrosion width is large, corrosion width values used in this section were densely clustered for smaller corrosion widths and were sparse for larger corrosion widths. To investigate the effect of corrosion width on pipe cracking, corrosion width values of \(0^{\circ}\), \(20^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), and \(180^{\circ}\) were calculated. As in Section 4.1, the maximum values of the maximum principal stress at the crown, the springline and the invert under different corrosion width were extracted (Figure 15).  
Figure 15 shows that as corrosion width increases, the maximum principal stress at the invert increases slowly, and the maximum principal stress at the springline does not change significantly.  
Figure 14: Circumferential strain curves of (**a**) inside and (**b**) outside of the pipe spigot wall at different corrosion widths.  
Figure 15: Relationship between the maximum principal stress of the pipe and corrosion width.  
However, the maximum principal stress at the crown rapidly increases (0-10\({}^{\circ}\)), then rapidly decreases (10-45\({}^{\circ}\)), and lastly gradually decreases (45-180\({}^{\circ}\)). We infer that corrosion width has a great influence on the crown where there is corrosion, but has little effect on the springline or the invert, where there is no corrosion. This is consistent with the conclusions obtained from Figures 13 and 14. There is a stress concentration that causes the strain at the corroded area to be greater than for other areas. This phenomenon becomes less pronounced as corrosion width increases.  
In summary, the maximum principal stress of the pipe is negatively correlated with corrosion width. As corrosion width decreases, the probability of pipe failure increases. Therefore, when the pipe corrosion width is small, measures must be taken to prevent the rapid deterioration of the pipeline.