## 6 Analysis of Ultimate Axial Load under Various Service Conditions
### Effect of Crack Size  
The effect of the crack depth ratio on the ultimate axial load was analyzed based on the evaluation results without and with 1 mm pipe misalignment under a fixed crack length-to-cycle ratio of 0.01 (Figure 11).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Influencing Factors** & **Values** \\ \hline Crack depth ratio \(a/B\) & 0.1, 0.2, 0.3 \\ Crack length-to-cycle ratio \(2c/\pi D\) & 0.01, 0.03, 0.05, 0.07 \\ Wall thickness \(B\) (mm) & 11.0, 12.5, 14.2, 16.0, 17.5 \\ Misalignment \(e\) (mm) & 0, 1, 2, 3 \\ Tensile strength \(\sigma_{u}\) (MPa) & 535, 647.5, 760 \\ Yield ratio \(\lambda\) & 0.842, 0.865, 0.888 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Value ranges of the investigated influencing factors.  
Figure 10: Effect of material properties on the evaluation results of a circumferential weld crack on the \(\mathcal{O}813\times 11\) mm pipeline. (**a**) \(\sigma_{u}\) = 535 MPa (minimum value); (**b**) \(\sigma_{u}\) = 647.5 MPa (mean value); (**c**) \(\lambda\) = 0.842; (**d**) \(\lambda\) = 0.865.  
It can be observed that the larger the crack depth ratio, the lower the ultimate axial tensile load that the girth welded joint can withstand. The conservative degree of Option 2 evaluation was lower than that of Option 1 evaluation; thus, the ultimate axial load of the Option 2 evaluation was higher than that of the Option 1 evaluation. According to the Option 1 evaluation, when the crack depth ratio is 0.3, the maximum axial load should not exceed 0.93 times the specified minimum yield strength of the pipeline without misalignment during operation. Under the same conditions and 1 mm misalignment, the maximum axial load should not exceed 0.78 times the specified minimum yield strength during operation.  
The effect of crack perimeter ratio on the ultimate axial load was analyzed based on the evaluation results without and with 1 mm pipe misalignment under a fixed crack depth ratio of _a/B_ = 0.3.  
According to Figure 12, the larger the crack length-to-cycle ratio, the lower the ultimate axial tensile load that the girth welded joint can withstand. In addition, the Option 2 evaluation was less conservative than the Option 1 evaluation; thus, the ultimate axial load under the Option 2 evaluation was higher than that under the Option 1 evaluation. According to the Option 1 evaluation, when there is no pipeline misalignment and the crack length-to-cycle ratio has the maximum value of 0.07, the maximum axial load should not exceed 0.77 times the specified minimum yield strength during operation. Under the same conditions and 1 mm misalignment, the maximum axial load should not exceed 0.67 times the specified minimum yield strength during operation.  
Without pipeline misalignment, the ultimate axial load value decreases slightly with increasing wall thickness. This is because the width of the weld toe increases with the increase of the wall thickness, and the effect of stress concentration becomes more significant. The load is at the limit of plastic collapse, and its non-conservative degree increases. However, when there is pipeline misalignment, the ultimate axial load value increases slightly with the increasing wall thickness, which is attributed to the fact that the stress concentration of the weld toe is weakened with the occurrence of misalignment. In general, the greater the wall thickness, the higher the safety of the pipeline, and the ultimate axial load value increases as well.  
Figure 11: Ultimate axial load of girth weld cracks in pipes with different wall thickness values (2_c/\(\pi\)D_ = 0.01). (**a**) \(e\) = 0 mm; (**b**) \(e\) = 1 mm.