## 4 Results
### Effect of Non-Uniform Corrosion  
The uniform corroded tubular joint and 10 non-uniform corroded tubular joints are analysed under axial loading, and the SCFs are compared to illustrate the effect of non-uniform corrosion degradation as shown in Figure 14. The exposure time of these joints is assumed to be 15 years, resulting in d = 1.5 mm (corrosion rate 0.1 mm/year) and Ra = 57.822 um based on the linear equation shown in Figure 9. Non-uniform corrosion can result in significant fluctuation of the hot-spot stress around the uniform corrosion results. The SCF can be underestimated if only the uniform corrosion is considered.  
The SCF deviation caused by non-uniform corrosion is statistically analysed. The crown toe along the intersection is divided into four regions: two crown regions and two saddle regions [11], as shown in Figure 1. The SCF deviation for each weld toe node in the critical region where the maximum SCF appears is obtained as follows:  
\[\mathrm{x_{i}}=\mathrm{SCF_{nu,i}}-\mathrm{SCF_{nu,i}} \tag{3}\]  
where \(\mathrm{x_{i}}\) is the SCF deviation of weld toe node i, \(\mathrm{SCF_{nu,i}}\) is the SCF of the non-uniformly corroded tubular joint at the node, and \(\mathrm{SCF_{u,i}}\) is the SCF of the uniformly corroded tubular joint at the node. Statistical analyses can be conducted based on the results for all the  
Figure 14: (**a**) SCF distributions along the intersection and (**b**) partial enlarged SCF distribution for the uniformly corroded tubular joint with d = 1.5 mm (black line) and 10 non-uniformly corroded tubular joints with Ra = 57.822 um (other lines) under axial loading.  
Figure 13: SCFs between grooving corrosion and uniform corrosion.  
nodes in the critical region. It has been found that the SCF deviation conforms to normal distributions. The SCF deviation at the critical region can be described by a normal distributed random variable. Normal distributions are regressed for the exposure time of 1, 2, 5, 10 and 15 years, respectively. The regressed distributions for various conditions are shown in Figure 15. The mean values of the SCF deviation are close to zero, and the standard deviation of the SCF deviation increases with the exposure time.  
The relationship between the standard deviation of the SCF deviation \(\sigma_{\text{X}}\) and Ra is investigated. The \(\sigma_{\text{X}}\) for the saddle region under axial loading, crown region under IPB and saddle region under OPB are evaluated, and the results are shown in Figure 16. It can be seen that \(\sigma_{\text{X}}\) increases with Ra, and the relationship between \(\sigma_{\text{X}}\) and Ra is approximately linear for all three loading conditions. The variation of \(\sigma_{\text{X}}\) to Ra depends on the loading conditions.  
Figure 15: PDF of the SCF deviation between uniform and non-uniform corrosion: (**a**) saddle region under axial loading; (**b**) crown region under axial loading; (**c**) crown region under IPB; (**d**) saddle region under OPB.  
The analyses of the non-uniformly corroded tubular joint are time-consuming because of the complex modelling procedures. To obtain a conservative maximum SCF only accounting for non-uniform corrosion, the following equation is proposed:  
\[\text{SCF}_{\text{c}}=\text{SCF}_{\text{u}}+2\sigma_{X} \tag{4}\]  
where \(\text{SCF}_{\text{c}}\) and \(\text{SCF}_{\text{u}}\) are the maximum SCF accounting for the non-uniform corrosion and the maximum SCF of the uniformly corroded tubular joint, respectively. \(2\sigma_{\text{X}}\) indicates that the exceeding probability is about 2.3%.