## 5 Result Analysis
### Discussion of Burst Pressure  
In the burst pressure tests, 16 full size tests were carried out, and the burst pressures of those specimens were obtained. However, the experiments data indicated that the burst pressures decreased with increased SDR. Hence, theoretical approaches and various full size experimental data of burst pressure for PVC pipes were compared in Figure 21. The data from the 16 full size tests carried out in the experimental study were involved for various SDR grades ranging from 21 to 51. It can be seen from Figure 21 that the same trend of burst pressure derived from the four failure criteria was observed while the ASSY solution was the closest to the test data. However, significant differences have also been noticed in these methods; the TSSY overestimated the burst pressure of pipe and provided the upper limit of burst pressure while the Tresca solution did just the opposite. Based on other yield criteria such as Mises and ASSY, the burst pressure is between those two approaches. In the comparison of Mises and ASSY results, ASSY results are closer to the experimental test values.  
Normally, nominal stress is used as the primary parameter of materials for safety assessment. Therefore, to directly address the role of the yield criteria solution, we analyzed the corresponding equivalent stress \(\sigma_{e}\) and hoop stress \(\sigma_{\theta}\) in burst pressure solutions. The equivalent stress and hoop stress can be expressed as  
\[\left(\sigma_{e}\right)_{b}=\left(\frac{k}{2}\right)^{n}\sigma_{t}^{\prime}, \left(\sigma_{\theta}\right)_{b}=2\left(\frac{k}{2}\right)^{n}\sigma_{t}^{\prime} \tag{18}\]  
\[k=\left\{\begin{array}{ll}1,&\text{for Tresca criteria}\\ 2/\sqrt{3},&\text{for Mises criteria}\\ 1/2+1/\sqrt{3},&\text{for ASSY criteria}\\ 4/3,&\text{for TSSY criteria}\\ \end{array}\right. \tag{19}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Evaluation** & **RMSE (MPa)** & **MAE (MPa)** & **ME (MPa)** & **R\({}^{2}\)** \\ \hline ASSY solution & **0.05** & **0.04** & **0.11** & **0.99960** \\ FEM approach & **0.04** & **0.04** & **0.08** & **0.99975** \\ TSSY solution & 0.78 & 0.77 & 1.05 & 0.99962 \\ Tresca solution & 0.28 & 0.27 & 0.45 & 0.99960 \\ von Mises solution & 0.22 & 0.21 & 0.26 & 0.99961 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistical comparison of burst pressure prediction.  
Figure 21: The relationship between burst pressure and SDR.  
2. The test data revealed that the ASSY approach exhibited excellent performance in evaluating PVC pipe burst pressure. The TSSY approach and Tresca criterion provided an upper and lower bound, respectively, while they overestimated or underestimated burst pressure to a certain extent.
3. The theoretical value of water burst pressure was reduced with increasing strain hardening exponent \(n\)-value, while it increased with increasing SDR. The equivalent stress and the hoop stress derived from the four theoretical solutions showed a similar tendency. However, a significant discrepancy among them can be recognized.  
Consequently, we are convinced that the ASSY approach proposed in this study can be applied as a practical tool for evaluating the PVC pipe bursting pressures.  
Conceptualization, [PERSON] and S.H.; methodology, J.Y.; software, J.Y.; validation, [PERSON] and S.H.; formal analysis, J.Y.; investigation, [PERSON]; resources, J.Y.; data curation, J.Y.; writing--original draft preparation, J.Y.; writing--review and editing, [PERSON] and S.H.; visualization, [PERSON]; supervision, [PERSON] and S.H.; project administration, [PERSON] and S.H.; funding acquisition, S.H. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the National Natural Science Foundation of China (51739008).  
Not applicable.  
This work was supported by the National Natural Science Foundation of China (51739008).  
The authors declare no conflict of interest.