## 2 Experimental Testing
### Experimental Result
#### 2.2.2 Critical Buckling Pressure  
According to the test results in Table 2, in T1 and T2, with the increase of lining diameter, the critical buckling pressure value presents a downward trend, and the data anomalies of T3 are explained in the foregoing contents. The test results of T1 and T4 show that, in thin-walled structures, the wall thickness has a significant impact on structural buckling, and the critical buckling pressure of the lining with a wall thickness of 1.61 mm decreases by nearly 25% compared with lining with a wall thickness of 1.79 mm. As for the influence of loading mode, the results concluded that the shorter the time for the pressure differentials to reach the threshold of critical buckling, the lower the critical buckling pressure of the lining structure. Compared with the T1 with continuous ventilation, the critical buckling pressure of the T5 decreased by 13.7%. Figure 6 illustrates the curves of pressure-displacement in the logarithmic coordinates of several groups of tests, which all show the same law. The curve can be described as four stages during the extraction of the internal cavity. They stages are as follows: (1) the linear segment where the vacuum degree of the system increases and the displacement has minimal changes; (2) the nonlinear segment whose displacement increases with the increase of vacuum degree; (3) when the critical buckling pressure is reached, the pressure value remains constant and the displacement changes rapidly; and (4) with the increase of displacement, the system pressure begins to decrease, respectively. It can be found from the curve that, under the same wall thickness, the larger the pipe diameter, the more the liner reaches the third stage (T1 and T2). The displacements of the experimental groups (T1, T4) with the same pipe diameter and different wall thickness at the third stage were basically the same. In addition, instantaneous change of pressure differentials will also advance the lining into the third stage (T1 and T5). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen Number** & **n = 1** & **Gr** & **n = 2** & **Gr** & **n = 3** & **Gr** & **n = 4** & **Gr** \\ \hline T1 & 55.12 & 0 & 52.44 & \(-\)4.86\% & 54.45 & +3.82\% & 68.84 & +26.43\% \\ T2 & 28.47 & 0 & 29.46 & +3.49\% & 28.16 & \(-\)4.42\% & / & / \\ T3 & 34.44 & 0 & 53.59 & +55.60\% & 47.70 & \(-\)10.99\% & 47.84 & \(-\)0.29\% \\ T4 & 41.37 & 0 & 40.30 & \(-\)2.58\% & / & / & / & / \\ T5 & 47.57 & 0 & 52.87 & +11.15\% & 54.02 & +2.17\% & 54.38 & +0.67\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test result (buckling pressure of different lobes and gradient, Gr). Figure 6: Pressure displacement curves from T1 to T5. After the first buckling value was observed, the post-buckling of the lining in several groups of tests was also observed in subsequent tests (Figure 7). The second column of each set of tests in Table 2 presents the increment of the system pressure at the time of each lobe generation compared to the previous buckling pressure. In groups T1, T2 and T4, the pressure values generated by several lobes were relatively close, with the mean values being 54.00, 28.70 and 40.84 kPa, respectively. In group T3, the circumscribed length of the liner rolled by steel plate was 1436 mm, exceeding the DN1200 pipe by 236 mm, which made part of the liner overlap repeatedly. Thus, it showed two platforms in the peak value of buckling, with the mean values of 34.44 and 49.71 kPa, respectively. The post-buckling model results of group T5 show that, during the rapid \"loading\" process, the critical pressure values generated by several lobes were reduced. The critical pressure generated by the first lobe was 47.57 kPa, and the average pressure of the second to the fifth lobe was 53.76 kPa. Through the data of PIV targets, the reduction regularity of lining area in several stages was obtained, and it is shown in Figure 8. [PERSON] and [PERSON] [27] presented the order of buckling state and cross-sectional area change of pipelines under external pressure.