## 4 Conclusions  
In this paper, the buckling behavior of a loosely fitted FIPP liner under external pressure was investigated experimentally; the sensitivity of the critical buckling pressure of the loosely fitted FIPP liner to different parameters was investigated by 2D finite element model and a prediction method of the critical buckling pressure was proposed. Based on the results, the following conclusions can be obtained.  
(1) A loosely fitted FIPP liner will float under the action of buoyancy. While rotation may occur, the buckling lobe of the initial elliptical liner is likely to appear in the direction of the short axis of the liner cross-section when the pressure reaches the critical buckling pressure, the buckling lobe will move in the axial direction, the buckling part has not had plastic deformation and the liner will rebound after the movement of the buckling lobe.  
(2) Through test and simulation, results indicate that the value of critical buckling pressure calculated by the equation from ASTM 1216 is significantly lower than the results under working conditions. The difference in the critical buckling pressure between the calculated result and actual result will increase when the installation condition of the liner is closed to the tightly fitted status.  
(3) The decrease in the value of \(a/R\) causes a change in the contact conditions between the liner and the host pipe under the loosely fitted condition, the increase in the gap between the liner and the host pipe will lead to the movement of the contact point between the liner and the original pipe and the range of the buckling portion increases under external pressure conditions, resulting in a reduction in the critical buckling pressure.  
(4) The effects of changes in the dimensional parameters of the liner on the critical buckling pressure are not independent of each other. With the determined value of \(DR\), a  
Figure 14: Comparing the critical buckling pressure between the simulation result and result calculated by the prediction model.  
decrease in the value of \(a/R\) will diminish the effect of \(DR\) and \(q\) on the critical buckling pressure, while an increase in the value of \(q\) will diminish the effect of \(a/R\) on the critical buckling pressure with the determined value of \(DR\). Considering the interaction between the dimensional parameters, a polynomial fit is used to propose the equation for the enhancement factor \(K_{\Delta}\) and the average difference rate was reduced from 23.43% to 5.52%.  
The present study only considers 2D plane conditions; any possible deformation in the axial direction is ignored, while the possible rotation of the liner under the water pressure is also ignored and the results are idealized. Future research can focus on the buckling behavior of the FIPP liner which is suspended in the host pipe under water pressure and not in contact with the inner surface of the host pipe.  
Conceptualization, Z.Z., X.Y. and S.T.A.; methodology, Z.Z. and Y.Z.; software, Z.Z. and Y.Z.; validation, X.Y. and W.X.; formal analysis, Z.Z.; investigation, X.Y. and S.T.A.; resources, X.Y. and S.T.A.; data curation, W.X. and Z.Z.; writing--original draft preparation, Z.Z.; writing--review and editing, S.T.A., Y.Z. and X.Y.; visualization, Z.Z.; supervision, X.Y.; project administration, X.Y.; funding acquisition, X.Y. All authors have read and agreed to the published version of the manuscript.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.