## 4 Summary and Conclusions  
The buckling of stainless-steel liner encased in host pipe under continuous negative pressure (instantaneous negative pressure) was investigated experimentally in this paper. The buckling and post-buckling behavior of the liner pipe were expounded from the measurement of critical pressure, strain and displacement of liner. Finally, based on the thin-shell theory, an enhanced prediction model considering the support of existing pipelines was proposed, and an analytical solution was given. It should be noted that there  
Figure 17: Critical pressure envelope under different wall thickness. will be more or less imperfections due to the installation of the on-site lining. Therefore, the research in this paper is carried out when the ovality is less than 1.6% and the annular gap is less than 2.0%. According to the research results of this paper, the following conclusions can be drawn:  
1. When the pump and valve are switched on and off in the water supply network system, the inertia of the medium causes negative pressure and positive pressure, which can be considered as the local failure of the pipeline. The test equipment employed in this study is reliable and effective for the study of application of thin-wall stainless-steel trenchless repair technology to update the system stability of water-supply pipe network. 2. In the pre-buckling stage, the critical buckling pressure is closely related to the lining wall thickness and lining diameter. The smaller the lining wall thickness is, the smaller the critical buckling pressure is. Moreover, with the increase of pipe diameter, the critical buckling pressure of liner pipe with the same wall thickness tended to decrease. 3. The results show that the buckling behavior of the pipeline lining system is affected by the pressure change velocity. Under the condition of instantaneous negative pressure, it is easier to form lobes, but after the first lobe, the subsequent critical buckling pressure to form new lobes increases less than that of the continuous negative pressure test. 4. The buckling mode of inner liner under negative vacuum pressure is different from that of buried pipeline and deep-sea pipeline. The strain results indicate that with the increase of vacuum degree, the lining shows the elastic deformation of the full section, such as the elastic deformation of the lower end of the pipeline in Figure 12(c-1). After the material exceeds the elastic stage, the first lobe appears in the lining, and then the vacuum degree of the system decreases obviously. The system will reach a new equilibrium. With the increase of vacuum degree, new lobes will be formed. This process shows certain cyclic characteristics. The buckling position of several test liners is not the same, which is determined by the boundary constraints of the liners and host pipe. 5. One of the most important factors to consider in a water-supply pipeline is its ability to overflow. The critical buckling pressure of the subsequent lobes differs little from the critical buckling pressure of the first lobe. That is, as long as the buckling occurs, the subsequent lobes will be generated quickly. We believe that the overflow section in post-buckling is easier to reduce to the level of 50-60% of the original pipeline, which is unacceptable in the water supply network. Therefore, a reasonable design method should be applied to obtain the economic and reliable lining design's wall thickness. 6. With the support of the existing pipe, the position where lining buckling produces greater tensile strain. The critical pressure of lining buckling deviates significantly from the theory of free ring. By comparing the two, the enhancement coefficient \(\mathbf{k}\), which ranges from 11.22 to 14.02, is obtained. The critical pressure calculation Equation given in the thin-shell theory can predict the number of buckling waves and critical buckling pressure, but it does not consider the supporting role of existing pipelines.