###### Abstract  
This paper presents a study about the buckling behavior of thin stainless-steel lining (SSL) for trenches repair of urban water supply networks under negative pressure. The critical buckling pressure and displacement (\(p\)-\(\delta\)) curves, temperature changing curves, hoop and axial strain of the lining monitoring section and the strain changes with system pressure (\(p\)-\(\epsilon\)) of the lining under the action of different diameters, different lining wall thickness and different ventilation modes were obtained through five groups of full-scale tests. The variation principles of the post-buckling pressure and the reduction regularity of the flowing section of the lining were further investigated. By comparing different pipeline buckling models and introducing thin-shell theory, the buckling model of liner supported by existing pipe was established. The comparison between the test results and thin-shell theory indicates that one of the significances of the enhancement coefficient \(k\) value is to change the constraint condition of the aspect ratio, \(l\)/\(R\), thus increasing the critical buckling pressure of the lining. Finally, an improved lining buckling prediction model (enhancement model) is presented. A previous test is used as a case study with the results showing that the enhanced model is able to predict critical buckling pressure and lobe-starting amount of the liner, which can provide guidance for trenches restoration of the liner with thin-walled stainless steel. water supply; buckling and post buckling; stainless-steel pipe; thin-shell structure +
Footnote †: journal: Applied Sciences  
1 Faculty of Engineering, China University of Geosciences-Wuhan, Wuhan 430074, China; [EMAIL_ADDRESS] (C.L. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (W.X.) 20 June 2021  
21 July 2021  
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**[PERSON] 1 Faculty of Engineering, China University of Geosciences-Wuhan, Wuhan 430074, China; [EMAIL_ADDRESS] (C.L. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (W.X. )**  
**[PERSON] 1 Faculty of Engineering, China University of Geosciences-Wuhan, Wuhan 430074, China; [EMAIL_ADDRESS] (C.L. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (W.  
Water-supply networks are often installed in the underground space of urban built-up areas, thereby making it difficult to dig and repair broken pipes. Trenchless technology has been used for more than 25 years in China [10]. ISO 11298-1(2018) [11] provides seven methods for trenchless repair of water-supply pressure pipelines, namely lining with continuous pipes, lining with close-fit pipes, lining with cured-in-place pipes, lining with discrete pipes, lining with adhesive-backed hoses, lining with sprayed polymeric materials and lining with inserted hoses. However, the relevant theories and processes in design and construction are not perfected at present. Trenchless technology applied to water supply pressure defective pipelines includes the following categories: stainless-steel liner (SSL), folding of plastic liner, PVC liner and polymer liner [12]. Stainless steel has many desirable characteristics, including corrosion-resistant, long-lasting, tough, hygienic, adaptable and recyclable [13; 14; 15; 16]. As early as the mid-1960s, Europe and the United States began to use stainless-steel pipes, gradually accounting for more than 85% of the water pipe market. Japan began to implement stainless-steel pipes around 1980 fully, and the market share gradually rose to 90%. East and Southeast Asia are the fastest growing regions for stainless-steel pipes, with an annual sales rate of stainless-steel pipes growing by 10%. At the beginning of the 21 st century, the Chinese government made it mandatory to use plastic, aluminum-plastic composite water-supply pipes or stainless-steel and copper pipes as the materials of choice for water-supply pipelines.