{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T19:17:12Z","timestamp":1775330232813,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,12]],"date-time":"2021-12-12T00:00:00Z","timestamp":1639267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51578550"],"award-info":[{"award-number":["51578550"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51538009"],"award-info":[{"award-number":["51538009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51978668"],"award-info":[{"award-number":["51978668"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The deformation of existing pipelines caused by the tunneling of a shield machine along curved sections has not been sufficiently researched, and a corresponding theoretical prediction formula is lacking. This paper derives a prediction formula for the deformation of an existing pipeline caused by shield machine tunneling along a curved section. Further, a finite difference model (FDM) corresponding to an actual project is built. Finally, the deformation of the surface and existing pipelines caused by shield machine tunneling along the curved section is analyzed. The research results show that the results of theoretical prediction, FDM calculation, and field monitoring data are consistent. In addition, the deformation of the surface and the existing pipeline are asymmetrically distributed when the shield machine tunnels along the curve section instead of symmetrically distributed (for straight line segment). When the pipeline is perpendicular to the tunnel axis, the maximum deformation position of the existing pipeline deviates from the tunnel axis by about 0.5 times the tunnel radius. In addition, as the angle \u03b2 between the pipeline axis and the tunnel axis increases, the maximum deformation position of the pipeline gradually approaches the tunnel axis.<\/jats:p>","DOI":"10.3390\/sym13122396","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T01:29:33Z","timestamp":1639358973000},"page":"2396","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Analysis of Asymmetrical Deformation of Surface and Oblique Pipeline Caused by Shield Tunneling along Curved Section"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6572-8620","authenticated-orcid":false,"given":"Huangshi","family":"Deng","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Central South University, Changsha 410075, China"},{"name":"National Engineering Laboratory for Construction Technology of High-Speed Railway, Central South University, Changsha 410075, China"}]},{"given":"Helin","family":"Fu","sequence":"additional","affiliation":[{"name":"National Engineering Laboratory for Construction Technology of High-Speed Railway, Central South University, Changsha 410075, China"}]},{"given":"Yue","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Central South University, Changsha 410075, China"},{"name":"National Engineering Laboratory for Construction Technology of High-Speed Railway, Central South University, Changsha 410075, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2026-5893","authenticated-orcid":false,"given":"Zhen","family":"Huang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Disaster Prevention and Structural Safety, College of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China"}]},{"given":"Qibing","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Central South University, Changsha 410075, China"},{"name":"National Engineering Laboratory for Construction Technology of High-Speed Railway, Central South University, Changsha 410075, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.tust.2019.01.015","article-title":"Estimating the effects of tunnelling on existing jointed pipelines based on Winkler model","volume":"86","author":"Huang","year":"2019","journal-title":"Tunn. 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