{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T15:19:31Z","timestamp":1776525571631,"version":"3.51.2"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T00:00:00Z","timestamp":1580083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005022","name":"Beijing Jiaotong University","doi-asserted-by":"publisher","award":["2019JBM093"],"award-info":[{"award-number":["2019JBM093"]}],"id":[{"id":"10.13039\/501100005022","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004254","name":"Ministry of Railways","doi-asserted-by":"publisher","award":["J2017G001"],"award-info":[{"award-number":["J2017G001"]}],"id":[{"id":"10.13039\/501100004254","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004254","name":"Ministry of Railways","doi-asserted-by":"publisher","award":["N2018G029"],"award-info":[{"award-number":["N2018G029"]}],"id":[{"id":"10.13039\/501100004254","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Cracks in the lining significantly reduce the safety of a tunnel during operation. It is urgent to figure out the influence of cracks on tunnel carrying capacity. In this paper, three-dimensional model tests were conducted to investigate deformation, internal force, and deterioration laws of the lining with prefabricated cracks at different positions. The main conclusions were obtained as follows: (1) The carrying capacity of the lining structure with prefabricated cracks was reduced, and the deformation of the lining structure increased. The penetration of the vault crown crack accelerated the damage of the lining structure, and structural failure occurred when the crack went through at the left arch spring. (2) The internal force of the lining was greatly affected by the positions of prefabricated cracks. The internal forces of the lining structure decreased with the existence of prefabricated cracks. Whether or not there were prefabricated cracks, tension cracks appeared in the inside fiber of the vault and inverted arch. (3) The deformation of the lining structure with the existence of prefabricated cracks increased. When the prefabricated crack was located at the vault, the deformation was the largest, followed by the arch spring, side wall, and arch shoulder. (4) The analysis shows that prefabricated cracks at the vault are the most damaging under stress and deformation of the lining structure, so longitudinal cracks at the vault should be strengthened.<\/jats:p>","DOI":"10.3390\/sym12020194","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T11:41:57Z","timestamp":1580125317000},"page":"194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Mechanical Behavior of Tunnel Lining with Cracks at Different Positions"],"prefix":"10.3390","volume":"12","author":[{"given":"Jie","family":"Su","sequence":"first","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinming","family":"Jie","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaokai","family":"Niu","sequence":"additional","affiliation":[{"name":"Beijing Municipal Engineering Research Institute, Beijing 100037, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuan","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.tust.2015.08.007","article-title":"Face stability analysis of shallow circular tunnels in cohesive-frictional soils","volume":"50","author":"Zhang","year":"2015","journal-title":"Tunn. 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