{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T13:07:09Z","timestamp":1776690429169,"version":"3.51.2"},"reference-count":42,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,17]],"date-time":"2019-06-17T00:00:00Z","timestamp":1560729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The presence of symmetric and asymmetric voids directly affects the mechanical behaviors of tunnel linings and further induces tunnel diseases among influence factors. In this paper, 1:5-scale model tests were carried out to study the mechanical behaviors of reinforced concrete (RC) linings considering the voids located at the crown and at the spandrel. Based on the experimental results and concrete plastic damage (CDP) model, the effects of void (i.e., location and size), subgrade stiffness, and lining size on bearing capacity of RC lining were investigated using numerical simulation. The results of model test and parametric analysis showed that the existence of voids significantly affected the mechanical behavior of the lining during inelastic deformation period. The lining with a larger void size corresponded to low bearing capacity and larger deformation around the void, thus increasing the damage possibility of linings. The influence of voids on the bearing capacity of linings varied with the void location, load direction (especially under horizontal symmetrical loads), and subgrade stiffness. High soil stiffness corresponded to a great influence of the void size on the lining bearing capacity. In addition, the lining strength increased inconsistently with the increase of model size. On the basis of parameter sensitivity analysis, the Levenberg\u2013Marquardt (L-M) optimization algorithm and Logistic model were used to establish the equation of lining bearing capacity loss rate considering the void effect.<\/jats:p>","DOI":"10.3390\/sym11060802","type":"journal-article","created":{"date-parts":[[2019,6,17]],"date-time":"2019-06-17T11:24:45Z","timestamp":1560770685000},"page":"802","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Influence of Symmetric and Asymmetric Voids on Mechanical Behaviors of Tunnel Linings: Model Tests and Numerical Simulations"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6140-1885","authenticated-orcid":false,"given":"Zude","family":"Ding","sequence":"first","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiafei","family":"Ji","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqin","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhihua","family":"Ren","sequence":"additional","affiliation":[{"name":"Yunnan Research Institute of Highway Science and Technology, Kunming 650051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sen","family":"Zhang","sequence":"additional","affiliation":[{"name":"Yunnan Research Institute of Highway Science and Technology, Kunming 650051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,17]]},"reference":[{"key":"ref_1","unstructured":"Zhao, Y. 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