{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T19:52:52Z","timestamp":1780516372710,"version":"3.54.1"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T00:00:00Z","timestamp":1706227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100015282","name":"China Academy of Railway Sciences Corporation Limited","doi-asserted-by":"publisher","award":["2023YJ090"],"award-info":[{"award-number":["2023YJ090"]}],"id":[{"id":"10.13039\/501100015282","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The environmental vibrations of tunnels and soil caused by metro operations is one of the most important issues in the field of environmental geotechnical engineering. Recent studies in metro-induced vibrations have revealed significant uncertainties in the vibration responses of tunnels and the surrounding soil. A two-step method of obtaining train loads considering uncertainty was introduced. The first step was to obtain the train loads via an inverse model based on measurements, and the second step was to quantify the uncertainty of train loads based on complex principal component analysis. A portion of a tunnel of the Beijing metro was selected as the object of study, where the vertical accelerations on the rail and on the tunnel wall were measured under different train speeds of 35, 45 and 55 km\/h. Inputting the train loads based on the measured rail accelerations into an axisymmetric numerical model, established using ANSYS, the vibration responses of the tunnel wall in a probabilistic framework were calculated and were compared with the measured results. By using an accuracy index that considers both calculation bias and uncertainty, the accuracy of the calculated vibration response was quantitatively evaluated. It can be concluded that the calculated vibration response can reflect the actual vibration level and uncertainty of the tunnel wall. The accuracies of the calculated results under different speeds were generally high while showing a slight difference in amplitude.<\/jats:p>","DOI":"10.3390\/sym16020145","type":"journal-article","created":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T08:56:01Z","timestamp":1706259361000},"page":"145","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Analysis of Vibration Responses Induced by Metro Operations Using a Probabilistic Method"],"prefix":"10.3390","volume":"16","author":[{"given":"Zongzhen","family":"Wu","sequence":"first","affiliation":[{"name":"Urban Rail Transit Centre, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chunyang","family":"Li","sequence":"additional","affiliation":[{"name":"Urban Rail Transit Centre, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6523-564X","authenticated-orcid":false,"given":"Weifeng","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donghai","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenbin","family":"Wang","sequence":"additional","affiliation":[{"name":"Urban Rail Transit Centre, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Zhu","sequence":"additional","affiliation":[{"name":"Urban Rail Transit Centre, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107106","DOI":"10.1016\/j.jobe.2023.107106","article-title":"Train-induced vibration mitigation based on foundation improvement","volume":"76","author":"Li","year":"2023","journal-title":"J. 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