{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:43:21Z","timestamp":1760233401479,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T00:00:00Z","timestamp":1609977600000},"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":["51908371"],"award-info":[{"award-number":["51908371"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, numerical simulations of face stability of shallow tunnels are carried out by using the particle discrete element codes PFC2D from the microscopic view. Progressive instability of the tunnel face is achieved through the withdrawal of the baffle used to simulate the tunnel face. Under different retreating displacement of the tunnel face, the evolution laws of support pressure on the tunnel face, the ground deformation, ground surface settlement and contact force chain in front of the tunnel face are studied. The results show that with the withdrawal of the tunnel face, the support pressure on the tunnel face can be divided into four stages, namely, the rapid decline stage, the minimum stage, the slow rising stage, and the horizontal stability stage. Moreover, based on the simulation results of the particle contact force chain, discriminated methods of failure zones are proposed. The research results obtained from this paper will provide theoretical support for the reasonable value of support pressure of a tunnel face in practical engineering.<\/jats:p>","DOI":"10.3390\/sym13010094","type":"journal-article","created":{"date-parts":[[2021,1,10]],"date-time":"2021-01-10T23:03:42Z","timestamp":1610319822000},"page":"94","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Two-Dimensional Numerical Model for Stability Analysis of Tunnel Face Based on Particle Flow Code"],"prefix":"10.3390","volume":"13","author":[{"given":"Tingwei","family":"Xie","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5623-6376","authenticated-orcid":false,"given":"Kaihang","family":"Han","sequence":"additional","affiliation":[{"name":"College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China"},{"name":"Underground Polis Academy, Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, L., Han, K., Xie, T., and Luo, J. 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