{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T18:21:06Z","timestamp":1778782866575,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,7]],"date-time":"2023-03-07T00:00:00Z","timestamp":1678147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Anhui Province Postdoctoral Research Activities Funding Project","award":["2022B642"],"award-info":[{"award-number":["2022B642"]}]},{"name":"Anhui Province Postdoctoral Research Activities Funding Project","award":["U1934210"],"award-info":[{"award-number":["U1934210"]}]},{"name":"Key Project of the High-Speed Rail Joint Fund of the National Natural Science Foundation of China","award":["2022B642"],"award-info":[{"award-number":["2022B642"]}]},{"name":"Key Project of the High-Speed Rail Joint Fund of the National Natural Science Foundation of China","award":["U1934210"],"award-info":[{"award-number":["U1934210"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Compared with single or twin tunnels, the pressure arch effect of deeply buried, symmetrically distributed triple tunnels are more complex and less studied. In this paper, the arching responses are in-situ measured in the deeply buried, symmetrically distributed triple tunnels of Badaling Great Wall station. Numerical research is subsequently conducted to investigate the formation and development of the pressure arch of triple tunnels. Then, the influencing law of buried depth on pressure arch behavior is systematically studied. Based on monitoring data, the rock pressure distribution is asymmetric about the axis of the triple tunnels, and the arching response of the middle tunnels is more significant than that of the left and right tunnels. According to numerical analysis, a combined large pressure arch may be easily formed across the triple tunnels. The pre-arching and double-arching effects are also numerically observed during triple tunnel excavations. The inner boundary of the pressure arch of the middle tunnel is 14.0 m, nearly two times higher than those of the left and right tunnels. This simulation result indicates that the mechanical state of the middle tunnel is the least desirable. Moreover, the critical arching depth of closely spaced tunnels is 1.75 times that of a single tunnel. Compared with a single tunnel, the support of triple tunnels should be additionally strengthened.<\/jats:p>","DOI":"10.3390\/sym15030673","type":"journal-article","created":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T03:29:05Z","timestamp":1678246145000},"page":"673","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Pressure Arch Effect of Deeply Buried Symmetrically Distributed Triple Tunnels"],"prefix":"10.3390","volume":"15","author":[{"given":"Ran","family":"Li","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"},{"name":"Key Laboratory for Urban Underground Engineering of the Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"},{"name":"China Tiesiju Civil Engineering Group Co., Ltd., Hefei 230023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dingli","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory for Urban Underground Engineering of the Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Song","sequence":"additional","affiliation":[{"name":"Key Laboratory for Urban Underground Engineering of the Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"},{"name":"School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ao","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory for Urban Underground Engineering of the Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiwei","family":"Luo","sequence":"additional","affiliation":[{"name":"Key Laboratory for Urban Underground Engineering of the Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,7]]},"reference":[{"key":"ref_1","first-page":"91","article-title":"\u00dcber Den Erddruck Gegen Innere St\u00fctzw\u00e4nde (Tunnelw\u00e4nde)","volume":"16","author":"Engesser","year":"1882","journal-title":"Deutsche Bauzeitung"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Terzaghi, K.T. (1943). Theoretical Soil Mechanics, John Wiley & Sons. Inc.","DOI":"10.1002\/9780470172766"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/0148-9062(79)90003-2","article-title":"Deformational Response in Discontinua","volume":"16","author":"Chappell","year":"1979","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0886-7798(02)00010-X","article-title":"Cavern Roof Stability\u2014Mechanism of Arching and Stabilization by Rockbolting","volume":"17","author":"Huang","year":"2002","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.tust.2010.06.012","article-title":"Stress Redistribution and Ground Arch Development during Tunneling","volume":"26","author":"Chen","year":"2011","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.tust.2016.09.005","article-title":"A New Model to Predict Soil Pressure Acting on Deep Burial Jacked Pipes","volume":"60","author":"Zhang","year":"2016","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/j.tust.2017.09.004","article-title":"A Method to Estimate the Pressure Arch Formation Above Underground Excavation in Rock Mass","volume":"71","author":"Kong","year":"2018","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.tust.2016.03.009","article-title":"A Model to Assess the Response of an Arched Roof of a Lined Tunnel","volume":"56","author":"Dancygier","year":"2016","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2503","DOI":"10.1007\/s11431-022-2158-9","article-title":"Analytical Solutions for Deep Tunnels in Strain-Softening Rocks Modeled by Different Elastic Strain Definitions with the Unified Strength Theory","volume":"65","author":"Sun","year":"2022","journal-title":"Sci. China Technol. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Sun, Z., Zhang, D., Fang, Q., Huangfu, N., and Chu, Z. (2022). Convergence-Confinement Analysis for Tunnels with Combined Bolt\u2013Cable System Considering the Effects of Intermediate Principal Stress. Acta Geotech.","DOI":"10.1007\/s11440-022-01758-4"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103104","DOI":"10.1016\/j.tust.2019.103104","article-title":"Three-Dimensional Stress-Transfer Mechanism and Soil Arching Evolution Induced by Shield Tunneling in Sandy Ground","volume":"93","author":"Lin","year":"2019","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ram, S., Waclawik, P., Nemcik, J., Kukutsch, R., Kumar, A., Singh, A.K., and Gong, L. Mechanical Behaviors of Deep Pillar Sandwiched between Strong and Weak Layers. J. Rock. Mech. Geo Eng., 2022. in press.","DOI":"10.1016\/j.jrmge.2022.11.006"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4013005","DOI":"10.1061\/(ASCE)GT.1943-5606.0000998","article-title":"Investigation of Soil Arching with Centrifuge Tests","volume":"140","author":"Iglesia","year":"2014","journal-title":"J. Geotech. Geoenviron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.tust.2005.06.003","article-title":"Tunnel Stability and Arching Effects during Tunneling in Soft Clayey Soil","volume":"21","author":"Lee","year":"2006","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_15","first-page":"83","article-title":"Numerical Research and Engineering Practice of Rock Stability of Large Section Triple Tunnels","volume":"11","author":"Ran","year":"2022","journal-title":"China Civ. Eng. J."},{"key":"ref_16","unstructured":"Anwar, K. (2003). A Study On Stress Rock Arch Development Around Dual Caverns, Nanyang Technological Univerisity."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2380","DOI":"10.1007\/s11771-012-1285-x","article-title":"Pressure From Surrounding Rock of Three Shallow Tunnels with Large Section and Small Spacing","volume":"19","author":"Yang","year":"2012","journal-title":"J. Cent. South Univ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.tust.2018.10.007","article-title":"Analytical Scrutiny of Loosening Pressure on Deep Twin-Tunnels in Rock Formations","volume":"83","author":"Li","year":"2019","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104118","DOI":"10.1016\/j.tust.2021.104118","article-title":"Infrared Thermography for Detecting Cracks in Pillar Models with Different Reinforcing Systems","volume":"116","author":"Seo","year":"2021","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S1365-1609(02)00130-2","article-title":"Methodology for Tunnel and Portal Support Design in Mixed Limestone, Schist and Phyllite Conditions: A Case Study in Turkey","volume":"40","author":"Kokar","year":"2003","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S1365-1609(03)00073-X","article-title":"Design of Anchorage and Assessment of the Stability of Openings in Silty, Sandy Limestone: A Case Study in Turkey","volume":"41","year":"2004","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.tust.2013.10.018","article-title":"Geotechnical Investigations and Preliminary Support Design for the Ge\u00e7ilmez Tunnel: A Case Study Along the Black Sea Coastal Highway, Giresun, Northern Turkey","volume":"40","year":"2014","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Azarafza, Mohammad, Akgun, Haluk, Asghari-Kaljahi, and Ebrahim (2018). Stochastic Geometry Model of Rock Mass Fracture Network in Tunnels. Q. J. Eng. Geol. Hydrogeol., 51, 379\u2013386.","DOI":"10.1144\/qjegh2017-136"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103357","DOI":"10.1016\/j.tust.2020.103357","article-title":"Displacement Monitoring, Displacement Verification and Stability Assessment of the Critical Sections of the Konak Tunnel, \u0130zmir, Turkey","volume":"101","author":"Yertutanol","year":"2020","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"8637837","DOI":"10.1155\/2019\/8637837","article-title":"Ground Settlements Due to Construction of Triplet Tunnels with Different Construction Arrangements","volume":"2019","author":"Naseem","year":"2019","journal-title":"Adv. Civ. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Naseem, A., Kashif, M., Iqbal, N., Schotte, K., and De Backer, H. (2020). Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking. Appl. Sci., 10.","DOI":"10.3390\/app10010334"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Li, R., Zhang, D., Wu, P., Fang, Q., Li, A., and Cao, L. (2020). Combined Application of Pipe Roof Pre-Support and Curtain Grouting Pre-Reinforcement in Closely Spaced Large Span Triple Tunnels. Appl. Sci., 10.","DOI":"10.3390\/app10093186"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1061\/(ASCE)GT.1943-5606.0000823","article-title":"Protection of Buildings Against Damages as a Result of Adjacent Large-Span Tunneling in Shallowly Buried Soft Ground","volume":"139","author":"Zhang","year":"2013","journal-title":"J. Geotech. Geoenviron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/S0013-7952(02)00204-1","article-title":"Engineering Geological Investigations Along the Il\u0131ksu Tunnels, Alanya, Southern Turkey","volume":"68","year":"2003","journal-title":"Eng. Geol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.enggeo.2007.09.005","article-title":"Engineering Geological Investigations and the Preliminary Support Design for the Proposed Ordu Peripheral Highway Tunnel, Ordu, Turkey","volume":"96","author":"Akgun","year":"2008","journal-title":"Eng. Geol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"103574","DOI":"10.1016\/j.tust.2020.103574","article-title":"Mechanical Responses of Closely Spaced Large Span Triple Tunnels","volume":"105","author":"Li","year":"2020","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Yan, Q.X., Zhang, C., Lin, G., and Wang, B. (2017). Field Monitoring of Deformations and Internal Forces of Surrounding Rocks and Lining Structures in the Construction of the Gangkou Double-Arched Tunnel\u2014A Case Study. Appl. Sci., 7.","DOI":"10.3390\/app7020169"},{"key":"ref_33","first-page":"168","article-title":"Evaluation of Tunnels Under Squeezing Rock Condition","volume":"10","author":"Ghiasi","year":"2012","journal-title":"J. Eng. Des. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.tust.2016.09.007","article-title":"Deformation and Mechanical Model of Temporary Support Sidewall in Tunnel Cutting Partial Section","volume":"61","author":"Luo","year":"2017","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"103816","DOI":"10.1016\/j.tust.2021.103816","article-title":"Soil Movement Mechanism Associated with Arching Effect in a Multi-Strutted Excavation in Soft Clay","volume":"110","author":"Li","year":"2021","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.21595\/jve.2019.20615","article-title":"Geotechnical Monitoring and Safety Assessment of Large-Span Triple Tunnels Using Drilling and Blasting Method","volume":"21","author":"Li","year":"2019","journal-title":"J. Vib."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/3\/673\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:50:01Z","timestamp":1760122201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/3\/673"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,7]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["sym15030673"],"URL":"https:\/\/doi.org\/10.3390\/sym15030673","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,7]]}}}