{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T23:24:21Z","timestamp":1773703461326,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Chinese National Natural Science Foundation","doi-asserted-by":"publisher","award":["52068044"],"award-info":[{"award-number":["52068044"]}],"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 practice, asymmetric formation disturbance occurs due to the sequence of excavation though parallel double-track tunnel is a typical symmetrical engineering. Based on a shield tunneling project of a section of the Suzhou Rail Transit under the subgrade of the Shanghai\u2013Nanjing Expressway, a finite element model was established to obtain a numerical solution that was validated by the measured data to guarantee reliability. According to the construction characteristics of the shield method, two correction coefficients\u2014namely the soil loss rate correction coefficient \u03b1 and the settlement trough width correction coefficient \u03b2\u2014were introduced. A modified Peck formula suitable for the preceding tunnel and the subsequent tunnel was proposed. The applicability of the modified Peck formula was verified by another similar project. The results showed that the numerical solution can better reflect the actual settlement of the highway subgrade under shield tunneling. The results calculated by the classic Peck formula had a large error in comparison with the measured data. The modified empirical formula could more accurately predict the settlement of the expressway subgrade caused by the shield method when \u03b11 = 0.38 and \u03b21 = 2.08 for the preceding tunnel and \u03b12 = 0.29 and \u03b22 = 1.99 for the subsequent tunnel.<\/jats:p>","DOI":"10.3390\/sym14091904","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T22:37:28Z","timestamp":1663108648000},"page":"1904","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Modification of the Peck Formula for a Double-Track Shield Tunnel under Expressway Subgrade"],"prefix":"10.3390","volume":"14","author":[{"given":"Yuxiang","family":"Li","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juncen","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Songhong","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaxuan","family":"Du","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2896","DOI":"10.1007\/s12205-017-0761-0","article-title":"Control of surface settlement by considering shield tunneling technology","volume":"21","author":"Zhu","year":"2017","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_2","first-page":"164","article-title":"Application of modified Peck formula in surface subsidence prediction of Changsha subway tunnel construction","volume":"24","author":"Duan","year":"2013","journal-title":"J. Nat. Disasters"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, X., Zhang, D., and Hou, Y. (2022). Analysis of Shield Tunnel Ground Deformation Characteristics and Affecting Factors in Water-Rich Soft Stratum: A Case Study on the Section Tunnel of Tianjin Metro Line 6. Appl. Sci., 12.","DOI":"10.3390\/app12126208"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"9637838","DOI":"10.1155\/2018\/9637838","article-title":"A structural calculation model of shield tunnel segment: Heterogeneous equivalent beam model","volume":"2018","author":"Lei","year":"2018","journal-title":"Adv. Civ. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tan, Z., Li, Z., Tang, W., Chen, X., and Duan, J. (2020). 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Eng."},{"key":"ref_12","first-page":"1270","article-title":"Improvement of Peck formula of surface construction settlement of rectangular tunnel in soft soil area","volume":"14","author":"Yusheng","year":"2017","journal-title":"J. Railw. Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1680\/geot.1993.43.2.315","article-title":"Subsurface settlement profiles above tunnels in clays","volume":"43","author":"Bracegirdle","year":"1993","journal-title":"G\u00e9otechnique"},{"key":"ref_14","first-page":"1354","article-title":"Selection and distribution of ground loss ratio induced by shield tunnel construction","volume":"32","author":"Gang","year":"2010","journal-title":"Chin. J. Geotech. Eng."},{"key":"ref_15","unstructured":"Peixian, Q. (2021). Deformation Law and Control Strategy of the Subgrade under Shield Crossing High Railway. [Master\u2019s Thesis, Anhui Jianzhu University]."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1904\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:29:50Z","timestamp":1760142590000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1904"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,12]]},"references-count":15,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["sym14091904"],"URL":"https:\/\/doi.org\/10.3390\/sym14091904","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,12]]}}}