{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T04:33:05Z","timestamp":1773117185453,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,11]],"date-time":"2018-07-11T00:00:00Z","timestamp":1531267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51778025"],"award-info":[{"award-number":["51778025"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Based on the mirror image method and superposition principle, an analytical model of seepage field for symmetrical underwater tunnels is proposed. The condition is assumed as two-dimensional steady water inflow into symmetrical and horizontal underwater tunnels in a fully saturated, homogeneous, isotropic, and semi-infinite aquifer. Analytical solutions of pore water distribution and water inflow into tunnels are obtained. Two different boundary conditions at the perimeter of symmetrical tunnels are considered, constant total hydraulic head and constant water pressure. Taking the subsea tunnels of Xiamen Xiang\u2019an in China as an example, comparisons between analytical solutions and numerical solutions are analyzed in the case of zero water pressure at the perimeter of symmetrical tunnels. The results show that the analytical solutions for pore pressure distribution and water inflow match well with the numerical solutions and that the relative deviations are all in an acceptable range. The solutions derived from the analytical model in this paper can analyze the steady seepage field of symmetrical underwater tunnels accurately and reasonably.<\/jats:p>","DOI":"10.3390\/sym10070273","type":"journal-article","created":{"date-parts":[[2018,7,11]],"date-time":"2018-07-11T10:50:09Z","timestamp":1531306209000},"page":"273","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["An Analytical Model of Seepage Field for Symmetrical Underwater Tunnels"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7410-342X","authenticated-orcid":false,"given":"Fan","family":"Wang","sequence":"first","affiliation":[{"name":"The Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China"}]},{"given":"Pengfei","family":"Li","sequence":"additional","affiliation":[{"name":"The Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1111\/j.1745-6584.1999.tb00953.x","article-title":"An analytical solution for steady flow into a tunnel","volume":"37","author":"Lei","year":"1999","journal-title":"Ground Water"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.tust.2012.06.007","article-title":"Steady-state groundwater inflow into a circular tunnel","volume":"32","author":"Butscher","year":"2012","journal-title":"Tunn. 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