{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:14:24Z","timestamp":1760148864770,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T00:00:00Z","timestamp":1686528000000},"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":["51978621","U2006225","LTZ21E080001","101025312"],"award-info":[{"award-number":["51978621","U2006225","LTZ21E080001","101025312"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["51978621","U2006225","LTZ21E080001","101025312"],"award-info":[{"award-number":["51978621","U2006225","LTZ21E080001","101025312"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Marie Sklodowska-Curie Individual Fellowships","award":["51978621","U2006225","LTZ21E080001","101025312"],"award-info":[{"award-number":["51978621","U2006225","LTZ21E080001","101025312"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A model of consolidation for a single-drain well under vacuum preloading, based on Biot\u2019s axisymmetric theory and considering the \u201creal strain\u201d hypothesis, was established using the finite element method. Degenerating the consolidation equation of real strain yielded the Barron\u2019s classical free strain and equal strain equations. The free strain and equal strain finite element models were derived by imposing boundary and constraint conditions on the real strain FEM model. The validation of the simulation process confirmed that the numerical model achieved consistent outcomes, with the theoretical values postulating its effectiveness. The real strain model revealed the Mandel\u2013Cryer effect of soil near the vertical drain during the initial vacuum preloading consolidation process, causing the effective stress to increase more than the effective stress generated by the vacuum pressure and leading to a greater reduction in the void ratio. This phenomenon is one of the reasons for clogging during the vacuum preloading process. However, the free strain and equal strain models cannot produce this effect because they cannot describe the coupling between soil deformation and fluid flow. The parameter analysis of the real strain model showed that as Poisson\u2019s ratio for soil decreased, the consolidation rate of soil also decreased, while the Mandel\u2013Cryer effect of soil increased.<\/jats:p>","DOI":"10.3390\/sym15061245","type":"journal-article","created":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T01:35:30Z","timestamp":1686620130000},"page":"1245","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of Consolidation by Vertical Drain with Vacuum Preloading Based on Axisymmetric Biot\u2019s Consolidation Theory"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiaodong","family":"Pan","sequence":"first","affiliation":[{"name":"College of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China"},{"name":"School of Engineering, University of Warwick, Coventry CV4 7AL, UK"},{"name":"Zhejiang Key Laboratory of Civil Engineering Structures & Disaster Prevention and Mitigation Technology, Hangzhou 310014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haijun","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huailin","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Honglei","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China"},{"name":"Zhejiang Key Laboratory of Civil Engineering Structures & Disaster Prevention and Mitigation Technology, Hangzhou 310014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueyu","family":"Geng","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Warwick, Coventry CV4 7AL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xie, L., Liang, Z., Feng, G., Li, Y., and Wu, T. 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