{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:15:36Z","timestamp":1760228136588,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T00:00:00Z","timestamp":1651795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Science and technology planning project of Zhejiang Provincial Highway and Transportation Management Center","award":["211821200009","211821220089"],"award-info":[{"award-number":["211821200009","211821220089"]}]},{"name":"the Science and technology planning project of Zhejiang Provincial Department of Transportation","award":["211821200009","211821220089"],"award-info":[{"award-number":["211821200009","211821220089"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the field of civil engineering and architecture, the concept of symmetry has been widely accepted. The bridge can be treated as a typical symmetrical structure of civil engineering buildings. Among them, the Subgrade can be identified as an important part to bear the vehicle loads. Severe pavement problems and bridge service capabilities will be caused by problems of the bridge\u2013subgrade transition section. Therefore, setting the rigid\u2013flexible transition is an important method to solve this problem. The bridge\u2013subgrade transition section has been set at both ends of the bridge, which can be regarded as a typical symmetrical structure. Based on nonlinear finite element numerical simulation and synergistic theory, the cooperative control problems of the bridge\u2013subgrade transition section were studied in this work. The change rule of the stiffness of the transition section was discussed and the influence of stiffness variation of the bridge\u2013subgrade transition section on the stress state of the structure was also analyzed. Furthermore, the influence of subgrade stiffness change on the stress and strain field was analyzed. A permanent strain prediction model was established and stiffness or subsidence difference coordination control was also discussed.<\/jats:p>","DOI":"10.3390\/sym14050950","type":"journal-article","created":{"date-parts":[[2022,5,8]],"date-time":"2022-05-08T23:27:25Z","timestamp":1652052445000},"page":"950","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Cooperative Control of Subgrade Stiffness on Symmetrical Bridge\u2013Subgrade Transition Section"],"prefix":"10.3390","volume":"14","author":[{"given":"Yang","family":"Zhang","sequence":"first","affiliation":[{"name":"Jinhua Highway and Transportation Management Center, Jinhua 321000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9736-6468","authenticated-orcid":false,"given":"Rui","family":"Li","sequence":"additional","affiliation":[{"name":"Highway School, Chang\u2019an University, Xi\u2019an 710064, China"}]},{"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"Jinhua Wucheng District Highway and Transportation Management Center, Jinhua 321000, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,6]]},"reference":[{"key":"ref_1","unstructured":"Wahls, H.E. 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Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1520\/STP24562S","article-title":"Prediction of Permanent Deformation in Flexible Pavement Materials","volume":"Volume 1016","author":"Tseng","year":"1989","journal-title":"Implication of Aggregates in the Design, Construction, and Performance of Flexible Pavements"},{"key":"ref_20","unstructured":"NCHRP (2004). Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures, NCHRP."},{"key":"ref_21","unstructured":"Huang, Y.H. (1993). Pavement Analysis and Design, Pearson."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"105719","DOI":"10.1016\/j.ijfatigue.2020.105719","article-title":"Stress concentration factors in tubular T\/Y-joints strengthened with FRP subjected to compressive load in offshore structures","volume":"140","author":"Nassiraei","year":"2020","journal-title":"Int. J. Fatigue"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"103413","DOI":"10.1016\/j.compgeo.2019.103413","article-title":"Modeling humidity and stress-dependent subgrade soils in flexible pavements","volume":"120","author":"Peng","year":"2020","journal-title":"Comput. Geotech."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/950\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:07:17Z","timestamp":1760137637000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/950"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,6]]},"references-count":23,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14050950"],"URL":"https:\/\/doi.org\/10.3390\/sym14050950","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,5,6]]}}}