{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T05:02:25Z","timestamp":1789448545936,"version":"build-2803163510"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T00:00:00Z","timestamp":1789257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Scientific Research Projects of Universities in Henan Province","award":["26B580002"],"award-info":[{"award-number":["26B580002"]}]},{"DOI":"10.13039\/501100004761","name":"Henan Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["262300421967"],"award-info":[{"award-number":["262300421967"]}],"id":[{"id":"10.13039\/501100004761","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Key Research and Development Projects of Henan Province","award":["262102240001"],"award-info":[{"award-number":["262102240001"]}]},{"name":"Key Research and Development Projects of Henan Province","award":["261111241000"],"award-info":[{"award-number":["261111241000"]}]},{"name":"Planned Project Supported by the Science and Technology Innovation Team of Universities and Colleges in Henan province","award":["24IRTSTHN011"],"award-info":[{"award-number":["24IRTSTHN011"]}]},{"name":"Key Scientific and Technological Projects in Henan Province","award":["252102240031"],"award-info":[{"award-number":["252102240031"]}]},{"name":"Special Plan for Key Scientific Research Projects of Higher Education Institutions in Henan Province to Serve Industry Development","award":["25CY022"],"award-info":[{"award-number":["25CY022"]}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"crossref","award":["BK20250986"],"award-info":[{"award-number":["BK20250986"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["25KJB580015"],"award-info":[{"award-number":["25KJB580015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Gels"],"abstract":"<jats:p>The fatigue of an SBS asphalt mixture with physical gel structures under repeated loading is a variable-rate mechanical process. However, there is a lack of a mechanical characterization mechanism to accurately quantify this process. This study aims to propose a method for mechanically characterizing the variable-rate fatigue process of the SBS asphalt mixture based on kinetics theory. First, indirect tensile monotonic and repeated-loading tests with advantages of easy specimen fabrication, good test repeatability, and widespread use in pavement fatigue evaluation were conducted at 15 \u00b0C, 20 \u00b0C, and 25 \u00b0C to obtain the mechanical response of SBS asphalt mixtures. Then, a permanent strain model accounting for damage of the SBS asphalt mixture was established based on viscoelastic damage theory. Finally, a fatigue damage kinetic model was developed. The parameters, represented in terms of lumped damage sensitivity exponent (\u03b2) and fatigue activation energy (Ea), were determined to quantitatively characterize the variable-rate fatigue behavior of the SBS asphalt mixture. The results show that the established permanent strain model accounting for damage can accurately capture the nonlinear evolution of fatigue damage and permanent strain in SBS asphalt mixtures. The parameter \u03b2 can serve as a reliable mechanical indicator for quantifying the fatigue process rate. The fitted kinetic parameter Ea can reasonably characterize the magnitude of the energy barrier governing the temperature-dependent variable-rate fatigue process. Macroscopically, the SBS asphalt mixture presents an elevated fatigue damage energy threshold compared with the base mixture. According to existing literature, this difference may be associated with three-dimensional physical gel structures from the SBS polymer. Within the scope of the present test conditions, kinetics theory shows potential as a theoretical framework for quantifying and characterizing the variable-rate fatigue behavior observed for SBS asphalt mixtures.<\/jats:p>","DOI":"10.3390\/gels12090839","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T13:05:26Z","timestamp":1789391126000},"page":"839","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigating Kinetic Characterization of Variable-Rate Fatigue Process of SBS Asphalt Mixture with Physical Gel Structures"],"prefix":"10.3390","volume":"12","author":[{"given":"Chenze","family":"Fang","sequence":"first","affiliation":[{"name":"School of Civil Engineering and Transportation, North China University of Water Resources and Electric Power, Zhengzhou 450045, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Jiahao","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Transportation, North China University of Water Resources and Electric Power, Zhengzhou 450045, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Menghao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0555-0824","authenticated-orcid":false,"given":"Hongbin","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Transportation Engineering, Dalian Maritime University, Dalian 116026, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4362-1210","authenticated-orcid":false,"given":"Pingfan","family":"Hu","sequence":"additional","affiliation":[{"name":"Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122, USA"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1016\/j.conbuildmat.2013.07.100","article-title":"Fatigue performance evaluation of SBS modified mastic asphalt mixtures","volume":"48","author":"Kim","year":"2013","journal-title":"Constr. 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Polymers, 18.","DOI":"10.3390\/polym18172103"}],"container-title":["Gels"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2310-2861\/12\/9\/839\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T04:12:13Z","timestamp":1789445533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2310-2861\/12\/9\/839"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,13]]},"references-count":34,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["gels12090839"],"URL":"https:\/\/doi.org\/10.3390\/gels12090839","relation":{},"ISSN":["2310-2861"],"issn-type":[{"value":"2310-2861","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,13]]}}}