{"paper_id":"3a744c8d-afe2-432f-87ef-fd205d7fc0de","body_text":"Research on microscopic parameter characteristics based on Cambridge-like model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Research on microscopic parameter characteristics based on Cambridge-like model Feng Yue, Zhenhai Wei, Jianhua Dong, Ying Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4337837/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The Cambridge model reveals the basic characteristics of saturated remolded soil and establishes the constitutive equation of soil, which is one of the most important models in soil mechanics. However, the Cambridge model is still a phenomenological macroscopic model, which cannot consider the influence of soil microstructure. In this paper, based on the basic theory of complex material mechanics, a microscopic model of materials is established by point element method, and the governing equations of strain energy density function and state set function of material structure are obtained. Through simplified analysis, an envelope surface equation describing the set of structural states of the material is obtained. It is found that the envelope surface equation is similar to the Cambridge model critical state surface equation. This state envelope surface can not only reflect the similar characteristics of the Cambridge model, but also introduce the microscopic characteristic parameters of materials, so that the Cambridge theory describing the macroscopic properties of materials can be developed into a macro-microscopic method describing the properties of materials at multiple scales. More importantly, the Cambridge model is built based on experiments, and the macromicro equation obtained here is derived from the basic theory of complex material mechanics. Soil Mechanics Mechanics of complex materials Cambridge model State geometry function Macro-micro-multiscale analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-4337837\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":299733332,\"identity\":\"db21dcc8-2578-4f02-a847-cc628ab39f99\",\"order_by\":0,\"name\":\"Feng Yue\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYJCCDyCCn7354IOEihqidDDOAJGSPceSDR6cOUaCFoMZPmqSD1uYCas3uJF8sOHjjloGAwketorEBjYG/vbuBAJa0hIbZ545zmAu3XvsRuIOGQaJM2c3ENCSY/6Yt+0Yg+Wcc2k3Es+wAa3LJaQl/2PzX6AWoF6zgsQ2ZmK05DA2M7bVgLUwEKVF8swzw8betgPgQJZIOHOMh6Bf+I4nP2z42VYHjsqPPypq5Pjbe/FrUTgApg7XN0AFePAqBwF5iNI6ggpHwSgYBaNgBAMAkehShm7+5L0AAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Lanzhou University of Technology\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Feng\",\"middleName\":\"\",\"lastName\":\"Yue\",\"suffix\":\"\"},{\"id\":299733334,\"identity\":\"716808b1-6e3d-4390-bcf8-4424aa825c21\",\"order_by\":1,\"name\":\"Zhenhai Wei\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"China People's Liberation Army National Defence University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Zhenhai\",\"middleName\":\"\",\"lastName\":\"Wei\",\"suffix\":\"\"},{\"id\":299733336,\"identity\":\"273b5961-3c21-48f6-922a-0467926e8b99\",\"order_by\":2,\"name\":\"Jianhua Dong\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Lanzhou University of Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Jianhua\",\"middleName\":\"\",\"lastName\":\"Dong\",\"suffix\":\"\"},{\"id\":299733338,\"identity\":\"730c955f-beb5-4cad-9714-2f8fdf40ca99\",\"order_by\":3,\"name\":\"Ying Wang\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Lanzhou University of Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Ying\",\"middleName\":\"\",\"lastName\":\"Wang\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-04-28 12:07:19\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-4337837/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-4337837/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":69008565,\"identity\":\"44c95e5c-46f3-41fe-8bf8-e7dc4406a2f4\",\"added_by\":\"auto\",\"created_at\":\"2024-11-14 13:17:32\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":355368,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"Manuscript428.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4337837/v1_covered_c8a87037-4d34-46bd-848e-96f8c1ea91e4.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Research on microscopic parameter characteristics based on Cambridge-like model\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Soil Mechanics, Mechanics of complex materials, Cambridge model, State geometry function, Macro-micro-multiscale analysis \",\"lastPublishedDoi\":\"10.21203/rs.3.rs-4337837/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-4337837/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThe Cambridge model reveals the basic characteristics of saturated remolded soil and establishes the constitutive equation of soil, which is one of the most important models in soil mechanics. However, the Cambridge model is still a phenomenological macroscopic model, which cannot consider the influence of soil microstructure. In this paper, based on the basic theory of complex material mechanics, a microscopic model of materials is established by point element method, and the governing equations of strain energy density function and state set function of material structure are obtained. Through simplified analysis, an envelope surface equation describing the set of structural states of the material is obtained. It is found that the envelope surface equation is similar to the Cambridge model critical state surface equation. This state envelope surface can not only reflect the similar characteristics of the Cambridge model, but also introduce the microscopic characteristic parameters of materials, so that the Cambridge theory describing the macroscopic properties of materials can be developed into a macro-microscopic method describing the properties of materials at multiple scales. 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