Strength of sand in plane strain conditions: insights from legacy experimental data

Strength of sand in plane strain conditions: insights from legacy experimental data | 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 Strength of sand in plane strain conditions: insights from legacy experimental data Jos de Greef, Henri John Lengkeek, Vahid Galavi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7648179/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 plane strain assumption is widely used in geotechnical engineering for boundary value problems such as retaining structures and embankments. In practice, the peak friction angle of cohesionless soils under plane strain conditions is frequently approximated by increasing the friction angle obtained from triaxial compression tests by a factor 9/8 to account for the experimentally observed strength surplus. This paper demonstrates, both theoretically and experimentally, that this factor is neither constant nor consistently conservative. Using a comprehensive database of legacy experiments -including both independent stress control and plane strain tests, with matching triaxial compression data- a multi-linear regression analysis is performed to identify key predictors of the plane strain strength surplus. In addition to relative density and confining stress, two geometric parameters are significant: (i) the ratio of sample height to the height for a shear band to freely develop across the sample, and (ii) the ratio of sample height to sample length (distance between the zero strain boundaries). Based on these findings, two empirical relations are proposed for estimating the plane strain strength surplus as a function of relative density and confining stress, conditioned on typical sample geometries: one for uniform strain conditions and one for localized strain conditions. A case study on slope stability demonstrates that the effect of selecting either of these empirical relations on the calculated factor of safety is comparable to (in)adequately capturing localized strain behavior in the model environment. This highlights that the appropriate plane strain strength surplus depends both on soil state and the model’s capacity to capture localized strain behavior. plane strain friction angle shear band localization sand Full Text Additional Declarations The authors declare no competing interests. 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7648179","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":517001070,"identity":"e1eb0998-9552-424a-b13a-6a2614c76832","order_by":0,"name":"Jos de Greef","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Jos","middleName":"","lastName":"de Greef","suffix":""},{"id":517001085,"identity":"c8454ed1-668d-498b-b750-d555e1d7f96a","order_by":1,"name":"Henri John Lengkeek","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Henri","middleName":"John","lastName":"Lengkeek","suffix":""},{"id":517001086,"identity":"e950a883-3944-4654-8c47-69066896fa26","order_by":2,"name":"Vahid Galavi","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Vahid","middleName":"","lastName":"Galavi","suffix":""}],"badges":[],"createdAt":"2025-09-18 09:55:46","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7648179/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7648179/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91691628,"identity":"22e676cc-db44-47ad-a3af-b64b36c1a149","added_by":"auto","created_at":"2025-09-19 08:48:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2655283,"visible":true,"origin":"","legend":"","description":"","filename":"Strengthofsandinplanestrainconditionsinsightsfromlegacyexperimentaldata.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7648179/v1_covered_84e9b6ef-bae0-408c-942c-cd75a34cdfa3.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eStrength of sand in plane strain conditions: insights from legacy experimental data\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Port of Rotterdam Authority","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","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":"plane strain, friction angle, shear band, localization, sand","lastPublishedDoi":"10.21203/rs.3.rs-7648179/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7648179/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe plane strain assumption is widely used in geotechnical engineering for boundary value problems such as retaining structures and embankments. In practice, the peak friction angle of cohesionless soils under plane strain conditions is frequently approximated by increasing the friction angle obtained from triaxial compression tests by a factor 9/8 to account for the experimentally observed strength surplus.\u003c/p\u003e\n\u003cp\u003eThis paper demonstrates, both theoretically and experimentally, that this factor is neither constant nor consistently conservative. Using a comprehensive database of legacy experiments -including both independent stress control and plane strain tests, with matching triaxial compression data- a multi-linear regression analysis is performed to identify key predictors of the plane strain strength surplus. 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