Static Analysis of Cantilever Retaining Wall With Shelves using Rankine and Klien’s Approach

Static Analysis of Cantilever Retaining Wall With Shelves using Rankine and Klien’s Approach | 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 Static Analysis of Cantilever Retaining Wall With Shelves using Rankine and Klien’s Approach Purnanand Savoikar, Smita Aldonkar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7139966/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 Rankine's solution offers a simple and conservative approach for estimating earth pressure, based on idealized assumptions such as a smooth, vertical retaining wall, uniform soil, and a linear pressure distribution. Rankine’s theory shows its limitations when applied to more complex scenarios, such as retaining walls with shelves, varying soil layers, or significant friction between the wall and soil. In such cases, Rankine’s method may either overestimate or underestimate the actual earth pressures, potentially compromising the safety or cost-effectiveness of the design. Klein's solution estimates that the earth's pressure above the shelf remains largely unaffected, while the pressure below the shelf decreases significantly, approaching zero just below the shelf. This reduction is due to the redistribution of earth forces, with the shelf acting as a point of pressure relief. In the present study, the configuration-based analysis of retaining walls with shelves in which a comparative study of earth pressure distribution by the Rankine and Klein method, the effect of variation of the position of shelves on the stem, the effect of increasing shelf widths from top to bottom, decreasing shelf widths and keeping shelf widths uniform on bending moments in the stem is studied. Based on these studies suitable method for shelf placement is suggested to have an economical shelf design and reduce the cost of retaining walls. Retaining wall with shelves factor of safety sliding overturning Klien’s solution Rankine Method 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-7139966","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":500434011,"identity":"0119db20-3612-444e-8cf2-db45e883db6c","order_by":0,"name":"Purnanand Savoikar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYNACgwQGBvYGEMOCFC08B0AMCaKtAWqRSAAxiNBizn/4mcSHgjR585nPr274USDBwN/enYBXi+WMNDPJGQY5hnNu55Td7AE6TOLM2Q14tRjcYDA25jGoYJwhnZN2gweoxUAil4CW88c/g7TYz5A8k3bzD1FaDuQYPuYxyEmcIcF+7DZRtljOyCl8OMMgLXkGTw7bbRkDCR6CfjHnP77hwIc/ybYz2I8/u/nmj40cf3svAYchmDxgNg9e5Wha2B8QVD0KRsEoGAUjEwAADwdFSjkoCq8AAAAASUVORK5CYII=","orcid":"","institution":"Goa Enineering College","correspondingAuthor":true,"prefix":"","firstName":"Purnanand","middleName":"","lastName":"Savoikar","suffix":""},{"id":500434012,"identity":"5d7722d2-75d7-45bb-8672-800ce49600b7","order_by":1,"name":"Smita Aldonkar","email":"","orcid":"","institution":"Goa Enineering College","correspondingAuthor":false,"prefix":"","firstName":"Smita","middleName":"","lastName":"Aldonkar","suffix":""}],"badges":[],"createdAt":"2025-07-16 12:23:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7139966/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7139966/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102749149,"identity":"c866cb64-7cf7-4cb9-9015-b10cc4f12c83","added_by":"auto","created_at":"2026-02-16 09:12:07","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1064228,"visible":true,"origin":"","legend":"","description":"","filename":"1StaticAnalysisofCantileverRetainingWallWithShelvesusingRankineandKliensApproach.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7139966/v1_covered_c88bd79e-1bba-480b-8540-e0494940cf02.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Static Analysis of Cantilever Retaining Wall With Shelves using Rankine and Klien’s Approach","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":"[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":"Retaining wall with shelves, factor of safety, sliding, overturning, Klien’s solution, Rankine Method","lastPublishedDoi":"10.21203/rs.3.rs-7139966/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7139966/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRankine's solution offers a simple and conservative approach for estimating earth pressure, based on idealized assumptions such as a smooth, vertical retaining wall, uniform soil, and a linear pressure distribution. Rankine\u0026rsquo;s theory shows its limitations when applied to more complex scenarios, such as retaining walls with shelves, varying soil layers, or significant friction between the wall and soil. In such cases, Rankine\u0026rsquo;s method may either overestimate or underestimate the actual earth pressures, potentially compromising the safety or cost-effectiveness of the design. Klein's solution estimates that the earth's pressure above the shelf remains largely unaffected, while the pressure below the shelf decreases significantly, approaching zero just below the shelf. This reduction is due to the redistribution of earth forces, with the shelf acting as a point of pressure relief. 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