A Nonlinear Winkler–FEM Framework for Consolidation-Driven Negative Skin Friction in Pile Foundations

A Nonlinear Winkler–FEM Framework for Consolidation-Driven Negative Skin Friction in Pile Foundations | 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 A Nonlinear Winkler–FEM Framework for Consolidation-Driven Negative Skin Friction in Pile Foundations Leonardo Nascimento This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9378025/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Negative skin friction (NSF, downdrag) arises when consolidating soils settle relative to piles, reversing interface shear and increasing axial compression along the foundation. This paper presents a framework coupling an elastic beam on a depth-dependent nonlinear Winkler foundation with a rigid cap endowed with six Degrees of Freedom (DOF). Depthwise reactions are obtained from tabulated \(\:p-y\) and \(\:\:t-z\) curves using secant stiffness and linear interpolation, while consolidation settlements are applied incrementally as equivalent nodal actions. A fixed-point iteration updates soil spring levels consistently with recovered pile displacements and enforces cap equilibrium. The formulation retains closed-form element expressions when coefficients are constant and uses numerical quadrature otherwise, avoiding locking and ensuring robust convergence. The paper details condensation to pile group head, also known as pile cap, global assembly, convergence monitoring, and recovery of along-depth field variables for obtaining axial force, shear, torsion, and bending moments along the piles. Referenced results for a benchmark pile traversing clay over sand under service load illustrate NSF build-up and stabilization as \(\:t-z\) resistances reach plastic plateaus, and adequate comparison with the classical De Beer-Wallays estimate. Skin friction Consolidation Pile foundation Nonlinear Winkler model Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 29 Apr, 2026 Editor assigned by journal 20 Apr, 2026 Submission checks completed at journal 20 Apr, 2026 First submitted to journal 10 Apr, 2026 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. 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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-9378025","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":621318159,"identity":"5f4597bd-2904-4f3c-8eba-bfee1bfa38f8","order_by":0,"name":"Leonardo Nascimento","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYBACPhDB2CDBY9/eAxbg4SOkhQ2kAahFxoDnDAPDAaAWNiK1MNgYSOSAtTAQ1sLefPwx7w4LHnPJtwcff8yxk2FjYH746AY+LTzHEpt5z0jwWM7OSzY4uC0Z6DA2Y+McfFokcgybedskeBhu55hJHNzGDNTCwyaNV4v8G6iWm2dAWuqJ0CLBA9FicIMHpOUwEVp40hJnzgX6RbInx9jg7LbjPGzMBPzCz374wIe3O+rs+dnPGD6o3FYNZDQ/fIxPCxbATJryUTAKRsEoGAVYAACyHD+dFkEUKAAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Leonardo","middleName":"","lastName":"Nascimento","suffix":""}],"badges":[],"createdAt":"2026-04-10 10:09:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9378025/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9378025/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106753937,"identity":"8b10795a-cd2c-4215-bdb8-d47490edadec","added_by":"auto","created_at":"2026-04-13 07:37:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":345125,"visible":true,"origin":"","legend":"","description":"","filename":"2026NascimentoPaperNegativeFrictionPiles.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9378025/v1_covered_056ee92f-64df-464b-b544-49aaebe45112.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Nonlinear Winkler–FEM Framework for Consolidation-Driven Negative Skin Friction in Pile Foundations","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"discover-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Civil Engineering](https://www.springer.com/journal/44290)","snPcode":"44290","submissionUrl":"https://submission.nature.com/new-submission/44290","title":"Discover Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Skin friction, Consolidation, Pile foundation, Nonlinear Winkler model","lastPublishedDoi":"10.21203/rs.3.rs-9378025/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9378025/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNegative skin friction (NSF, downdrag) arises when consolidating soils settle relative to piles, reversing interface shear and increasing axial compression along the foundation. This paper presents a framework coupling an elastic beam on a depth-dependent nonlinear Winkler foundation with a rigid cap endowed with six Degrees of Freedom (DOF). Depthwise reactions are obtained from tabulated \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p-y\\)\u003c/span\u003e\u003c/span\u003e and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:t-z\\)\u003c/span\u003e\u003c/span\u003e curves using secant stiffness and linear interpolation, while consolidation settlements are applied incrementally as equivalent nodal actions. A fixed-point iteration updates soil spring levels consistently with recovered pile displacements and enforces cap equilibrium. The formulation retains closed-form element expressions when coefficients are constant and uses numerical quadrature otherwise, avoiding locking and ensuring robust convergence. The paper details condensation to pile group head, also known as pile cap, global assembly, convergence monitoring, and recovery of along-depth field variables for obtaining axial force, shear, torsion, and bending moments along the piles. 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