Hybrid a node-based smoothed radial point interpolation method and artificial neural networks for stability evaluation of dual square tunnels at different depths in cohesive-frictional soils

Hybrid a node-based smoothed radial point interpolation method and artificial neural networks for stability evaluation of dual square tunnels at different depths in cohesive-frictional soils | 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 Hybrid a node-based smoothed radial point interpolation method and artificial neural networks for stability evaluation of dual square tunnels at different depths in cohesive-frictional soils G. Mai-Hai, Thanh Danh Tran, T. Vo-Minh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7314210/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Nov, 2025 Read the published version in Transportation Infrastructure Geotechnology → Version 1 posted You are reading this latest preprint version Abstract This study introduces a hybrid approach combining the node-based smoothed radial point interpolation method (NS-RPIM) and Artificial neural networks (ANN) to evaluate the limit load capacity of dual square tunnels at different depths in cohesive-frictional soils. NS-RPIM performs effectively in upper bound limit analysis by eliminating mesh dependency and enhances accuracy through smoothed strain fields, while enabling flexible node distribution for complex tunnel geometries. Its integration with second-order cone programming ensures precise computation of critical surcharge loads with improved computational efficiency. ANN complements NS-RPIM provides reliable predictions of stability numbers N = σ s /c , and its ability to model nonlinear soil-tunnel interactions and adapt to diverse geotechnical conditions. Trained on extensive NS-RPIM-generated datasets, the ANN model achieves high predictive accuracy with minimal computational cost. The hybrid framework is validated against numerical simulations demonstrating superior performance in capturing the effects of tunnel depth H/B , the horizontal spacing ratio S/B and vertical spacing ratio L/B , soil properties γB/c and internal friction angle φ . This approach offers significant advantages over traditional finite element methods, including reduced computational time, enhanced robustness, and applicability to practical tunneling design. Hybrid NS-RPIM and ANN approach is a powerful tool for geotechnical engineers addressing the stability of dual square tunnels under complex loading conditions. ANN Cohesive-frictional soils Dual square tunnels NS-RPIM Tunnel stability Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Nov, 2025 Read the published version in Transportation Infrastructure Geotechnology → 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-7314210","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":501149700,"identity":"b720ca0f-ce4f-4e94-a885-f402ee99774c","order_by":0,"name":"G. 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NS-RPIM performs effectively in upper bound limit analysis by eliminating mesh dependency and enhances accuracy through smoothed strain fields, while enabling flexible node distribution for complex tunnel geometries. Its integration with second-order cone programming ensures precise computation of critical surcharge loads with improved computational efficiency. ANN complements NS-RPIM provides reliable predictions of stability numbers \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eσ\u003c/em\u003e \u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/c\u003c/em\u003e, and its ability to model nonlinear soil-tunnel interactions and adapt to diverse geotechnical conditions. Trained on extensive NS-RPIM-generated datasets, the ANN model achieves high predictive accuracy with minimal computational cost. The hybrid framework is validated against numerical simulations demonstrating superior performance in capturing the effects of tunnel depth \u003cem\u003eH/B\u003c/em\u003e, the horizontal spacing ratio \u003cem\u003eS/B\u003c/em\u003e and vertical spacing ratio \u003cem\u003eL/B\u003c/em\u003e, soil properties \u003cem\u003eγB/c\u003c/em\u003e and internal friction angle \u003cem\u003eφ\u003c/em\u003e. This approach offers significant advantages over traditional finite element methods, including reduced computational time, enhanced robustness, and applicability to practical tunneling design. Hybrid NS-RPIM and ANN approach is a powerful tool for geotechnical engineers addressing the stability of dual square tunnels under complex loading conditions.\u003c/p\u003e","manuscriptTitle":"Hybrid a node-based smoothed radial point interpolation method and artificial neural networks for stability evaluation of dual square tunnels at different depths in cohesive-frictional soils","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-25 10:11:25","doi":"10.21203/rs.3.rs-7314210/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"45e7aff9-df6b-4084-9b68-17cd720c3217","owner":[],"postedDate":"August 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-24T16:11:39+00:00","versionOfRecord":{"articleIdentity":"rs-7314210","link":"https://doi.org/10.1007/s40515-025-00749-8","journal":{"identity":"transportation-infrastructure-geotechnology","isVorOnly":false,"title":"Transportation Infrastructure Geotechnology"},"publishedOn":"2025-11-21 15:58:47","publishedOnDateReadable":"November 21st, 2025"},"versionCreatedAt":"2025-08-25 10:11:25","video":"","vorDoi":"10.1007/s40515-025-00749-8","vorDoiUrl":"https://doi.org/10.1007/s40515-025-00749-8","workflowStages":[]},"version":"v1","identity":"rs-7314210","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7314210","identity":"rs-7314210","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}