Creep Strain Analysis and an Improved Creep Model of Granite Based on the Ratio of Deviatoric Stress-Peak Strength under Different Confining Pressures

Creep Strain Analysis and an Improved Creep Model of Granite Based on the Ratio of Deviatoric Stress-Peak Strength under Different Confining Pressures | 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 Creep Strain Analysis and an Improved Creep Model of Granite Based on the Ratio of Deviatoric Stress-Peak Strength under Different Confining Pressures Li Qian, Jianhai Zhang, Xianliang Wang, Yonghong Li, Ru Zhang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-317168/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Feb, 2022 Read the published version in Environmental Earth Sciences → Version 1 posted You are reading this latest preprint version Abstract Creep refers to the deformation of rock with time under long-term applied stress, which occur in most underground engineering. The creep behavior of granite in Shuang jiangkou underground powerhouse in Western Sichuan Province, China, was studied by creep tests. Based on test results, a new parameter DPR , the ratio of deviatoric stress to peak strength, is proposed. DPR is found to be a key parameter to describe creep parameters such as instantaneous elastic modulus, creep elastic modulus, and viscosity coefficient of rock under different confining pressures. Creep tests show that instantaneous elastic modulus increases with the increase of DPR . Creep elastic modulus increases when DPR changes from 0.54 to 0.7004, but decreases when DPR is from 0.7004 to 0.88, indicating fractures in rock closes firstly and then new fractures are generated. The viscosity coefficient of the rock increases first and then decreases with the increase of DPR , and when DPR = 0.7171, viscosity coefficient is maximum, indicating the time for rock to reach stability is the longest in creep tests. By introducing DPR and confining pressure into creep model, which interconnect creep parameters in a unified expression, an improved generalized Kelvin creep model is proposed which can accurately describe the primary and the secondary creep behavior of granite under given deviatoric stresses and confining pressures. Environmental Engineering Environmental Policy Deviatoric stress to peak strength ratio Instantaneous strain Creep strain analysis Improved generalized Kelvin model Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Full Text Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the latest manuscript can be downloaded and accessed as a PDF. Cite Share Download PDF Status: Published Journal Publication published 01 Feb, 2022 Read the published version in Environmental Earth Sciences → 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-317168","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":15955973,"identity":"4b0db77f-9856-4a9d-9beb-3e09928603d5","order_by":0,"name":"Li Qian","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYDACZiB+UMEmx8DAQ4qWhDN8xiRoAYHEFrnEBqK18B1nfvYgscEsfcPxswcffGCwk9NtIKBF8jCbuUHijrTcDWfykg1nMCQbmx0goMXgMIOZROKZY7kbDuSYSfMwHEjcRlgL+zeJxLb/6Qbn3xCthQdoSxtbgsENYm2RPMxTJpFwhs1w5o03xoYzDIjwC9/549skPlSwyfOdzzF88KHCTo6gFgaYAgUww4CQcmQt8g3EqB4Fo2AUjIIRCQCZA0OgKn73ywAAAABJRU5ErkJggg==","orcid":"","institution":"Sichuan University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Qian","suffix":""},{"id":15955974,"identity":"2ab655a2-89d7-4c16-bd16-e26a1c422309","order_by":1,"name":"Jianhai Zhang","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jianhai","middleName":"","lastName":"Zhang","suffix":""},{"id":15955975,"identity":"3269d111-4938-4092-8eff-f5affeb0083f","order_by":2,"name":"Xianliang Wang","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xianliang","middleName":"","lastName":"Wang","suffix":""},{"id":15955976,"identity":"6c559f0b-9f69-48fa-8491-5e804d18ffde","order_by":3,"name":"Yonghong Li","email":"","orcid":"","institution":"Power China Chengdu Engineering Corporation Limited","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yonghong","middleName":"","lastName":"Li","suffix":""},{"id":15955977,"identity":"95caa465-02cc-4550-9b97-68649b66fc36","order_by":4,"name":"Ru Zhang","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ru","middleName":"","lastName":"Zhang","suffix":""},{"id":15955978,"identity":"66da7119-1199-467d-a01f-6dba9ddca158","order_by":5,"name":"Nuwen Xu","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Nuwen","middleName":"","lastName":"Xu","suffix":""},{"id":15955979,"identity":"6c781b81-db3e-435c-a09c-6c91ecbbc6dd","order_by":6,"name":"Zhiguo Li","email":"","orcid":"","institution":"power china chengdu engineering corporation Limited","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhiguo","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2021-03-10 21:40:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-317168/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-317168/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s12665-022-10241-y","type":"published","date":"2022-02-01T06:19:03+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":7130151,"identity":"65ed76c4-214c-4930-9196-69a491865c62","added_by":"auto","created_at":"2021-03-18 22:55:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":11824,"visible":true,"origin":"","legend":"A schematic presentation of rheological behavior of rock","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/b6fa8c9d8de8a5db794140f0.png"},{"id":7130544,"identity":"ac8b0edd-00e5-4910-b0b1-b976667059e5","added_by":"auto","created_at":"2021-03-18 22:58:05","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":9834,"visible":true,"origin":"","legend":"Representative strain-time curve with the different types of strains","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/2f0b5f471b341ac2539cd628.png"},{"id":7130144,"identity":"2501e15b-84a5-4af2-b9fa-8b46b8ebc7ec","added_by":"auto","created_at":"2021-03-18 22:55:05","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":142659,"visible":true,"origin":"","legend":"Granite sample","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/2fc44fd34c00ce8241140a9d.png"},{"id":7130146,"identity":"9dcb5f60-eb05-4585-ad50-a218605c708b","added_by":"auto","created_at":"2021-03-18 22:55:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":199741,"visible":true,"origin":"","legend":"Test equipment","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/957df97d35b6283eb61f030e.png"},{"id":7130147,"identity":"99d6a840-ba6b-46ce-86c9-b3f2ed7825ce","added_by":"auto","created_at":"2021-03-18 22:55:05","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":117424,"visible":true,"origin":"","legend":"Curves for granite creep tests under different confining pressures and deviatoric stresses","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/adf562e0f113e832e3af8d41.png"},{"id":7130947,"identity":"4d8cf7c5-1d52-4a2c-8bd3-c04c5676cb51","added_by":"auto","created_at":"2021-03-18 23:01:06","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":55944,"visible":true,"origin":"","legend":"Relationship between EM and DPR","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/cadc544a491900a517c1d672.png"},{"id":7130546,"identity":"5c1260b6-d1bc-4ce3-8a42-a52016f9f02b","added_by":"auto","created_at":"2021-03-18 22:58:06","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":17659,"visible":true,"origin":"","legend":"Illustration of Kelvin model.","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/dd8fee55283f84421666450e.png"},{"id":7130548,"identity":"a3b29dcd-fcf1-435d-9e48-db78cde95a9a","added_by":"auto","created_at":"2021-03-18 22:58:06","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":67828,"visible":true,"origin":"","legend":"Relationship between EK and DPR under different confining pressures","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/b8cfaecdc92c19749cbbdf9c.png"},{"id":7130156,"identity":"2f37f9a1-a848-4c26-ac01-0a5b9d1100ce","added_by":"auto","created_at":"2021-03-18 22:55:06","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":42624,"visible":true,"origin":"","legend":"Relationship between Dcr(σ) and DPR under different confining pressures","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/d9486b41c334181b5a02d04c.png"},{"id":7130545,"identity":"36bdb625-5181-4cfe-a07c-25d017ff97fd","added_by":"auto","created_at":"2021-03-18 22:58:05","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":36990,"visible":true,"origin":"","legend":"Relationship between ηK and DPR under different confining pressures","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/a3d4bc4b44fb0d7495d87591.png"},{"id":7130150,"identity":"8b215661-f19b-4b7c-91ee-3d3d9ebe6ea6","added_by":"auto","created_at":"2021-03-18 22:55:06","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":15410,"visible":true,"origin":"","legend":"Illustrations of the generalized Kelvin model","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/00f63c9cb3f7420f16648839.png"},{"id":7130153,"identity":"5b70bf3a-6370-42cd-b25a-51c78f1e3eef","added_by":"auto","created_at":"2021-03-18 22:55:06","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":160884,"visible":true,"origin":"","legend":"Creep test results and calculated curves for different confining pressures and deviatoric stresses","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/77a6f93dfe45730a5acdb094.png"},{"id":7130154,"identity":"8122eb0a-bf64-4f39-ac8a-cb61519a377e","added_by":"auto","created_at":"2021-03-18 22:55:06","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":760965,"visible":true,"origin":"","legend":"Relationship of creep strain with time and DPR under different confining pressures","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1/82bcd1cc3d676b1199f947e5.png"},{"id":18085217,"identity":"3fc6f433-11bf-4cf6-ab03-52dd9f67f772","added_by":"auto","created_at":"2022-02-10 06:19:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1544486,"visible":true,"origin":"","legend":"","description":"","filename":"CreepStrain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1_covered.pdf"},{"id":13609522,"identity":"81c0e8db-c278-486a-9cab-c5090c9d2499","added_by":"auto","created_at":"2021-09-17 06:20:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1539462,"visible":true,"origin":"","legend":"","description":"","filename":"CreepStrain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1_covered.pdf"},{"id":7131266,"identity":"0bbe57a2-b8d4-45a0-be9d-1988d28557fe","added_by":"auto","created_at":"2021-03-18 23:04:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1458605,"visible":true,"origin":"","legend":"","description":"","filename":"CreepStrain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-317168/v1_stamped.pdf"}],"financialInterests":"","formattedTitle":"Creep Strain Analysis and an Improved Creep Model of Granite Based on the Ratio of Deviatoric Stress-Peak Strength under Different Confining Pressures","fulltext":[{"header":"Full Text","content":"Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the latest manuscript can be downloaded and \u003ca href='/article/rs-317168/latest.pdf' target='_blank'\u003e accessed as a PDF.\u003c/a\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"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":"Deviatoric stress to peak strength ratio, Instantaneous strain, Creep strain analysis, Improved generalized Kelvin model","lastPublishedDoi":"10.21203/rs.3.rs-317168/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-317168/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCreep refers to the deformation of rock with time under long-term applied stress, which occur in most underground engineering. The creep behavior of granite in Shuang jiangkou underground powerhouse in Western Sichuan Province, China, was studied by creep tests. Based on test results, a new parameter \u003cem\u003eDPR\u003c/em\u003e, the ratio of deviatoric stress to peak strength, is proposed. \u003cem\u003eDPR\u003c/em\u003e is found to be a key parameter to describe creep parameters such as instantaneous elastic modulus, creep elastic modulus, and viscosity coefficient of rock under different confining pressures. Creep tests show that instantaneous elastic modulus increases with the increase of \u003cem\u003eDPR\u003c/em\u003e. Creep elastic modulus increases when \u003cem\u003eDPR\u003c/em\u003e changes from 0.54 to 0.7004, but decreases when \u003cem\u003eDPR\u003c/em\u003e is from 0.7004 to 0.88, indicating fractures in rock closes firstly and then new fractures are generated. The viscosity coefficient of the rock increases first and then decreases with the increase of \u003cem\u003eDPR\u003c/em\u003e, and when \u003cem\u003eDPR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.7171, viscosity coefficient is maximum, indicating the time for rock to reach stability is the longest in creep tests. By introducing \u003cem\u003eDPR\u003c/em\u003e and confining pressure into creep model, which interconnect creep parameters in a unified expression, an improved generalized Kelvin creep model is proposed which can accurately describe the primary and the secondary creep behavior of granite under given deviatoric stresses and confining pressures.\u003c/p\u003e","manuscriptTitle":"Creep Strain Analysis and an Improved Creep Model of Granite Based on the Ratio of Deviatoric Stress-Peak Strength under Different Confining Pressures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-03-18 22:55:03","doi":"10.21203/rs.3.rs-317168/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":"e104a69c-b3c9-47e9-b941-29a0c5637ab2","owner":[],"postedDate":"March 18th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":3054394,"name":"Environmental Engineering"},{"id":3054395,"name":"Environmental Policy"}],"tags":[],"updatedAt":"2022-02-10T06:19:03+00:00","versionOfRecord":{"articleIdentity":"rs-317168","link":"https://doi.org/10.1007/s12665-022-10241-y","journal":{"identity":"environmental-earth-sciences","isVorOnly":false,"title":"Environmental Earth Sciences"},"publishedOn":"2022-02-01 06:19:03","publishedOnDateReadable":"February 1st, 2022"},"versionCreatedAt":"2021-03-18 22:55:03","video":"","vorDoi":"10.1007/s12665-022-10241-y","vorDoiUrl":"https://doi.org/10.1007/s12665-022-10241-y","workflowStages":[]},"version":"v1","identity":"rs-317168","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-317168","identity":"rs-317168","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}