Research on the relationship between macroscopic and mesoscopic mechanical parameters of limestone based on Hertz Mindlin with bonding model

The mesoscopic parameters of numerical simulation cannot be directly obtained from laboratory test, and it is necessary to calibrate the parameters by comparing the numerical simulation results with the experimental results. To quickly and reasonably determine the mesoscopic parameters of limestone,...

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Veröffentlicht in:Geomechanics and geophysics for geo-energy and geo-resources. 2020-12, Vol.6 (4), Article 68
Hauptverfasser: Yang, Weimin, Wang, Meixia, Zhou, Zongqing, Li, Liping, Yang, Geng, Ding, Ruosong
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container_title Geomechanics and geophysics for geo-energy and geo-resources.
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creator Yang, Weimin
Wang, Meixia
Zhou, Zongqing
Li, Liping
Yang, Geng
Ding, Ruosong
description The mesoscopic parameters of numerical simulation cannot be directly obtained from laboratory test, and it is necessary to calibrate the parameters by comparing the numerical simulation results with the experimental results. To quickly and reasonably determine the mesoscopic parameters of limestone, a unique variable principle is used to comprehensively analyze the quantitative relationship between mesoscopic and macroscopic parameters. The results show that: The elastic modulus is positively correlated with the shear and normal stiffness per unit area. The compressive strength increases linearly with the increase of normal and shear stiffness per unit area, and it has a power function growth relation to critical normal stress and shear stress. The cohesion is mainly affected by critical normal and shear stress. With an increase of the critical normal and shear stress, the cohesion decreases. The normal stiffness per unit area, shear stiffness per unit area, critical shear stress, and critical normal stress have little influence on the internal friction angle. But there is a linear relationship between the internal friction angle and shear stiffness per unit area, and the internal friction angle is linearly related to the critical shear stress. Considering the interaction of multiple parameters, the correlation criterion and empirical formula between the mesoscopic parameters and rock mechanical parameters in the Hertz–Mindlin with Bonding contact model are proposed. The peak load, elastic modulus, and stress–strain curve variation law obtained by laboratory test and numerical simulation are close to each other, which indicates the correlation criterion can accurately simulate the mechanical properties of limestone.
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To quickly and reasonably determine the mesoscopic parameters of limestone, a unique variable principle is used to comprehensively analyze the quantitative relationship between mesoscopic and macroscopic parameters. The results show that: The elastic modulus is positively correlated with the shear and normal stiffness per unit area. The compressive strength increases linearly with the increase of normal and shear stiffness per unit area, and it has a power function growth relation to critical normal stress and shear stress. The cohesion is mainly affected by critical normal and shear stress. With an increase of the critical normal and shear stress, the cohesion decreases. The normal stiffness per unit area, shear stiffness per unit area, critical shear stress, and critical normal stress have little influence on the internal friction angle. But there is a linear relationship between the internal friction angle and shear stiffness per unit area, and the internal friction angle is linearly related to the critical shear stress. Considering the interaction of multiple parameters, the correlation criterion and empirical formula between the mesoscopic parameters and rock mechanical parameters in the Hertz–Mindlin with Bonding contact model are proposed. The peak load, elastic modulus, and stress–strain curve variation law obtained by laboratory test and numerical simulation are close to each other, which indicates the correlation criterion can accurately simulate the mechanical properties of limestone.</description><identifier>ISSN: 2363-8419</identifier><identifier>EISSN: 2363-8427</identifier><identifier>DOI: 10.1007/s40948-020-00184-8</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Adhesion ; Bonding ; Cohesion ; Compressive strength ; Contact stresses ; Correlation ; Criteria ; Empirical analysis ; Energy ; Engineering ; Environmental Science and Engineering ; Foundations ; Friction ; Geoengineering ; Geophysics/Geodesy ; Geotechnical Engineering &amp; Applied Earth Sciences ; Hydraulics ; Interaction parameters ; Internal friction ; Laboratories ; Laboratory tests ; Limestone ; Mathematical models ; Mechanical properties ; Mindlin plates ; Modulus of elasticity ; Original Article ; Parameters ; Peak load ; Shear stiffness ; Shear stress ; Simulation ; Stress-strain curves ; Stress-strain relations</subject><ispartof>Geomechanics and geophysics for geo-energy and geo-resources., 2020-12, Vol.6 (4), Article 68</ispartof><rights>Springer Nature Switzerland AG 2020</rights><rights>Springer Nature Switzerland AG 2020.</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-df326b21bc8a98cf4fe8e194b8d5ebe977cfce672fc8866f146287e83450d5013</citedby><cites>FETCH-LOGICAL-c319t-df326b21bc8a98cf4fe8e194b8d5ebe977cfce672fc8866f146287e83450d5013</cites><orcidid>0000-0003-4418-1264</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40948-020-00184-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40948-020-00184-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Yang, Weimin</creatorcontrib><creatorcontrib>Wang, Meixia</creatorcontrib><creatorcontrib>Zhou, Zongqing</creatorcontrib><creatorcontrib>Li, Liping</creatorcontrib><creatorcontrib>Yang, Geng</creatorcontrib><creatorcontrib>Ding, Ruosong</creatorcontrib><title>Research on the relationship between macroscopic and mesoscopic mechanical parameters of limestone based on Hertz Mindlin with bonding model</title><title>Geomechanics and geophysics for geo-energy and geo-resources.</title><addtitle>Geomech. Geophys. Geo-energ. Geo-resour</addtitle><description>The mesoscopic parameters of numerical simulation cannot be directly obtained from laboratory test, and it is necessary to calibrate the parameters by comparing the numerical simulation results with the experimental results. To quickly and reasonably determine the mesoscopic parameters of limestone, a unique variable principle is used to comprehensively analyze the quantitative relationship between mesoscopic and macroscopic parameters. The results show that: The elastic modulus is positively correlated with the shear and normal stiffness per unit area. The compressive strength increases linearly with the increase of normal and shear stiffness per unit area, and it has a power function growth relation to critical normal stress and shear stress. The cohesion is mainly affected by critical normal and shear stress. With an increase of the critical normal and shear stress, the cohesion decreases. The normal stiffness per unit area, shear stiffness per unit area, critical shear stress, and critical normal stress have little influence on the internal friction angle. But there is a linear relationship between the internal friction angle and shear stiffness per unit area, and the internal friction angle is linearly related to the critical shear stress. Considering the interaction of multiple parameters, the correlation criterion and empirical formula between the mesoscopic parameters and rock mechanical parameters in the Hertz–Mindlin with Bonding contact model are proposed. The peak load, elastic modulus, and stress–strain curve variation law obtained by laboratory test and numerical simulation are close to each other, which indicates the correlation criterion can accurately simulate the mechanical properties of limestone.</description><subject>Adhesion</subject><subject>Bonding</subject><subject>Cohesion</subject><subject>Compressive strength</subject><subject>Contact stresses</subject><subject>Correlation</subject><subject>Criteria</subject><subject>Empirical analysis</subject><subject>Energy</subject><subject>Engineering</subject><subject>Environmental Science and Engineering</subject><subject>Foundations</subject><subject>Friction</subject><subject>Geoengineering</subject><subject>Geophysics/Geodesy</subject><subject>Geotechnical Engineering &amp; Applied Earth Sciences</subject><subject>Hydraulics</subject><subject>Interaction parameters</subject><subject>Internal friction</subject><subject>Laboratories</subject><subject>Laboratory tests</subject><subject>Limestone</subject><subject>Mathematical models</subject><subject>Mechanical properties</subject><subject>Mindlin plates</subject><subject>Modulus of elasticity</subject><subject>Original Article</subject><subject>Parameters</subject><subject>Peak load</subject><subject>Shear stiffness</subject><subject>Shear stress</subject><subject>Simulation</subject><subject>Stress-strain curves</subject><subject>Stress-strain relations</subject><issn>2363-8419</issn><issn>2363-8427</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kNtKxDAQhosouKz7Al4FvK7m1Ca9lMUTrAii1yFNJ9tIm9Sky6LP4EPbdT3ceTUz8P3_zPxZdkrwOcFYXCSOKy5zTHGOMZE8lwfZjLKS5ZJTcfjbk-o4W6TkaswILRkndJZ9PEICHU2LgkdjCyhCp0cXfGrdgGoYtwAe9drEkEwYnEHaN6iH9DP2YFrtndEdGnTUPYwQEwoWdW6ixuAB1TpBs_O_hTi-o3vnm855tHVji-rgG-fXqA8NdCfZkdVdgsV3nWfP11dPy9t89XBzt7xc5YaRaswby2hZU1IbqStpLLcggVS8lk0BNVRCGGugFNQaKcvSEl5SKUAyXuCmwITNs7O97xDD62a6Ur2ETfTTSkW5YKIqhNxRdE_tfk8RrBqi63V8UwSrXfBqH7yagldfwSs5idhelCbYryH-Wf-j-gQTzIkn</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Yang, Weimin</creator><creator>Wang, Meixia</creator><creator>Zhou, Zongqing</creator><creator>Li, Liping</creator><creator>Yang, Geng</creator><creator>Ding, Ruosong</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TN</scope><scope>F1W</scope><scope>H96</scope><scope>L.G</scope><orcidid>https://orcid.org/0000-0003-4418-1264</orcidid></search><sort><creationdate>20201201</creationdate><title>Research on the relationship between macroscopic and mesoscopic mechanical parameters of limestone based on Hertz Mindlin with bonding model</title><author>Yang, Weimin ; 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Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy &amp; Non-Living Resources</collection><collection>Aquatic Science &amp; Fisheries Abstracts (ASFA) Professional</collection><jtitle>Geomechanics and geophysics for geo-energy and geo-resources.</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yang, Weimin</au><au>Wang, Meixia</au><au>Zhou, Zongqing</au><au>Li, Liping</au><au>Yang, Geng</au><au>Ding, Ruosong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Research on the relationship between macroscopic and mesoscopic mechanical parameters of limestone based on Hertz Mindlin with bonding model</atitle><jtitle>Geomechanics and geophysics for geo-energy and geo-resources.</jtitle><stitle>Geomech. 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The cohesion is mainly affected by critical normal and shear stress. With an increase of the critical normal and shear stress, the cohesion decreases. The normal stiffness per unit area, shear stiffness per unit area, critical shear stress, and critical normal stress have little influence on the internal friction angle. But there is a linear relationship between the internal friction angle and shear stiffness per unit area, and the internal friction angle is linearly related to the critical shear stress. Considering the interaction of multiple parameters, the correlation criterion and empirical formula between the mesoscopic parameters and rock mechanical parameters in the Hertz–Mindlin with Bonding contact model are proposed. 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subjects Adhesion
Bonding
Cohesion
Compressive strength
Contact stresses
Correlation
Criteria
Empirical analysis
Energy
Engineering
Environmental Science and Engineering
Foundations
Friction
Geoengineering
Geophysics/Geodesy
Geotechnical Engineering & Applied Earth Sciences
Hydraulics
Interaction parameters
Internal friction
Laboratories
Laboratory tests
Limestone
Mathematical models
Mechanical properties
Mindlin plates
Modulus of elasticity
Original Article
Parameters
Peak load
Shear stiffness
Shear stress
Simulation
Stress-strain curves
Stress-strain relations
title Research on the relationship between macroscopic and mesoscopic mechanical parameters of limestone based on Hertz Mindlin with bonding model
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