On a statistical damage constitutive model for rock materials
A statistical damage constitutive model for rocks with strain softening behaviour is put forward, using the theory of continuous damage mechanics together with statistical mesoscopic strength theory based on maximum entropy distribution. In statistical constitutive modelling, the probabilistic distr...
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| Published in | Computers & geosciences Vol. 37; no. 2; pp. 122 - 128 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Ltd
01.02.2011
Elsevier |
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| Online Access | Get full text |
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| Abstract | A statistical damage constitutive model for rocks with strain softening behaviour is put forward, using the theory of continuous damage mechanics together with statistical mesoscopic strength theory based on maximum entropy distribution. In statistical constitutive modelling, the probabilistic distribution of mesoscopic element strength in rocks is a critical piece of information, which was conventionally described by various empirical distributions among which the Weibull distribution was extensively used. In this paper, an alternative and universal distribution, i.e. maximum entropy distribution, is proposed to describe the statistical property of mesoscopic strength in rocks. By incorporating the entropy distribution information into a damage variable, the paper derives a new constitutive model, which is verified by conventional triaxial experiments and dynamic experiments on rock specimens. To illustrate suitability and flexibility, the new model is compared to the well-established Weibull-distribution-based models. |
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| AbstractList | A statistical damage constitutive model for rocks with strain softening behaviour is put forward, using the theory of continuous damage mechanics together with statistical mesoscopic strength theory based on maximum entropy distribution. In statistical constitutive modelling, the probabilistic distribution of mesoscopic element strength in rocks is a critical piece of information, which was conventionally described by various empirical distributions among which the Weibull distribution was extensively used. In this paper, an alternative and universal distribution, i.e. maximum entropy distribution, is proposed to describe the statistical property of mesoscopic strength in rocks. By incorporating the entropy distribution information into a damage variable, the paper derives a new constitutive model, which is verified by conventional triaxial experiments and dynamic experiments on rock specimens. To illustrate suitability and flexibility, the new model is compared to the well-established Weibull-distribution-based models. |
| Author | Deng, Jian Gu, Desheng |
| Author_xml | – sequence: 1 givenname: Jian surname: Deng fullname: Deng, Jian email: jdengj@sina.com – sequence: 2 givenname: Desheng surname: Gu fullname: Gu, Desheng |
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| Cites_doi | 10.36487/ACG_repo/808_167 10.1115/1.4010337 10.1016/j.probengmech.2008.12.002 10.1016/j.ceramint.2007.10.003 10.1016/0029-5493(84)90169-9 10.1016/S0148-9062(96)00039-3 10.1016/j.cageo.2006.02.011 10.1016/S1365-1609(00)00049-6 10.1016/j.renene.2004.10.003 |
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| Keywords | Maximum entropy distribution Constitutive model Rock materials Weibull distribution strain experimental studies damage models strength data processing metamorphic rocks quartzites entropy confining pressure triaxial compression computers theory |
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| References_xml | – year: 1983 ident: bib9 article-title: Probabilistic Engineering Design contributor: fullname: Siddall – volume: 3 start-page: 453 year: 2007 end-page: 457 ident: bib8 article-title: A statistical damage softening constitutive model for rock and back analysis of its parameters publication-title: Chinese Journal of Underground Space and Engineering contributor: fullname: Cao – year: 1979 ident: bib4 article-title: Fundamentals of Rock Mechanics contributor: fullname: Cook – volume: 18 start-page: 293 year: 1951 end-page: 297 ident: bib13 article-title: A statistical distribution function of wide applicability publication-title: Journal of Applied Mechanics contributor: fullname: Weibull – volume: 32 start-page: 11 year: 2008 end-page: 14 ident: bib2 article-title: On statistical damage constitutive model and its parameters for rock based on normal distribution publication-title: Chinese Hydrogeology & Engineering Geology contributor: fullname: Zhao – volume: 37 start-page: 1115 year: 2000 end-page: 1121 ident: bib14 article-title: Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock publication-title: International Journal of Rock Mechanics and Mining Sciences contributor: fullname: Zhao – volume: 80 start-page: 233 year: 1984 end-page: 245 ident: bib5 article-title: How to use damage mechanics publication-title: Nuclear Engineering and Design contributor: fullname: Lemaitre – volume: 35 start-page: 237 year: 2009 end-page: 246 ident: bib1 article-title: Is Weibull distribution the most appropriate statistical strength distribution for brittle materials? 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publication-title: Ceramics International doi: 10.1016/j.ceramint.2007.10.003 contributor: fullname: Basu – volume: 80 start-page: 233 issue: 3 year: 1984 ident: 10.1016/j.cageo.2010.05.018_bib5 article-title: How to use damage mechanics publication-title: Nuclear Engineering and Design doi: 10.1016/0029-5493(84)90169-9 contributor: fullname: Lemaitre – year: 1983 ident: 10.1016/j.cageo.2010.05.018_bib9 contributor: fullname: Siddall – volume: 34 start-page: 249 issue: 2 year: 1997 ident: 10.1016/j.cageo.2010.05.018_bib10 article-title: Numerical simulation of progressive rock failure and associated seismicity publication-title: International Journal of Rock Mechanics and Mining Sciences doi: 10.1016/S0148-9062(96)00039-3 contributor: fullname: Tang – volume: 33 start-page: 1 issue: 1 year: 2007 ident: 10.1016/j.cageo.2010.05.018_bib12 article-title: A damage-softening statistical constitutive model considering rock residual strength publication-title: Computers & Geosciences doi: 10.1016/j.cageo.2006.02.011 contributor: fullname: Wang – year: 1979 ident: 10.1016/j.cageo.2010.05.018_bib4 contributor: fullname: Jaeger – volume: 37 start-page: 1115 issue: 7 year: 2000 ident: 10.1016/j.cageo.2010.05.018_bib14 article-title: Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock publication-title: International Journal of Rock Mechanics and Mining Sciences doi: 10.1016/S1365-1609(00)00049-6 contributor: fullname: Zhao – volume: 30 start-page: 1221 issue: 8 year: 2005 ident: 10.1016/j.cageo.2010.05.018_bib6 article-title: MEP-type distribution function: a better alternative to Weibull function for wind speed distributions publication-title: Renewable Energy doi: 10.1016/j.renene.2004.10.003 contributor: fullname: Li |
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| SubjectTerms | Constitutive model Constitutive relationships Damage Earth sciences Earth, ocean, space Engineering and environment geology. Geothermics Engineering geology Entropy Exact sciences and technology Mathematical models Maximum entropy Maximum entropy distribution Rock Rock materials Strain softening Strength Weibull distribution |
| Title | On a statistical damage constitutive model for rock materials |
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