高应力区岩石统计损伤本构模型研究
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摘要
为了反映高应力区岩石变形破坏全过程,通过引入双参数抛物线型Mohr强度准则,建立适用于高应力区岩体的微元强度度量方式,并假定由该度量方式得到的微元强度服从幂函数概率密度分布,结合连续损伤理论,考虑损伤变量修正,建立一个新的适用于高应力区岩体的统计损伤本构模型。以高应力区英安岩为验证对象,进行常规三轴压缩试验,依据岩石应力-应变曲线特征,给出模型参数确定方法。引用基于线性Mohr强度准则而建适用于浅部低应力水平岩体的相关统计损伤模型,利用该模型和所建模型对高应力区英安岩和相关文献中的高应力区砂岩、花岗岩试验数据进行验证,对比试验曲线和理论曲线,证明所建模型的可行性和适用性,并对英安岩累积损伤的扩展过程进行分析。
In order to reflect the whole process of rock deformation and failure in high stress areas,the parabolic Mohr strength criterion is introduced.The micro-unit strength measurement method for rock mass in high stress areas is established,and it is assumed that the element strength obeys the power function probability density distribution.The continuum damage theory is combined and the correction of damage variable is considered.A new statistical damage constitutive model of rock in high stress areas is also established.The conventional triaxial compression test of dacite in high stress areas is conduced,and the method of determining the model parameters is given according to the characteristics of stress-strain curves of rock.A related statistical damage model based on the linear Mohr strength criterion for rock under a shallow low stress level is quoted,and the quoted model and the model built in this paper are used to verify the test data of the dacite,sandstone and granite in high stress areas in related literatures.The feasibility of the modelis proved by comparing the test curves with the theoretical curves.The damage accumulation and energy dissipation of dacite in high stress areas are analyzed.The correctness of damage correction factor is proved from the energy point of view and the energy change law during rock deformation and failure is studied.The rationality of the model is reflected.
In order to reflect the whole process of rock deformation and failure in high stress areas,the parabolic Mohr strength criterion is introduced.The micro-unit strength measurement method for rock mass in high stress areas is established,and it is assumed that the element strength obeys the power function probability density distribution.The continuum damage theory is combined and the correction of damage variable is considered.A new statistical damage constitutive model of rock in high stress areas is also established.The conventional triaxial compression test of dacite in high stress areas is conduced,and the method of determining the model parameters is given according to the characteristics of stress-strain curves of rock.A related statistical damage model based on the linear Mohr strength criterion for rock under a shallow low stress level is quoted,and the quoted model and the model built in this paper are used to verify the test data of the dacite,sandstone and granite in high stress areas in related literatures.The feasibility of the modelis proved by comparing the test curves with the theoretical curves.The damage accumulation and energy dissipation of dacite in high stress areas are analyzed.The correctness of damage correction factor is proved from the energy point of view and the energy change law during rock deformation and failure is studied.The rationality of the model is reflected.
引文
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[14]石崇,蒋新兴,朱珍德,等.基于Hoek-Brown准则的岩石损伤本构模型研究及其参数探讨[J].岩石力学与工程学报,2011,30(增刊1):2647-2652.[SHI C,JIANG X X,ZHU Z D,et al.Study of rock damage constitutive model and discussion of its parameters based on Hoek-Brown criterion[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Sup 1):2647-2652.(in Chinese)]
[15]ZHU C Q,YIN Z Q,LI C M.Elastoplastic Analysis of Tunnel Surrounding Rocks based on the Statistical Damage Constitutive Model[J].Journal of Engineering Science&Technology Review,2016,9(3):27-34.
[16]LEMAITRE J.A continuous damage mechanics model for ductile fracture[J].Journal of Engineering Materials&Technology,1985,107(1):83-89.
[17]周永强,盛谦,冷先伦,等.考虑残余强度和阈值影响的岩石弹性损伤统计模型[J].长江科学院院报,2016,33(3):48-53.[ZHOU Y Q,SHENG Q,LENG X L,et al.Statistical constitutive model of elastic damage for rock considering residual strength and threshold[J].Journal of Yangtze River Scientific Research Institute,2016,33(3):48-53.(in Chinese)]
[18]佘成学,刘杰.基于Mohr强度理论的双参数抛物线型屈服准则[J].武汉大学学报(工学版),2008,41(1):31-34.[SHE C X,LIU J.Two-parameter parabolic-type yield criterion based on Mohr strength theory[J].Engineering Journal of Wuhan University,2008,41(1):31-34.(in Chinese)]
[19]李顺群,焦学英,王芳.Mohr包线的二次曲线形式[J].辽宁工程技术大学学报,2005,24(6):853-855.[LI S Q,JIAO X Y,WANG F.Study on conic for Mohr curve[J].Journal of Liaoning Technical University(Natural Science),2005,24(6):853-855.(in Chinese)]
[20]曹瑞琅,贺少辉,韦京,等.基于残余强度修正的岩石损伤软化统计本构模型研究[J].岩土力学,2013,34(6):1652-1667.[CAO R L,HE S H,WEI J,et al.Study of modified statistical damage softening constitutive model for rock considering residual strength[J].Rock and Soil Mechanics,2013,34(6):1652-1667.(in Chinese)]
[21]温韬,刘佑荣,胡政,等.高应力区砂岩加卸载条件下能量变化规律及损伤分析[J].地质科技情报,2015,34(2):200-206.[WEN T,LIU Y R,HU Z,et al.Energy Change law damage analysis of sandstone under loading and unloading conditions in high stress area[J].Geological Science and Technology Information,2015,34(2):200-206.(in Chinese)]
[22]张帆,盛谦,朱泽奇,等.三峡花岗岩峰后力学特性及应变软化模型研究[J].岩石力学与工程学报,2008,27(增刊1):2651-2655.[ZHANG F,SHENG Q,ZHU Z Q,et al.Study on post-peak mechanical behaviour and strain-softening model of three gorges granite[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(Sup 1):2651-2655.(in Chinese)]
[2]陈菲,何川,邓建辉.高地应力定义及其定性定量判据[J].岩土力学,2015,36(4):971-980.[CHENF,HE C,DENG J H.Concept of high geostress and its qualitative and quantitative Definitions[J].Rock and Soil Mechanics,2015,36(4):971-980.(in Chinese)]
[3]COOK N G W.The failure of rock[J].International Journal of Rock Mechanics&Mining Sciences&Geomechanics Abstracts,1965,2(4):389-403.
[4]李兆霞.损伤力学及其应用[M].北京:科学出版社,2002.[LI Z X.Damage mechanics and its application[M].Beijing:Science Press,2002.(in Chinese)]
[5]邓华锋,胡安龙,李建林,等.水岩作用下砂岩劣化损伤统计本构模型[J].岩土力学,2017,38(3):631-639.[DENG H F,HU A L,LI J L,et al.Statistical damage constitutive model of sandstone under water-rock interaction[J].Rock and Soil Mechanics,2017,38(3):631-639.(in Chinese)]
[6]KRAJCINOVIC D.Damage mechanics[J].Mechanics of Materials,1989,8(2):117-197.
[7]曹文贵,莫瑞,李翔,等.基于正态分布的岩石软硬化损伤统计本构模型及其参数确定方法探讨[J].岩土工程学报,2007,29(5):671-675.[CAO WG,MO R,LI X,et al.Study on statistical constitutive model and determination of parameters of rock based on normal distribution[J].Chinese Journal of Geotechnical Engineering,2007,29(5):671-675.(in Chinese)]
[8]曹文贵,戴笠,张超.深部岩石统计损伤本构模型研究[J].水文地质工程地质,2016,43(4):60-65.[CAO W G,DAI L,ZHANG C.A study of statistical damage constitutive models for deep earth rocks[J].Hydrogeology&Engineering Geology,2016,43(4):60-65.(in Chinese)]
[9]曹文贵,张升.基于Mohr-Coulomb准则的岩石损伤统计分析方法研究[J].湖南大学学报(自然科学版),2005,32(1):43-47.[CAO W G,ZHANG S.Study on the statistical analysis of rock damage based on Mohr-coulomb Criterion[J].Journal of Hunan University(Natural Sciences),2005,32(1):43-47.(in Chinese)]
[10]曹文贵,赵衡,张玲,等.考虑损伤阀值影响的岩石损伤统计软化本构模型及其参数确定方法[J].岩石力学与工程学报,2008,27(6):1148-1154.[CAO W G,ZHAO H,ZHANG L,et al.Damage statistical softening constitutive model for rock considering effect of damage threshold and its parameters determination method[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(6):1148-1154.(in Chinese)]
[11]刘成学,杨林德,曹文贵.岩石统计损伤软化本构模型及其参数反演[J].地下空间与工程学报,2007,3(3):453-457.[LIU C X,YANG L D,CAO WG.A statistical damage softening constitutive model for rock and back analysis of its parameters[J].Chinese Journal of Underground Space and Engineering,2007,3(3):453-457.(in Chinese)]
[12]韦立德,徐卫亚,杨春和,等.具有统计损伤的岩石弹塑性本构模型研究[J].岩石力学与工程学报,2004,23(12):1971-1975.[WEI L D,XU W Y,YANG C H,et al.Study on elastoplastic constitutive model of rock with statistical damage[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(12):1971-1975.(in Chinese)]
[13]蒋维,邓建,李隐,等.基于对数正态分布的岩石损伤本构模型研究[J].地下空间与工程学报,2010,6(6):1190-1194.[JIANG W,DENG J,LI Y,et al.Study on constitutive model of rock damage based on lognormal distribution[J].Chinese Journal of Underground Space and Engineering,2010,6(6):1190-1194.(in Chinese)]
[14]石崇,蒋新兴,朱珍德,等.基于Hoek-Brown准则的岩石损伤本构模型研究及其参数探讨[J].岩石力学与工程学报,2011,30(增刊1):2647-2652.[SHI C,JIANG X X,ZHU Z D,et al.Study of rock damage constitutive model and discussion of its parameters based on Hoek-Brown criterion[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Sup 1):2647-2652.(in Chinese)]
[15]ZHU C Q,YIN Z Q,LI C M.Elastoplastic Analysis of Tunnel Surrounding Rocks based on the Statistical Damage Constitutive Model[J].Journal of Engineering Science&Technology Review,2016,9(3):27-34.
[16]LEMAITRE J.A continuous damage mechanics model for ductile fracture[J].Journal of Engineering Materials&Technology,1985,107(1):83-89.
[17]周永强,盛谦,冷先伦,等.考虑残余强度和阈值影响的岩石弹性损伤统计模型[J].长江科学院院报,2016,33(3):48-53.[ZHOU Y Q,SHENG Q,LENG X L,et al.Statistical constitutive model of elastic damage for rock considering residual strength and threshold[J].Journal of Yangtze River Scientific Research Institute,2016,33(3):48-53.(in Chinese)]
[18]佘成学,刘杰.基于Mohr强度理论的双参数抛物线型屈服准则[J].武汉大学学报(工学版),2008,41(1):31-34.[SHE C X,LIU J.Two-parameter parabolic-type yield criterion based on Mohr strength theory[J].Engineering Journal of Wuhan University,2008,41(1):31-34.(in Chinese)]
[19]李顺群,焦学英,王芳.Mohr包线的二次曲线形式[J].辽宁工程技术大学学报,2005,24(6):853-855.[LI S Q,JIAO X Y,WANG F.Study on conic for Mohr curve[J].Journal of Liaoning Technical University(Natural Science),2005,24(6):853-855.(in Chinese)]
[20]曹瑞琅,贺少辉,韦京,等.基于残余强度修正的岩石损伤软化统计本构模型研究[J].岩土力学,2013,34(6):1652-1667.[CAO R L,HE S H,WEI J,et al.Study of modified statistical damage softening constitutive model for rock considering residual strength[J].Rock and Soil Mechanics,2013,34(6):1652-1667.(in Chinese)]
[21]温韬,刘佑荣,胡政,等.高应力区砂岩加卸载条件下能量变化规律及损伤分析[J].地质科技情报,2015,34(2):200-206.[WEN T,LIU Y R,HU Z,et al.Energy Change law damage analysis of sandstone under loading and unloading conditions in high stress area[J].Geological Science and Technology Information,2015,34(2):200-206.(in Chinese)]
[22]张帆,盛谦,朱泽奇,等.三峡花岗岩峰后力学特性及应变软化模型研究[J].岩石力学与工程学报,2008,27(增刊1):2651-2655.[ZHANG F,SHENG Q,ZHU Z Q,et al.Study on post-peak mechanical behaviour and strain-softening model of three gorges granite[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(Sup 1):2651-2655.(in Chinese)]