考虑初始损伤和残余强度的岩石变形过程模拟
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摘要
针对现有损伤模型的不足,提出同时反映岩石初始损伤和残余强度的岩石变形过程模拟方法.将岩石材料分为未损伤部分、损伤部分和微缺陷,未损伤部分和损伤部分共同承担岩石所受的应力.通过岩石材料几何条件及微观受力分析建立未损伤部分的应变分析.再考虑岩石的形变比能只与损伤部分材料相关,从而建立损伤部分的应变分析.然后探讨岩石损伤和耗散能的关系,提出了可以反映岩石初始损伤的损伤演化方程,基于各部分应变分析建立模拟岩石变形过程的损伤本构模型,同时给出模型各参数的确定方法.结果表明:损伤演化方程不仅表现了岩石的初始损伤特征,也可以完整地体现岩石变形破坏过程的5个阶段;与前人模型相比,提出的岩石变形模拟方法与试验曲线更加吻合,体现了岩石的变形全过程,特别是更加直观地反映了岩石的初始损伤和残余强度特征.综合体现了本文模型在模拟岩石变形全过程时的优势.
Aiming at the limitations of previous rock damage constitutive models,a comprehensive simulation method of rock deformation to present simultaneously initial damage and residual strength is developed.With consideration of the initial damage of rock and the fact that the damage portion still can bear certain stress,deformation mechanism models of each portion are established by decomposing rock materials into three portions,undamaged material,damaged material and micro-defects.Firstly,on the basis of geometry conditions and micro-force for rocks,the strain analysis for undamaged material is proposed.Meanwhile,considering that the deformation energy of rock is only related to damaged material,the strain analysis for damaged material is developed.Then,discussing the relationships between damage evolution and energy dissipation,and putting forward a damage evolution model to reflect the initial damage for rocks,a rock damage constitutive model to simulate the complete processes of deformation for rocks is established based on the strain analysis and the determination methods of model parameters are also provided.The results show that damage evolution model not only reflects the initial damage for rocks,but also presents the rock deformation stages.Compared with previous models,the proposed damage constitutive model is more consistent with the experimental curve.In addition,the proposed model reflects the complete processes of deformation for rocks,and presents intuitively the characteristics of the initial damage and the residual strength.Thus,the superiority of the model is validated.
Aiming at the limitations of previous rock damage constitutive models,a comprehensive simulation method of rock deformation to present simultaneously initial damage and residual strength is developed.With consideration of the initial damage of rock and the fact that the damage portion still can bear certain stress,deformation mechanism models of each portion are established by decomposing rock materials into three portions,undamaged material,damaged material and micro-defects.Firstly,on the basis of geometry conditions and micro-force for rocks,the strain analysis for undamaged material is proposed.Meanwhile,considering that the deformation energy of rock is only related to damaged material,the strain analysis for damaged material is developed.Then,discussing the relationships between damage evolution and energy dissipation,and putting forward a damage evolution model to reflect the initial damage for rocks,a rock damage constitutive model to simulate the complete processes of deformation for rocks is established based on the strain analysis and the determination methods of model parameters are also provided.The results show that damage evolution model not only reflects the initial damage for rocks,but also presents the rock deformation stages.Compared with previous models,the proposed damage constitutive model is more consistent with the experimental curve.In addition,the proposed model reflects the complete processes of deformation for rocks,and presents intuitively the characteristics of the initial damage and the residual strength.Thus,the superiority of the model is validated.
引文
Cao,W.G.,Zhang,C.,He,M.,et al.,2016a.Deformation Simulation of Brittle Rock Based on Micromechanical Properties.Rock and Soil Mechanics,37(10):2753-2760(in Chinese with English abstract).
Cao,W.G.,Zhang,C.,He,M.,et al.,2016b.Statistical Damage Simulation Method of Strain Softening Deformation Process for Rocks Considering Characteristics of Void Compaction Stage.Chinese Journal of Geotechnical Engineering,38(10):1754-1761(in Chinese with English abstract).
Cao,W.G.,Zhang,S.,2005.Study on the Statistical Analysis of Rock Damage Based on Mohr-Coulomb Criterion.Journal of Hunan University(Natural Sciences),32(1):43-47(in Chinese with English abstract).
Cao,W.G.,Zhang,S.,Zhao,M.H.,2006.Study on Statistical Damage Constitutive Model of Rock Based on New Definition of Damage.Rock and Soil Mechanics,27(1):41-46(in Chinese with English abstract).
Cao,W.G.,Zhao,H.,Zhang,Y.J.,et al.,2011.Strain Softening and Hardening Damage Constitutive Model for Rock Considering Effect of Volume Change and Its Parameters Determination Method.Rock and Soil Mechanics,32(3):647-654(in Chinese with English abstract).
Cao,W.G.,Zhao,M.H.,Liu,C.X.,2004.Study on the Model and Its Modifying Method for Rock Softening and Damage Based on Weibull Random Distribution.Chinese Journal of Rock Mechanics and Engineering,23(19):3226-3231(in Chinese with English abstract).
Cui,D.S.,Xiang,W.,Chen,Q.,et al.,2016.Experiment of Energy Dissipation and Energy Release during StickSlip within Glass Beads.Earth Science,41(9):1603-1610(in Chinese with English abstract).
Diederichs,M.S.,Kaiser,P.K.,Eberhardt,E.,2004.Damage Initiation and Propagation in Hard Rock during Tunnelling and the Influence of Near-Face Stress Rotation.International Journal of Rock Mechanics and Mining Sciences,41(5):785-812.https://doi.org/10.1016/j.ijrmms.2004.02.003
Fairhurst,C.E.,Hudson,J.A.,1999.Draft ISRM Suggested Method for the Complete Stress-Strain Curve for Intact Rock in Uniaxial Compression.International Journal of Rock Mechanics and Mining Sciences,36(3):279-289.https://doi.org/10.1016/S0148-9062(99)00006-6
Fan,H.L.,Jin,F.N.,2000.Effective Modulus Method in Damage Mechanics of Rock.Chinese Journal of Rock Mechanics and Engineering,19(4):432-435(in Chinese with English abstract).
Gong,X.N.,2000.Prospects for the Development of Geotechnical Engineering in the 21th Century.Chinese Journal of Geotechnical Engineering,22(2):238-242(in Chinese with English abstract).
Hu,L.M.,Pu,J.L.,2002.Damage of Soil-Structure Interface.RockandSoil Mechanics,23(1):6-11(in Chinese with English abstract).
Hu,Z.,Liu,Y.R.,Wu,S.,et al.,2014.Experimental Study of Deformation Parameters Degradation of Sandstone in High Geostress Regions under Unloading Conditions.Rock and Soil Mechanics,35(Suppl.1):78-84(in Chinese with English abstract).
Li,X.,Cao,W.G.,Su,Y.H.,2012.A Statistical Damage Constitutive Model for Softening Behavior of Rocks.Engineering Geology,143-144:1-17.https://doi.org/10.1016/j.enggeo.2012.05.005
Peng,J.,Cai,M.,Liu,D.Q.,et al.,2015a.A Phenomenological Model of Brittle Rocks under Uniaxial Compression.International Journal of Geohazards and Environment,1(2):53-62.https://doi.org/10.1016/j.enggeo.2015.12.011
Peng,J.,Cai,M.,Rong,G.,et al.,2015b.Stresses for Crack Closure and Its Application to Assessing StressInducing Microcrack Damage.Chinese Journal of Rock Mechanics and Engineering,34(6):1091-1100(in Chinese with English abstract).
Tian,H.M.,Chen,W.Z.,Tian,T.,et al.,2012.Experimental and Theoretical Studies of Creep Damage Behavior of Soft Rock.Chinese Journal of Rock Mechanics and Engineering,31(3):610-617(in Chinese with English abstract).
Wang,X.G.,Hu,B.,Tang,H.M.,et al.,2016.Triaxial Rheological Experiments and Rheological Constitutive of Mudstone under Hydro-Mechanical Coupling State.Earth Science,41(5):886-894(in Chinese with English abstract).
Wen,T.,Liu,Y.R.,Yang,C.G.,et al.,2017.A Rock Damage Constitutive Model and Damage Energy Dissipation Rate Analysis for Characterising the Crack Closure Effect.Geomechanics and Geoengineering,13(1):54-63.https://doi.org/10.1080/17486025.2017.1330969
Wen,T.,Tang,H.M.,Liu,Y.R.,et al.,2016a.Newly Modified Damage Statistical Constitutive Model of Rock Based on Impact Factor.Journal of China University of Mining&Technology,45(1):141-149(in Chinese with English abstract).
Wen,T.,Tang,H.M.,Liu,Y.R.,et al.,2016b.Energy and Damage Analysis of Slate during Triaxial Compression under Different Confining Pressures.Coal Geology&Exploration,44(3):80-86(in Chinese with English abstract).
Wu,E.L.,Wei,C.F.,Wei,H.Z.,et al.,2013.A Statistical Damage Constitutive Model of Hydrate-Bearing Sediments.Rock and Soil Mechanics,34(1):60-65(in Chinese with English abstract).
Xie,H.P.,1990.Damage Mechanics of Rock and Concrete.China University of Mining&Technology Press,Xuzhou,173-186(in Chinese).
Yang,M.H.,Zhao,M.H.,Cao,W.G.,2005.Method for Determining the Parameters of Statistical Damage Softening Constitutive Model for Rock.Journal of Hydraulic Engineering,36(3):345-349(in Chinese with English abstract).
Yang,S.Q.,Xu,P.,Ranjith,P.G.,2015.Damage Model of Coal under Creep and Triaxial Compression.International Journal of Rock Mechanics and Mining Sciences,80:337-345.https://doi.org/10.1016/j.ijrmms.2015.10.006
Yang,S.Q.,Xu,W.Y.,Wei,L.D.,et al.,2004.Statistical Constitutive Model for Rock Damage under Uniaxial Compression and Its Experimental Study.Journal of Hohai University(Natural Sciences),32(2):200-203(in Chinese with English abstract).
Zhang,K.,Liu,S.Wei,C.Y.,et al.,2016.Constitutive Model and Damage Evolution of Rock under Different Loads.Journal of Shenyang Jianzhu University(Natural Science),32(5):896-903(in Chinese with English abstract).
Zhao,H.,Shi,C.J.,Zhao,M.H.,et al.,2016.Statistical Damage Constitutive Model for Rocks Considering Residual Strength.International Journal of Geomechanics,17(1):04016033.https://doi.org/10.1061/(asce)gm.1943-5622.0000680
Zhu,J.M.,Xu,B.Y.,Ren,T.G.,et al.,2000.Establishing the Damage Evolution Equation of the Fractured Rocks Based on the Triaxial Compression Tests.Journal of Engineering Geology,8(2):175-179(in Chinese with English abstract).
曹文贵,张超,贺敏,等,2016a.基于微观力学特性的脆性岩石变形过程模拟.岩土力学,37(10):2753-2760.
曹文贵,张超,贺敏,等,2016b.考虑空隙压密阶段特征的岩石应变软化统计损伤模拟方法.岩土工程学报,38(10):1754-1761.
曹文贵,张升,2005.基于Mohr-Coulomb准则的岩石损伤统计分析方法研究.湖南大学学报(自然科学版),32(1):43-47.
曹文贵,赵衡,张永杰,等,2011.考虑体积变化影响的岩石应变软硬化损伤本构模型及参数确定方法.岩土力学,32(3):647-654.
曹文贵,张升,赵明华,2006.基于新型损伤定义的岩石损伤统计本构模型探讨.岩土力学,27(1):41-46.
曹文贵,赵明华,刘成学,2004.基于Weibull分布的岩石损伤软化模型及其修正方法研究.岩石力学与工程学报,23(19):3226-3231.
崔德山,项伟,陈琼,等,2016.细颗粒粘滑运动的能量耗散与释放试验.地球科学,41(9):1603-1610.
范华林,金丰年,2000.岩石损伤定义中的有效模量法.岩石力学与工程学报,19(4):432-435.
龚晓南,2000.21世纪岩土工程发展展望.岩土工程学报,22(2):238-242.
胡黎明,濮家骝,2002.土与结构物接触面损伤本构模型.岩土力学,23(1):6-11.
胡政,刘佑荣,武尚,等,2014.高地应力区砂岩在卸荷条件下的变形参数劣化试验研究.岩土力学,35(增刊1):78-84.
彭俊,蔡明,荣冠,等,2015.裂纹闭合应力及其岩石微裂纹损伤评价.岩石力学与工程学报,34(6):1091-1100.
田洪铭,陈卫忠,田田,等,2012.软岩蠕变损伤特性的试验与理论研究.岩石力学与工程学报,31(3):610-617.
王新刚,胡斌,唐辉明,等,2016.渗透压-应力耦合作用下泥岩三轴流变实验及其流变本构.地球科学,41(5):886-894.
温韬,唐辉明,刘佑荣,等,2016a.影响因子修正的新型岩石损伤统计本构模型.中国矿业大学学报,45(1):141-149.
温韬,唐辉明,刘佑荣,等,2016b.不同围压下板岩三轴压缩过程能量及损伤分析.煤田地质与勘探,44(3):80-86.
吴二林,韦昌富,魏厚振,等,2013.含天然气水合物沉积物损伤统计本构模型.岩土力学,34(1):60-65.
谢和平,1990.岩石、混凝土损伤力学,徐州:中国矿业大学出版社,173-186.
杨明辉,赵明华,曹文贵,2005.岩石损伤软化统计本构模型参数的确定方法.水利学报,36(3):345-349.
杨圣奇,徐卫亚,韦立德,等,2004.单轴压缩下岩石损伤统计本构模型与试验研究.河海大学学报(自然科学版),32(2):200-203.
张珂,刘帅,魏春雨,等,2016.岩石在不同应力条件下的本构模型与损伤演化.沈阳建筑大学学报(自然科学版),32(5):896-903.
朱建明,徐秉业,任天贵,等,2000.基于三轴压缩试验的破裂岩损伤演化方程的建立.工程地质学报,8(2):175-179.
Cao,W.G.,Zhang,C.,He,M.,et al.,2016b.Statistical Damage Simulation Method of Strain Softening Deformation Process for Rocks Considering Characteristics of Void Compaction Stage.Chinese Journal of Geotechnical Engineering,38(10):1754-1761(in Chinese with English abstract).
Cao,W.G.,Zhang,S.,2005.Study on the Statistical Analysis of Rock Damage Based on Mohr-Coulomb Criterion.Journal of Hunan University(Natural Sciences),32(1):43-47(in Chinese with English abstract).
Cao,W.G.,Zhang,S.,Zhao,M.H.,2006.Study on Statistical Damage Constitutive Model of Rock Based on New Definition of Damage.Rock and Soil Mechanics,27(1):41-46(in Chinese with English abstract).
Cao,W.G.,Zhao,H.,Zhang,Y.J.,et al.,2011.Strain Softening and Hardening Damage Constitutive Model for Rock Considering Effect of Volume Change and Its Parameters Determination Method.Rock and Soil Mechanics,32(3):647-654(in Chinese with English abstract).
Cao,W.G.,Zhao,M.H.,Liu,C.X.,2004.Study on the Model and Its Modifying Method for Rock Softening and Damage Based on Weibull Random Distribution.Chinese Journal of Rock Mechanics and Engineering,23(19):3226-3231(in Chinese with English abstract).
Cui,D.S.,Xiang,W.,Chen,Q.,et al.,2016.Experiment of Energy Dissipation and Energy Release during StickSlip within Glass Beads.Earth Science,41(9):1603-1610(in Chinese with English abstract).
Diederichs,M.S.,Kaiser,P.K.,Eberhardt,E.,2004.Damage Initiation and Propagation in Hard Rock during Tunnelling and the Influence of Near-Face Stress Rotation.International Journal of Rock Mechanics and Mining Sciences,41(5):785-812.https://doi.org/10.1016/j.ijrmms.2004.02.003
Fairhurst,C.E.,Hudson,J.A.,1999.Draft ISRM Suggested Method for the Complete Stress-Strain Curve for Intact Rock in Uniaxial Compression.International Journal of Rock Mechanics and Mining Sciences,36(3):279-289.https://doi.org/10.1016/S0148-9062(99)00006-6
Fan,H.L.,Jin,F.N.,2000.Effective Modulus Method in Damage Mechanics of Rock.Chinese Journal of Rock Mechanics and Engineering,19(4):432-435(in Chinese with English abstract).
Gong,X.N.,2000.Prospects for the Development of Geotechnical Engineering in the 21th Century.Chinese Journal of Geotechnical Engineering,22(2):238-242(in Chinese with English abstract).
Hu,L.M.,Pu,J.L.,2002.Damage of Soil-Structure Interface.RockandSoil Mechanics,23(1):6-11(in Chinese with English abstract).
Hu,Z.,Liu,Y.R.,Wu,S.,et al.,2014.Experimental Study of Deformation Parameters Degradation of Sandstone in High Geostress Regions under Unloading Conditions.Rock and Soil Mechanics,35(Suppl.1):78-84(in Chinese with English abstract).
Li,X.,Cao,W.G.,Su,Y.H.,2012.A Statistical Damage Constitutive Model for Softening Behavior of Rocks.Engineering Geology,143-144:1-17.https://doi.org/10.1016/j.enggeo.2012.05.005
Peng,J.,Cai,M.,Liu,D.Q.,et al.,2015a.A Phenomenological Model of Brittle Rocks under Uniaxial Compression.International Journal of Geohazards and Environment,1(2):53-62.https://doi.org/10.1016/j.enggeo.2015.12.011
Peng,J.,Cai,M.,Rong,G.,et al.,2015b.Stresses for Crack Closure and Its Application to Assessing StressInducing Microcrack Damage.Chinese Journal of Rock Mechanics and Engineering,34(6):1091-1100(in Chinese with English abstract).
Tian,H.M.,Chen,W.Z.,Tian,T.,et al.,2012.Experimental and Theoretical Studies of Creep Damage Behavior of Soft Rock.Chinese Journal of Rock Mechanics and Engineering,31(3):610-617(in Chinese with English abstract).
Wang,X.G.,Hu,B.,Tang,H.M.,et al.,2016.Triaxial Rheological Experiments and Rheological Constitutive of Mudstone under Hydro-Mechanical Coupling State.Earth Science,41(5):886-894(in Chinese with English abstract).
Wen,T.,Liu,Y.R.,Yang,C.G.,et al.,2017.A Rock Damage Constitutive Model and Damage Energy Dissipation Rate Analysis for Characterising the Crack Closure Effect.Geomechanics and Geoengineering,13(1):54-63.https://doi.org/10.1080/17486025.2017.1330969
Wen,T.,Tang,H.M.,Liu,Y.R.,et al.,2016a.Newly Modified Damage Statistical Constitutive Model of Rock Based on Impact Factor.Journal of China University of Mining&Technology,45(1):141-149(in Chinese with English abstract).
Wen,T.,Tang,H.M.,Liu,Y.R.,et al.,2016b.Energy and Damage Analysis of Slate during Triaxial Compression under Different Confining Pressures.Coal Geology&Exploration,44(3):80-86(in Chinese with English abstract).
Wu,E.L.,Wei,C.F.,Wei,H.Z.,et al.,2013.A Statistical Damage Constitutive Model of Hydrate-Bearing Sediments.Rock and Soil Mechanics,34(1):60-65(in Chinese with English abstract).
Xie,H.P.,1990.Damage Mechanics of Rock and Concrete.China University of Mining&Technology Press,Xuzhou,173-186(in Chinese).
Yang,M.H.,Zhao,M.H.,Cao,W.G.,2005.Method for Determining the Parameters of Statistical Damage Softening Constitutive Model for Rock.Journal of Hydraulic Engineering,36(3):345-349(in Chinese with English abstract).
Yang,S.Q.,Xu,P.,Ranjith,P.G.,2015.Damage Model of Coal under Creep and Triaxial Compression.International Journal of Rock Mechanics and Mining Sciences,80:337-345.https://doi.org/10.1016/j.ijrmms.2015.10.006
Yang,S.Q.,Xu,W.Y.,Wei,L.D.,et al.,2004.Statistical Constitutive Model for Rock Damage under Uniaxial Compression and Its Experimental Study.Journal of Hohai University(Natural Sciences),32(2):200-203(in Chinese with English abstract).
Zhang,K.,Liu,S.Wei,C.Y.,et al.,2016.Constitutive Model and Damage Evolution of Rock under Different Loads.Journal of Shenyang Jianzhu University(Natural Science),32(5):896-903(in Chinese with English abstract).
Zhao,H.,Shi,C.J.,Zhao,M.H.,et al.,2016.Statistical Damage Constitutive Model for Rocks Considering Residual Strength.International Journal of Geomechanics,17(1):04016033.https://doi.org/10.1061/(asce)gm.1943-5622.0000680
Zhu,J.M.,Xu,B.Y.,Ren,T.G.,et al.,2000.Establishing the Damage Evolution Equation of the Fractured Rocks Based on the Triaxial Compression Tests.Journal of Engineering Geology,8(2):175-179(in Chinese with English abstract).
曹文贵,张超,贺敏,等,2016a.基于微观力学特性的脆性岩石变形过程模拟.岩土力学,37(10):2753-2760.
曹文贵,张超,贺敏,等,2016b.考虑空隙压密阶段特征的岩石应变软化统计损伤模拟方法.岩土工程学报,38(10):1754-1761.
曹文贵,张升,2005.基于Mohr-Coulomb准则的岩石损伤统计分析方法研究.湖南大学学报(自然科学版),32(1):43-47.
曹文贵,赵衡,张永杰,等,2011.考虑体积变化影响的岩石应变软硬化损伤本构模型及参数确定方法.岩土力学,32(3):647-654.
曹文贵,张升,赵明华,2006.基于新型损伤定义的岩石损伤统计本构模型探讨.岩土力学,27(1):41-46.
曹文贵,赵明华,刘成学,2004.基于Weibull分布的岩石损伤软化模型及其修正方法研究.岩石力学与工程学报,23(19):3226-3231.
崔德山,项伟,陈琼,等,2016.细颗粒粘滑运动的能量耗散与释放试验.地球科学,41(9):1603-1610.
范华林,金丰年,2000.岩石损伤定义中的有效模量法.岩石力学与工程学报,19(4):432-435.
龚晓南,2000.21世纪岩土工程发展展望.岩土工程学报,22(2):238-242.
胡黎明,濮家骝,2002.土与结构物接触面损伤本构模型.岩土力学,23(1):6-11.
胡政,刘佑荣,武尚,等,2014.高地应力区砂岩在卸荷条件下的变形参数劣化试验研究.岩土力学,35(增刊1):78-84.
彭俊,蔡明,荣冠,等,2015.裂纹闭合应力及其岩石微裂纹损伤评价.岩石力学与工程学报,34(6):1091-1100.
田洪铭,陈卫忠,田田,等,2012.软岩蠕变损伤特性的试验与理论研究.岩石力学与工程学报,31(3):610-617.
王新刚,胡斌,唐辉明,等,2016.渗透压-应力耦合作用下泥岩三轴流变实验及其流变本构.地球科学,41(5):886-894.
温韬,唐辉明,刘佑荣,等,2016a.影响因子修正的新型岩石损伤统计本构模型.中国矿业大学学报,45(1):141-149.
温韬,唐辉明,刘佑荣,等,2016b.不同围压下板岩三轴压缩过程能量及损伤分析.煤田地质与勘探,44(3):80-86.
吴二林,韦昌富,魏厚振,等,2013.含天然气水合物沉积物损伤统计本构模型.岩土力学,34(1):60-65.
谢和平,1990.岩石、混凝土损伤力学,徐州:中国矿业大学出版社,173-186.
杨明辉,赵明华,曹文贵,2005.岩石损伤软化统计本构模型参数的确定方法.水利学报,36(3):345-349.
杨圣奇,徐卫亚,韦立德,等,2004.单轴压缩下岩石损伤统计本构模型与试验研究.河海大学学报(自然科学版),32(2):200-203.
张珂,刘帅,魏春雨,等,2016.岩石在不同应力条件下的本构模型与损伤演化.沈阳建筑大学学报(自然科学版),32(5):896-903.
朱建明,徐秉业,任天贵,等,2000.基于三轴压缩试验的破裂岩损伤演化方程的建立.工程地质学报,8(2):175-179.
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