A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China
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摘要
Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and timedependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10-6 s-1 to 1×10-3 s-1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value(about 0.1 to 0.2), soon reaches its minimum(about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre's equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.
Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and timedependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10-6 s-1 to 1×10-3 s-1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value(about 0.1 to 0.2), soon reaches its minimum(about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre's equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.
Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and timedependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10-6 s-1 to 1×10-3 s-1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value(about 0.1 to 0.2), soon reaches its minimum(about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre's equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.
引文
Abousleiman,Y.N.,Hoang,S.K.,and Tran,M.H.,2010.Mechanical characterization of small shale samples subjected to fluid exposure using the inclined direct shear testing device.International Journal of Rock Mechanics and Mining Sciences,47(3):355-367.
Ulusay,R.,2015.The ISRM Suggested Methods for Rock Characterization,Testing and Monitoring 2007-2014.Switzerland:Springer International Publishing,1-293.
Bai,Y.,and Wierzbicki,T.,2010.Application of extended MohrCoulomb criterion to ductile fracture.International Journal of Fracture,161(1):1-20.
Benz,T.,Schwab,R.,Kauther,R.A.,and Vermeer,P.A.,2008.AHoek-Brown criterion with intrinsic material strength factorization.International Journal of Rock Mechanics and Mining Sciences,45(2):210-222.
Cai,M.F.,He,M.C.,and Liu,D.Y.,2002.Rock Mechanics and Engineering.Beijing:Science Press,131-134(in Chinese).
Cao,R.L.,He,S.H.,Wei,J.,and Wang,F.,2013.Study of modified statistical damage softening constitutive model for rock considering residual strength.Rock and Soil Mechanics,34(6):1652-1660(in Chinese).
Cao,W.G.,and Li,X.,and Zhao,H.,2007.Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination.Journal of Central South University of Technology,14(5):719-724.
Gong,F.Q.,and Zhao,G.F.,2014.Dynamic indirect tensile strength of sandstone under different loading rates.Rock Mechanics and Rock Engineering,47(6):2271-2278.
GT/T23561,2009.The Professional Standards Compilation Group of Peoples Republic of China:Methods for determining the physical and mechanical properties of coal and rock.Beijing:Standards Press of China(in Chinese).
Hao,Z.G.,Fei,H.C.,Hao,Q.Q.,and Liu L.,2017.China’s shale gas geological investigation and prospecting have made significant progress.Acta Geologica Sinica(English Edition),91(2):727-728.
Heng,S.,Guo,Y.,Yang,C.,Daemen,J.J.K.,and Li,Z.,2015.Experimental and theoretical study of the anisotropic properties of shale.International Journal of Rock Mechanics&Mining Sciences,74(1):58-68.
Hou,Z.K.,Yang,C.H.,Guo,Y.T.,Zhang,B.P.,Wei,Y.L.,Heng,S.,and Wang,L.,2015.Experimental study on anisotropic properties of Longmaxi Formation shale under uniaxial compression.Rock and Soil Mechanics,36(9):2541-2550(in Chinese).
Hou,Z.K.,Yang,C.H.,Wang,L.,Liu,P.J.,Guo,Y.T.,Wei,Y.L.,and Li,Z.,2016.Hydraulic fracture propagation of shale horizontal well by large-scale true triaxial physical simulation test.Rock and Soil Mechanics,37(2):407-414(in Chinese).
Hou,Z.K.,Yang,C.H.,Wang,L.,and Xu,F.,2016.Evaluation method of shale brittleness based on indoor experiments.Journal of Northeastern University,37(10):1496-1501(in Chinese).
Hou,Z.K.,Marte,G.,Wang,A.M.,Abdulhadi,A.,and Yang,C.H.,2018.Mechanical properties and brittleness of shale with different degrees of fracturing-fluid saturation.Current Science,09(115):1163-1174.
Hou,Z.K.,2018.Research on Hydraulic Fracturing Tests and Crack Extension Mechanism of Longmaxi Shale.Chongqing:Chonqing University(Ph.D thesis):1-180(in Chinese).
Hudson,J.,Harrison,J.,and Popescu,M.,1997.Engineering rock mechanics:an introduction to the principles.Applied Mechanics Reviews,55(2):72-78.
Katsuki,D.,and Gutierrez,M.,2011.Viscoelastic damage model for asphalt concrete.Acta Geotechnica,6(4):231-241.
Lemaitre,J.,1984.How to use damage mechanics.Nuclear Engineering and Design,80(2):233-245.
Li,M.H.,Yin,G.Z.,Xu,J.,Cao,J.,and Song,Z.L.,2016.Permeability evolution of shale under anisotropic true triaxial stress conditions.International Journal of Coal Geology,165:142-148.
Li,Y.S.,and Xia,C.C.,2000.Time-dependent tests on intact rocks in uniaxial compression.International Journal of Rock Mechanics and Mining Sciences,37(3):467-475.
Liang,W.G.,Zhao,Y.S.,Xu,S.G.,and Dusseault,M.B.,2011.Effect of strain rate on the mechanical properties of salt rock.International Journal of Rock Mechanics and Mining Sciences,48(1):161-167.
Ma,T.S.,and Chen,P.,2014.Study of meso-damage characteristics of shale hydration based on CT scanning technology.Petroleum Exploration and Development,41(2):249-256.
Mahanta,B.,Tripathy,A.,Vishal,V.,Singh,T.N.,and Ranjith,P.G.,2016.Effects of strain rate on fracture toughness and energy release rate of gas shales.Engineering Geology,218:39-19.
Middleton,R.S.,Carey,J.W.,Currier,R.P.,Hyman,J.D.,Kang,Q.,and Karra,S.,2015.Shale gas and non-aqueous fracturing fluids:opportunities and challenges for supercritical CO2.Applied Energy,147(3):500-509.
Nie,H.K.,Zhang,J.C.,and Jiang,S.L.,2015.Types and characteristics of the Lower Silurian shale gas reservoirs in and around the Sichuan Basin.Acta Geologica Sinica(English Edition),89(6):1973-1985.
Peng,T.,Yan,J.,Bing,H.,Ke,H.,Zhou,Y.,and Meng,S.,2017.Experimental investigation on fracture initiation and nonplanar propagation of hydraulic fractures in coal seams.Petroleum Exploration&Development,44(3):439-445.
Sedman,A.,Talviste,P.,M?tlep,R.,J?eleht,A.,Kirsim?e,K.,2012.Geotechnical characterization of Estonian oil shale semi-coke deposits with prime emphasis on their shear strength.Engineering Geology,131:37-44.
Vervoort,A.,Min,K.B.,Konietzky,H.,Cho,J.W.,Debecker,B.,and Dinh,Q.D.,2014.Failure of transversely isotropic rock under brazilian test conditions.International Journal of Rock Mechanics&Mining Sciences,70(70):343-352.
Weibull,G.W.,1951.A statistical distribution function of wide applicability.Journal of Applied Mechanics,18:293-297.
Zhai,G.Y.,Wang,Y.F.,Zhou,Z.,Yu,S.F.,Chen,X.L.,and Zhang,Y.X.,2018.Exploration and research progress of shale gas in China.China Geology,1,257-272.
Zhang,G.,Lan,Z.,and Peng,L.,2009.Fracturing control method for deep volcanic rock gas reservoirs in Daqing exploration area.Petroleum Exploration&Development,36(4):529-534.
Zhang,S.W.,Shou,K.J.,Xian,X.F.,Zhou,J.P.,and Liu,G.J.,2018.Fractal characteristics and acoustic emission of anisotropic shale in Brazilian tests.Tunnelling and Underground Space Technology,71:298-308.
Zhou,W.,1990.Advanced Rock Mechanics.Beijing:China Water and Power Press,219(in Chinese).
Zhou,W.,2006.The characteristics of in-situ earth stress and its application research in engineering geology of petroleum on compact reservoir in western Sichuan depression.Chengdu:Chengdu University of Technology(Ph.D thesis):1-150(in Chinese with English abstract).
Ulusay,R.,2015.The ISRM Suggested Methods for Rock Characterization,Testing and Monitoring 2007-2014.Switzerland:Springer International Publishing,1-293.
Bai,Y.,and Wierzbicki,T.,2010.Application of extended MohrCoulomb criterion to ductile fracture.International Journal of Fracture,161(1):1-20.
Benz,T.,Schwab,R.,Kauther,R.A.,and Vermeer,P.A.,2008.AHoek-Brown criterion with intrinsic material strength factorization.International Journal of Rock Mechanics and Mining Sciences,45(2):210-222.
Cai,M.F.,He,M.C.,and Liu,D.Y.,2002.Rock Mechanics and Engineering.Beijing:Science Press,131-134(in Chinese).
Cao,R.L.,He,S.H.,Wei,J.,and Wang,F.,2013.Study of modified statistical damage softening constitutive model for rock considering residual strength.Rock and Soil Mechanics,34(6):1652-1660(in Chinese).
Cao,W.G.,and Li,X.,and Zhao,H.,2007.Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination.Journal of Central South University of Technology,14(5):719-724.
Gong,F.Q.,and Zhao,G.F.,2014.Dynamic indirect tensile strength of sandstone under different loading rates.Rock Mechanics and Rock Engineering,47(6):2271-2278.
GT/T23561,2009.The Professional Standards Compilation Group of Peoples Republic of China:Methods for determining the physical and mechanical properties of coal and rock.Beijing:Standards Press of China(in Chinese).
Hao,Z.G.,Fei,H.C.,Hao,Q.Q.,and Liu L.,2017.China’s shale gas geological investigation and prospecting have made significant progress.Acta Geologica Sinica(English Edition),91(2):727-728.
Heng,S.,Guo,Y.,Yang,C.,Daemen,J.J.K.,and Li,Z.,2015.Experimental and theoretical study of the anisotropic properties of shale.International Journal of Rock Mechanics&Mining Sciences,74(1):58-68.
Hou,Z.K.,Yang,C.H.,Guo,Y.T.,Zhang,B.P.,Wei,Y.L.,Heng,S.,and Wang,L.,2015.Experimental study on anisotropic properties of Longmaxi Formation shale under uniaxial compression.Rock and Soil Mechanics,36(9):2541-2550(in Chinese).
Hou,Z.K.,Yang,C.H.,Wang,L.,Liu,P.J.,Guo,Y.T.,Wei,Y.L.,and Li,Z.,2016.Hydraulic fracture propagation of shale horizontal well by large-scale true triaxial physical simulation test.Rock and Soil Mechanics,37(2):407-414(in Chinese).
Hou,Z.K.,Yang,C.H.,Wang,L.,and Xu,F.,2016.Evaluation method of shale brittleness based on indoor experiments.Journal of Northeastern University,37(10):1496-1501(in Chinese).
Hou,Z.K.,Marte,G.,Wang,A.M.,Abdulhadi,A.,and Yang,C.H.,2018.Mechanical properties and brittleness of shale with different degrees of fracturing-fluid saturation.Current Science,09(115):1163-1174.
Hou,Z.K.,2018.Research on Hydraulic Fracturing Tests and Crack Extension Mechanism of Longmaxi Shale.Chongqing:Chonqing University(Ph.D thesis):1-180(in Chinese).
Hudson,J.,Harrison,J.,and Popescu,M.,1997.Engineering rock mechanics:an introduction to the principles.Applied Mechanics Reviews,55(2):72-78.
Katsuki,D.,and Gutierrez,M.,2011.Viscoelastic damage model for asphalt concrete.Acta Geotechnica,6(4):231-241.
Lemaitre,J.,1984.How to use damage mechanics.Nuclear Engineering and Design,80(2):233-245.
Li,M.H.,Yin,G.Z.,Xu,J.,Cao,J.,and Song,Z.L.,2016.Permeability evolution of shale under anisotropic true triaxial stress conditions.International Journal of Coal Geology,165:142-148.
Li,Y.S.,and Xia,C.C.,2000.Time-dependent tests on intact rocks in uniaxial compression.International Journal of Rock Mechanics and Mining Sciences,37(3):467-475.
Liang,W.G.,Zhao,Y.S.,Xu,S.G.,and Dusseault,M.B.,2011.Effect of strain rate on the mechanical properties of salt rock.International Journal of Rock Mechanics and Mining Sciences,48(1):161-167.
Ma,T.S.,and Chen,P.,2014.Study of meso-damage characteristics of shale hydration based on CT scanning technology.Petroleum Exploration and Development,41(2):249-256.
Mahanta,B.,Tripathy,A.,Vishal,V.,Singh,T.N.,and Ranjith,P.G.,2016.Effects of strain rate on fracture toughness and energy release rate of gas shales.Engineering Geology,218:39-19.
Middleton,R.S.,Carey,J.W.,Currier,R.P.,Hyman,J.D.,Kang,Q.,and Karra,S.,2015.Shale gas and non-aqueous fracturing fluids:opportunities and challenges for supercritical CO2.Applied Energy,147(3):500-509.
Nie,H.K.,Zhang,J.C.,and Jiang,S.L.,2015.Types and characteristics of the Lower Silurian shale gas reservoirs in and around the Sichuan Basin.Acta Geologica Sinica(English Edition),89(6):1973-1985.
Peng,T.,Yan,J.,Bing,H.,Ke,H.,Zhou,Y.,and Meng,S.,2017.Experimental investigation on fracture initiation and nonplanar propagation of hydraulic fractures in coal seams.Petroleum Exploration&Development,44(3):439-445.
Sedman,A.,Talviste,P.,M?tlep,R.,J?eleht,A.,Kirsim?e,K.,2012.Geotechnical characterization of Estonian oil shale semi-coke deposits with prime emphasis on their shear strength.Engineering Geology,131:37-44.
Vervoort,A.,Min,K.B.,Konietzky,H.,Cho,J.W.,Debecker,B.,and Dinh,Q.D.,2014.Failure of transversely isotropic rock under brazilian test conditions.International Journal of Rock Mechanics&Mining Sciences,70(70):343-352.
Weibull,G.W.,1951.A statistical distribution function of wide applicability.Journal of Applied Mechanics,18:293-297.
Zhai,G.Y.,Wang,Y.F.,Zhou,Z.,Yu,S.F.,Chen,X.L.,and Zhang,Y.X.,2018.Exploration and research progress of shale gas in China.China Geology,1,257-272.
Zhang,G.,Lan,Z.,and Peng,L.,2009.Fracturing control method for deep volcanic rock gas reservoirs in Daqing exploration area.Petroleum Exploration&Development,36(4):529-534.
Zhang,S.W.,Shou,K.J.,Xian,X.F.,Zhou,J.P.,and Liu,G.J.,2018.Fractal characteristics and acoustic emission of anisotropic shale in Brazilian tests.Tunnelling and Underground Space Technology,71:298-308.
Zhou,W.,1990.Advanced Rock Mechanics.Beijing:China Water and Power Press,219(in Chinese).
Zhou,W.,2006.The characteristics of in-situ earth stress and its application research in engineering geology of petroleum on compact reservoir in western Sichuan depression.Chengdu:Chengdu University of Technology(Ph.D thesis):1-150(in Chinese with English abstract).