黑色页岩动载破坏的层理效应及损伤本构模型研究
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摘要
为了探究不同层理方向下页岩动载破坏的各向异性行为,针对龙马溪组黑色页岩制备7组层理倾角试样,利用分离式霍普金森压杆(SHPB)进行3种应变率下的动态压缩试验,研究层理方向对页岩动载破坏模式、强度、能量耗散特征的影响,揭示层理页岩动载破坏的机制,并建立综合考虑初始损伤、受荷损伤的层理页岩动载损伤本构模型。试验及理论分析结果表明:(1)不同层理方向页岩动载破坏模式分为劈裂拉伸破坏、剪切破坏和混合破坏。小层理倾角及大层理倾角情况下容易发生劈裂拉伸破坏,中等倾角情况下容易发生混合破坏和剪切破坏。(2)3种应变率下抗压强度随层理倾角的变化都会呈现先减小后增大的趋势,显示出明显的层理效应,同时抗压强度还具有率相关效应,但其与层理效应呈竞争关系,即应变率增大强度增大,强度各向异性减弱。(3)能量耗散特征与强度特征类似,也随倾角变化有先减小后增大的趋势。但能量耗散值有率相关效应,吸能率却对应变率不敏感。(4)新建立的损伤本构模型综合考虑了岩体结构效应与载荷耦合作用,具有结构简单,物理意义明确的特点,与试验数据吻合较好,尤其对于不出现应力–应变回弹的中高应变率情况,理论预测数据与试验数据相关程度更高,有助于更为准确地描述层理页岩试样在动载下的变形破坏行为。
In order to investigate the anisotropic properties of layered shale under dynamic loading,seven groups of samples with different bedding inclinations were cored from the black shale in Longmaxi formation,and dynamic compressive experiments at three strain rate levels were carried out by using the split Hopkinson pressure bar. The influence of the bedding direction on failure mode,strength and energy consumption characteristics of shale was investigated,and the failure mechanism of shale was revealed. A dynamic loading damage constitutive model of shale considering both initial and loading damage was established. The results show that the failure modes of shale with different bedding inclinations under dynamic loading can be divided into splitting tensile failure,shear failure and mixed failure. Splitting tensile failure is more likely to occur in the case of small or large bedding inclination,while shear or mixed failure is more prone to appear at a medium inclination. The compressive strength shows a trend of decreasing first and then increasing with increasing the inclination at three strain rates,which manifests an obvious bedding effect. The compressive strength also has a rate-dependent effect,which is in competition with the bedding effect. In other words,as the strain rate increases,the strength will increase as well but the strength anisotropy will attenuate. The change trend of the energy consumption characteristics with the inclination is similar to that of the strength. The value of the energy consumption is rate-dependent,but the energy consumption rate is not sensitive to the strain rate. The established damage model considering the coupling effect of rock mass structure and loading is simple in structure and clear in physical meaning. It is shown that the model is in good agreement with the experimental data,especially for the situation of medium to high strain rate without stress-strain rebound. The established model can be of benefit to more accurately describe the deformation and failure behavior of layered shale specimen under dynamic loading.
In order to investigate the anisotropic properties of layered shale under dynamic loading,seven groups of samples with different bedding inclinations were cored from the black shale in Longmaxi formation,and dynamic compressive experiments at three strain rate levels were carried out by using the split Hopkinson pressure bar. The influence of the bedding direction on failure mode,strength and energy consumption characteristics of shale was investigated,and the failure mechanism of shale was revealed. A dynamic loading damage constitutive model of shale considering both initial and loading damage was established. The results show that the failure modes of shale with different bedding inclinations under dynamic loading can be divided into splitting tensile failure,shear failure and mixed failure. Splitting tensile failure is more likely to occur in the case of small or large bedding inclination,while shear or mixed failure is more prone to appear at a medium inclination. The compressive strength shows a trend of decreasing first and then increasing with increasing the inclination at three strain rates,which manifests an obvious bedding effect. The compressive strength also has a rate-dependent effect,which is in competition with the bedding effect. In other words,as the strain rate increases,the strength will increase as well but the strength anisotropy will attenuate. The change trend of the energy consumption characteristics with the inclination is similar to that of the strength. The value of the energy consumption is rate-dependent,but the energy consumption rate is not sensitive to the strain rate. The established damage model considering the coupling effect of rock mass structure and loading is simple in structure and clear in physical meaning. It is shown that the model is in good agreement with the experimental data,especially for the situation of medium to high strain rate without stress-strain rebound. The established model can be of benefit to more accurately describe the deformation and failure behavior of layered shale specimen under dynamic loading.
引文
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[3]王倩,王鹏,项德贵,等.页岩力学参数各向异性研究[J].天然气工业,2012,32(12):62-65.(WANG Qian,WANG Peng,XIANG Degui,et al.Anisotropic property of mechanical parameters of shales[J].Natural Gas Industry,2012,32(12):62-65.(in Chinese))
[4]LIU X W,GUO Z Q,LIU C,et al.Anisotropy rock physics model for the Longmaxi shale gas reservoir,Sichuan Basin,China[J].Applied Geophysics,2017,14(1):21-30.
[5]JOSH M,ESTEBAN L,DELLE PIANE C,et al.Laboratory characterisation of shale properties[J].Journal of Petroleum Science and Engineering,2012,88(2):107-124.
[6]WANG Y,LI C H.Investigation of the P-and S-wave velocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxial deformation[J].Journal of Petroleum Science and Engineering,2017,158(1):253-267.
[7]陈天宇,冯夏庭,张希巍,等.黑色页岩力学特性及各向异性特性试验研究[J].岩石力学与工程学报,2014,33(9):1 772-1 779.(CHEN Tianyu,FENG Xiating,ZHANG Xiwei,et al.Experimental study on mechanical and anisotropic properties of black shale[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(9):1 772-1 779.(in Chinese))
[8]侯鹏,高峰,杨玉贵,等.黑色页岩巴西劈裂破坏的层理效应研究及能量分析[J].岩土工程学报,2016,38(5):930-937.(HOUPeng,GAO Feng,YANG Yugui,et al.Effect of bedding orientation on failure of black shale under Brazilian tests and energy analysis[J].Chinese Journal of Geotechnical Engineering,2016,38(5):930-937.(in Chinese))
[9]HENG S,GUO Y,YANG C,et al.Experimental and theoretical study of the anisotropic properties of shale[J].International Journal of Rock Mechanics and Mining Sciences,2015,74(1):58-68.
[10]衡帅,杨春和,曾义金,等.基于直剪试验的页岩强度各向异性研究[J].岩石力学与工程学报,2014,33(5):874-883.(HENGShuai,YANG Chunhe,ZENG Yijin,et al.Anisotropy of shear strength of shale based on direct shear test[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(5):874-883.(in Chinese))
[11]YAN C,DENG J,CHENG Y,et al.Mechanical properties of gas shale during drilling operations[J].Rock Mechanics and Rock Engineering,2017,50(7):1 753-1 765.
[12]SONE H,ZOBACK M D.Time-dependent deformation of shale gas reservoir rocks and its long-term effect on the in situ state of stress[J].International Journal of Rock Mechanics and Mining Sciences,2014,69(1):120-132.
[13]YANG Y,ZOBACK M.Viscoplastic deformation of the Bakken and adjacent formations and its relation to hydraulic fracture growth[J].Rock Mechanics and Rock Engineering,2016,49(2):689-698.
[14]SHENG M,CHENG Z,TIAN S,et al.Experimental study on dynamic failure behaviors of gas shale and the relation to drilling fluid[C]//The4th ISRM Young Scholars Symposium on Rock Mechanics.[S.l.]:[s.n.],2017:359-362.
[15]LIU J,LI Y,ZHANG H.Study on shale’s dynamic damage constitutive model based on statistical distribution[J].Shock and Vibration,2015,33(4):343-351.
[16]张慧娟.页岩动态本构关系及应用初探[硕士学位论文][D].成都:西南石油大学,2014.(ZHANG Huijuan.Study on dynamic constitutive relation and application of shale[M.S.Thesis][D].Chengdu:Southwest Petroleum University,2014.(in Chinese))
[17]宫凤强,李夕兵,饶秋华,等.岩石SHPB试验中确定试样尺寸的参考方法[J].振动与冲击,2013,32(17):24-28.(GONG Fengqiang,LI Xibing,RAO Qiuhua,et al.Reference method for determination of specimen size in rock SHPB test[J].Vibration and Shock,2013,32(17):24-28.(in Chinese))
[18]ZHANG Q B,ZHAO J.A review of dynamic experimental techniques and mechanical behaviour of rock materials[J].Rock Mechanics and Rock Engineering,2014,47(4):1 411-1 478.
[19]宫凤强,李夕兵,董陇军.圆盘冲击劈裂试验中岩石拉伸弹性模量的求解算法[J].岩石力学与工程学报,2013,32(4):705-713.(GONG Fengqiang,LI Xibing,DONG Longjun.Algorithm to estimate tensile modulus of rock in disk impact splitting test[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(4):705-713.(in Chinese))
[20]尹土兵,李夕兵,殷志强,等.高温后砂岩静、动态力学特性研究与比较[J].岩石力学与工程学报,2012,31(2):273-279.(YINTubing,LI Xibing,YIN Zhiqiang,et al.Study and comparison of mechanical properties of sandstone under static and dynamic loadings after high temperature[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(2):273-279.(in Chinese))
[21]DAI F,HUANG S,XIA K,et al.Some Fundamental issues in dynamic compression and tension tests of rocks using split hopkinson pressure bar[J].Rock Mechanics and Rock Engineering,2010,43(6):657-666.
[22]CHO J W,KIM H,JEON S,et al.Deformation and strength anisotropy of Asan gneiss,Boryeong shale,and Yeoncheon schist[J].International Journal of Rock Mechanics and Mining Sciences,2012,50(1):158-169.
[23]DAI F,XIA K,ZUO J P,et al.Static and dynamic flexural strength anisotropy of Barre granite[J].Rock Mechanics and Rock Engineering,2013,46(6):1 589-1 602.
[24]张志镇,高峰.单轴压缩下红砂岩能量演化试验研究[J].岩石力学与工程学报,2012,31(5):953-962.(ZHANG Zhizhen,GAO Feng.Experimental research on energy evolution of red sandstone samples under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):953-962.(in Chinese))
[25]尹土兵,李夕兵,叶洲元,等.温-压耦合及动力扰动下岩石破碎的能量耗散[J].岩石力学与工程学报,2013,32(6):1 197-1 202.(YIN Tubing,LI Xibing,YE Zhouyuan,et al.Energy dissipation of rock fracture under thermo-mechanical coupling and dynamic disturbances[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1 197-1 202.(in Chinese))
[26]王登科,刘淑敏,魏建平,等.冲击破坏条件下煤的强度型统计损伤本构模型与分析[J].煤炭学报,2016,41(12):3 024-3 031.(WANG Dengke,LIU Shumin,WEI Jianping,et al.Analysis and strength statistical damage constitutive model of coal under impacting failure[J].Journal of China Coal Society,2016,41(12):3 024-3 031.(in Chinese))
[27]DENG J,GU D.On a statistical damage constitutive model for rock materials[J].Computers and Geosciences,2011,37(2):122-128.
[28]朱晶晶,李夕兵,宫凤强,等.单轴循环冲击下岩石的动力学特性及其损伤模型研究[J].岩土工程学报,2013,35(3):531-539.(ZHUJingjing,LI Xibing,GONG Fengqiang,et al.Dynamic characteristics and damage model for rock under uniaxial cyclic impact compressive loads[J].Chinese Journal of Geotechnical Engineering,2013,35(3):531-539.(in Chinese))
[29]汪杰,宋卫东,付建新.考虑节理倾角的岩体损伤本构模型及强度准则[J].岩石力学与工程学报,2018,37(10):2 253-2 263.(WANG Jie,SONG Weidong,FU Jianxin.Damage constitutive model and strength criterion of rock mass considering joint dip angle[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(10):2 253-2 263.(in Chinese))
[30]李夕兵,宫凤强,ZHAO J,等.一维动静组合加载下岩石冲击破坏试验研究[J].岩石力学与工程学报,2010,29(2):251-260.(LIXibing,GONG Fengqiang,ZHAO J,et al.Impact failure characteristics study of rock subjected to 1D coupled static and dynamic loads[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):251-260.(in Chinese))
[2]张金川,徐波,聂海宽,等.中国页岩气资源勘探潜力[J].天然气工业,2008,28(6):136-140.(ZHANG Jinchuan,XU Bo,NIEHaikuan,et al.Exploration potential of shale gas resources in China[J].Natural Gas Industry,2008,28(6):136-140.(in Chinese))
[3]王倩,王鹏,项德贵,等.页岩力学参数各向异性研究[J].天然气工业,2012,32(12):62-65.(WANG Qian,WANG Peng,XIANG Degui,et al.Anisotropic property of mechanical parameters of shales[J].Natural Gas Industry,2012,32(12):62-65.(in Chinese))
[4]LIU X W,GUO Z Q,LIU C,et al.Anisotropy rock physics model for the Longmaxi shale gas reservoir,Sichuan Basin,China[J].Applied Geophysics,2017,14(1):21-30.
[5]JOSH M,ESTEBAN L,DELLE PIANE C,et al.Laboratory characterisation of shale properties[J].Journal of Petroleum Science and Engineering,2012,88(2):107-124.
[6]WANG Y,LI C H.Investigation of the P-and S-wave velocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxial deformation[J].Journal of Petroleum Science and Engineering,2017,158(1):253-267.
[7]陈天宇,冯夏庭,张希巍,等.黑色页岩力学特性及各向异性特性试验研究[J].岩石力学与工程学报,2014,33(9):1 772-1 779.(CHEN Tianyu,FENG Xiating,ZHANG Xiwei,et al.Experimental study on mechanical and anisotropic properties of black shale[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(9):1 772-1 779.(in Chinese))
[8]侯鹏,高峰,杨玉贵,等.黑色页岩巴西劈裂破坏的层理效应研究及能量分析[J].岩土工程学报,2016,38(5):930-937.(HOUPeng,GAO Feng,YANG Yugui,et al.Effect of bedding orientation on failure of black shale under Brazilian tests and energy analysis[J].Chinese Journal of Geotechnical Engineering,2016,38(5):930-937.(in Chinese))
[9]HENG S,GUO Y,YANG C,et al.Experimental and theoretical study of the anisotropic properties of shale[J].International Journal of Rock Mechanics and Mining Sciences,2015,74(1):58-68.
[10]衡帅,杨春和,曾义金,等.基于直剪试验的页岩强度各向异性研究[J].岩石力学与工程学报,2014,33(5):874-883.(HENGShuai,YANG Chunhe,ZENG Yijin,et al.Anisotropy of shear strength of shale based on direct shear test[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(5):874-883.(in Chinese))
[11]YAN C,DENG J,CHENG Y,et al.Mechanical properties of gas shale during drilling operations[J].Rock Mechanics and Rock Engineering,2017,50(7):1 753-1 765.
[12]SONE H,ZOBACK M D.Time-dependent deformation of shale gas reservoir rocks and its long-term effect on the in situ state of stress[J].International Journal of Rock Mechanics and Mining Sciences,2014,69(1):120-132.
[13]YANG Y,ZOBACK M.Viscoplastic deformation of the Bakken and adjacent formations and its relation to hydraulic fracture growth[J].Rock Mechanics and Rock Engineering,2016,49(2):689-698.
[14]SHENG M,CHENG Z,TIAN S,et al.Experimental study on dynamic failure behaviors of gas shale and the relation to drilling fluid[C]//The4th ISRM Young Scholars Symposium on Rock Mechanics.[S.l.]:[s.n.],2017:359-362.
[15]LIU J,LI Y,ZHANG H.Study on shale’s dynamic damage constitutive model based on statistical distribution[J].Shock and Vibration,2015,33(4):343-351.
[16]张慧娟.页岩动态本构关系及应用初探[硕士学位论文][D].成都:西南石油大学,2014.(ZHANG Huijuan.Study on dynamic constitutive relation and application of shale[M.S.Thesis][D].Chengdu:Southwest Petroleum University,2014.(in Chinese))
[17]宫凤强,李夕兵,饶秋华,等.岩石SHPB试验中确定试样尺寸的参考方法[J].振动与冲击,2013,32(17):24-28.(GONG Fengqiang,LI Xibing,RAO Qiuhua,et al.Reference method for determination of specimen size in rock SHPB test[J].Vibration and Shock,2013,32(17):24-28.(in Chinese))
[18]ZHANG Q B,ZHAO J.A review of dynamic experimental techniques and mechanical behaviour of rock materials[J].Rock Mechanics and Rock Engineering,2014,47(4):1 411-1 478.
[19]宫凤强,李夕兵,董陇军.圆盘冲击劈裂试验中岩石拉伸弹性模量的求解算法[J].岩石力学与工程学报,2013,32(4):705-713.(GONG Fengqiang,LI Xibing,DONG Longjun.Algorithm to estimate tensile modulus of rock in disk impact splitting test[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(4):705-713.(in Chinese))
[20]尹土兵,李夕兵,殷志强,等.高温后砂岩静、动态力学特性研究与比较[J].岩石力学与工程学报,2012,31(2):273-279.(YINTubing,LI Xibing,YIN Zhiqiang,et al.Study and comparison of mechanical properties of sandstone under static and dynamic loadings after high temperature[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(2):273-279.(in Chinese))
[21]DAI F,HUANG S,XIA K,et al.Some Fundamental issues in dynamic compression and tension tests of rocks using split hopkinson pressure bar[J].Rock Mechanics and Rock Engineering,2010,43(6):657-666.
[22]CHO J W,KIM H,JEON S,et al.Deformation and strength anisotropy of Asan gneiss,Boryeong shale,and Yeoncheon schist[J].International Journal of Rock Mechanics and Mining Sciences,2012,50(1):158-169.
[23]DAI F,XIA K,ZUO J P,et al.Static and dynamic flexural strength anisotropy of Barre granite[J].Rock Mechanics and Rock Engineering,2013,46(6):1 589-1 602.
[24]张志镇,高峰.单轴压缩下红砂岩能量演化试验研究[J].岩石力学与工程学报,2012,31(5):953-962.(ZHANG Zhizhen,GAO Feng.Experimental research on energy evolution of red sandstone samples under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):953-962.(in Chinese))
[25]尹土兵,李夕兵,叶洲元,等.温-压耦合及动力扰动下岩石破碎的能量耗散[J].岩石力学与工程学报,2013,32(6):1 197-1 202.(YIN Tubing,LI Xibing,YE Zhouyuan,et al.Energy dissipation of rock fracture under thermo-mechanical coupling and dynamic disturbances[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1 197-1 202.(in Chinese))
[26]王登科,刘淑敏,魏建平,等.冲击破坏条件下煤的强度型统计损伤本构模型与分析[J].煤炭学报,2016,41(12):3 024-3 031.(WANG Dengke,LIU Shumin,WEI Jianping,et al.Analysis and strength statistical damage constitutive model of coal under impacting failure[J].Journal of China Coal Society,2016,41(12):3 024-3 031.(in Chinese))
[27]DENG J,GU D.On a statistical damage constitutive model for rock materials[J].Computers and Geosciences,2011,37(2):122-128.
[28]朱晶晶,李夕兵,宫凤强,等.单轴循环冲击下岩石的动力学特性及其损伤模型研究[J].岩土工程学报,2013,35(3):531-539.(ZHUJingjing,LI Xibing,GONG Fengqiang,et al.Dynamic characteristics and damage model for rock under uniaxial cyclic impact compressive loads[J].Chinese Journal of Geotechnical Engineering,2013,35(3):531-539.(in Chinese))
[29]汪杰,宋卫东,付建新.考虑节理倾角的岩体损伤本构模型及强度准则[J].岩石力学与工程学报,2018,37(10):2 253-2 263.(WANG Jie,SONG Weidong,FU Jianxin.Damage constitutive model and strength criterion of rock mass considering joint dip angle[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(10):2 253-2 263.(in Chinese))
[30]李夕兵,宫凤强,ZHAO J,等.一维动静组合加载下岩石冲击破坏试验研究[J].岩石力学与工程学报,2010,29(2):251-260.(LIXibing,GONG Fengqiang,ZHAO J,et al.Impact failure characteristics study of rock subjected to 1D coupled static and dynamic loads[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):251-260.(in Chinese))