围压对红砂岩应力波传播特性的影响
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摘要
围压可以改变岩石内部微观结构,导致波阻抗发生变化,进而影响应力波在岩石中的透反射能力。为探索围压对岩石应力波传播特性的影响,通过一维应力波理论推导,得到了岩石应力波透射系数和反射系数随波阻抗值的变化关系。用红砂岩制备短试件和长试件,基于动静组合加载实验系统进行不同围压下的应力波传播试验,分析岩石的纵波波速、波阻抗、反射系数和透射系数与围压的关系。根据岩石波阻抗与围压的经验模型,结合理论分析所得的透射系数与波阻抗的关系,得到不同围压下透射系数的理论值,并与相应的试验值进行对比,证明理论分析结果的正确性。综合分析了岩石的纵波波速、波阻抗、透射系数和反射系数与围压的关系,得到围压对红砂岩应力波传播衰减特性的影响规律。结果表明,岩石短试件和长试件的纵波波速及波阻抗与围压之间均具有正向相关性。随着围压的增加,短试件反射系数的绝对值逐渐减小,透射系数逐渐增大,长试件的透射系数逐渐减小,透射系数和反射系数均与围压呈二次函数关系。纵波波速、波阻抗、透射系数及反射系数与围压的关系都表明,增大围压有利于应力波穿过岩石,减小其幅值的衰减。
Confining pressure has a great effect on the internal microstructure of the rock,and results in a change in wave impedance,which affects the propagation attenuation laws of the stress wave in the porous rock subjected to high stress.In order to investigate the effect of confining pressure on the characteristics of stress wave propagation in rock,the relationships between both reflection coefficient and transmission coefficient with the wave impedance of rock were established based on one dimensional stress wave theory. Then the short and long rock specimens were made of red sandstone,and the experiments of stress wave propagation in specimens under different confining pressures were carried out based on the modified Split Hopkinson Pressure Bar( SHPB).Also,the experimental longitudinal wave velocities,wave impedances,reflection coefficients and transmission coefficients of rock under different confining pressures were analyzed.Based on the empirical relationship between wave impedance and confining pressure,and the theoretical relationship between wave impedance and transmission coefficient,the theoretical transmission coefficients under different confining pressures were obtained and compared with experimental values.The comparison shows that the differences between theoretical and experiment values were very small,and verifies the theoretical analysis of transmission and reflection coefficients are valid.The influence laws of confining pressure on the stress wave propagation along red sandstone were obtained by the comprehensive analysis of longitudinal wave velocity,wave impedance,transmitted and reflected coefficients of rock under different confining pressures.The results show that both the longitudinal wave velocity and wave impedance of rock specimen increase with the increase in confining pressure.With the increase of confining pressure,the transmission coefficient of short specimen increases,and the absolute value of reflection coefficient decreases,the transmission coefficient of long specimen,however,decreases gradually.The variation trends of both the reflection coefficient and trans-mission coefficient with confining pressure can be fitted with quadratic function.All of the above variation tendencies show that the increase of confining pressure decreases the attenuation of its amplitude.
Confining pressure has a great effect on the internal microstructure of the rock,and results in a change in wave impedance,which affects the propagation attenuation laws of the stress wave in the porous rock subjected to high stress.In order to investigate the effect of confining pressure on the characteristics of stress wave propagation in rock,the relationships between both reflection coefficient and transmission coefficient with the wave impedance of rock were established based on one dimensional stress wave theory. Then the short and long rock specimens were made of red sandstone,and the experiments of stress wave propagation in specimens under different confining pressures were carried out based on the modified Split Hopkinson Pressure Bar( SHPB).Also,the experimental longitudinal wave velocities,wave impedances,reflection coefficients and transmission coefficients of rock under different confining pressures were analyzed.Based on the empirical relationship between wave impedance and confining pressure,and the theoretical relationship between wave impedance and transmission coefficient,the theoretical transmission coefficients under different confining pressures were obtained and compared with experimental values.The comparison shows that the differences between theoretical and experiment values were very small,and verifies the theoretical analysis of transmission and reflection coefficients are valid.The influence laws of confining pressure on the stress wave propagation along red sandstone were obtained by the comprehensive analysis of longitudinal wave velocity,wave impedance,transmitted and reflected coefficients of rock under different confining pressures.The results show that both the longitudinal wave velocity and wave impedance of rock specimen increase with the increase in confining pressure.With the increase of confining pressure,the transmission coefficient of short specimen increases,and the absolute value of reflection coefficient decreases,the transmission coefficient of long specimen,however,decreases gradually.The variation trends of both the reflection coefficient and trans-mission coefficient with confining pressure can be fitted with quadratic function.All of the above variation tendencies show that the increase of confining pressure decreases the attenuation of its amplitude.
引文
[1] AMOS NUR. Effects of stress on velocity anisotropy in rock with cracks[J]. Journal of Geophysical Research,1971,76(8):2022-2034.
[2] WEI Yujie,LALLIT ANAND.On micro-cracking,inelastic dilatancy,and the brittle-ductile transition in compact rocks:A micro-mechanical study[J]. International Journal of Solids and Structures,2008,45(10):2785-2798.
[3] ZONG Yijiang,HAN Lijun,WEI Jianjun,et al.Mechanical and damage evolution properties of sandstone under triaxial compression[J].International Journal of Mining Science and Technology,2016,26(4):601-607.
[4] YANG Chunhe,DAEMEN J J K,YIN Jianhua.Experimental investigation of creep behavior of salt rock[J]. International Journal of Rock Mechanics and Mining Sciences,1999,36(2):233-242.
[5]嵇少丞,王茜,DENIS MARCOTTE,等.苏鲁超高压变质岩中地震波速随围压的变化规律[J].地质学报,2006,80(12):1807-1812.JI Shaocheng,WANG Qian,DENIS MARCOTTE,et al.Pressure-dependence of P-Wave velocities in Sulu UHP metamorphic rocks[J].Acta Geologica Sinica,2006,80(12):1807-1812.
[6]李阿伟,孙东生,王红才.致密砂岩波速各向异性及弹性参数随围压变化规律的实验研究[J].地球物理学进展,2014,29(2):754-760.LI Awei,SUN Dongsheng,WANG Hongcai.Seismic anisotropy and elastic parameter of tight sandstone with confining pressure[J]. Progress in Geophysics,2014,29(2):754-760.
[7] AMOS NUR. Effects of stress on velocity anisotropy in rock with cracks[J]. Journal of Geophysical Research,1971,76(8):2022-2034.
[8]巩思园,窦林名,徐晓菊,等.冲击倾向煤岩纵波波速与应力关系试验研[J].采矿与安全工程学报,2012,29(1):67-71.GONG Siyuan,DOU Linming,XU Xiaoju,et al. Experimental study on the correlation between stress and P-wave velocity for burst tendency coal-rock samples[J].Journal of Mining&Safety Engineering,2012,29(1):67-71.
[9]尹帅,丁文龙,孙圆辉,等.不同围压条件下含气致密砂岩孔裂隙形态演化试验研究[J].石油物探,2016,55(3):326-332.YIN Shuai,DING Wenlong,SUN Yuanhui,et al. Experimental study on pore fracture morphology evolution of gas-bearing tight sandstone under different confining pressure[J]. Geophysical Prospecting for Petroleum,2016,55(3):326-332.
[10] GARDNER G H F,GARDNER L W,GREGORY A R.Formation velocity and density-the diagnostic basics for stratigraphic traps[J].Geophysics,1974,39(6):770-780.
[11]朱广生,桂志先,熊新斌,等.密度与纵横波速度关系[J].地球物理学报,1995,38(S1):260-264.ZHU Guangsheng,GUI Zhixian,XIONG Xinbin,et al.Relationships between density and P-wave,S-wave velocities[J].Chinese Journal of Geophysics,1995,38(S1):260-264.
[12]金解放,李夕兵,殷志强,等.轴压和循环冲击次数对砂岩动态力学特性的影响[J].煤炭学报,2012,37(6):923-930.JIN Jiefang,LI Xibing,YIN Zhiqiang,et al.Effects of axial pressure and number of cyclic impacts on dynamic mechanical characteristics of sandstone[J].Journal of China Coal Society,2012,37(6):923-930.
[13]金解放,李夕兵,钟海兵,等.三维静载与循环冲击组合作用下砂岩动态力学特性研究[J].岩石力学与工程学报,2013,32(7):1358-1372.JIN Jiefang,LI Xibing,ZHONG Haibing,et al. Study of dynamic mechanical characteristic of sandstone subjected to three-dimensional coupled static-cyclic impact loadings[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(7):1358-1372.
[14]吕晓聪,许金余,葛洪海,等.围压对砂岩动态冲击力学性能的影响[J].岩石力学与工程学报,2010,29(1):193-201.LXiaocong,XU Jinyu,GE Honghai,et al. Effects of confining pressure on mechanical behaviors of sandstone under dynamic impact loads[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(1):193-201.
[15] LI Xibing,TAO Ming,WU Chengqing,et al. Spalling strength of rock under different static pre-confining pressures[J].International Journal of Impact Engineering,2017,99:69-74.
[16]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.LI Xibing,GONG Fengqiang,ZHAO J,et al. Test study of impact failure of rock subjected to one-dimensional coupled static and dynamic loads[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):251-260.
[17]尤业超,李二兵,谭跃虎,等.基于能量耗散原理的盐岩动力特性及破坏特征分析[J].岩石力学与工程学报,2017,36(4):843-851.YOU Yechao,LI Erbing,TAN Yuehu,et al. Analysis on dynamic properties and failure characteristics of salt rock based on energy dissipation principle[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(4):843-851.
[18]白羽,朱万成,魏晨慧,等.不同地应力条件下双孔爆破的数值模拟[J].岩土力学,2013,34(S1):466-471.BAI Yu,ZHU Wancheng,WEI ChenHui,et al. Numerical simulation on two-hole blasting under different in-situ stress conditions[J].Rock and Soil Mechanics,2013,34(S1):466-471.
[19]范勇,江璐,卢文波,等.圆形隧洞爆破荷载与瞬态卸荷作用围岩应变能效应研究[J].岩石力学与工程学报,2017,36(8):1855-1866.FAN Yong,JIANG Lu,LU Wenbo,et al. Strain energy characteristics of surrounding rock under blasting load and transient release of geostress during excavation of circular tunnel[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(8):1855-1866.
[20]李夕兵,姚金蕊,杜坤.高地应力硬岩矿山诱导致裂非爆连续开采初探———以开阳磷矿为例[J].岩石力学与工程学报,2013,32(6):1101-1111.LI Xibing,YAO Jinrui,DU Kun.Preliminary study for induced fracture and non-explosive continuous mining in high-geostress hard rock mine-a case study of Kaiyang phosphate mine[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1101-1111.
[21] DOU Linming,MU Zonglong,LI Zhenlei,et al. Research progress of monitoring,forecasting,and prevention of rockburst in underground coal mining in China[J].International Journal of Coal Science&Technology,2014,1(3):278-288.
[22] XU Jialin,XUAN Dayang,HE Changchun. Innovative backfilling longwall panel layout for better subsidence control effect-separating adjacent subcritical panels with pillars[J]. International Journal of Coal Science&Technology,2014,1(3):297-305.
[23]刘少虹,毛德兵,齐庆新,等.动静加载下组合煤岩的应力波传播机制与能量耗散[J].煤炭学报,2014,39(S1):15-22.LIU Shaohong,MAO Debing,QI Qingxin,et al.Under static loading stress wave propagation mechanism and energy dissipation in compound coal-rock[J]. Journal of China Coal Society,2014,39(S1):15-22.
[24]李新平,赵航,罗忆,等.深部裂隙岩体中弹性波传播与衰减规律试验研究[J].岩石力学与工程学报,2015,34(11):2319-2326.LI Xinping,ZHAO Hang,LUO Yi,et al. Experimental study of propagation and attenuation of elastic wave in deep rock mass with joints[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(11):2319-2326.
[25]金解放,程昀,昌晓旭,等.轴向静载对红砂岩中应力波传播特性的影响试验研究[J].岩石力学与工程学报,2017,36(8):1939-1950.JIN Jiefang,CHENG Yun,CHANG Xiaoxu,et al. Experimental study on stress wave propagation characteristics in red sandstone under axial static stress[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(8):1939-1950.
[26] FAN L F,SUN H Y.Seismic wave propagation through an in-situ stressed rock mass[J]. Journal of Applied Geophysics,2015,121:13-20.
[27]王礼立.应力波基础[M].北京:国防工业出版社,2005.
[28]孟召平,张吉昌,JOACHIM Tiedemann.煤系岩石物理力学参数与声波速度之间的关系[J].地球物理学报,2006,49(5):1505-1510.MENG Zhaoping,ZHANG Jichang,JOACHIM Tiedemann.Relationship between physical and mechanical parameters and acoustic wave velocity of coal measures rocks[J]. Chinese Journal of Geophysics,2006,49(5):1505-1510.
[2] WEI Yujie,LALLIT ANAND.On micro-cracking,inelastic dilatancy,and the brittle-ductile transition in compact rocks:A micro-mechanical study[J]. International Journal of Solids and Structures,2008,45(10):2785-2798.
[3] ZONG Yijiang,HAN Lijun,WEI Jianjun,et al.Mechanical and damage evolution properties of sandstone under triaxial compression[J].International Journal of Mining Science and Technology,2016,26(4):601-607.
[4] YANG Chunhe,DAEMEN J J K,YIN Jianhua.Experimental investigation of creep behavior of salt rock[J]. International Journal of Rock Mechanics and Mining Sciences,1999,36(2):233-242.
[5]嵇少丞,王茜,DENIS MARCOTTE,等.苏鲁超高压变质岩中地震波速随围压的变化规律[J].地质学报,2006,80(12):1807-1812.JI Shaocheng,WANG Qian,DENIS MARCOTTE,et al.Pressure-dependence of P-Wave velocities in Sulu UHP metamorphic rocks[J].Acta Geologica Sinica,2006,80(12):1807-1812.
[6]李阿伟,孙东生,王红才.致密砂岩波速各向异性及弹性参数随围压变化规律的实验研究[J].地球物理学进展,2014,29(2):754-760.LI Awei,SUN Dongsheng,WANG Hongcai.Seismic anisotropy and elastic parameter of tight sandstone with confining pressure[J]. Progress in Geophysics,2014,29(2):754-760.
[7] AMOS NUR. Effects of stress on velocity anisotropy in rock with cracks[J]. Journal of Geophysical Research,1971,76(8):2022-2034.
[8]巩思园,窦林名,徐晓菊,等.冲击倾向煤岩纵波波速与应力关系试验研[J].采矿与安全工程学报,2012,29(1):67-71.GONG Siyuan,DOU Linming,XU Xiaoju,et al. Experimental study on the correlation between stress and P-wave velocity for burst tendency coal-rock samples[J].Journal of Mining&Safety Engineering,2012,29(1):67-71.
[9]尹帅,丁文龙,孙圆辉,等.不同围压条件下含气致密砂岩孔裂隙形态演化试验研究[J].石油物探,2016,55(3):326-332.YIN Shuai,DING Wenlong,SUN Yuanhui,et al. Experimental study on pore fracture morphology evolution of gas-bearing tight sandstone under different confining pressure[J]. Geophysical Prospecting for Petroleum,2016,55(3):326-332.
[10] GARDNER G H F,GARDNER L W,GREGORY A R.Formation velocity and density-the diagnostic basics for stratigraphic traps[J].Geophysics,1974,39(6):770-780.
[11]朱广生,桂志先,熊新斌,等.密度与纵横波速度关系[J].地球物理学报,1995,38(S1):260-264.ZHU Guangsheng,GUI Zhixian,XIONG Xinbin,et al.Relationships between density and P-wave,S-wave velocities[J].Chinese Journal of Geophysics,1995,38(S1):260-264.
[12]金解放,李夕兵,殷志强,等.轴压和循环冲击次数对砂岩动态力学特性的影响[J].煤炭学报,2012,37(6):923-930.JIN Jiefang,LI Xibing,YIN Zhiqiang,et al.Effects of axial pressure and number of cyclic impacts on dynamic mechanical characteristics of sandstone[J].Journal of China Coal Society,2012,37(6):923-930.
[13]金解放,李夕兵,钟海兵,等.三维静载与循环冲击组合作用下砂岩动态力学特性研究[J].岩石力学与工程学报,2013,32(7):1358-1372.JIN Jiefang,LI Xibing,ZHONG Haibing,et al. Study of dynamic mechanical characteristic of sandstone subjected to three-dimensional coupled static-cyclic impact loadings[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(7):1358-1372.
[14]吕晓聪,许金余,葛洪海,等.围压对砂岩动态冲击力学性能的影响[J].岩石力学与工程学报,2010,29(1):193-201.LXiaocong,XU Jinyu,GE Honghai,et al. Effects of confining pressure on mechanical behaviors of sandstone under dynamic impact loads[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(1):193-201.
[15] LI Xibing,TAO Ming,WU Chengqing,et al. Spalling strength of rock under different static pre-confining pressures[J].International Journal of Impact Engineering,2017,99:69-74.
[16]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.LI Xibing,GONG Fengqiang,ZHAO J,et al. Test study of impact failure of rock subjected to one-dimensional coupled static and dynamic loads[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):251-260.
[17]尤业超,李二兵,谭跃虎,等.基于能量耗散原理的盐岩动力特性及破坏特征分析[J].岩石力学与工程学报,2017,36(4):843-851.YOU Yechao,LI Erbing,TAN Yuehu,et al. Analysis on dynamic properties and failure characteristics of salt rock based on energy dissipation principle[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(4):843-851.
[18]白羽,朱万成,魏晨慧,等.不同地应力条件下双孔爆破的数值模拟[J].岩土力学,2013,34(S1):466-471.BAI Yu,ZHU Wancheng,WEI ChenHui,et al. Numerical simulation on two-hole blasting under different in-situ stress conditions[J].Rock and Soil Mechanics,2013,34(S1):466-471.
[19]范勇,江璐,卢文波,等.圆形隧洞爆破荷载与瞬态卸荷作用围岩应变能效应研究[J].岩石力学与工程学报,2017,36(8):1855-1866.FAN Yong,JIANG Lu,LU Wenbo,et al. Strain energy characteristics of surrounding rock under blasting load and transient release of geostress during excavation of circular tunnel[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(8):1855-1866.
[20]李夕兵,姚金蕊,杜坤.高地应力硬岩矿山诱导致裂非爆连续开采初探———以开阳磷矿为例[J].岩石力学与工程学报,2013,32(6):1101-1111.LI Xibing,YAO Jinrui,DU Kun.Preliminary study for induced fracture and non-explosive continuous mining in high-geostress hard rock mine-a case study of Kaiyang phosphate mine[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1101-1111.
[21] DOU Linming,MU Zonglong,LI Zhenlei,et al. Research progress of monitoring,forecasting,and prevention of rockburst in underground coal mining in China[J].International Journal of Coal Science&Technology,2014,1(3):278-288.
[22] XU Jialin,XUAN Dayang,HE Changchun. Innovative backfilling longwall panel layout for better subsidence control effect-separating adjacent subcritical panels with pillars[J]. International Journal of Coal Science&Technology,2014,1(3):297-305.
[23]刘少虹,毛德兵,齐庆新,等.动静加载下组合煤岩的应力波传播机制与能量耗散[J].煤炭学报,2014,39(S1):15-22.LIU Shaohong,MAO Debing,QI Qingxin,et al.Under static loading stress wave propagation mechanism and energy dissipation in compound coal-rock[J]. Journal of China Coal Society,2014,39(S1):15-22.
[24]李新平,赵航,罗忆,等.深部裂隙岩体中弹性波传播与衰减规律试验研究[J].岩石力学与工程学报,2015,34(11):2319-2326.LI Xinping,ZHAO Hang,LUO Yi,et al. Experimental study of propagation and attenuation of elastic wave in deep rock mass with joints[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(11):2319-2326.
[25]金解放,程昀,昌晓旭,等.轴向静载对红砂岩中应力波传播特性的影响试验研究[J].岩石力学与工程学报,2017,36(8):1939-1950.JIN Jiefang,CHENG Yun,CHANG Xiaoxu,et al. Experimental study on stress wave propagation characteristics in red sandstone under axial static stress[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(8):1939-1950.
[26] FAN L F,SUN H Y.Seismic wave propagation through an in-situ stressed rock mass[J]. Journal of Applied Geophysics,2015,121:13-20.
[27]王礼立.应力波基础[M].北京:国防工业出版社,2005.
[28]孟召平,张吉昌,JOACHIM Tiedemann.煤系岩石物理力学参数与声波速度之间的关系[J].地球物理学报,2006,49(5):1505-1510.MENG Zhaoping,ZHANG Jichang,JOACHIM Tiedemann.Relationship between physical and mechanical parameters and acoustic wave velocity of coal measures rocks[J]. Chinese Journal of Geophysics,2006,49(5):1505-1510.