岩石粘弹性质的实验研究
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摘要
衰减、波速及其频散和加卸载响应比与岩石的粘弹性密切相关,本文从以上几个方面研究岩石的粘弹性质。
关于衰减的研究很多,主要集中在地震波、超声波频率内,与之相比,对于作用周期较长、有一定应力(应变)振幅的循环衰减研究较少。本文对衰减的研究侧重于不同初应力水平(即振幅的基线)下衰减与应力振幅及作用周期之间的关系；在此基础上为了获得更宽频域内的衰减,在一定的初应力下,进行了一系列蠕变实验和超声波实验,并将两者结果进行对比分析。由于两者应力振幅都为零,前面加压过程都一样,消除了应力振幅对衰减的影响,两者结果只与应力作用时间有关而具有可比性,而作用时间与蠕变(应变)量对应,将衰减与蠕变时间关系转化为衰减与蠕变量关系后,发现二者线性相关,将蠕变的衰减向小应变(小蠕变量)方向进行了外推,发现蠕变衰减的外延值跟超声波下测得的衰减很接近,再联合已有的0.1-1MHz下Q值近似常量的规律,说明衰减-蠕变量相关性在小应变方向也适用。将蠕变的衰减向大蠕变量方向外推可以找到蠕变破裂时蠕变量对应的衰减,一旦向破裂蠕变量方向外推被实验验证,根据破裂时蠕变量来估算蠕变时间,这样就得到同一块样品蠕变破裂对应的最低频率到MHz相当宽频域内衰减关系。
具体而言,为了找出衰减同初应力水平、应力加载振幅及作用周期之间的关系,对大庆油田砂岩,分别在不同的初应力水平下,进行了一系列地震学中感兴趣的应变范围内的等振幅变周期、等周期变振幅、三角波单轴压缩试验,找出了衰减与三者关系,并用线性粘弹理论、内时理论、P-M模型给予了解释,利用已有的实验结果计算了内时理论模型参数a,用实验规律对未知应力振幅和作用周期下衰减值进行了预测并和实验值进行了对比,预测值和实验值符合很好。
为了获得长周期下衰减,对大庆砂岩、郯庐断裂带合肥段紫蓬山干燥砂岩,在扣除应力振幅对衰减影响的基础上,在一定的初应力水平下进行时间为1小时、2小时、4小时、12小时、1天、2天、3天的蠕变实验,发现衰减随蠕变时间增大而增大。并将用应力应变曲线法计算出长时间较大应变量下的衰减对比了相同初应力水平下超声波频率470KHz、700KHz下测得的衰减。实验结果显示蠕变实验衰减要大于超声波衰减,两者最小相差40%左右,两种不同方法的差异可能与应变量有关。将蠕变衰减与周期的关系转化为衰减与蠕变量关系后发现二者线性相关系数95%以上,以此为据,将衰减向小蠕变量方向外推,发现蠕变衰减外推后的结果和超声波衰减很接近,将应变量考虑进去后两种方法的结果是比较符合的,同时也从应变角度说明了为什么在0.1-1MHz内衰减几乎不变。地下岩石长时间处于一定应力作用状态因此蠕变作用下衰减比其他方法测得的结果更接近于地层条件下岩石衰减。
波速测量的研究也很多,通常强调的是实验的结果和规律性,而实验条件对结果造成的影响讨论较少,不同的测量条件会对实验结果造成偏差,即使同一块样品同一个人在不同的测量条件下获取的波速值也可能不同,研究各种因素对波速影响对规范测量条件获取准确波速是必要的。
为了总结出测量条件对波速的影响,对上百块不同尺寸、不同衰减、空气干燥的样品(砂岩、大理岩、花岗岩、铁、铝、有机玻璃)用不同频率的换能器进行了波速测量,定量地得出样品长度、换能器频率、放大器倍数、耦合强度和耦合剂对波速的影响,揭示了尺寸和本征衰减对频散的影响,其中关于稳定波速所需的样品长度比现有推荐长度要小,说明推荐标准还有放宽可能。尝试了频散法测衰减得到了与频谱振幅比法相一致的结果,修正了岩体完整性系数,降低了不同频率完整性系数平均差。
加卸载响应比理论对岩石破裂实验数据处理已取得很好效果,但对蠕变破裂过程的响应比的变化研究较少。为了从响应比的角度来研究整个蠕变破裂过程,本文通过逐级加载的蠕变实验获得了大理岩蠕变破裂全过程曲线,并进行了分解,计算了蠕变破裂过程中杨氏模量、蠕变量、蠕变速率等参数的加卸载响应比,讨论了蠕变各阶段响应比的变化。发现与已有的孕震破裂过程中响应比一致；杨氏模量随应力的响应曲线异于典型本构曲线,可能与岩石的弱化和稳态蠕变向加速蠕变过渡有关。
Attenuation, velocity and its dispersion, Load/Unload response ratio are closely related to the rock's viscoelastic properties. From the three acpects, this paper studied the viscoelastic properties of the rock.
Many studies on the attenuation has been done-mainly concentrated in the frequencies of seismic wave, compared with this, the researches of attenuation under a longer period driven by a certain cycle of stress (strain) amplitude were less. This paper focused on the relationship among the attenuation, the stress amplitude and cycle time under different initial stress levels (the baseline of the amplitude).On this basis, in order to obtain the attenuation in a wider frequency domain, under unchanged initial stress, a series of creep and ultrasonic tests were performed, then the results were compared with. As the two stress amplitudes were zero with the same pressing process, the effect from stress amplitude on the attenuation was eliminated. Both results were only concerned with the keeping time and could be comparable. Because of testing time corresponding to the amount of creep, after changing the relationship between attenuation and creep time into the relationship between attenuation and the amount of creep, the attenuation was extrapolated in the smaller strain (small amount of creep) direction, it was found that the attenuation value of zero creep was close to the attenuation measured by ultrasonic. Combining the existing constant-Q under 0.1～1MHz, the correlation between the attenuation frequency relationship and attenuation-strain was suitable. The creep attenuation was extrapolated in the bigger strain direction, the attenuation of creep rupture could be found and the creep time could been estimated according to the amount of rupture creep, once the correctness of extrapolating in the direction of creep rupture was tested by experiments, then the attenuation for one sample within the lowest frequency to MHz could be obtained.
Specifically, to find out the relationship between attenuation and the initial stress, amplitude and cycle time of the stress, a series of uniaxial stress cycling tests performed in triangle waveform loading with equivalent amplitude but different cycle time or equivalent frequency but different amplitude under different initial stress levels were conducted on dry Taching sandstones and sandstones from the Zipeng mountain of the Tan-Lu fault zone using MTS testing machine. And then, the relationships among Q, the initial stress level, the strain (or stress) amplitude and the frequency were obtained. With the help of Endochronic theory, linear viscoelastic theory and P-M model theory, I gave a suitable reason for the results.Using the experimental results I calculated the parameter of Endochronic theory, and the attenuation of unknown stress amplitude and frequency were well predicted compared with experimental values.
In order to obtain attenuation under a long period, according to the results, except the effe(?) of stress amplitude on the attenuation, the attenuations from the different creep time which respectively continued 1 hour,2 hours,4 hours,12 hours,1 day,2 days and 3 days under certain initial stress level were jointly considered with the results from the ultrasonic frequencies 470KHz,700KHz. The results showed that the attenuation of creep was higher than that of ultrasonic, the smallest difference between them was about 40%, which might be related to the strain of different methods. After changing the relationship between attenuation and creep time into the relationship between attenuation and strain, the linear correlation coefficient was above 95%. The result of creep attenuation extrapolated in the smaller strain (small amount of creep) direction was very close to the ultrasonic attenuation. Taking the strain into account, the results of two methods were in line with. At the same time, from the point of strain, why the attenuation in 0.1～1MHz almost was unchanged could be explained. The rock underground in a certain state of stress for a long time, the results of attenuation measured by creep is closer to the attenuation of layer rock than other methods.
Many studies also have been done on velocity, but often emphasized the experimental results and the regularity, the discussion of the influence from experimental conditions on the results was less. For different measurement conditions would result in deviation of experimental results, even the velocity values from the same sample by the same person might be different, because of different measurement conditions. So it was necessary to study the impact of various factors on the velocity for standardizing the measurement conditions.
Transducers with different frequencies (550KHz,50KHz) were used to measured the velocities of nearly a hundred samples(sandstone, marble, steel, aluminum, plexiglass) with different lengths to quantitatively understand the effects of the length of the samples, the transducer's frequency, signal amplification, coupling agents, coupling strength on the testing results. The results revealed the effects of sample sizes, intrinsic attenuation on the velocity dispersion. The length caused stable velocity was smaller than the recommended length, which meant the recommended standards could be relaxed.Base on the results, I measured the attenuation by the dispersion method and corrected the coefficient of rock mass integrity tested by seismograph and acoustic instrument.
Load/Unload response ratio(LURR) theory has been achieved well in processing the rock fracture data, but the study on the change of LURR of the whole creep rupture process was relatively lack. In order to study the whole process of creep rupture in the point view of LURR, experiments on the granite sample at uniaxial stress were performed by using grade loading method to obtain the creep curves at grade loading process and creep fracture curve. After decomposing the creep fracture curve, the Young modulus, creep value and creep rate during the fracture process were analyzed by Load/Unload response ratio method. It was found that the law of the load/unload response ratio's variation in the fracture were consistent with that during the rupture process of earthquake, and the response curve of the Young modulus changing with the stress was different from the typical constitutive curve, which was probably because of the weakening of the rock and the transition from the steady creep to the accelerating creep.
关于衰减的研究很多,主要集中在地震波、超声波频率内,与之相比,对于作用周期较长、有一定应力(应变)振幅的循环衰减研究较少。本文对衰减的研究侧重于不同初应力水平(即振幅的基线)下衰减与应力振幅及作用周期之间的关系；在此基础上为了获得更宽频域内的衰减,在一定的初应力下,进行了一系列蠕变实验和超声波实验,并将两者结果进行对比分析。由于两者应力振幅都为零,前面加压过程都一样,消除了应力振幅对衰减的影响,两者结果只与应力作用时间有关而具有可比性,而作用时间与蠕变(应变)量对应,将衰减与蠕变时间关系转化为衰减与蠕变量关系后,发现二者线性相关,将蠕变的衰减向小应变(小蠕变量)方向进行了外推,发现蠕变衰减的外延值跟超声波下测得的衰减很接近,再联合已有的0.1-1MHz下Q值近似常量的规律,说明衰减-蠕变量相关性在小应变方向也适用。将蠕变的衰减向大蠕变量方向外推可以找到蠕变破裂时蠕变量对应的衰减,一旦向破裂蠕变量方向外推被实验验证,根据破裂时蠕变量来估算蠕变时间,这样就得到同一块样品蠕变破裂对应的最低频率到MHz相当宽频域内衰减关系。
具体而言,为了找出衰减同初应力水平、应力加载振幅及作用周期之间的关系,对大庆油田砂岩,分别在不同的初应力水平下,进行了一系列地震学中感兴趣的应变范围内的等振幅变周期、等周期变振幅、三角波单轴压缩试验,找出了衰减与三者关系,并用线性粘弹理论、内时理论、P-M模型给予了解释,利用已有的实验结果计算了内时理论模型参数a,用实验规律对未知应力振幅和作用周期下衰减值进行了预测并和实验值进行了对比,预测值和实验值符合很好。
为了获得长周期下衰减,对大庆砂岩、郯庐断裂带合肥段紫蓬山干燥砂岩,在扣除应力振幅对衰减影响的基础上,在一定的初应力水平下进行时间为1小时、2小时、4小时、12小时、1天、2天、3天的蠕变实验,发现衰减随蠕变时间增大而增大。并将用应力应变曲线法计算出长时间较大应变量下的衰减对比了相同初应力水平下超声波频率470KHz、700KHz下测得的衰减。实验结果显示蠕变实验衰减要大于超声波衰减,两者最小相差40%左右,两种不同方法的差异可能与应变量有关。将蠕变衰减与周期的关系转化为衰减与蠕变量关系后发现二者线性相关系数95%以上,以此为据,将衰减向小蠕变量方向外推,发现蠕变衰减外推后的结果和超声波衰减很接近,将应变量考虑进去后两种方法的结果是比较符合的,同时也从应变角度说明了为什么在0.1-1MHz内衰减几乎不变。地下岩石长时间处于一定应力作用状态因此蠕变作用下衰减比其他方法测得的结果更接近于地层条件下岩石衰减。
波速测量的研究也很多,通常强调的是实验的结果和规律性,而实验条件对结果造成的影响讨论较少,不同的测量条件会对实验结果造成偏差,即使同一块样品同一个人在不同的测量条件下获取的波速值也可能不同,研究各种因素对波速影响对规范测量条件获取准确波速是必要的。
为了总结出测量条件对波速的影响,对上百块不同尺寸、不同衰减、空气干燥的样品(砂岩、大理岩、花岗岩、铁、铝、有机玻璃)用不同频率的换能器进行了波速测量,定量地得出样品长度、换能器频率、放大器倍数、耦合强度和耦合剂对波速的影响,揭示了尺寸和本征衰减对频散的影响,其中关于稳定波速所需的样品长度比现有推荐长度要小,说明推荐标准还有放宽可能。尝试了频散法测衰减得到了与频谱振幅比法相一致的结果,修正了岩体完整性系数,降低了不同频率完整性系数平均差。
加卸载响应比理论对岩石破裂实验数据处理已取得很好效果,但对蠕变破裂过程的响应比的变化研究较少。为了从响应比的角度来研究整个蠕变破裂过程,本文通过逐级加载的蠕变实验获得了大理岩蠕变破裂全过程曲线,并进行了分解,计算了蠕变破裂过程中杨氏模量、蠕变量、蠕变速率等参数的加卸载响应比,讨论了蠕变各阶段响应比的变化。发现与已有的孕震破裂过程中响应比一致；杨氏模量随应力的响应曲线异于典型本构曲线,可能与岩石的弱化和稳态蠕变向加速蠕变过渡有关。
Attenuation, velocity and its dispersion, Load/Unload response ratio are closely related to the rock's viscoelastic properties. From the three acpects, this paper studied the viscoelastic properties of the rock.
Many studies on the attenuation has been done-mainly concentrated in the frequencies of seismic wave, compared with this, the researches of attenuation under a longer period driven by a certain cycle of stress (strain) amplitude were less. This paper focused on the relationship among the attenuation, the stress amplitude and cycle time under different initial stress levels (the baseline of the amplitude).On this basis, in order to obtain the attenuation in a wider frequency domain, under unchanged initial stress, a series of creep and ultrasonic tests were performed, then the results were compared with. As the two stress amplitudes were zero with the same pressing process, the effect from stress amplitude on the attenuation was eliminated. Both results were only concerned with the keeping time and could be comparable. Because of testing time corresponding to the amount of creep, after changing the relationship between attenuation and creep time into the relationship between attenuation and the amount of creep, the attenuation was extrapolated in the smaller strain (small amount of creep) direction, it was found that the attenuation value of zero creep was close to the attenuation measured by ultrasonic. Combining the existing constant-Q under 0.1～1MHz, the correlation between the attenuation frequency relationship and attenuation-strain was suitable. The creep attenuation was extrapolated in the bigger strain direction, the attenuation of creep rupture could be found and the creep time could been estimated according to the amount of rupture creep, once the correctness of extrapolating in the direction of creep rupture was tested by experiments, then the attenuation for one sample within the lowest frequency to MHz could be obtained.
Specifically, to find out the relationship between attenuation and the initial stress, amplitude and cycle time of the stress, a series of uniaxial stress cycling tests performed in triangle waveform loading with equivalent amplitude but different cycle time or equivalent frequency but different amplitude under different initial stress levels were conducted on dry Taching sandstones and sandstones from the Zipeng mountain of the Tan-Lu fault zone using MTS testing machine. And then, the relationships among Q, the initial stress level, the strain (or stress) amplitude and the frequency were obtained. With the help of Endochronic theory, linear viscoelastic theory and P-M model theory, I gave a suitable reason for the results.Using the experimental results I calculated the parameter of Endochronic theory, and the attenuation of unknown stress amplitude and frequency were well predicted compared with experimental values.
In order to obtain attenuation under a long period, according to the results, except the effe(?) of stress amplitude on the attenuation, the attenuations from the different creep time which respectively continued 1 hour,2 hours,4 hours,12 hours,1 day,2 days and 3 days under certain initial stress level were jointly considered with the results from the ultrasonic frequencies 470KHz,700KHz. The results showed that the attenuation of creep was higher than that of ultrasonic, the smallest difference between them was about 40%, which might be related to the strain of different methods. After changing the relationship between attenuation and creep time into the relationship between attenuation and strain, the linear correlation coefficient was above 95%. The result of creep attenuation extrapolated in the smaller strain (small amount of creep) direction was very close to the ultrasonic attenuation. Taking the strain into account, the results of two methods were in line with. At the same time, from the point of strain, why the attenuation in 0.1～1MHz almost was unchanged could be explained. The rock underground in a certain state of stress for a long time, the results of attenuation measured by creep is closer to the attenuation of layer rock than other methods.
Many studies also have been done on velocity, but often emphasized the experimental results and the regularity, the discussion of the influence from experimental conditions on the results was less. For different measurement conditions would result in deviation of experimental results, even the velocity values from the same sample by the same person might be different, because of different measurement conditions. So it was necessary to study the impact of various factors on the velocity for standardizing the measurement conditions.
Transducers with different frequencies (550KHz,50KHz) were used to measured the velocities of nearly a hundred samples(sandstone, marble, steel, aluminum, plexiglass) with different lengths to quantitatively understand the effects of the length of the samples, the transducer's frequency, signal amplification, coupling agents, coupling strength on the testing results. The results revealed the effects of sample sizes, intrinsic attenuation on the velocity dispersion. The length caused stable velocity was smaller than the recommended length, which meant the recommended standards could be relaxed.Base on the results, I measured the attenuation by the dispersion method and corrected the coefficient of rock mass integrity tested by seismograph and acoustic instrument.
Load/Unload response ratio(LURR) theory has been achieved well in processing the rock fracture data, but the study on the change of LURR of the whole creep rupture process was relatively lack. In order to study the whole process of creep rupture in the point view of LURR, experiments on the granite sample at uniaxial stress were performed by using grade loading method to obtain the creep curves at grade loading process and creep fracture curve. After decomposing the creep fracture curve, the Young modulus, creep value and creep rate during the fracture process were analyzed by Load/Unload response ratio method. It was found that the law of the load/unload response ratio's variation in the fracture were consistent with that during the rupture process of earthquake, and the response curve of the Young modulus changing with the stress was different from the typical constitutive curve, which was probably because of the weakening of the rock and the transition from the steady creep to the accelerating creep.
引文
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