动静组合加载下岩石力学特性和动态强度准则的试验研究
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摘要
针对目前深部硬岩矿山开采的特点和深部岩石力学实验与理论研究相对还不足这一现状,开展动静组合加载下岩石力学的理论和实验研究具有十分重要的意义。本文利用改进的动静组合加载装置,对受不同预应力状态下的岩石开展了冲击载荷下力学特性的试验研究,在此基础上进行了相关的理论研究。主要内容和结论性成果如下：
(1)定义了应力波峰值因子和应力波上升沿时间因子两个系数,利用三维数值模拟,从弹性杆的轴向和径向传播两个方面,分析了矩形波、三角波和半正弦波在5种不同直径SHPB中的传播规律。研究结果表明,针对大直径(≥50mm)的SHPB装置,半正弦应力波在传播过程中能够较好的满足一维应力假定。
(2)根据应力波在弹性杆和岩石试样内的透反射规律,给出了利用反射系数和应力波在试样间来回传播最低次数获得应力差相对值的查值表。提出了岩石波速跟岩样最大长度之间存在二次函数关系式,为具体试验条件下确定岩石试样尺寸提供了一种参考方法。
(3)对均质砂岩进行的动态单轴抗压试验结果标明：岩石在应变率低于102/s情况下,抗压强度的增加跟应变率的量级成正比；在高于应变率102/s时,岩石的抗压强度增加趋势跟应变率的1/3次方成正比。冲击时存在着岩石吸能为零的临界入射能,当入射能小于临界入射能时,岩石内部不参与能量的吸收。
(4)动三轴试验中围压相同时,岩石在应变率低于102/s情况下抗压强度的增加跟应变率的量级成正比。在应变率102/s时,岩石的抗压强度增加趋势跟应变率的1/3次方成正比。在应变率一定时,岩石的抗压强度会随着围压的增大基本呈线性关系显著增大。对于动三轴冲击试验,存在着临界入射能和临界应变率。
(5)一维动静组合加载试验中,相同应变率下,动静组合加载抗压强度会随着轴压比的增加出现先增加后减小的趋势,大约会在轴压比为0.6～0.7时达到最大值。在相同轴压下,抗压强度会随着应变率的增加而增加,呈现指数函数关系。一维动静组合加载破坏试验中,岩石对外界动能的响应受轴压比影响很大。在轴压比递增的情况下,先后会经历“吸收能量-释放能量-吸收能量”三个阶段。这三个阶段可以较好的解释高应力下岩石的动态强度递增、岩爆发生和诱导致裂三者之间的互相转化机制,对深部岩石工程的实践可以提供理论上的指导。
(6)在三维动静组合冲击加载试验中,同一应变率下,当围压一定时,岩石的抗压强度都会随着轴压的增大呈现先增大后减小的趋势。在围压为5MPa时,岩石的抗压强度跟无围压情况下差别不大。但是当围压增大到10MPa,岩石的抗压强度会有较大提高。在轴压一定时,随着围压的增大,抗压强度有增大的趋势。
(7)根据圆盘对心受力的弹性解以及岩石材料受拉过程中线弹性变化的特点,基于微积分原理,分别得到了常规劈裂和冲击劈裂试验中拉伸弹模的解析算法。劈裂试验的结果表明,在低于应变率102/s的范围内,抗拉强度增加比较缓慢,强度增加跟应变率的对数值呈线性关系。在高于应变率102/s内,抗拉强度迅速增加,强度增加跟应变率的1/3次方呈线性关系。利用高速摄像仪对动态劈裂过程进行了记录,证实了劈裂起始位置是从加载方向试样中心位置开始的。并对动态冲击下的劈裂破坏发展模式进行了讨论。
(8)通过对动态单轴压缩、三轴压缩和拉伸试验数据的整理分析,并结合莫尔-库伦准则、霍克-布朗准则和格里菲斯准则的原理,给出了不同应变率范围内动态莫尔-库伦准则、动态霍克布朗准则的具体表达形式。研究结果表明,在低应变率情况下,动态莫尔-库伦准则和动态霍克布朗准则均适用,但是格里菲斯准则判别结果误差很大。在高应变率情况下,动态莫尔-库伦准则比较适用,格里菲斯准则仅适用于判别高应变率单轴抗压强度和抗拉强度。
Aiming at the characteristics of the deep hard-rock metal mines and the relative shortage status of experimental and theoretical research on deep rock mechanics, it is essential to study and understand the mechnical properties of deep rock under coupled static-dynamic loads. For deep rocks with different pre-stress state, the dynamic experiments were conducted with impact loads by using an innovative testing system, and some theoretical researches were also carried on in this paper. The main contents and conclusive results are as follows:
(1) Two indexes, the stress wave peak-value factor and stress wave rising-edge time factor, were defined to analyze the propagation rules of stress wave (rectangular waves, triangular waves and half-sine wave) in 5 different diameters SHPB. For large diameter (>50mm) SHPB device, the results show that half-sine stress wave is able to meet the one-dimensional assumptions in the propagation process.
(2) According to the transmission-reflection laws of stress waves between elastic bar with rock sample, a look-up table to obtain the relative stress difference value was given by using the reflection coefficient and the back-forth communication number of stress wave in rock. The quadratic function relationship between the wave velocity of rock with the maximum length of sample was obtained, which provides a reference method to determine the sample size for specific test condition.
(3) The dynamic uniaxial compression tests show that the compressive strength of rock increases with the magnitude of strain rate when the strain rate is less than 102/s and the upward trend in the compressive strength is proportional to 1/3 power of strain rate when the strain rate is larger than 102/s. There is a critical incident energy value when the shock wave incidents in the rock. When the incident energy is less than the critical incident energy, the rock sample does not participate in the energy absorption.
(4) In the dynamic triaxial tests with different strain-rate, the compressive strength increases with the magnitude of strain rate when the confining pressure is the same and the strain rate is less than 102/s, and the compressive strength increases with the 1/3 power of strain rate when the strain rate is larger than 102/s. When the strain rate is a constant, the compressive strength of the rock will linear increase with the increases of confining pressure. For the dynamic triaxial impact test, the critical incident energy and the critical strain rate were obtained.
(5) In the one-dimensional dynamis tests coupled loads, when the strain rate is a constant, the impact compressive strength will first increase and then decrease as the axial static pressure increases and also reach the maximum value when the axial static pressure is about 60%-70%of static compressive strength. When the axial static pressure is a constant, the impact strength will increase with exponential function when the strain rate increases. The ratio axial compressive pressure will influence the response of rock specimen to impact energy and the specimen will experience three phases "energy absorption-energy release-energy absorption" when the ratio axial compressive pressure increases. The transformation mechanism of dynamic strength increase, rock burst and induced fracture of rock under high in-situ stress can be explained better by the above three phases.The results can also provide a theoretical guide for the deep rock engineering practice.
(6) When the strain rate is a constant in three-dimensional coupled static-dynamic loading tests and the confining pressure is also a constant, the impact strength of rock will increase firstly and then decrease with the axial compression pressure increases. When the confining pressure is 5MPa, there is no obvious difference between the impact strength with that of one-dimensional coupled tests. But when the confining pressure increased to lOMPa, the impact strength of rock will be greatly enhanced. In the situation with the axial compression is a constant, the impact strength will show an increasing trend as the confining pressure increases.
(7) Combined the theoretical clastic solution of disc on cardiac force and the physical parameters obtained in actual measure of experiments and based on the principle of calculus, two analytic algorithms to estimate the static and dynamic tensile modulus in Brazilian disk splitting tests were presented. The Brazilian tensile test results show that the tensile strength of rock will increase with the magnitude of strain rate when the strain rate is less than 102/s and the upward trend in the tensile strength is proportional to 1/3 power of strain rate when the strain rate is larger than 102/s. The splitting processes in static and dynamic tensile tests were photographed by using high-speed camera and confirmed that the split starting position is the center of the specimen in loading direction from the loading beginning. The splitting destruct developing mode under impact loading is summarized.
(8) Combined the analysis of data in dynamic uniaxial tests, dynamic triaxial tests and dynamic tensile tests and the principle of Mohr-coulomb criterion, Hoek-Brown criterion and Griffith criterion, the dynamic Mohr-coulomb criterion and dynmaic Hoek-Brown criterion were given. The experimental results show that dynamic Mohr-coulomb criterion and dynmaic Hoek-Brown criterion can be used to estimate the dynamic strength in low strain rate range. In high strain rate range, the dynamic strength can be estimated by using dynamic Mohr-coulomb criterion, and the Griffith criterion can be used to estimate the dynamic uniaxial compressive strength and dynmaic tensile strength.
(1)定义了应力波峰值因子和应力波上升沿时间因子两个系数,利用三维数值模拟,从弹性杆的轴向和径向传播两个方面,分析了矩形波、三角波和半正弦波在5种不同直径SHPB中的传播规律。研究结果表明,针对大直径(≥50mm)的SHPB装置,半正弦应力波在传播过程中能够较好的满足一维应力假定。
(2)根据应力波在弹性杆和岩石试样内的透反射规律,给出了利用反射系数和应力波在试样间来回传播最低次数获得应力差相对值的查值表。提出了岩石波速跟岩样最大长度之间存在二次函数关系式,为具体试验条件下确定岩石试样尺寸提供了一种参考方法。
(3)对均质砂岩进行的动态单轴抗压试验结果标明：岩石在应变率低于102/s情况下,抗压强度的增加跟应变率的量级成正比；在高于应变率102/s时,岩石的抗压强度增加趋势跟应变率的1/3次方成正比。冲击时存在着岩石吸能为零的临界入射能,当入射能小于临界入射能时,岩石内部不参与能量的吸收。
(4)动三轴试验中围压相同时,岩石在应变率低于102/s情况下抗压强度的增加跟应变率的量级成正比。在应变率102/s时,岩石的抗压强度增加趋势跟应变率的1/3次方成正比。在应变率一定时,岩石的抗压强度会随着围压的增大基本呈线性关系显著增大。对于动三轴冲击试验,存在着临界入射能和临界应变率。
(5)一维动静组合加载试验中,相同应变率下,动静组合加载抗压强度会随着轴压比的增加出现先增加后减小的趋势,大约会在轴压比为0.6～0.7时达到最大值。在相同轴压下,抗压强度会随着应变率的增加而增加,呈现指数函数关系。一维动静组合加载破坏试验中,岩石对外界动能的响应受轴压比影响很大。在轴压比递增的情况下,先后会经历“吸收能量-释放能量-吸收能量”三个阶段。这三个阶段可以较好的解释高应力下岩石的动态强度递增、岩爆发生和诱导致裂三者之间的互相转化机制,对深部岩石工程的实践可以提供理论上的指导。
(6)在三维动静组合冲击加载试验中,同一应变率下,当围压一定时,岩石的抗压强度都会随着轴压的增大呈现先增大后减小的趋势。在围压为5MPa时,岩石的抗压强度跟无围压情况下差别不大。但是当围压增大到10MPa,岩石的抗压强度会有较大提高。在轴压一定时,随着围压的增大,抗压强度有增大的趋势。
(7)根据圆盘对心受力的弹性解以及岩石材料受拉过程中线弹性变化的特点,基于微积分原理,分别得到了常规劈裂和冲击劈裂试验中拉伸弹模的解析算法。劈裂试验的结果表明,在低于应变率102/s的范围内,抗拉强度增加比较缓慢,强度增加跟应变率的对数值呈线性关系。在高于应变率102/s内,抗拉强度迅速增加,强度增加跟应变率的1/3次方呈线性关系。利用高速摄像仪对动态劈裂过程进行了记录,证实了劈裂起始位置是从加载方向试样中心位置开始的。并对动态冲击下的劈裂破坏发展模式进行了讨论。
(8)通过对动态单轴压缩、三轴压缩和拉伸试验数据的整理分析,并结合莫尔-库伦准则、霍克-布朗准则和格里菲斯准则的原理,给出了不同应变率范围内动态莫尔-库伦准则、动态霍克布朗准则的具体表达形式。研究结果表明,在低应变率情况下,动态莫尔-库伦准则和动态霍克布朗准则均适用,但是格里菲斯准则判别结果误差很大。在高应变率情况下,动态莫尔-库伦准则比较适用,格里菲斯准则仅适用于判别高应变率单轴抗压强度和抗拉强度。
Aiming at the characteristics of the deep hard-rock metal mines and the relative shortage status of experimental and theoretical research on deep rock mechanics, it is essential to study and understand the mechnical properties of deep rock under coupled static-dynamic loads. For deep rocks with different pre-stress state, the dynamic experiments were conducted with impact loads by using an innovative testing system, and some theoretical researches were also carried on in this paper. The main contents and conclusive results are as follows:
(1) Two indexes, the stress wave peak-value factor and stress wave rising-edge time factor, were defined to analyze the propagation rules of stress wave (rectangular waves, triangular waves and half-sine wave) in 5 different diameters SHPB. For large diameter (>50mm) SHPB device, the results show that half-sine stress wave is able to meet the one-dimensional assumptions in the propagation process.
(2) According to the transmission-reflection laws of stress waves between elastic bar with rock sample, a look-up table to obtain the relative stress difference value was given by using the reflection coefficient and the back-forth communication number of stress wave in rock. The quadratic function relationship between the wave velocity of rock with the maximum length of sample was obtained, which provides a reference method to determine the sample size for specific test condition.
(3) The dynamic uniaxial compression tests show that the compressive strength of rock increases with the magnitude of strain rate when the strain rate is less than 102/s and the upward trend in the compressive strength is proportional to 1/3 power of strain rate when the strain rate is larger than 102/s. There is a critical incident energy value when the shock wave incidents in the rock. When the incident energy is less than the critical incident energy, the rock sample does not participate in the energy absorption.
(4) In the dynamic triaxial tests with different strain-rate, the compressive strength increases with the magnitude of strain rate when the confining pressure is the same and the strain rate is less than 102/s, and the compressive strength increases with the 1/3 power of strain rate when the strain rate is larger than 102/s. When the strain rate is a constant, the compressive strength of the rock will linear increase with the increases of confining pressure. For the dynamic triaxial impact test, the critical incident energy and the critical strain rate were obtained.
(5) In the one-dimensional dynamis tests coupled loads, when the strain rate is a constant, the impact compressive strength will first increase and then decrease as the axial static pressure increases and also reach the maximum value when the axial static pressure is about 60%-70%of static compressive strength. When the axial static pressure is a constant, the impact strength will increase with exponential function when the strain rate increases. The ratio axial compressive pressure will influence the response of rock specimen to impact energy and the specimen will experience three phases "energy absorption-energy release-energy absorption" when the ratio axial compressive pressure increases. The transformation mechanism of dynamic strength increase, rock burst and induced fracture of rock under high in-situ stress can be explained better by the above three phases.The results can also provide a theoretical guide for the deep rock engineering practice.
(6) When the strain rate is a constant in three-dimensional coupled static-dynamic loading tests and the confining pressure is also a constant, the impact strength of rock will increase firstly and then decrease with the axial compression pressure increases. When the confining pressure is 5MPa, there is no obvious difference between the impact strength with that of one-dimensional coupled tests. But when the confining pressure increased to lOMPa, the impact strength of rock will be greatly enhanced. In the situation with the axial compression is a constant, the impact strength will show an increasing trend as the confining pressure increases.
(7) Combined the theoretical clastic solution of disc on cardiac force and the physical parameters obtained in actual measure of experiments and based on the principle of calculus, two analytic algorithms to estimate the static and dynamic tensile modulus in Brazilian disk splitting tests were presented. The Brazilian tensile test results show that the tensile strength of rock will increase with the magnitude of strain rate when the strain rate is less than 102/s and the upward trend in the tensile strength is proportional to 1/3 power of strain rate when the strain rate is larger than 102/s. The splitting processes in static and dynamic tensile tests were photographed by using high-speed camera and confirmed that the split starting position is the center of the specimen in loading direction from the loading beginning. The splitting destruct developing mode under impact loading is summarized.
(8) Combined the analysis of data in dynamic uniaxial tests, dynamic triaxial tests and dynamic tensile tests and the principle of Mohr-coulomb criterion, Hoek-Brown criterion and Griffith criterion, the dynamic Mohr-coulomb criterion and dynmaic Hoek-Brown criterion were given. The experimental results show that dynamic Mohr-coulomb criterion and dynmaic Hoek-Brown criterion can be used to estimate the dynamic strength in low strain rate range. In high strain rate range, the dynamic strength can be estimated by using dynamic Mohr-coulomb criterion, and the Griffith criterion can be used to estimate the dynamic uniaxial compressive strength and dynmaic tensile strength.
引文
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