动载作用下砂岩变形速率及能量毫秒级模拟研究
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摘要
以中国科学院武汉岩土力学研究所研制的RMT-150C岩石力学试验系统为主要试验平台,以宜昌砂岩为研究对象,对砂岩在96 k N峰值、不同频率、不同波形加载下的垂向力变化速率、垂向变形速率、表观弹性模量、横向变形速率、瞬时泊松比与时间的关系等5方面内容进行分析得出不同频率、不同波形对上述关系的影响规律。在提出非滞后时间段内表观弹性模量与垂直力线性关系的基础上,给出不同频率下三角波和正弦波的计算公式及参数,计算和实测对比证明,其计算公式可以很好地拟合不同波形、不同频率下的变形速率随时间的毫秒级变化规律。在此基础上,给出了三角波和正弦波的能量计算方法,对比分析显示,计算公式和方法可以很好地对三角波和正弦波在不同频率和不同加载速度下的能量值作出毫秒级的精确预测。
Taking RMT-150 C rock mechanics testing system developed by Institute of Rock and Soil Mechanics,Chinese Academy of Sciences as the main test platform, five aspects of sandstone in the 96 k N peak with different frequencies and wave loadings in Yichang are studied:relationship between vertical force change rate and time, relationship between vertical deformation rate and time, relationship between apparent elastic modulus and time, relationship between the lateral deformation rate and time, relationship between instantaneous Poisson's ratio and time. Influence of different frequencies and waveforms on the relationships above is drawn.On the basis of putting forward the linear relationship between the non-lag period of apparent tangent modulus and vertical force,calculation formulas and parameters of the triangular wave and sine wave are obtained in different frequencies. The comparison of the calculation and measured values shows that the proposed calculation formulas can be well fitted with the changes rule with milliseconds of the deformation rate of different waveforms and different frequencies. On this basis, the paper gives the triangle and sine wave energy calculation methods, and comparative analysis shows that the listed computing formula and method can make accurate prediction of millisecond on the triangle and sine wave at different frequencies and energy value of different loading rates.
Taking RMT-150 C rock mechanics testing system developed by Institute of Rock and Soil Mechanics,Chinese Academy of Sciences as the main test platform, five aspects of sandstone in the 96 k N peak with different frequencies and wave loadings in Yichang are studied:relationship between vertical force change rate and time, relationship between vertical deformation rate and time, relationship between apparent elastic modulus and time, relationship between the lateral deformation rate and time, relationship between instantaneous Poisson's ratio and time. Influence of different frequencies and waveforms on the relationships above is drawn.On the basis of putting forward the linear relationship between the non-lag period of apparent tangent modulus and vertical force,calculation formulas and parameters of the triangular wave and sine wave are obtained in different frequencies. The comparison of the calculation and measured values shows that the proposed calculation formulas can be well fitted with the changes rule with milliseconds of the deformation rate of different waveforms and different frequencies. On this basis, the paper gives the triangle and sine wave energy calculation methods, and comparative analysis shows that the listed computing formula and method can make accurate prediction of millisecond on the triangle and sine wave at different frequencies and energy value of different loading rates.
引文
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[13]李顺群.关于粘弹模型中滞回圈的讨论[J].辽宁工学院学报(自然科学版),2004,24(5):58-60.LI Shun-qun.Discussion on delayed curve about soil viscoelasticity model[J].Journal of Liaoning Institute of Technology,2004,24(5):58-60.
[14]葛修润,卢应发.循环载荷作用下岩石疲劳破坏和不可逆变形问题的探讨[J].岩土工程学报,1992,14(3):56-60.GE Xiu-run,LU Ying-fa.To investigate the rock fatigue failure and irreversible deformation under cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,1992,14(3):56-60.
[15]葛修润,任建喜,蒲毅彬,等.岩石疲劳损伤扩展规律CT细观分析初探[J].岩土工程学报,2001,23(2):191-195.GE Xiu-run,REN Jian-xi,PU Yi-bin,et al.Primary study of CT real-time testing of fatigue meso-damage propagation law of rock[J].Chinese Journal of Geotechnical Engineering,2001,23(2):191-195.
[16]葛修润,蒋宇,卢允德,等.周期载荷作用下岩石疲劳应变特性试验研究[J].岩石力学与工程学报,2003,22(10):1581-1585.GE Xiu-run,JIANG Yu,LU Yun-de,et al.Testing study on fatigue deformationg law of rock under cyclic loading[J].Chinese Journal of Geotechnical Engineering,2003,22(10):1581-1585.
[17]刘杰,李建林,唐亮,等.三角波卸载段作用下钙质砂岩毫秒量级变形速率预测模型研究[J].岩土力学,2014,35(增刊1):63-70.LIU Jie,LI Jian-lin,TANG Liang.Study of prediction model for milliseconds deformation rate in triangular wave unloading segment of calcareous sandstone[J].Rock and Soil Mechanics,2014,35(Supp.1):63-70.
[18]巩思园,窦林名,何江,等.深部冲击倾向煤岩循环加卸载的纵波波速与应力关系试验研究[J].岩土力学,2012,35(1):41-47.GONG Si-yuan,DOU Lin-ming,HE Jiang.Study of correlation between stress and longitudinal wave velocity for deep burst tendency coal and rock samples in uniaxial cyclic loading and unloading experiment[J].Rock and Soil Mechanics,2014,35(1):41-47.
[19]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报,2007,26(增刊1):1581-1585.YANG Yong-jie,SONG Yang,CHU Jun.Experimental study on characteristics of strength and deformation of coal under cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp.1):1581-1585.
[20]郭印同,赵克烈,孙冠华,等.周期荷载下盐岩的疲劳变形及损伤特性研究[J].岩土力学,2011,32(5):1353-1359.GUO Yin-tong,ZHAO Ke-lie,SUN Guan-hua.Experimental study of fatigue deformation and damage characteristics of salt rock under cyclic loading[J].Rock and Soil Mechanics,2011,32(5):1353–1359.
[21]马林建,刘新宇,许宏发,等.循环荷载作用下盐岩三轴变形和强度特性试验研究[J].岩石力学与工程学报,2013,32(4):849-856.MA Lin-jian,LIU Xin-yu,XU Hong-fa,et al.Deformation and strength properties of rock salt subjected to triaxial compression with cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(4):849-856.
[22]周小平,季璇,钱七虎.强地震荷载作用下临水挡土墙的拟动力法稳定性分析[J].岩石力学与工程学报,2012,31(10):2071-2081.ZHOU Xiao-ping,JI Xuan,QIAN Qi-hu.Stability analysis of water front retaining wall subjected to seismic loads using pseudo-dynamic method[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(10):2071-2081.
[2]唐杰,孙成禹,周家惠,等.岩石非线性阻尼滞后响应特性研究[J].岩石力学与工程学报,2012,5(增刊1):2948-2955.TANG Jie,SUN Cheng-yu,ZHOU Jia-hui,et al.Study of nonlinear dampin g hysteresis response character for rock sample[J].Chinese Journal of Rock Mechanics and Engineering,2012,5(Supp.1):2948-2955.
[3]席道瑛,陈运平,陶月赞,等.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,2006,6(6):1086-1093.XI Dao-ying,CHEN Yun-ping,TAO Yue-zan,et al.Nonlinear elastic hysteric characteristics of rocks[J].Chinese Journal of Rock Mechanics and Engineering,2006,6(6):1086-1093.
[4]席道瑛,刘小燕,张程远.由宏观滞回曲线分析岩石的微细观损伤[J].岩石力学与工程学报,2003,22(2):182XI Dao-ying,LIU Xiao-yan,ZHANG Cheng-yuan.Analysis on micro and meso-damage of rock by macro-hysteresis curve[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):182-187.
[5]陈运平,席道瑛,薛彦伟.循环荷载下饱和岩石的滞后和衰减[J].地球物理学报,2004,47(4):672-679.CHEN Yun-Ping,XI Dao-Ying,XUE Yan-Wei.Hysteresis and attenuation of saturated rocks under cyclic loading[J].Chinese Journal of Geophysics,2004,47(4):672-679.
[6]陈运平,刘干斌,姚海林.岩石滞后非线性弹性模拟的研究[J].岩石力学与工程学报,2006,27(3):341-347.CHEN Yun-ping,LIU Gan-bin,YAO Hai-lin.Study on simulation for hysteretic nonlinear elasticity of rock[J].Chinese Journal of Rock Mechanics and Engineering,2006,27(3):341-347.
[7]许江,杨秀贵,王鸿,等.周期性载荷作用下岩石滞回曲线的演化规律[J].西南交通大学学报,2005,40(6):754-758.XU Jiang,YANG Xiu-gui,WANG Hong,et al.Evolution law of hysteresis curve of rock under cyclic loading[J].Journal of Southwest Jiaotong University,2005,40(6):754-758.
[8]王鸿,许江,杨秀贵.循环载荷条件下岩石塑性滞回环的演化规律[J].重庆大学学报(自然科学版),2006,29(4):80-82.WANG Hong,XU Jiang,YANG Xiu-gui.Evolvement of plastic-loop of fine-sandstone under the loading and unloading conditions[J].Journal of Chongqing University(Natural Science Edition),2006,29(4):80-82.
[9]王鸿,许江,李树春,等.不同水饱和度下岩石滞回曲线演化的实验研究[J].矿业研究与开发,2007,27(3):18-21.WANG Hong,XU Jiang,LI Shu-chun,et al.Experimental research on the evolution of hysteresis curve of fine-sandstone with different water saturation[J].Mining Research and Development,2007,27(3):18-21.
[10]MCCALL K R,GUYER R A.Equation of state and wave propagation in hysteretic nonlinear elastic material[J].Journal of Geophysical Research,1994,99(12):23897-25887.
[11]TUTUNCU A N,PODIO A L,SHARNA M M.Nonlinear visco-elastic behavior of sedimentary rocks,partⅠ:effect of frequency and strain amplitude[J].Geophysics,1998,63(1):184-190.
[12]TUTUNCU A N,PODIO A L,SHARNA M M.Nonlinear visco-elastic behavior of sedimentary rocks,part II:hysteresis effect and influence of type of fluid on elastic module[J].Geophysics,1998,63(1):195-203.
[13]李顺群.关于粘弹模型中滞回圈的讨论[J].辽宁工学院学报(自然科学版),2004,24(5):58-60.LI Shun-qun.Discussion on delayed curve about soil viscoelasticity model[J].Journal of Liaoning Institute of Technology,2004,24(5):58-60.
[14]葛修润,卢应发.循环载荷作用下岩石疲劳破坏和不可逆变形问题的探讨[J].岩土工程学报,1992,14(3):56-60.GE Xiu-run,LU Ying-fa.To investigate the rock fatigue failure and irreversible deformation under cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,1992,14(3):56-60.
[15]葛修润,任建喜,蒲毅彬,等.岩石疲劳损伤扩展规律CT细观分析初探[J].岩土工程学报,2001,23(2):191-195.GE Xiu-run,REN Jian-xi,PU Yi-bin,et al.Primary study of CT real-time testing of fatigue meso-damage propagation law of rock[J].Chinese Journal of Geotechnical Engineering,2001,23(2):191-195.
[16]葛修润,蒋宇,卢允德,等.周期载荷作用下岩石疲劳应变特性试验研究[J].岩石力学与工程学报,2003,22(10):1581-1585.GE Xiu-run,JIANG Yu,LU Yun-de,et al.Testing study on fatigue deformationg law of rock under cyclic loading[J].Chinese Journal of Geotechnical Engineering,2003,22(10):1581-1585.
[17]刘杰,李建林,唐亮,等.三角波卸载段作用下钙质砂岩毫秒量级变形速率预测模型研究[J].岩土力学,2014,35(增刊1):63-70.LIU Jie,LI Jian-lin,TANG Liang.Study of prediction model for milliseconds deformation rate in triangular wave unloading segment of calcareous sandstone[J].Rock and Soil Mechanics,2014,35(Supp.1):63-70.
[18]巩思园,窦林名,何江,等.深部冲击倾向煤岩循环加卸载的纵波波速与应力关系试验研究[J].岩土力学,2012,35(1):41-47.GONG Si-yuan,DOU Lin-ming,HE Jiang.Study of correlation between stress and longitudinal wave velocity for deep burst tendency coal and rock samples in uniaxial cyclic loading and unloading experiment[J].Rock and Soil Mechanics,2014,35(1):41-47.
[19]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报,2007,26(增刊1):1581-1585.YANG Yong-jie,SONG Yang,CHU Jun.Experimental study on characteristics of strength and deformation of coal under cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp.1):1581-1585.
[20]郭印同,赵克烈,孙冠华,等.周期荷载下盐岩的疲劳变形及损伤特性研究[J].岩土力学,2011,32(5):1353-1359.GUO Yin-tong,ZHAO Ke-lie,SUN Guan-hua.Experimental study of fatigue deformation and damage characteristics of salt rock under cyclic loading[J].Rock and Soil Mechanics,2011,32(5):1353–1359.
[21]马林建,刘新宇,许宏发,等.循环荷载作用下盐岩三轴变形和强度特性试验研究[J].岩石力学与工程学报,2013,32(4):849-856.MA Lin-jian,LIU Xin-yu,XU Hong-fa,et al.Deformation and strength properties of rock salt subjected to triaxial compression with cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(4):849-856.
[22]周小平,季璇,钱七虎.强地震荷载作用下临水挡土墙的拟动力法稳定性分析[J].岩石力学与工程学报,2012,31(10):2071-2081.ZHOU Xiao-ping,JI Xuan,QIAN Qi-hu.Stability analysis of water front retaining wall subjected to seismic loads using pseudo-dynamic method[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(10):2071-2081.
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