基于相关函数理论的动模量和阻尼比计算新方法
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摘要
基于相关函数理论,提出一种新的计算动三轴试验动模量和阻尼比的方法。假设土体为黏弹性体,采用自相关函数分析应力、应变波形的平均幅值,进而计算动模量;采用互相关函数分析应变滞后于应力时程波形的相位差,进而计算阻尼比。利用饱和珊瑚砂、南京细砂和原状粉质黏土的不排水应变控制分级循环加载试验数据,分析结果表明:动模量和阻尼比计算的相关函数法对不同土样具有普适性;应变幅值小于1×10~(-4)时,相关函数法计算动模量及阻尼比的精度明显优于传统的滞回圈法;应变幅值大于1×10~(-3)时,土体呈现强非线性特性,应力-应变滞回圈不对称,相关函数法计算的阻尼更为可靠。
Based on the theory of correlation function, a new method for calculating the dynamic modulus and damping ratio of dynamic triaxial test is proposed. Based on viscoelastic constitutive model, the amplitudes of strain and stress can be captured by analyzing the autocorrelative function of strain and stress variations with time, respectively. Thus, the dynamic modulus can be calculated. The damping ratio is determined through the characterization of the phase lag between the strain and stress time-histories which can be captured by the cross-correlation function. A series of undrained multistage strain-controlled cyclic triaxial test was conducted on saturated coral sand, Nanjing fine sand, and a type of undisturbed silty clay. The dynamic modulus and damping ratios were calculated from the experimental results using both the correlation function(CF) method and the conventional hysteresis loop(HL) method. The results show that the CF method is applicable for the calculation of dynamic modulus and damping ratio of different types of soils. The results show that the precision of the CF method for the modulus and damping ratio is significantly higher than that of the HL method within the strain amplitude of 1×10~(-4). When the strain amplitude is greater than 1×10~(-3), because of the strong nonlinearity of soil as well as the asymmetry of the stress-strain hysteresis loop, the damping ratio of soil calculated by the CF method is more reliable.
Based on the theory of correlation function, a new method for calculating the dynamic modulus and damping ratio of dynamic triaxial test is proposed. Based on viscoelastic constitutive model, the amplitudes of strain and stress can be captured by analyzing the autocorrelative function of strain and stress variations with time, respectively. Thus, the dynamic modulus can be calculated. The damping ratio is determined through the characterization of the phase lag between the strain and stress time-histories which can be captured by the cross-correlation function. A series of undrained multistage strain-controlled cyclic triaxial test was conducted on saturated coral sand, Nanjing fine sand, and a type of undisturbed silty clay. The dynamic modulus and damping ratios were calculated from the experimental results using both the correlation function(CF) method and the conventional hysteresis loop(HL) method. The results show that the CF method is applicable for the calculation of dynamic modulus and damping ratio of different types of soils. The results show that the precision of the CF method for the modulus and damping ratio is significantly higher than that of the HL method within the strain amplitude of 1×10~(-4). When the strain amplitude is greater than 1×10~(-3), because of the strong nonlinearity of soil as well as the asymmetry of the stress-strain hysteresis loop, the damping ratio of soil calculated by the CF method is more reliable.
引文
[1]陈国兴.岩土地震工程学[M].北京:科学出版社,2007.CHEN Guo-xing.Geotechnical earthquake engineering[M].Beijing:Science Press,2007.
[2]ISHIHARA K.Soil behaviour in earthquake geotechnics[M].[S.l.]:Clarendon Press,1996.
[3]何昌荣.动模量和阻尼的动三轴试验研究[J].岩土工程学报,1997,19(2):39-48.HE Chang-rong.Dynamic triaxial test on modulus and damping[J].Chinese Journal of Geotechnical Engineering,1997,19(2):39-48.
[4]孙静,袁晓铭.土的动模量和阻尼比研究述评[J].世界地震工程,2003,19(1):88-95.SUN Jing,YUAN Xiao-ming.A state-of-art of research on dynamic modulus and damping ratio of soils[J].World Earthquake Engineering,2003,19(1):88-95.
[5]CHEN Guo-xing,ZHOU Zheng-long,PAN Hua,et al.The influence of undrained cyclic loading patterns and consolidation states on the deformation features of saturated fine sand over a wide strain range[J].Engineering Geology,2016,204:77-93.
[6]SEED H B,WONG R T,IDRISS I M,et al.Moduli and damping factors for dynamic analyses of cohesionless soil[J].Journal of Geotechnical Engineering,1986,112(11):1016-1032.
[7]袁晓铭,孙锐,孙静,等.常规土类动剪切模量比和阻尼比试验研究[J].地震工程与工程振动,2000,20(4):133-139.YUAN Xiao-ming,SUN Rui,SUN Jing,et al.Laboratory experimental study on dynamic shear modulus ratio and damping ratio of soils[J].Earthquake Engineering and Engineering Dynamics,2000,20(4):133-139.
[8]汪明元,单治钢,王亚军,等.应变控制下舟山岱山海相软土动弹性模量及阻尼比试验研究[J].岩石力学与工程学报,2014,33(7):1503-1512.WANG Ming-yuan,SHAN Zhi-gang,WANG Ya-jun,et al.Dynamic elastic moduli and damping ratios of marine sediments at Zhoushan Daishan based on dynamic triaxial tests under strain control[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(7):1503-1512.
[9]魏茂杰,林木春.一种确定土的等效阻尼比的新方法[J].水利水电技术,1993(8):50-53.WEI Mao-jie,LIN Mu-chun.A new method to determine the damping ratio of soils[J].Water Resources and Hydropower Engineering,1993(8):50-53.
[10]陈伟,孔令伟,朱建群.一种土的阻尼比近似计算方法[J].岩土力学,2007,28(增刊1):789-791.CHEN Wei,KONG Ling-wei,ZHU Jian-qun.A simple method to approximately determine the damping ratio of soils[J].Rock and Soil Mechanics,2007,28(Suppl.1):789-791.
[11]FONSECA AVD,FERREIRA C,FAHEY M A.Framework interpreting bender element tests,combining time-domain and frequency-domain methods[J].Geotechnical Testing Journal,2009,32(2):59-63.
[12]侯兴民,薄景山,杨学山,等.互相关函数在单孔法剪切波速测量中的应用[J].地震工程与工程振动,2004,24(2):59-63.HOU Xing-min,BO Jing-shan,YANG Xue-shan,et al.Applications of correlation function in shear-velocity measurement of single-hole method[J].Earthquake Engineering and Engineering Vibration,2004,24(2):59-63.
[13]葛新成,罗大成,曹勇.相关函数在数字信号处理中的应用[J].电光与控制,2006,13(6):78-80.GE Xin-cheng,LUO Da-cheng,CAO Yong.Application of correlation function in digital signal processing[J].Electronics Optics and Control,2006,13(6):78-80.
[14]KUMAR J,MADHUSUDHAN B N.A note on the measurement of travel times using bender and extender elements[J].Soil Dynamics and Earthquake Engineering,2010,30(7):630-634.
[15]王炳辉,陈国兴,胡庆兴.南京细砂动剪切模量和阻尼比的试验研究[J].世界地震工程,2010,26(3):7-15.WANG Bing-hui,CHEN Guo-xing,HU Qing-xing.Experiment of dynamic shear modulus and damping of Nanjing fine sand[J].World Earthquake Engineering,2010,26(3):7-15.
[16]左熹,陈国兴,孙田.考虑孔压效应的饱和细砂剪切模量衰减规律研究[J].世界地震工程,2017,33(1):194-201.ZUO Xi,CHEN Guo-xing,SUN Tian.Research on shear modulus attenuation law of saturated fine sand considering pore pressure effect[J].World Earthquake Engineering,2017,33(1):194-201.
[17]陈国兴,刘雪珠.南京及邻近地区新近沉积土的动剪切模量和阻尼比的试验研究[J].岩石力学与工程学报,2004,24(8):1403-1410.CHEN Guo-xing,LIU Xue-zhu.Testing study on ratio of dynamic shear moduli and ratio of damping for recently deposited soils in Nanjing and its neighboring areas[J].Chinese Journal of Rock Mechanics and Engineering,2004,24(8):1403-1410.
[18]陈国兴,王炳辉,孙田.南京细砂动剪切模量特性的大型振动台试验研究[J].岩土工程学报,2012,34(4):582-590.CHEN Guo-xing,WANG Bing-hui,SUN Tian.Dynamic shear modulus of saturated Nanjing fine sand in large scaleshaking table tests[J].Chinese Journal of Geotechnical Engineering,2012,34(4):582-590.
[19]KUMAR S S,KRISHNA A M,DEY A.Evaluation of dynamic properties of sandy soil at high cyclic strains[J].Soil Dynamics and Earthquake Engineering,2017,99:157-167.
[2]ISHIHARA K.Soil behaviour in earthquake geotechnics[M].[S.l.]:Clarendon Press,1996.
[3]何昌荣.动模量和阻尼的动三轴试验研究[J].岩土工程学报,1997,19(2):39-48.HE Chang-rong.Dynamic triaxial test on modulus and damping[J].Chinese Journal of Geotechnical Engineering,1997,19(2):39-48.
[4]孙静,袁晓铭.土的动模量和阻尼比研究述评[J].世界地震工程,2003,19(1):88-95.SUN Jing,YUAN Xiao-ming.A state-of-art of research on dynamic modulus and damping ratio of soils[J].World Earthquake Engineering,2003,19(1):88-95.
[5]CHEN Guo-xing,ZHOU Zheng-long,PAN Hua,et al.The influence of undrained cyclic loading patterns and consolidation states on the deformation features of saturated fine sand over a wide strain range[J].Engineering Geology,2016,204:77-93.
[6]SEED H B,WONG R T,IDRISS I M,et al.Moduli and damping factors for dynamic analyses of cohesionless soil[J].Journal of Geotechnical Engineering,1986,112(11):1016-1032.
[7]袁晓铭,孙锐,孙静,等.常规土类动剪切模量比和阻尼比试验研究[J].地震工程与工程振动,2000,20(4):133-139.YUAN Xiao-ming,SUN Rui,SUN Jing,et al.Laboratory experimental study on dynamic shear modulus ratio and damping ratio of soils[J].Earthquake Engineering and Engineering Dynamics,2000,20(4):133-139.
[8]汪明元,单治钢,王亚军,等.应变控制下舟山岱山海相软土动弹性模量及阻尼比试验研究[J].岩石力学与工程学报,2014,33(7):1503-1512.WANG Ming-yuan,SHAN Zhi-gang,WANG Ya-jun,et al.Dynamic elastic moduli and damping ratios of marine sediments at Zhoushan Daishan based on dynamic triaxial tests under strain control[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(7):1503-1512.
[9]魏茂杰,林木春.一种确定土的等效阻尼比的新方法[J].水利水电技术,1993(8):50-53.WEI Mao-jie,LIN Mu-chun.A new method to determine the damping ratio of soils[J].Water Resources and Hydropower Engineering,1993(8):50-53.
[10]陈伟,孔令伟,朱建群.一种土的阻尼比近似计算方法[J].岩土力学,2007,28(增刊1):789-791.CHEN Wei,KONG Ling-wei,ZHU Jian-qun.A simple method to approximately determine the damping ratio of soils[J].Rock and Soil Mechanics,2007,28(Suppl.1):789-791.
[11]FONSECA AVD,FERREIRA C,FAHEY M A.Framework interpreting bender element tests,combining time-domain and frequency-domain methods[J].Geotechnical Testing Journal,2009,32(2):59-63.
[12]侯兴民,薄景山,杨学山,等.互相关函数在单孔法剪切波速测量中的应用[J].地震工程与工程振动,2004,24(2):59-63.HOU Xing-min,BO Jing-shan,YANG Xue-shan,et al.Applications of correlation function in shear-velocity measurement of single-hole method[J].Earthquake Engineering and Engineering Vibration,2004,24(2):59-63.
[13]葛新成,罗大成,曹勇.相关函数在数字信号处理中的应用[J].电光与控制,2006,13(6):78-80.GE Xin-cheng,LUO Da-cheng,CAO Yong.Application of correlation function in digital signal processing[J].Electronics Optics and Control,2006,13(6):78-80.
[14]KUMAR J,MADHUSUDHAN B N.A note on the measurement of travel times using bender and extender elements[J].Soil Dynamics and Earthquake Engineering,2010,30(7):630-634.
[15]王炳辉,陈国兴,胡庆兴.南京细砂动剪切模量和阻尼比的试验研究[J].世界地震工程,2010,26(3):7-15.WANG Bing-hui,CHEN Guo-xing,HU Qing-xing.Experiment of dynamic shear modulus and damping of Nanjing fine sand[J].World Earthquake Engineering,2010,26(3):7-15.
[16]左熹,陈国兴,孙田.考虑孔压效应的饱和细砂剪切模量衰减规律研究[J].世界地震工程,2017,33(1):194-201.ZUO Xi,CHEN Guo-xing,SUN Tian.Research on shear modulus attenuation law of saturated fine sand considering pore pressure effect[J].World Earthquake Engineering,2017,33(1):194-201.
[17]陈国兴,刘雪珠.南京及邻近地区新近沉积土的动剪切模量和阻尼比的试验研究[J].岩石力学与工程学报,2004,24(8):1403-1410.CHEN Guo-xing,LIU Xue-zhu.Testing study on ratio of dynamic shear moduli and ratio of damping for recently deposited soils in Nanjing and its neighboring areas[J].Chinese Journal of Rock Mechanics and Engineering,2004,24(8):1403-1410.
[18]陈国兴,王炳辉,孙田.南京细砂动剪切模量特性的大型振动台试验研究[J].岩土工程学报,2012,34(4):582-590.CHEN Guo-xing,WANG Bing-hui,SUN Tian.Dynamic shear modulus of saturated Nanjing fine sand in large scaleshaking table tests[J].Chinese Journal of Geotechnical Engineering,2012,34(4):582-590.
[19]KUMAR S S,KRISHNA A M,DEY A.Evaluation of dynamic properties of sandy soil at high cyclic strains[J].Soil Dynamics and Earthquake Engineering,2017,99:157-167.