不同概率水准下动剪切模量比与阻尼比上、下限的计算
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摘要
采用试验方法,研究不同概率水平下常规土类动剪切模量比和阻尼比非线性曲线上限和下限变化范围,提出典型剪应变下黏性土和无黏性土动剪切模量比和阻尼比落在不同区间概率大小的计算方法和计算公式。计算方法形成的基本思路为:将试验资料整理成标准结果,利用频数分布图、概率纸法检验图和SAS软件得到典型剪应变下2个参数变异性分布形态,根据不同分布形态采用2种不同方法计算典型剪应变下2个动力参数上、下限概率参考值。分析结果表明:不同剪应变下动剪切模量比和阻尼比上、下限值随概率水准的变化具有规律性,不同剪应变下2个动力参数的上限和下限与其出现的概率之间均满足Boltzmann方程,但方程中参数随剪应变和土类而变化;所有概率水平下不同剪应变的动剪切模量比上、下限区间大小均有明显差异,剪应变在10-4～10-3范围内的动剪切模量比上、下限范围最大;同一概率水平下阻尼比上、下限区间大小随剪应变增大而明显增大。提出的2个动力参数的概率计算公式为土动力学和地震工程可靠性理论研究奠定一定基础,也为工程结构的抗震设计和地震安全的风险评估提供直接的技术支持。
By using experimental results,the upper and lower limits of the nonlinear curves of the dynamic shear modulus ratio and damping ratio for conventional soils under different probabilities are investigated. The method and formula for calculating the probabilistic zones of the two dynamic parameters for the cohesive and cohesionless soils under the typical shear strains are presented. The approach is that the experimental results are ordered by the standard way,and the distribution form of variability of two dynamic parameters is obtained by the frequency distribution diagram,the tests of normality diagram and the SAS software. According to different distribution forms,the probabilities of the upper and lower limits of the two parameters under typical shear strains are calculated. The results indicate that the relation between the upper and lower limits of the two dynamic parameters and their probabilities can be described by the Boltzmann equation,in which the parameters depend on the soil type and the shear strain. For all probabilities,the ranges of the shear modulus ratio for different shear stains are obviously different while the most ones appear at 10-4–10-3 of the shear strain. For the same probability,the range of the damping ratio increases with increasing shear strain. The proposed formula for calculating the probabilistic zones of the two dynamic parameters lays a foundation for the reliability theory in soil dynamics and earthquake engineering to some extent;and it also can directly supply the technical support to the risk evaluation of a seismic design and seismic safety of engineering structures.
By using experimental results,the upper and lower limits of the nonlinear curves of the dynamic shear modulus ratio and damping ratio for conventional soils under different probabilities are investigated. The method and formula for calculating the probabilistic zones of the two dynamic parameters for the cohesive and cohesionless soils under the typical shear strains are presented. The approach is that the experimental results are ordered by the standard way,and the distribution form of variability of two dynamic parameters is obtained by the frequency distribution diagram,the tests of normality diagram and the SAS software. According to different distribution forms,the probabilities of the upper and lower limits of the two parameters under typical shear strains are calculated. The results indicate that the relation between the upper and lower limits of the two dynamic parameters and their probabilities can be described by the Boltzmann equation,in which the parameters depend on the soil type and the shear strain. For all probabilities,the ranges of the shear modulus ratio for different shear stains are obviously different while the most ones appear at 10-4–10-3 of the shear strain. For the same probability,the range of the damping ratio increases with increasing shear strain. The proposed formula for calculating the probabilistic zones of the two dynamic parameters lays a foundation for the reliability theory in soil dynamics and earthquake engineering to some extent;and it also can directly supply the technical support to the risk evaluation of a seismic design and seismic safety of engineering structures.
引文
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[10]刘江平,罗银河,张英德.黏土动、静弹性模量相关性试验研究[J].岩石力学与工程学报,2007,26(2):417–432.(LIU Jiangping,LUO Yinhe,ZHANG Yingde.Test research on relativity between dynamic and static elastic modulus of clay[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(2):417–432.(in Chinese))
[11]刘建锋,谢和平,徐进,等.循环荷载作用下岩石阻尼特性的试验研究[J].岩石力学与工程学报,2008,27(4):712–717.(LIU Jianfeng,XIE Heping,XU Jin,et al.Experimental study on damping characteristics of rock under cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(4):712–717.(in Chinese))
[12]聂影,肖启华,梁义聪.重塑黏土和原状粉质黏土的动力特性试验研究[J].重庆建筑大学学报,2008,30(6):66–71.(NIE Ying,XIAO Qihua,LIANG Yicong.Dynamic properties of saturated clay and undisturbed silty clay[J].Journal of Chongqing Jianzhu University,2008,30(6):66–71.(in Chinese))
[13]蒋寿田,王幸幸.郑州地区地基原状土动模量和阻尼比[C]//第三届全国土动力学学术会议.上海:同济大学出版社,1990:151–155.(JIANG Shoutian,WANG Xingxing.Dynamic shear modulus and damping ratio of undisturbed soil in Zhengzhou area[C]//Proceedings of the3rd National Conference on Soil Dynamics.Shanghai:Tongji University Press,1990:151–155.(in Chinese))
[14]祝龙根,杜坚.不同类型共振柱仪对比试验[J].水电自动化与大坝监测,1990,(3):26–32.(ZHU Longgen,DU Jian.Comparison tests with different types of resonant column devices[J].Hydropower Automation and Dam Monitoring,1990,(3):26–32.(in Chinese))
[15]袁晓铭,孙静.非均等固结下砂土最大动剪切模量的增长模式及Hardin公式的修正[J].岩土工程学报,2005,27(3):264–269.(YUAN Xiaoming,SUN Jing.Model of maximum dynamic shear modulus of sand under anisotropic consolidation and revision of Hardin′s formula[J].Chinese Journal of Geotechnical Engineering,2005,27(3):264–269.(in Chinese))
[2]李小勇,谢康和,虞颜.太原粉质黏土强度指标概率特征[J].浙江大学学报(工程科学版),2001,35(5):492–496.(LI Xiaoyong,XIE Kanghe,YU Yan.Probabilistic characteristics of strength indexes for Taiyuan silty clay[J].Journal of Zhejiang University(Engineering Science),2001,35(5):492–496.(in Chinese))
[3]吴长富,朱向荣,刘雪梅.杭州地区典型土层抗剪强度指标的变异性研究[J].岩土工程学报,2005,27(1):94–99.(WU Changfu,ZHU Xiangrong,LIU Xuemei.Studies on variability of shear strength indexes for several typical stratums in Hangzhou area[J].Chinese Journal of Geotechnical Engineering,2005,27(1):94–99.(in Chinese))
[4]倪万魁,韩启龙.黄土土性参数的统计分析[J].工程地质学报,2001,9(1):62–67.(NI Wankui,HAN Qilong.Statistical analysis of physical and mechanical indexes of the typical loess[J].Journal of Engineering Geology.2001,9(1):62–67.(in Chinese))
[5]蒋建平,罗国煜.长江下游水下粉质黏土工程特性研究[J].岩石力学与工程学报,2007,26(增1):3215–3222.(JIANG Jianping,LUO Guoyu.Study on engineering characteristics of silty clay under water in lower reach of Yangtze River[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp.1):3215–3222.(in Chinese))
[6]王绍博,丁海平.土动力学参数对土层动力反应的影响[J].地震工程与工程振动,2001,21(1):105–108.(WANG Shaobo,DING Haiping.Effect of soil dynamic parameters on seismic response of soil layers[J].Earthquake Engineering and Engineering Vibration,2001,21(1):105–108.(in Chinese))
[7]陈国兴,刘雪珠,王炳辉.土动力参数变异性对深软场地地表地震动参数的影响[J].防灾减灾工程学报,2007,27(1):1–10.(CHEN Guoxing,LIU Xuezhu,WANG Binghui.Effect of variability of soil dynamic parameters on ground motion parameters for deep soft sites[J].Journal of Disaster Prevention and Mitigation Engineering.2007,27(1):1–10.(in Chinese))
[8]兰青龙,贺明华,安卫平.太原地区场地土动力性能的统计分析[J].山西地震,1997,(3):6–11.(LAN Qinglong,HE Minghua,AN Weiping.Several features of earthquake swarm in Taiyuan basin[J].Earthquake Research in Shan Xi,1997,(3):6–11.(In Chinese))
[9]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 Xiaoming.A state of art of research on dynamic modulus and damping ratio of soils[J].World Earthquake Engineering,2003,19(1):88–95.(in Chinese))
[10]刘江平,罗银河,张英德.黏土动、静弹性模量相关性试验研究[J].岩石力学与工程学报,2007,26(2):417–432.(LIU Jiangping,LUO Yinhe,ZHANG Yingde.Test research on relativity between dynamic and static elastic modulus of clay[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(2):417–432.(in Chinese))
[11]刘建锋,谢和平,徐进,等.循环荷载作用下岩石阻尼特性的试验研究[J].岩石力学与工程学报,2008,27(4):712–717.(LIU Jianfeng,XIE Heping,XU Jin,et al.Experimental study on damping characteristics of rock under cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(4):712–717.(in Chinese))
[12]聂影,肖启华,梁义聪.重塑黏土和原状粉质黏土的动力特性试验研究[J].重庆建筑大学学报,2008,30(6):66–71.(NIE Ying,XIAO Qihua,LIANG Yicong.Dynamic properties of saturated clay and undisturbed silty clay[J].Journal of Chongqing Jianzhu University,2008,30(6):66–71.(in Chinese))
[13]蒋寿田,王幸幸.郑州地区地基原状土动模量和阻尼比[C]//第三届全国土动力学学术会议.上海:同济大学出版社,1990:151–155.(JIANG Shoutian,WANG Xingxing.Dynamic shear modulus and damping ratio of undisturbed soil in Zhengzhou area[C]//Proceedings of the3rd National Conference on Soil Dynamics.Shanghai:Tongji University Press,1990:151–155.(in Chinese))
[14]祝龙根,杜坚.不同类型共振柱仪对比试验[J].水电自动化与大坝监测,1990,(3):26–32.(ZHU Longgen,DU Jian.Comparison tests with different types of resonant column devices[J].Hydropower Automation and Dam Monitoring,1990,(3):26–32.(in Chinese))
[15]袁晓铭,孙静.非均等固结下砂土最大动剪切模量的增长模式及Hardin公式的修正[J].岩土工程学报,2005,27(3):264–269.(YUAN Xiaoming,SUN Jing.Model of maximum dynamic shear modulus of sand under anisotropic consolidation and revision of Hardin′s formula[J].Chinese Journal of Geotechnical Engineering,2005,27(3):264–269.(in Chinese))
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