Abstract:Dynamic shear modulus and damping ratio are significant dynamic indicators of soil dynamics and geotechnical earthquake engineering,and their constitutive relationships are mostly established and recognized based on unit tests. Compared with the unit tests,the centrifuge model tests have more realistic stress boundaries,loading schemes and drainage conditions,but there are rarely studies on dynamic modulus and damping ratio. The form differences of the shear stress- strain hysteresis loop of dry sand and saturated sand are revealed,and the characteristics and laws of dynamic modulus and damping ratio with burial depth,shear strain and vibration order are compared based on the centrifuge model comparison tests. The results show that the hysteresis cycle of dry sand is oval,but the hysteresis cycle of saturated sand is irregular and non-smooth dumbbell shape. The shear strain of saturated sand increases rapidly after liquefaction,and the maximum shear strains of dry sand and saturated sand under 0.2 g load are 0.3% and 1%,respectively. The dynamic shear moduli of dry sand and saturated sand obey the Hardin hyperbola model well,which decrease with the increase of shear strain,increase with the increase of burial depth,and increase with the increase of vibration times,which causes the soil vibration density. The maximum dynamic shear modulus and their changes with depth and vibration order are basically the same,and are less affected by saturation. The reference strains of dry sand and saturated sand are 0.1%–0.35% and 0.05%–0.18%,respectively,and the reference strains of dry sand under different depths and loads are about twice that of the saturated sand,and they increase with the increase of burial depth and density. The damping ratio of dry sand has a good law with the variation of shear strain and burial depth,and the discreteness is small. However,the damping ratio of saturated sand is not obvious,and the discreteness is large,which is related to the change of sensor position,the test accuracy and the reliability of the analysis method caused by the failure of the soil strength after liquefaction. The research results provide technical support and guidance for understanding the response characteristics of the dynamic modulus and damping ratio of the centrifuge model test and for comparing the reliability of the dynamic modulus and damping ratio in the unit test.
王体强1,2,王永志1,2,梁小丛3,王德咏3,陈卓识1,2. 超重力模型试验干–饱和砂动剪切模量阻尼比特性研究[J]. 岩石力学与工程学报, 2023, 42(6): 1546-1559.
WANG Tiqiang1,2,WANG Yongzhi1,2,LIANG Xiaocong3,WANG Deyong3,CHEN Zhuoshi1,2. Study on the characteristics of shear modulus and damping ratio between dry sand and saturated sand in centrifuge model test. , 2023, 42(6): 1546-1559.
[1] 黄文熙. 土的弹塑性应力–应变模型理论[J]. 岩土力学,1979,1(1):1–20.(HUANG Wenxi. Theory of elastoplastic stress-strain model for soil[J]. Rock and Soil Mechanics,1979,1(1):1–20.(in Chinese))
[2] 黄茂松,边学成,陈育民,等. 土动力学与岩土地震工程[J]. 土木工程学报,2020,53(8):64–86.(HUANG Maosong,BIAN Xuecheng,CHEN Yumin,et al. Soil dynamics and geotechnical earthquake engineering[J]. China Civil Engineering Journal,2020,53(8):64–86.(in Chinese))
[3] 孙 静,袁晓铭,陶夏新. 共振柱试验机试验误差分析[J]. 哈尔滨工业大学学报,2007,39(4):510–513.(SUN Jing,YUAN Xiaoming,TAO Xiaxin. Error analysis of resonant column device tests[J]. Journal of Harbin Institute of Technology,2007,39(4):510–513.(in Chinese))
[4] 李晓飞,孙 锐,袁晓铭. 砂土动剪切模量比和阻尼比共振柱试验误差研究[J]. 哈尔滨工业大学学报,2016,48(11):155–161.(LI Xiaofei,SUN Rui,YUAN Xiaoming. Resonant column test error analysis for dynamic shear modulus ratio and damping ratio of sand[J]. Journal of Harbin Institute of Technology,2016,48(11):155–161.(in Chinese))
[5] ZEGHAL M,ELGAMAL A W,TANG H T,et al. Lotung downhole array. II:Evaluation of soil nonlinear properties[J]. Journal of Geotechnical Engineering,1995,121(4):363–378.
[6] ELGAMAL A W,ZEGHAL M,PARRA E. Liquefaction of reclaimed island in Kobe,Japan[J]. Journal of Geotechnical Engineering,1996,122(1):39–49.
[7] BRENNAN A J,THUSYANTHAN N I,MADABHUSHI S P G. Evaluation of shear modulus and damping in dynamic centrifuge tests[J]. Journal of Geotechnical and Geoenvironmental Engineering,2005,131(12):1 488–1 497.
[8] KAMAI R,BOULANGER R. Characterizing localization processes during liquefaction using inverse analysis of instrumentation arrays[M]. California:CRC Press,2009:219–238.
[9] 周燕国,梁 甜,李永刚,等. 含黏粒砂土场地液化离心机振动台试验研究[J]. 岩土工程学报,2012,35(9):1 650–1 658.(ZHOU Yanguo,LIANG Tian,LI Yonggang,et al. Dynamic centrifuge tests on liquefaction of clayey sand ground[J]. Chinese Journal of Geotechnical Engineering,2012,35(9):1 650–1 658.(in Chinese))
[10] 陈国兴,王炳辉,孙 田. 饱和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 Guoxing,WANG Binghui,SUN Tian. Dynamic shear modulus of saturated Nanjing fine sand in large scale shaking table tests[J]. Chinese Journal of Geotechnical Engineering,2012,34(4):582–590. (in Chinese))
[11] KUTTER B L,CAREY T J,HASHIMOTO T,et al. LEAP-GWU-2015 experiment specifications,results,and comparisons[J]. Soil Dynamic and Earthquake Engineering,2018,113(10):616–628.
[12] CONTI R,VIGGIANI G M B. Evaluation of soil dynamic properties in centrifuge tests[J]. Journal of Geotechnical and Geoenvironmental Engineering,2012,138(7):850–859.
[13] AFACAN K B,BRANDENBERG S J,STEWART J P. Centrifuge modeling studies of site response in soft clay over wide strain range[J]. Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):04013003.
[14] 王体强,王永志,袁晓铭,等. 自适应鲁棒加速度积分新方法与可靠度分析[J]. 岩石力学与工程学报,2021,40(增1):2 724–2 737. (WANG Tiqiang,WANG Yongzhi,YUAN Xiaoming,et al. A new type of adaptive robust acceleration integration approach and reliability analysis[J]. Chinese Journal of Rock Mechanics and Engineering,2021,40(Supp.1):2 724–2 737.(in Chinese))
[15] 王体强,王永志,陈 苏,等. 基于加速度阵列反演循环剪应力–剪应变的积分位移方法影响[J]. 岩土工程学报,2022,44(1):115–124 +202–203.(WANG Tiqiang,WANG Yongzhi,CHEN Su,et al. Influence of double-integral-displacement methods on inverse analysis of accelerograph arrays for cyclic shear stress-strain response[J]. Chinese Journal of Geotechnical Engineering,2022,44(1):115–124+202–203.(in Chinese))
[16] 王永志,王体强,袁晓铭,等. 动力离心试验反演分析砂土模量阻尼比特征与可靠性[J]. 岩石力学与工程学报,2022,41(8):1 717–1 727.(WANG Yongzhi,WANG Tiqiang,YUAN Xiaoming,et al. Characteristics and reliability of sand shear modulus and damping ratio evaluated by inverse analysis in dynamic centrifuge tests[J]. Chinese Journal of Rock Mechanics and Engineering,2022,41(8):1 717–1 727.(in Chinese))
[17] 王永志,WILSON D W,KHOSRAVI M,等. 动力离心模型试验循环剪应力–剪应变反演方法对比[J]. 岩土工程学报,2016,38(2):271–277.(WANG Yongzhi,WILSON D W,KHOSRAVI M,et al. Evaluation of cyclic shear stress-strain using inverse analysis techniques in dynamic centrifuge tests[J]. Chinese Journal of Geotechnical Engineering,2016,38(2):271–277.(in Chinese))
[18] CHEN G X,LIANG K,ZHAO K,et al. Shear modulus and damping ratio of saturated coral sand under generalised cyclic loadings[J]. Géotechnique,2023.(to be pressed)
[19] HARDIN B O,DRNEVICH V P. Shear modulus and damping in soils:design equations and curves[J]. Journal of the Soil Mechanics and Foundations Division,1972,98(7):667–692.
[20] JAMIOLKOWSKI M,LANCELLOTTA R,PRETI D. Remarks on the stiffness at small strains of six Italian clays[J]. Prefailure Deformation of Geomaterials,1995,2(1):817–836.
[21] SEED H B,WONG R T,IDRISS I M,et al. Moduli and damping factors for dynamic analyses of cohesionless soils[J]. Journal of Geotechnical Engineering,1986,112(11):1 016–1 032.
[22] OTSUBO M,O'SULLIVAN C,SIM W W,et al. Quantitative assessment of the influence of surface roughness on soil stiffness[J]. Géotechnique,2015,65(8):694–700.
[23] 梁 珂,陈国兴,杭天柱,等. 砂类土最大动剪切模量的新预测模型[J]. 岩土力学,2020,41(6):1 963–1 970.(LIANG Ke,CHEN Guoxing,HANG Tianzhu,et al. A new prediction model of small-strain shear modulus of sandy soils[J]. Rock and Soil Mechanics,2020,41(6):1 963–1 970.(in Chinese))
[24] WICHTMANN T,TRIANTAFYLLIDIS T. On the influence of the grain size distribution curve of quartz sand on the small strain shear modulus Gmax[J]. Journal of Geotechnical and Geoenvironmental Engineering,2009,135(10):1 404–1 418.
[25] 柏立懂. 荷载历史对砂土最大剪切模量影响的共振柱试验研究[J]. 岩石力学与工程学报,2011,30(11):2 366–2 374.(BAI Lidong. Effects of loading history on maximum shear modulus of sand by resonant column tests[J]. Chinese Journal of Rock Mechanics and Engineering,2011,30(11):2 366–2 374.(in Chinese))
[26] 吴 杨,崔 杰,李 晨,等. 细粒含量对岛礁吹填珊瑚砂最大动剪切模量影响的试验研究[J]. 岩石力学与工程学报,2022,41(1):205–216.(WU Yang,CUI Jie,LI Chen,et al. Experimental study on the effect of fines on the maximum dynamic shear modulus of coral sand in a hydraulic fill island-reef[J]. Chinese Journal of Rock Mechanics and Engineering,2022,41(1):205–216.(in Chinese))
[27] DONG Y,LU N. Dependencies of shear wave velocity and shear modulus of soil on saturation[J]. Journal of Engineering Mechanics,2016,142(11):04016083.
[28] FIORAVANTE V,GIRETTI D,JAMIOLKOWSKI M. Small strain stiffness of carbonate Kenya Sand[J]. Engineering Geology,2013,161(4):65–80.
[29] PAYAN M,KHOSHGHALB A,SENETAKIS K,et al. Effect of particle shape and validity of Gmax models for sand:A critical review and a new expression[J]. Computers and Geotechnics,2016,72(2):28–41.
[30] CASCANTE G,SANTAMARINA C,YASSIR N. Flexural excitation in a standard torsional-resonant column device[J]. Canadian Geotechnical Journal,1998,35(3):478–490.