条形荷载作用下梯度饱和土的动力响应分析
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摘要
根据Biot波动理论,研究了条形均布荷载作用下非均匀饱和土地基的动力响应问题。利用Fourier积分变换,通过Helmholtz矢量分解原理,建立了饱和土层在动荷载作用下的回传射线矩阵法计算列式,考虑饱和土的物理力学性质沿深度方向按幂函数连续变化,采用数值Fourier逆变换获得了饱和土地基的位移、应力和孔隙压力等物理量的数值解。分析讨论了材料非均匀性对饱和土介质动力特性的影响。结果表明,非均匀饱和土的动力行为与均匀饱和土有着明显的不同,当土体的非均匀程度越高,条形荷载中点下流体压力和应力幅值越大,而位移、流体压力以及应力等物理量在水平方向的振动频率均随着土体非均匀变化程度的增强而增大。
Based on the Biot’s theory of porous media,the dynamic response of heterogeneous saturated soil subjected to strip loading is researched.Applying the Helmholtz vector decomposition and Fourier transformation,the calculation formula of reverberation ray matrix method(RRMM) is established for two-dimensional transient response of fluid-saturated soil.Assuming that the material properties of the saturated soil have an exponential law distribution along the thickness-coordinate,by using numerical inverse Fourier transformation,the displacement,the stress and the pore pressure are obtained.The effect of heterogeneity on transient responses of graded saturated soil is demonstrated and discussed.The numerical result shows that there is a significant difference on dynamic response between heterogeneous saturated soil and homogeneous saturated soil.The amplitude of fluid pressure and stresses that right below the middle point of the strip load is increased when the soil heterogeneous degree becomes high.In addition,the vibration frequencies of displacement,fluid pressure and stress increase with the increasing of soil heterogeneous degree along the horizontal direction.
Based on the Biot’s theory of porous media,the dynamic response of heterogeneous saturated soil subjected to strip loading is researched.Applying the Helmholtz vector decomposition and Fourier transformation,the calculation formula of reverberation ray matrix method(RRMM) is established for two-dimensional transient response of fluid-saturated soil.Assuming that the material properties of the saturated soil have an exponential law distribution along the thickness-coordinate,by using numerical inverse Fourier transformation,the displacement,the stress and the pore pressure are obtained.The effect of heterogeneity on transient responses of graded saturated soil is demonstrated and discussed.The numerical result shows that there is a significant difference on dynamic response between heterogeneous saturated soil and homogeneous saturated soil.The amplitude of fluid pressure and stresses that right below the middle point of the strip load is increased when the soil heterogeneous degree becomes high.In addition,the vibration frequencies of displacement,fluid pressure and stress increase with the increasing of soil heterogeneous degree along the horizontal direction.
引文
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[2]PAK R Y S,GUZINA B B.Three-dimensional wavepropagation analysis of a smoothly heterogeneous solid[J].Journal of the Mechanics and Physics of Solids,1995,43(4):533-551.
[3]雷鸣,廖红建,黄理兴,等.应力波在功能梯度土介质中传播的特性研究[J].岩石力学与工程学报,2005,24(增刊1):4798-4804.LEI Ming,LIAO Hong-jian,HUANG Li-xing,et al.Study on characters of stress propagation in functionallygraded soil[J].Chinese Journal of Rock Mechanics andEngineering,2005,24(Supp.1):4798-4804.
[4]秦小军,陈少林,曾心传.二维非均匀饱和上体的地震反应分析[J].地震工程与工程振动,1999,19(1):7-14.QIN Xiao-jun,CHEN Shao-lin,ZENG Xin-chuan.Analysis of nonhomogeneous fluid-saturated soil in twodimensions under earthquake load[J].Earthquake Engi-neering and Engineering Vibration,1999,19(1):7-14.
[5]KE Liao-liang,WANG Yue-sheng,ZHENG Zi-mao.Propagation of love waves in an inhomogeneous fluidsaturated porous layered half-space with propertiesvarying exponentially[J].Journal of EngineeringMechanics,2005,131(12):1322-1328.
[6]KE Liao-liang,WANG Yue-sheng,ZHENG Zi-mao.Lovewave in an inhomogeneous fluid saturated porous layeredhalf space with linearly varying properties[J].SoilDynamics and Earthquake Engineering,2006,26(6/7):574-581.
[7]ZHOU Xiang-Lian,XU Bin,WANG Jian-hua,et al.Ananalytical solution for wave-induced seabed response in amulti-layered poro-elastic seabed[J].Ocean Engineering,2011,38:119-129.
[8]徐满清,金腊华,黎剑华,等.水平简谐荷载作用下层状饱和土体动力响应[J].岩土力学,2009,30(9):2633-2642.XU Man-qing,JIAN La-hua,LI Jian-hua,et al.Dynamicresponses of a layered saturated soil subjected toharmonic horizontal loads[J].Rock and Soil Mechanics,2009,30(9):2633-2642.
[9]徐斌,陆建飞,王建华,等.移动荷载作用下层状饱和土的动力响应[J].岩土力学,2008,29(12):3186-3192.XU Bin,LU Jian-fei,WANG Jian-hua,et al.Dynamicresponse of layered saturated soil under moving loads[J].Rock and Soil Mechanics,2008,29(12):3186-3192.
[10]诸骏,陈伟球,叶贵如,等.基于回传射线矩阵法的迭代算法及其应用[J].中国科学G辑,2009,39(3):103-111.
[11]PAO YH,KEH D C,HOWARD S M.Dynamic responseand wave propagation in plane trusses and frames[J].AIAAJ,1999,37:594-603
[12]PAO Y H,SU X Y,TIAN J Y.Reverberation matrixmethod for propagation of sound in a multilayeredliquid[J].Journal of Sound and Vibration,2000,230:743-760
[13]SU X Y,TIAN J Y,PAO Y H.Application of thereverberation-ray matrix to the propagation of elasticwaves in a layered solid[J].International Journal ofSolids and Structures,2002,39:5447-5463.
[14]TABATABAIE Y J,VALLIAPPAN S,ZHAO C B.Analytical and numerical solutions for wave propagationin water-saturated porous layered half-space[J].SoilDynamics and Earthquake Engineering,1994,13:249-257.
[15]SCHANZ M,CHENG A H D.Transient wavepropagation in a one-dimensional poroelastic column[J].Acta Mechanica,2000,145:1-8.
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