梯度饱和土瞬态响应分析
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摘要
基于Biot多孔介质理论,建立了饱和土体在动载荷作用下的一维回传射线矩阵法的计算列式,其中考虑了土体的非均匀性、惯性、黏滞以及固体颗粒和流体的可压缩性.利用计算结果与已有结果相比较,二者相吻合,验证了算法的正确性.作为数值算例,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,利用数值Laplace逆变换求解了在冲击性载荷作用下的位移,应力和孔隙压力等物理量的瞬态响应,重点分析讨论了材料非均匀性对饱和土介质动力特性的影响.
Based on the Biot’s theory of porous media,the calculation formula of reverberation ray matrix method is established for one-dimensional transient response of fluid-saturated soil,where the non-homogeneous,inertial,viscous and the compressible of solid particles and fluid are taken into account.The present methodology is validated by comparing solutions with some known result.As numerical examples,assuming that the material properties of the saturated soil have an exponential law distribution along the thickness-coordinate,the transient response,in terms of displacement,stress and pore press,are examined using numerical inverse Laplace transform.The effect of non-homogeneous on transient responses of gradient saturated soil is demonstrated and discussed.
Based on the Biot’s theory of porous media,the calculation formula of reverberation ray matrix method is established for one-dimensional transient response of fluid-saturated soil,where the non-homogeneous,inertial,viscous and the compressible of solid particles and fluid are taken into account.The present methodology is validated by comparing solutions with some known result.As numerical examples,assuming that the material properties of the saturated soil have an exponential law distribution along the thickness-coordinate,the transient response,in terms of displacement,stress and pore press,are examined using numerical inverse Laplace transform.The effect of non-homogeneous on transient responses of gradient saturated soil is demonstrated and discussed.
引文
1 Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid I:low-frequency range.Journal ofthe Acoustical Society of America,1956,28:168-178
2 Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid II:higher frequncy range.Journalof the Acoustical Society of America,1956,28:179-191
3 de Boer R.Highlights in the historical development of theporous media theory-toward a consistent macroscopic the-ory.Applied Mechanics Reviews,1996,49:201-262
4黄茂松,李进军.饱和多孔介质土动力学理论与数值解法.同济大学学报(自然科学版),2004,32(7):851-856(HuangMaosong,Li Jinjun.Dynamics of fluid-saturated porousmedia and its numerical solution.Journal of Tongji Uni-versity,2004,32(7):851-856(in Chiniese))
5 Schanz M.Poroelastodynamics:linear models,analyticalsolutions,and numerical methods.Applied Mechanics Re-views,2009,62:1-15
6 Manolisa GD,Rangelov TV.Non-homogeneous elasticwaves in soils:notes on the vector decomposition tech-nique.Soil Dynamics and Earthquake Engineering,2006,26:952-959
7 Pak RYS,Guzina BB.Three-dimensional wave propaga-tion analysis of a smoothly heterogeneous solid.Journal ofthe Mechanics and Physics of Solids,1995,43(4):533-551
8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.岩石力学与工程学报,2005,24(s1):4798-4804(LeiMing,Liao Hongjian,Huang Lixing,et al.Study on charac-ters of stress propagation in functionally graded soil.Chi-nese Journal of Rock Mechanics and Engineering,2005,24(s1):4798-4804(in Chiniese))
9秦小军,陈少林,曾心传.二维非均匀饱和土体的地震反应分析.地震工程与工程振动,1999,19(1):7-14(Qin Xiaojun,Chen Shaolin,Zeng Xinchuan.Analysis of nonhomoge-neous fluid-saturated soil in two dimensions under earth-quake load.Earthquake Engineering And Engineering Vi-bration,1999,19(1):7-14(in Chiniese))
10 Ke LL,Wang YS,Zhang ZM.Propagation of love wavesin an inhomogeneous fluid saturated porous layered half-space with properties varying exponentially.Journal ofEngineering Mechanics,2005,131(12):1322-1328
11 Ke LL,Wang YS,Zhang ZM.Love wave in an inhomoge-neous fluid saturated porous layered half space with lin-early varying properties.Soil Dynamics and EarthquakeEngineering,2006,26(6/7):574-581
12 Zhou XL,Xu B,Wang JH,et al.An analytical solutionfor wave-induced seabed response in a multi-layered poro-elastic seabed.Ocean Engineering,2011,38:119-129
13 Hirai H,Chen L.Recent and prospective development ofFGM in Japan.Materials Science Forum,1999,308/311:509-514
14 Chen WQ,Wang HM,Bao RH.On calculating dispersioncurves of waves in a functionally graded elastic plate.Com-posite Structures,2007,81:233-242
15 Pao YH,Keh DC,Howard SM.Dynamic response and wavepropagation in plane trusses and frames.AIAA J,1999,37:594-603
16 Pao YH,Su XY,Tian JY.Reverberation matrix methodfor propagation of sound in a multilayered liquid.Journalof Sound and Vibration,2000,230:743-760
17 Su XY,Tian JY,Pao YH.Application of the reverberation-ray matrix to the propagation of elastic waves in a layeredsolid.International Journal of Solids and Structures,2002,39:5447-5463.
18 Honig G,Hirdes U.A method for the numerical inversionof Laplace transforms.Journal of Computational and Ap-plied Mathematics,1984,10:113-32
19 Schanz M,Cheng AHD.Transient wave propagation ina one-dimensional poroelastic column.Acta Mechanica,2000,145:1-18
2 Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid II:higher frequncy range.Journalof the Acoustical Society of America,1956,28:179-191
3 de Boer R.Highlights in the historical development of theporous media theory-toward a consistent macroscopic the-ory.Applied Mechanics Reviews,1996,49:201-262
4黄茂松,李进军.饱和多孔介质土动力学理论与数值解法.同济大学学报(自然科学版),2004,32(7):851-856(HuangMaosong,Li Jinjun.Dynamics of fluid-saturated porousmedia and its numerical solution.Journal of Tongji Uni-versity,2004,32(7):851-856(in Chiniese))
5 Schanz M.Poroelastodynamics:linear models,analyticalsolutions,and numerical methods.Applied Mechanics Re-views,2009,62:1-15
6 Manolisa GD,Rangelov TV.Non-homogeneous elasticwaves in soils:notes on the vector decomposition tech-nique.Soil Dynamics and Earthquake Engineering,2006,26:952-959
7 Pak RYS,Guzina BB.Three-dimensional wave propaga-tion analysis of a smoothly heterogeneous solid.Journal ofthe Mechanics and Physics of Solids,1995,43(4):533-551
8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.岩石力学与工程学报,2005,24(s1):4798-4804(LeiMing,Liao Hongjian,Huang Lixing,et al.Study on charac-ters of stress propagation in functionally graded soil.Chi-nese Journal of Rock Mechanics and Engineering,2005,24(s1):4798-4804(in Chiniese))
9秦小军,陈少林,曾心传.二维非均匀饱和土体的地震反应分析.地震工程与工程振动,1999,19(1):7-14(Qin Xiaojun,Chen Shaolin,Zeng Xinchuan.Analysis of nonhomoge-neous fluid-saturated soil in two dimensions under earth-quake load.Earthquake Engineering And Engineering Vi-bration,1999,19(1):7-14(in Chiniese))
10 Ke LL,Wang YS,Zhang ZM.Propagation of love wavesin an inhomogeneous fluid saturated porous layered half-space with properties varying exponentially.Journal ofEngineering Mechanics,2005,131(12):1322-1328
11 Ke LL,Wang YS,Zhang ZM.Love wave in an inhomoge-neous fluid saturated porous layered half space with lin-early varying properties.Soil Dynamics and EarthquakeEngineering,2006,26(6/7):574-581
12 Zhou XL,Xu B,Wang JH,et al.An analytical solutionfor wave-induced seabed response in a multi-layered poro-elastic seabed.Ocean Engineering,2011,38:119-129
13 Hirai H,Chen L.Recent and prospective development ofFGM in Japan.Materials Science Forum,1999,308/311:509-514
14 Chen WQ,Wang HM,Bao RH.On calculating dispersioncurves of waves in a functionally graded elastic plate.Com-posite Structures,2007,81:233-242
15 Pao YH,Keh DC,Howard SM.Dynamic response and wavepropagation in plane trusses and frames.AIAA J,1999,37:594-603
16 Pao YH,Su XY,Tian JY.Reverberation matrix methodfor propagation of sound in a multilayered liquid.Journalof Sound and Vibration,2000,230:743-760
17 Su XY,Tian JY,Pao YH.Application of the reverberation-ray matrix to the propagation of elastic waves in a layeredsolid.International Journal of Solids and Structures,2002,39:5447-5463.
18 Honig G,Hirdes U.A method for the numerical inversionof Laplace transforms.Journal of Computational and Ap-plied Mathematics,1984,10:113-32
19 Schanz M,Cheng AHD.Transient wave propagation ina one-dimensional poroelastic column.Acta Mechanica,2000,145:1-18
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