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基于非局部Biot理论下饱和土中深埋圆柱形衬砌对平面弹性波的散射

徐长节, 丁海滨, 童立红, 杨园野

徐长节, 丁海滨, 童立红, 杨园野. 基于非局部Biot理论下饱和土中深埋圆柱形衬砌对平面弹性波的散射[J]. 岩土工程学报, 2018, 40(9): 1563-1570. DOI: 10.11779/CJGE201809001
引用本文: 徐长节, 丁海滨, 童立红, 杨园野. 基于非局部Biot理论下饱和土中深埋圆柱形衬砌对平面弹性波的散射[J]. 岩土工程学报, 2018, 40(9): 1563-1570. DOI: 10.11779/CJGE201809001
XU Chang-jie, DING Hai-bin, TONG Li-hong, YANG Yuan-ye. Scattering waves generated by cylindrical lining in saturated soil based on nonlocal Biot theory[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(9): 1563-1570. DOI: 10.11779/CJGE201809001
Citation: XU Chang-jie, DING Hai-bin, TONG Li-hong, YANG Yuan-ye. Scattering waves generated by cylindrical lining in saturated soil based on nonlocal Biot theory[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(9): 1563-1570. DOI: 10.11779/CJGE201809001

基于非局部Biot理论下饱和土中深埋圆柱形衬砌对平面弹性波的散射  English Version

基金项目: 国家重点基础研究发展计划(“973”计划)项目(2015CB057801); 海底盾构隧道关键设计理论与工程对策项目(51338009); 江西省青年科学基金项目(20171BAB216047)
详细信息
    作者简介:

    徐长节(1972- ),男,教授,博士生导师,主要从事地下空间及隧道工程研究。E-mail: xucj@zju.edu.cn。

    通讯作者:

    童立红,E-mail:lhtong@ecjtu.edu.cn

  • 中图分类号: TU435

Scattering waves generated by cylindrical lining in saturated soil based on nonlocal Biot theory

  • 摘要: 基于Biot饱和多孔介质理论和非局部弹性理论,构建了非局部Biot运动方程及本构方程。利用波函数展开法及饱和土与衬砌边界连续条件和衬砌内边界自由边界条件,求解了饱和土体中圆柱形衬砌对平面波散射问题的解析解。并通过将该解退化为单相介质中及经典Biot理论下衬砌对平面P波散射稳态解,验证了计算结果的正确性。研究结果表明,衬砌内边界及外边界动应力集中因子均随非局部因子的增大而减小;隧道内边界动应力集中因子分布曲线随非局部因子的减小而扩大;当入射波频率大于0.045 MHz时,饱和土中空隙尺寸及空隙动力的影响将不可忽略;非局部因子一定时,衬砌外径与内径比越大则衬砌内边界动应力集中因子越大,且当衬砌较薄时,衬砌内边界动应力集中因子可能产生负值。
    Abstract: Based on the Biot theory and the nonlocal elastic theory, the nonlocal Biot governing equations are proposed. The analytical solutions to the scattering wave fields generated by the cylindrical lining structure under incident plane waves are obtained utilizing the wave function expansion method under specific boundary conditions. The solutions are verified by degenerating the two-phase materials into single-phase ones and by comparing with the classical Biot theory as well. It is shown that the dynamic stress concentration factors on the inner and outer surfaces of the lining decrease with the increasing nonlocal factor. The distribution curves of dynamic stress concentration factor on the inner surface of the tunnel increase with the decrease of nonlocal factor. The influences of pore size and porosity dynamics in saturated soils cannot be ignored when the frequency of incident waves is greater than 0.045 MHz. For a certain nonlocal factor, the dynamic stress concentration factor increases with the increase of the ratio of outer radius to inner radius of the lining. The dynamic stress concentration factor may be negative on the inner surface of the lining for a thin lining.
  • [1] PAO Y H, MOW C C, ACHENBACH J D.Diffraction of elastic waves and dynamic stress concentrations[M]. New York: Crane and Russak, 1973.
    [2] LEE V W.Response of tunnels to incident SH waves[J]. Journal of Engineering Mechanics, 1979, 105(4): 643-659.
    [3] LEE V W, KARL J.On deformation near a circular underground cavity subjected to incident plane P waves[J]. European Earthquake Engineering, 1993, 7(1): 29-41.
    [4] KARINSKI Y S, SHERSHNEV V V, YANKELEVSKY D Z.Analytical solution of the harmonic waves diffraction by a cylindrical lined cavity in poroelastic saturated medium[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2007, 31(5): 667-689.
    [5] 李伟华, 赵成刚. 饱和土半空间中圆柱形孔洞对平面P波的散射[J]. 岩土力学, 2004, 25(12): 1867-1872.
    (LI Wei-hua, ZHAO Cheng-gang.An analytical solution for diffraction of plane P-waves by cylindrical cavity in a fluid-saturated porous media semi-space[J]. Rock and Soil Mechanics, 2004, 25(12): 667-689. (in Chinese))
    [6] 李伟华, 张钊. 饱和土中深埋圆柱形衬砌洞室对瞬态平面波的散射[J]. 地球物理学报, 2013, 56(1): 325-334.
    (LI Wei-hua, ZHANG Zhao.Scattering of transient plane waves by deep buried cylindrical lining cavity in saturated soil[J]. Chinese Journal of Geophysics, 2013, 56(1): 325-334. (in Chinese))
    [7] 胡亚元, 王立忠, 陈云敏, 等. 饱和土中平面应变波在圆柱体上的散射和折射[J]. 地震学报, 1998(3): 300-307.
    (HU Ya-yuan, WANG Li-zhong, CHEN Yun-min, et al.Scattering and refraction of plane strain waves on a cylinder in saturated soil[J]. Acta Seismologica Sinica, 1983(3): 300-307. (in Chinese))
    [8] GATMIRI B, ESLAMI H.Scattering of harmonic waves by a circular cavity in a porous medium: complex functions theory approach[J]. International Journal of Geomechanics, 2007, 7(5): 371-381.
    [9] 周香莲, 周光明, 王建华. 饱和土中圆形衬砌结构对弹性波的散射[J]. 岩石力学与工程学报, 2005, 24(9): 1572-1576.
    (ZHOU Xiang-lian, ZHOU Guang-ming, WANG Jian-hua.Scattering of elastic wave by circular cavity with lining in saturated soil[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(9): 1572-1576. (in Chinese))
    [10] 丁光亚, 蔡袁强, 徐长节. 半空间饱和土中圆形壳结构对平面P波的散射[J]. 工程力学, 2008, 25(12): 35-41.
    (DING Guang-ya, CAI Yuan-qiang, XU Chang-jie.Scattering of P waves by a cylindrical shell in a saturated half-space[J]. Engineering Mechanics, 2008, 25(12): 35-41. (in Chinese))
    [11] BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid: 2 higher frequency range[J]. The Journal of the Acoustical Society of America, 1956, 28(2): 179-191.
    [12] BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J]. Journal of Applied Physics, 1962, 33(4): 1482-1498.
    [13] LEE K I, HUMPHREY V F, KIM B N, et al.Frequency dependencies of phase velocity and attenuation coefficient in a water-saturated sandy sediment from 0.3 to 1.0 MHz[J]. Journal of the Acoustical Society of America, 2007, 121(1): 2553-2560.
    [14] SAHAY P N.Biot constitutive relation and porosity perturbation equation[J]. Geophysics, 2013, 78(5): 57-67.
    [15] ERINGEN A C.On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves[J]. Journal of Applied Physics, 1983, 54(9): 4703-4710.
    [16] CHAKRABORTY A.Prediction of negative dispersion by a nonlocal poroelastic theory[J]. Journal of the Acoustical Society of America, 2008, 123(1): 56.
    [17] TONG L H, YU Y, HU W T, et al.On wave propagation characteristics in fluid saturated porous materials by a nonlocal Biot theory[J]. Journal of Sound & Vibration, 2016, 379: 106-118.
    [18] 宫全美. 轨道交通线路动力学[M]. 北京: 人民交通出版社股份有限公司, 2015.
    (GONG Quan-mei.Dynamics of rail transit engineering[M]. Beijing: China Communications Press, 2015. (in Chinese))
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出版历程
  • 收稿日期:  2017-02-26
  • 发布日期:  2018-09-24

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