姚署霖, 闻敏杰. 黏弹性土中衬砌隧道振动响应的解析解[J]. 工程力学, 2014, 31(3): 109-115. DOI: 10.6052/j.issn.1000-4750.2012.04.0222
引用本文: 姚署霖, 闻敏杰. 黏弹性土中衬砌隧道振动响应的解析解[J]. 工程力学, 2014, 31(3): 109-115. DOI: 10.6052/j.issn.1000-4750.2012.04.0222
YAO Shu-lin, WEN Min-jie. ANALYTICAL SOLUTIONS OF DYNAMIC RESPONSES OF A LINED TUNNEL IN VISCOELASTIC SOIL[J]. Engineering Mechanics, 2014, 31(3): 109-115. DOI: 10.6052/j.issn.1000-4750.2012.04.0222
Citation: YAO Shu-lin, WEN Min-jie. ANALYTICAL SOLUTIONS OF DYNAMIC RESPONSES OF A LINED TUNNEL IN VISCOELASTIC SOIL[J]. Engineering Mechanics, 2014, 31(3): 109-115. DOI: 10.6052/j.issn.1000-4750.2012.04.0222

黏弹性土中衬砌隧道振动响应的解析解

ANALYTICAL SOLUTIONS OF DYNAMIC RESPONSES OF A LINED TUNNEL IN VISCOELASTIC SOIL

  • 摘要: 该文采用解析方法在频率域内对黏弹土层和衬砌结构简谐振动特性进行了研究。首先, 将土骨架视为具有分数阶导数本构关系的黏弹性体, 根据黏弹性理论, 推导得到了简谐荷载作用下分数导数型黏弹性土层的位移和应力等解析表达式。其次, 建立了两种类型的衬砌运动方程:第一, 将衬砌结构视为均匀弹性介质, 研究了分数导数黏弹性土中弹性衬砌结构的动力特性;第二, 将衬砌等效为薄壁壳体结构, 利用Flügge薄壳理论, 得到了衬砌结构的运动方程, 并对分数导数黏弹性土和壳体衬砌的动力相互作用进行了分析。根据连续性边界条件, 得到了相关待定系数的表达式。再次, 与以往的解析解进行了对比。最后, 通过算例分析了土体和衬砌各参数对系统动力特性的影响, 结果表明:薄壁壳体衬砌结构条件下系统的动力响应大于均匀弹性衬砌结构条件下系统的动力响应;随着土体和衬砌模量比的增加, 响应幅值逐渐减小。分数导数本构参数对系统的动力特性有较大影响。

     

    Abstract: Using an analytical method, the harmonic vibration characteristics of viscoelastic soil and lining structure are presented in the frequency domain. Firstly, the soil skeleton is treated as a viscoelastic medium with the fractional derivative constitutive relations. By the viscoelastic theory, the analytical solutions for the displacement and stress of the fractional derivative type viscoelastic soil are obtained, subject to a harmonic axisymmetric load. Secondly, the lining is treated as a homogeneous elastic medium. The lining is equivalent for a thin shell structure. The motion equation of the lining structure is established by the Flügge theory of a thin shell. The dynamic interactions of fractional derivative viscoelastic soil and the shell are analyzed. The expressions of undetermined coefficients are based on continuity conditions. Thirdly, the analytical results are compared with the analytical solutions from current existing literatures. Finally, the system dynamic characteristics are analyzed for different parameters of the soil and the lining by the numerical examples. It is shown that the system dynamic responses with a thin shell are greater than those with homogeneous elastic lining conditions; the response amplitudes decrease gradually as the modulus ratio between soil and lining increases. The parameters of fractional derivative constitutive have great influences on the system dynamic characteristics.

     

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