半封闭分数导数粘弹性衬砌隧道的频域响应

混凝土衬砌具有粘弹性性质，以往的经典Kelvin模型、弹性理论和壳体理论都不能刻画其蠕变的全过程。本文基于饱和多孔介质理论，在频率域研究了轴对称荷载和流体压力作用下饱和粘弹性土中半封闭分数导数型衬砌隧洞的稳态动力响应。在引入隧洞部分透水边界条件的基础上，通过分数阶导数粘弹性模型描述衬砌的应力—位移本构关系，并利用衬砌内边界以及接触面的连续性条件，得到了饱和土和衬砌的应力、位移和孔压解答。考察了分数导数阶数、材料参数以及衬砌和土体相对渗透系数的影响。研究表明：分数导数阶数对系统响应影响较大，且依赖于衬砌的材料参数。另外，相对渗透系数对系统响应的影响很大。

FREQUENCY RESPONSES OF A PARTIAL SEALED TUNNEL WITH FRACTIONAL DERIVATIVE VISCOELASTIC LINING

The concrete lining has viscoelastic properties, none of previous classic Kelvin model, theory of elastic and shell can describe the whole process of its creep. Based on saturated porous medium theory, the steady state dynamic responses of a partial sealed tunnel with fractional derivative type viscoelastic lining in saturated viscoelastic soil are investigated in the frequency domain subject to the axisymmetric radial traction and interior water pressure. On the basis of introducing a partial permeable boundary condition, the analytical solutions of stress, displacement and pore pressure of the lining and saturated soil are respectively obtained by the inner boundary of the lining and continuity conditions of the interface, besides, the stress and displacement constitutive behavior of the lining is described by fractional derivative viscoelastic constitutive model. The influences of the order of fractional derivative, the material parameter of the lining, relative permeability coefficient on the dynamic characteristics of the system are examined.. It is shown that the order of fractional derivative has a greater influence on the system dynamic responses, and it depends on material parameter of the lining. In addition, relative permeability coefficient has significant effects on the system responses.