饱和横观各向同性分数导数黏弹性土中半封闭衬砌振动响应

在频率域内研究了饱和横观各向同性分数导数黏弹性土体中深埋圆形隧道半封闭衬砌振动响应问题。根据土体在长期沉积过程中存在各向异性的特点，将土骨架视为具有分数导数本构关系的横观各向同性黏弹性体，采用饱和多孔介质理论和弹性理论，利用衬砌内边界应力协调以及土体和衬砌界面处应力和位移连续，得到了简谐荷载作用下饱和横观各向同性黏弹性土和弹性衬砌的位移、应力和孔隙水压力解析表达式。考察了饱和经典弹性土、饱和分数导数性黏弹性土和饱和经典黏弹性土三种条件下饱和黏弹性土和衬砌各参数的影响，表明：横观各向同性面的弹性模量和衬砌厚度对系统动力响应的影响与分数导数阶数和土骨架的黏性有关；渗透系数较小时，系统存在明显的共振现象。另外，在三种条件下半封闭衬砌振动响应存在较大差异。

Dynamic responses of a partially sealed lining saturated transversely isotropic fractional derivative viscoelastic soil

The problem of dynamic responses of partially sealed lining with a deep buried circular tunnel in the saturated transversely isotropic fractional derivative viscoelastic soil is studied in the frequency domain. Regarding the soil skeleton as transversely isotropic viscoelastic medium with fractional derivative constitutive behavior because of the soils have the anisotropic characteristics in the long-term deposition, and based on the theory of saturated porous medium and elastic, the analytical expressions of the displacement, stress and pore water pressure of saturated transversely isotropic viscoelastic soil and lining subjected to the harmonic load are respectively derived by the stress coordination on the inner boundary of lining and the stress and displacement continuous at the interface between soil and lining. The parameter for saturated viscoelastic soil and lining under the three conditions of saturated classical elastic soil, saturated fractional derivative viscoelastic soil and saturated classical viscoelastic soil is investigated. It is reveal that the influences of the elastic modulus of transversely isotropic surface and the lining thickness on the system responses are relation to the order of fractional derivative and viscosity of the soil skeleton; the system has obvious resonance phenomena when the permeability coefficient is small. In addition, the dynamic responses of the partially lining have obvious difference in the three conditions.