具有半封闭隧道的饱和粘弹性土动力特性

Coupled Vibration of Saturated Fractional Derivative Type Viscoelastic Soil of a Circular Tunnel with Partially Sealed Shell Lining

考虑介质和流体的压缩性,根据Biot理论和弹性壳体理论,在频率域内研究了饱和分数导数粘弹性土体-半封闭圆形隧道壳体衬砌系统耦合振动。将土体视为液固饱和多孔介质,选择反映介质流变特性的分数导数模型描述土骨架的应力-位移本构关系,又引入部分透水的边界条件,得到了饱和粘弹性土体中半封闭隧洞内边界分别在轴对称荷载和流体压力作用下位移、应力和孔压的表达式。进行了参数分析,研究表明:轴对称荷载条件下,分数导数阶数对系统响应的影响远大于流体压力情形下的动力响应,且存在明显的共振效应,但流体压力条件下不产生共振现象。

Considering the compression of medium and fluid,coupled vibration of saturated fractional derivative type viscoelastic soil and a circular tunnel with partially sealed shell lining in the frequency domain is investigated according to theories of Biot and elastic shell.The stress and displacement constitutive behavior of the soil skeleton is described by fractional derivative model which reflects the rheological properties of the medium while regarding soil as a liquid-solid saturated porous medium.The expressions of displacement,stress and pore water pressure are obtained while the inner boundary of circular tunnel is subjected to axially symmetric radial traction and axially symmetric fluid pressure respectively by introducing a partially permeable boundary condition.With the parameter analysis,it is revealed that the order of fractional derivative model on the responses for the system subjected to the symmetric radial traction is much greater than that of the system under the axially symmetric fluid pressure.And resonance phenomenon occurs obviously.Nevertheless the system responses do not have remarkable resonance phenomenon under axially symmetric fluid pressure.