中文摘要：

采用解析方法在频率域内研究简谐荷载作用下具有分数导数黏弹性衬砌的圆形隧道准饱和黏弹性土振动响应.假定混凝土衬砌为黏弹性材料,利用分数导数模型描述动力学行为.将水-气混合物视为一种均匀流体,采用Biot波动理论模拟准饱和黏弹性土.利用分数导数黏弹性衬砌内边界以及准饱和黏弹性土和衬砌结构界面处的连续性条件,得到准饱和黏弹性土和分数导数型衬砌动力相互作用时土体和衬砌的位移、应力和孔隙水压力等的解析表达式.讨论饱和度、衬砌厚度及分数导数本构参数对系统动力响应的影响.数值结果表明,分数导数阶数对系统响应的影响与衬砌材料参数比有关;饱和度对衬砌和土体界面处孔隙水的渗透性有较大影响;弹性衬砌条件下的系统响应大于分数导数黏弹性衬砌条件下的系统动力响应.

英文摘要：

The dynamic response of the nearly saturated viscoelastic soil with a fractional derivative viscoelastic lined circular tunnel subjected to harmonic load was investigated in the frequency domain by using an analytical method. Assuming that the concrete lining is a viscoelastic material, its dynamic behavior was described by the fractional derivative model. The mixture of water and gas was considered as a uniform fluid and the Biot＇theory was used to describe the nearly saturated viscoelastic soil. By inner boundary conditions of the fractional derivative viscoelastic lining and the continuity boundary conditions on the interface between the nearly saturated viscoelastic soil and lining structure, the analytical expressions for the displacement ~ stress and pore water pressure of the soil and lining for the interaction of nearly saturated viscoelastic soil and fractional derivative viscoelastic lining were obtained. The influences of the saturation, lining thickness and the fractional derivative constitutive parameters on the system responses were discussed. Results show that the influences of the order of fractional derivative on the system responses relate to the material parameters; the saturation greatly influences on the permeability of pore water on the interface between the lining and soil. The system responses with the elastic lining are greater than those with the fractional derivative viscoelastic lining.