基于分数导数本构的粘弹性土层—隧洞衬砌系统的稳态动力响应

将混凝土衬砌材料视为具有分数导数本构的粘弹性体,在频率域研究了深埋圆形隧洞粘弹性土的稳态动力响应。利用衬砌的内边界条件和混凝土衬砌与土体界面处的连续性条件,得到了粘弹性土体和衬砌稳态振动的应力和位移解析解。进行了隧洞衬砌厚度、土体阻尼比、本构阶数、材料参数比等对土体的位移和应力幅值影响的算例分析,结果表明:材料参数比对系统动力特性有较大影响,随着材料参数比的增加,位移和应力幅值减小;随着土体的阻尼比、衬砌厚度的增加,位移和应力幅值减小;当材料参数比Tσ/Tε=3时,随着分数导数阶数增大,响应幅值减小。

Steady dynamic responses of viscoelastic soil and tunnel lining system based on fractional derivative constitutive relation

Regarding the concrete lining as a viscoelastic medium with fractional derivative constitutive relation,the steady dynamic responses of the viscoelastic soil with a deeply embedded circular tunnel are investigated in the frequency domain.By using the inner boundary condition of the lining and the continuity conditions between the lining and soil,the analytical solutions of the displacement and stress of the viscoelastic soil and lining system are obtained for the steady vibration.Numerical examples are presented to examine the influences of the thickness of the lining,the damping ratio of the soil and the orders and material parameter ratios of the constitutive relation on the amplitudes of the displacement and stress.It is shown that the material parameter ratio has a great influence on the dynamic characteristics of the system.The amplitudes of the displacement and stress decrease with the increasing of damping ratio of the soil increasing and attenuate with the increasing of order when Tσ /Tε=3.