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衬砌和土体具有黏弹性性质.将土骨架和衬砌结构视为具有分数阶导数本构的黏弹性体,在频率域内研究了深埋圆柱形隧洞衬砌和土体系统的动力特性.基于黏弹性理论,根据界面连续性条件,分别得到了黏弹性土体和衬砌结构的径向位移、应力等的解析表达式.在此基础上,对比分析了经典弹性土和弹性衬砌系统、分数导数黏弹性衬砌和土体系统的动力特性.考察了土体和衬砌的模量比、衬砌厚度、分数导数阶数、材料参数比对系统动力响应的影响.结果表明:经典弹性土和弹性衬砌系统与分数导数黏弹性衬砌和土体系统的动力特性存在较大差异.随着分数导数阶数的增加,衬砌的径向位移和环向应力幅值明显减小;土体的黏性对系统动力特性的影响大于衬砌黏性的影响.
The lining and soil are of viscoelastic nature. Considering the soil skeleton and lining structure as a viscoelastic body with fractional derivative constitutive law, the dynamic characteristics of the deep buried cylindrical tunnel lining and soil system are studied in the frequency domain. Theory, the analytical expressions of radial displacement and stress of viscoelastic soil and lining structures are obtained respectively according to the interface continuity conditions.On the basis of this, the classical elastic soil and elastic lining system are compared and analyzed, the fractional derivative viscoelasticity Lining and soil system.The effects of modulus ratio, lining thickness, fractional derivative order and material parameter ratio on the dynamic response of the system are investigated.The results show that the relationship between the classical elastic soil and the elastic lining system and the fraction The dynamic characteristics of the derivative viscoelastic lining and soil system are quite different. With the increase of the fractional derivative order, the radial displacements and hoop stress amplitude of the lining decrease obviously. The viscosity of the soil affects the dynamic characteristics of the system The impact is greater than the effect of lining stickiness.