深埋圆柱形隧洞黏弹性衬砌-土系统稳态振动的解析解

Analytical Solution for Steady State Vibration of Soil and Viscoelastic Lining with Deeply Embedded Cylindrical Tunnel

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.

Lining and soil have viscoelastic properties. The soil skeleton and the lining are equivalent to a viscoelastic medium with fractional derivative constitutive equation, respectively. The dynamic characteristics of the system of lining and soil with deeply embedded cylindrical tunnel were studied in the frequency domain. Based on the viscoelastic theory, the analytical expressions for the radial displacement and stress of viscoelastic soil and lining structure were by the continuity conditions between the lining and the soil, respectively. Based on this, the dynamic characterises between the system of classic elastic soil-elastic lining and fractional derivative viscoelastic lining-soil were analyzed by mtmerical methods. The influences of modulus ratio of lining and soil, the thickness of lining, the order of fractional derivative and material parameter on the system dynamic response were discussed. It shows that it has significantly differences between the system of classic elastic soil-elastic lining and fractional derivative viscoelastic lining-soil. With the order of fractional derivative increasing, the amplitudes of radial displacement and hoop stress are significantly reducing. The influence of viscosity of soil on the dynamic characteristics of the system is greater than the viscosity of lining.