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在频率域研究了分数导数型粘弹性饱和土体和深埋圆形隧洞弹性衬砌相互作用的耦合简谐振动。将土骨架视为具有分数阶导数型本构的粘弹性体,基于饱和多孔介质理论和平面弹性理论,分别给出了饱和粘弹性土、弹性衬砌简谐振动的解析解。通过弹性衬砌和饱和土接触面处的连续性条件和衬砌内边界条件,得到了饱和粘弹性土-衬砌系统的稳态动力响应,给出了衬砌和饱和粘弹性土位移、应力和孔隙压力的解析表达式。在此基础上,进行了参数研究,讨论了物理和几何参数对系统响应的影响。研究表明:饱和分数导数型粘弹性土-衬砌系统的动力响应与经典饱和弹性/粘弹性土-衬砌系统的动力响应差异很大。
In the frequency domain, the coupling harmonic vibration of the fractional derivative viscoelastic saturated soil and the elastic lining of a deep buried circular tunnel are studied. Considering the soil skeleton as a viscoelastic body with fractional derivative constitutive model, the analytic solutions of the simple harmonic vibration of saturated viscoelastic soil and elastic lining are given respectively based on the theory of saturated porous media and plane elasticity theory. The steady-state dynamic response of saturated viscoelastic soil-lining system is obtained through the continuity condition of elastic lining and saturated soil contact surface and lining internal boundary conditions. The displacement, stress and pore pressure of lining and saturated viscoelastic soil are given Analytical expression. Based on this, the parameter research is carried out and the influence of the physical and geometric parameters on the system response is discussed. The results show that the dynamic response of saturated fractional derivative viscoelastic soil-lining system is quite different from the dynamic response of classical saturated elastic / viscoelastic soil-lining system.