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将衬砌和土骨架分别视为多孔弹性材料和具有分数阶导数本构关系的粘弹性体,在频率域内研究了饱和度对分数导数型准饱和粘弹性土-半封闭圆形隧洞弹性衬砌系统动力特性的影响。将水-气混合物视为一种均匀流体,基于Biot两相动力固结理论和弹性理论,分别得到了简谐轴对称荷载和流体压力作用下分数导数型准饱和粘弹性土的位移、应力和孔压以及衬砌的位移和应力解析表达式。利用衬砌内边界上的边界条件及土体和衬砌界面处的连续性条件,得到了待定系数的具体表达式。通过算例分析,发现:衬砌和土体相对渗透系数对孔压幅值的影响与饱和度有关;流体压力作用下,随着饱和度的减小,位移幅值逐渐增大。另外,分数导数模型参数对系统动力响应有较大影响。
Considering the lining and the soil skeleton as the viscoelastic material of porous elastic material and fractional order derivative constitutive relation, the influence of the saturation on the fractional derivative quasi-saturated viscoelastic soil-semi-closed circular tunnel elastic lining system is studied in the frequency domain Effect of characteristics. The water-air mixture is regarded as a homogeneous fluid. Based on Biot’s two-phase dynamic consolidation theory and elastic theory, the displacement and stress of fractional-derivative quasi-saturated viscoelastic soil under simple harmonic axis and fluid pressure Pore pressure and lining displacement and stress analysis expressions. The concrete expression of the coefficient to be determined is obtained by using the boundary conditions on the inner boundary of lining and the continuity conditions on the interface between soil and lining. Through the example analysis, it is found that the influence of the relative permeability coefficient of lining and soil on the pore pressure amplitude is related to the saturation. With the decrease of the saturation pressure, the amplitude of displacement increases gradually with the fluid pressure. In addition, the fractional derivative model parameters have a greater impact on the system dynamic response.