准饱和粘弹性土-隧道衬砌系统的动力特性

DYNAMIC CHARACTERISTICS OF NEARLY SATURATED VISCOELASTIC SOIL AND LINING SYSTEM WITH A TUNNEL

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。

The lining and soil skeleton are respectively treated as a porous elastic material and a viscoelastic medium with fractional derivative constitutive relations. The influences of the water saturation on the dynamic characteristics of the fractional derivative viscoelastic nearly saturated soil and elastic lining system with partial sealed tunnel are investigated in the frequency domain. The mixture of water-gas is considered as a homogeneous fluid. By the Boit＇s theory and elastic one, the analytical expressions of displacement, stress and pore water pressure of the nearly saturated viscoelastic soil and lining are respectively obtained subjected to the harmonic axisymmetric load or fluid pressure. By utilizing the inner boundary condition of the lining and the continuity conditions between the soil and the lining, the specific expressions of undetermined coefficients are determined. It is found that the effects of the relative permeability coefficient of lining and soil on the pore water pressure amplitude are related to the value of water saturation; the displacement amplitude increases with the water saturation decreasing under the fluid pressure. In addition, the parameters of fractional derivative model have great impacts on the system dynamic responses.