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利用Darcy渗透定律,通过引入衬砌和土体的相对渗透系数,建立了隧洞边界部分透水条件。将土骨架视为具有分数导数粘弹性本构关系的粘弹性体,基于Biot理论,通过界面连续性条件在频率域内给出了简谐轴对称荷载或流体压力作用下饱和粘弹性土-弹性衬砌系统耦合振动时饱和土、衬砌的位移、应力、孔隙水压力表达式,并通过算例分别考察了简谐轴对称荷载、流体压力作用下的分数导数阶数、材料参数比、渗透系数对系统的径向位移幅值U、孔隙水压力幅值P的影响,结果表明:随着分数导数阶数和材料参数比的增加,系统的响应幅值逐渐减小;随着渗透系数κ的增加,轴对称荷载作用下的土体位移幅值和孔隙水压力幅值逐渐减小,当κ大于100时,U和P值无明显变化,流体压力作用下的土体位移幅值和孔隙水压力幅值逐渐增大,当κ大于1时,U和P值无明显变化。
Based on the Darcy’s law of permeability and the relative permeability coefficient of the lining and soil, the permeability of the boundary of the tunnel is established. Considering the soil skeleton as a viscoelastic body with fractional derivative viscoelastic constitutive relation, based on the Biot theory, the saturated viscoelastic soil-elastic lining under the harmonic axis load or the fluid pressure is given in the frequency domain by the interface continuity condition. The expressions of displacements, stresses and pore water pressure of saturated soil and lining when the system is coupled with vibration are investigated. The symmetric load of simple harmonic shaft, the fractional derivative order of fluid pressure, the material parameter ratio and the permeability coefficient of the system The results show that with the increase of the fractional derivative order and material parameter ratio, the response amplitude of the system decreases gradually. With the increase of the permeability coefficient κ, Under the axisymmetric load, the amplitude of displacement and the pressure of pore water gradually decrease. When κ is greater than 100, there is no obvious change of U and P. The amplitude of displacement and pore water pressure under the action of fluid pressure Value increases gradually, when κ is greater than 1, U and P values no significant change.