简谐荷载作用下饱和土体中圆形衬砌隧道三维动力响应分析

Analysis of three-dimensional dynamic response of a circular lining tunnel in saturated soil to harmonic loading

研究了全空间饱和土体中圆形衬砌隧道在径向简谐点荷载作用下的三维动力响应,将衬砌用无限长圆柱壳来模拟,土体用Biot饱和多孔介质模型来模拟,引入两类势函数来表示土骨架的位移和孔隙水压力,并利用修正Bessel方程来求解各势函数,结合边界条件,得到频率-波数域内衬砌和土骨架位移、孔隙水压力的解答,最后进行Fourier逆变换得到时间-空间域内的响应。通过算例分析了荷载振动频率和土体渗透性对土体和衬砌位移响应及土体孔压的影响。结果表明,饱和土体和弹性土体的位移响应具有明显区别。随着荷载频率的增大,土体和隧道位移幅值减小,土体孔压幅值增大;随着土体渗透性增大,土体位移及孔压幅值减小。

Three-dimensional dynamic response of a circular lining tunnel surrounded by a full-space saturated soil to a harmonic point load acting in the radial direction is investigated. The lining is modeled as a cylindrical shell of infinite length; and the soil is modeled as a saturated poroelastic medium using Biot＇s theory. Two kinds of potential functions are introduced to represent the displacements of the soil skeleton and the excess pore fluid pressure; and the modified Bessel equations are utilized to obtain the expressions of the potentials function. According to boundary conditions, the analytical solutions of displacements of lining and soil and pore pressure are derived in frequency-wave number domain. Finally, the time-space domain solutions of the dynamic responses are obtained by inverse Fourier transformation. The effects of load vibration frequency and soil permeability on displacement and pore pressure responses are investigated. Numerical results show that the displacement response of saturated soil is significantly different from that of single phase elastic soil. As the load vibration frequency increasing, the displacement amplitudes of soil and tunnel decrease, while the pore pressure amplitude increases. The displacement and pore pressure amplitudes of soil decrease as the soil permeability getting better.