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.docx

文章编号：1000－7598 (2014) 文章编号：1000－7598 (2014) 04－1147－10 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 晨 1, 2，孙宏磊 1, 2，蔡袁强 1, 2, 3，王 鹏 3 曾 （1. 浙江大学 滨海和城市岩土工程研究中心，杭州 310058；2. 浙江大学 软弱土与环境土工教育部重点实验室，杭州 310058； 3. 温州大学 建筑与土木工程学院，浙江 温州 325035） 摘 要：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。 关 键 词：简谐点荷载；衬砌隧道；饱和土；动力响应 中图分类号： U 451 文献标识码：A Analysis of three-dimensional dynamic response of a circular lining tunnel in saturated soil to harmonic loading ZENG Chen1, 2，SUN Hong-lei1, 2，CAI Yuan-qiang1, 2, 3，WANG Peng3 （1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China; 2. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058, China; 3. College of Architecture and Civil Engineering, Wenzhou University, Wenzhou, Zhejiang 325035, China） Abstract: 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 displ