饱和半空间瞬态加载衬砌隧道的动力响应研究  

A study of dynamic response of lined tunnel subjected to transient loads in saturated half space

作　　者：王滢[1,2] 高广运[1,2] 

机构地区：[1]同济大学地下建筑与工程系,上海200092 [2]同济大学岩土及地下工程教育部重点实验室,上海200092

出　　处：《岩土力学》2016年第3期850-858,共9页Rock and Soil Mechanics

基　　金：国家自然科学基金项目(No.41372271)~~

摘　　要：工程中,地下衬砌隧道会遇到水压破裂压力、爆炸及突然开挖等瞬态荷载作用,将这些荷载理想化为作用在衬砌内边界上的均布瞬态荷载,研究圆柱形衬砌隧道在突加荷载、阶跃荷载和三角形脉冲荷载作用下的动力响应规律。根据Biot波动理论推导出半空间饱和介质的控制方程;视衬砌结构为弹性材料导出衬砌结构的控制方程。用极大半径凸圆弧近似半空间直边界,采用Graff加法公式进行坐标变换,将直角坐标表示的通解转化为极坐标表示的通解。根据边界条件导出衬砌和土体的位移、应力和孔隙压力的Laplace变换域的解答。利用反Laplace变换数值计算方法,将解答转换为时域解,得出3种瞬态荷载作用下衬砌隧道地面位移峰值、衬砌应力和孔隙压力的分布规律。Underground lined tunnels are sometimes exposed to hydraulic fracturing, blasting loading and sudden excavations in operation. The loadings mentioned above are idealized the uniform axially symmetric transient radial loads acted on the internal lined tunnel and the dynamic responses of lined cylindrical tunnels due to the suddenly applied constant load, step load and triangular pulse load are analyzed. The governing equations of the lining and the surrounding saturated medium are derived based on Biot＇s theory and elastodynamic theory, respectively. The straight boundary of half space is modeled as a convex arc with the maximum large radius. A set of general solutions in rectangular coordinate system is transformed into solutions in polar coordinate system using addition theorem proposed by Graff. According to the boundary conditions, ground displacement, hoop stress in the lining and pore pressure between the lining and saturated soil are obtained in Laplace transform space and then transformed to solutions in time domain using the numerical calculation method of inverse Laplace transform. The distribution of ground displacement and hoop stress of lined cylindrical tunnel and pore pressure between the lining and saturated soil are obtained.

关 键 词：衬砌隧道 饱和半空间 瞬态荷载 LAPLACE变换 时域解 

分 类 号：U451.4[建筑科学—桥梁与隧道工程]