公路隧道开挖问题的复变函数解及应用

Complex Variable Function Solution and Its Application for Road Tunnel Excavation

为优化公路隧道开挖和支护的设计,通过将公路隧道的开挖视为弹性无限大板中的单孔问题,引入共形映射和柯西积分,采用复变函数解法推导了在支护压力与远场地应力作用下,任意形状公路隧道围岩应力与位移的解析解,并在MATLAB平台上编程求解数值解。在此基础上,通过大量的算例分析讨论了隧道洞形、洞室跨度、侧压力系数和支护压力等因素对公路隧道围岩应力场与位移场的影响。研究结果表明:隧道洞形对洞室围岩应力和位移的分布影响显著;隧道跨度的增加将明显加大隧道开挖后的拱顶沉降、底板隆起和净空收敛变形,也使得围岩应力的分布和变化更为复杂;对于水平向地应力较大的情形,将隧道分为上下台阶开挖来改善应力分布较为适宜。

To optimize road tunnel excavation and support design,by considering road tunnel excavation as single bore in the elastic infinite plate and introducing conformal mapping and Cauchy integral,complex variable function solutions were applied to deduce the stress and displacement distributions along the tunnel perimeter with arbitrary cross section,which was subjected to the non-uniform far-field stresses and the supporting pressure.The solutions were implemented in the platform of MATLAB.Then detailed case studies were carried out to discuss the influences of cavity shape of tunnel,cavern span,lateral pressure coefficient and supporting pressure on the stress and displacement distribution along tunnel perimeter.The results show that cavity shape of tunnel influences significantly the stress and displacement distributions within the surrounding rock mass of cavern.Increasing tunnel span will significantly enlarge the crown subsidence,invert upheaval and sidewall convergence after tunnel excavation,which makes the stress distribution and change within surrounding rock more complex.It is more appropriate to utilize the top-heading excavation method for the ground condition with higher horizontal in-situ stress.