层状地层中矩形隧洞围岩应力及位移

Stress and displacement of surrounding rock of rectangular tunnel in layered stratum

为从理论上探析层状地层中隧洞围岩应力和位移求解问题,基于Покровский当层法理论,将层状地层转化为均质地层,再利用复变函数将坐标平面z上均质地层中矩形隧洞映射为复平面ζ的单位圆。首先,针对浅埋隧洞,阐述计算其应力及位移的方法;其次,针对深埋隧洞,通过求解解析函数Φ(ζ)和Ψ(ζ),得出层状地层中深埋矩形隧洞围岩应力,进而获得围岩应变和位移;最后,针对某具体矩形隧洞,借助MATLAB软件求解其解析函数Φ(ζ)和Ψ(ζ),研究围岩侧压力系数、边界力和隧洞高宽比等对隧洞围岩应力的影响。

In order to theoretically solve the problem of stress and displacement of tunnel surrounding rock in layered stratum,based on the theory of theПокровскийequivalent layer method,the layered strata were cibverted into homogeneous strata,then the rectangular tunnel in the coordinate plane z was mapped to the unit circle of the complex planeζby using complex variable method.For shallow buried tunnels,was mapped the method of calculating its stress and displacement was described.For the deep-buried tunnel,by calculating the analytic functionΦ(ζ)andψ(ζ)with Matlab softwar,the stress of surrounding rock of deep-buried rectangular tunnel in layered strata was obtained,then the strain and the displacement of surrounding rock was obtained.Finally,the effects of lateral pressure coefficient of surrounding rock,boundary force and ratio of height to width of the tunnel on the stress of surrounding rock of the tunnel were obtained.