刘灯凯, 饶军应, 徐世军,等.层状地层中矩形隧洞围岩应力及位移[J].河南理工大学学报（自然科学版）,2020,39(5):168-176.

LIU D K, RAO J Y, XU S J,et al.Stress and displacement of surrounding rock of rectangular tunnel inlayered stratum[J].Journal of Henan Polytechnic University(Natural Science) ,2020,39(5):168-176.

层状地层中矩形隧洞围岩应力及位移

刘灯凯1, 饶军应1, 徐世军2, 谢财进1, 聂崇欣1

1.贵州大学 土木工程学院，贵州 贵阳 550025;2.中铁十八局集团第二工程有限公司，河北 唐山 063000

摘要: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，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。

关键词:层状地层;隧洞围岩;复变函数;围岩应力;围岩位移

doi:10.16186/j.cnki.1673-9787.2020.5.24

基金项目:国家自然科学基金资助项目（51608141 ）；贵州大学人才引进科研基金资助项目（（2015 ） 16）

收稿日期:2019/12/25

修回日期:2020/02/21

出版日期:2020/09/15

Stress and displacement of surrounding rock of rectangular tunnel inlayered stratum

LIU Dengkai1, RAO Junying1, XU Shijun2, XIE Caijin1, NIE Chongxin1

1.School of Civil Engineering, Guizhou University, Guvyang  550025，Guizhou，China;2.China Railway 18th Bureau Group Second Engineering Co. ，Ltd. ，Tangshan  063000，Hebei，China

Abstract:In order to theoretically solve the problem of stress and displacement of tunnel surrounding rock in layered stratum， based on the theory of the HoKpoBCKRK equivalent layer method， the layered strata were cib-verted into homogeneous strata, then the rectangular tunnel in the coordinate plane z was mapped to the unit circle of the complex planeζ by 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 function Φ(ζ) and Ψ(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.

Key words:layered stratum;surrounding rock of tunnel;complex variables function;stress of surrounding rock;displacement of surrounding rock

层状地层中矩形隧洞围岩应力及位移_刘灯凯.pdf