圆形洞室动态施工中围岩粘弹时变解析分析

Analytics Study of Underground Circular Tunnel Construction in Plane Viscoelasticity

针对深埋地下洞室,寻求洞室动态施工中围岩应力及位移场的解析解.在推导中考虑了岩体粘性时效和动态施工对位移影响的耦合作用.将开挖岩体模拟为Maxwell粘弹模型,从基本控制方程出发,导出双向等地应力情况下无限均匀介质中圆形洞室施工过程围岩位移解析解;应力解则由时变力学对应性原理得出.该结果可用于圆形洞室半径任意时变的情况.针对匀速和加速施工情况进一步求解施工至某一时刻结束后的位移粘弹解,定量分析最终形状相同时,不同时变速度和加速度对最终结果的影响,分析了粘性介质中圆洞施工的时径相关性现象.

An analytic study of stress and displacement during dynamic construction is conducted on the immerged underground tunnel. The coupling influence of viscous aging and construction on the displacement is considered during derivation. Rock mass is simulated to Maxwell viscoelastic model, and basic equations of this problem are presented then. Analytic displacement solution of infinite homogeneous plane with one circular tunnel under uniform ground stress is derived by solving basic equations directly. Solutions of stresses are obtained by correspondence principle method. Stress and displacement solutions available for the analysis of circular tunnel with radius random time varying. Then viscoelastic solution is obtained for the time after construction with radius linear and non-linear time-varying, For different construction path with the same ultimate shape, influence of construction speed and acceleration is analyzed quantitatively, and the phenomenon of time-radius correlation is also studied.