非静水压力场中考虑应力释放的圆形隧道黏弹性解

VISCOELASTIC SOLUTION OF CIRCULAR TUNNEL UNDER ASYMMETRIC HYDROSTATIC PRESSURE CONSIDERING STRESS RELEASE

在非静水压力场中考虑应力释放的圆形隧道弹性解基础上,先利用对应性原理求解应力释放率λ为常数时隧道的黏弹性解。然后考虑到施工过程中应力逐步释放,隧道内壁(r=R0)处边界条件随开挖面和研究断面之间距离x变化,距离x取决于掘进速度v和时间t,从而边界条件可以表示为时间t的函数。采用斯蒂尔杰斯积分法将常应力释放率时黏弹性解中的λFi(t)(i=1~11)转换为Fi(t)对应力释放率导数dλ(t)的积分形式,可得非静水压力场中考虑应力释放的圆形隧道黏弹性解。该解在侧压系数k0=1时,可转化为静水压力场中考虑应力释放的黏弹性解;在λ=1时,可以转化为非静水压力场中不考虑应力释放的黏弹性解,所以后2种解均为非静水压力场中考虑引起释放圆形隧道黏弹性解的特例。考虑非静水压力场,求解边界条件能较好地反应工程实际中原岩应力分布;考虑应力释放能够反应隧道掘进过程中围岩应力及变形分布情况。故所提出的黏弹性解能够为隧道设计、施工阶段及长期变形及稳定性预测提供理论依据。

Firstly,taking use of the correspondence principle,the viscoelastic solution for the circular tunnel with constant ratio of stress release is obtained,based on the elastic solution of the circular tunnel under non-hydrostatic pressure. Then,the stress is released step by step during construction,and the boundary condition at the intrados will change along with the distance x between excavating face and the studred section. The distance x could be expressed as a function of excavation speed v and time t. so the boundary condition could be expressed as a function of time t and speed v. According to the Stieltjes integrals, the items ofλFi(t)(i=1-11) in the solution for constant ratio of stress release are replaced with the integrals of Fi(t) with respect to dλ(t). The solution for the circular tunnel under non-hydrostatic pressure considering the ratio of stress release could be obtained. When the ratio of horizontal pressure coefficients k0=1,the solution could be transformed into the viscoelastic solution for the circular tunnel under hydrostatic pressure considering the ratio of stress release. When the ratio of stress release λ=1,the solution will be transformed into the viscoelastic solution for the circular tunnel under non-hydrostatic pressure without considering the ratio of stress release. So the latter two solutions are special cases of the solution in the paper. The non-hydrostatic pressure assumption accords with the engineering practice,and the ratio of stress release indicates the effects of construction procedure on the stress and deformation of rock. The results could be a reference for the design and construction of tunnels.