斜坡下浅埋偏压隧道地层响应的解析解答

Analytical solution of ground response induced by excavation of shallow-embedded bias tunnel under slope

针对斜坡下浅埋偏压隧道的开挖问题,考虑重力梯度作用,根据有限元模拟结果对现有解析偏压初始应力场进行修正,通过理论推导给出隧道开挖引发的地层响应解析解。求解采用复变函数法和Laurent级数解法,采用两种荷载释放方式建立隧道开挖边界的应力边界条件。结合地表边界条件求解得到完整的复位势表达,进而得到全域开挖增量应力和位移的理论解答。考虑到实际工程中隧道边界不存在不平衡力影响,采用洞心释放的理论解答分析了斜坡角度对隧道开挖后的地表位移和洞周应力、位移的影响。结果表明:随斜坡角度增大,偏压影响更加显著,地表位移整体向浅埋侧移动,浅埋侧隆起现象越加明显,地表最大沉降量减小,沉降槽整体向深埋侧移动。环向全应力在90°和270°区域出现拉应力极值,并随偏压角度增加向顺时针方向移动。研究成果对浅埋偏压隧道的初步设计具有参考价值。

Aiming at the excavation of shallow-embedded bias tunnel and considering the effect of gravity gradient, the existed analytical bias initial stress field is modified according to the result of the relevant finite element simulation, while the analytical solution of the ground response induced by the tunnel excavation is given out through then the oretical derivation concerned. The solving is made with complex-variable function method and Laurent series expansion, and then the boundary condition of the tunnelling boundary is established in accordance with two load releasing modes. Combined with the solving of ground surface boundary condition, the integral complex potential expression is obtained, and furthermore, the theoretical solutions of the universal incremental stress and displacement of the excavation are got as well. Under the consideration of that no impact from imbalance force is there on the tunnel boundary in the actual excavation, the effect from the slope angle on the ground surface displacement as well as the tunnel surrounding stress and displacement after the excavation of tunnel is analyzed with the theoretical solution of the releasing from tunnel center. The result shows that along with the increase of slope angle, the bias effect becomes more significant, for which the surface displacement integrally moves to the shallow-embedded side and the heaving phenomenon at the shallow- embedded side is more and more obvious, while the maximum surface settlement decreases and the settlement trough integrally moves to the deep-embedded side. The extreme values of the tensile stress appear in the regions of 90° and 180°for the circumferential total stress and move clockwise along with the increase of the bias angle. The study result has a referential value for the preliminary design of shallow-embedded bias tunnel.