基于对数曲线和塌落拱组合的砂卵石隧道开挖面稳定分析

Stability Analysis of Excavation Face in Sandy Pebble Tunnels Based on Combination of Logarithmic Curves and Collapse Arches

合理的支护力对于砂卵石土隧道开挖面的稳定性至关重要。借助已有对数螺旋曲线破坏模式,将塌落拱模型与极限分析法结合,建立砂卵石隧道开挖面破坏模型,并提出适用于砂卵石隧道的开挖面极限支护力计算方法。然后,将本文理论解析与数值模拟、已有理论进行对比,获得不同内摩擦角和黏聚力下的破坏区域。最后,利用理论解析与数值模拟方法对北京某盾构隧道进行开挖面稳定性分析。结果显示,本文解析解与已有研究获得的极限支护力吻合较好,计算便捷,精度较高。极限支护力随着内摩擦角的增大呈非线性减小,且在摩擦角较小时,极限支护力对内摩擦角变化更为敏感。极限支护力随着黏聚力的增大呈近似线性减小。当埋深比较小时,其对极限支护力有着较为明显的影响。当C/D>1.0时,隧道埋深的增加对极限支护力的大小没有明显影响,摩擦角对破坏区域有非常明显的影响。随着内摩擦角的增大,破坏区域显著减小。黏聚力对破坏区域的影响非常小,即不同黏聚力下耗能面的大小几乎不变。针对北京某盾构隧道计算可以发现,基于极限分析法提出的破坏模式优化塌陷范围及形状后,使得破坏模式更加合理,同时破坏范围更大,取得了很好的工程应用效果。

Reasonable support force is crucial for the stability of the excavation face in sandy pebble tunnels.By utilizing the existing failure mode of the logarithmic spiral curve,this study combined the collapse arch model with the limit analysis method to establish a failure model for the excavation face in sandy pebble tunnels.A calculation method for the ultimate supporting force applicable to the excavation face of sandy pebble tunnels was also proposed.Then,the theoretical analysis presented in this paper was compared with numerical simulation and existing theories to determine the failure areas under different internal friction angles and cohesion values.Finally,the excavation face stability of a shield tunnel in Beijing was analyzed using theoretical analysis and numerical simulation methods.The results showed that the analytical solution proposed in this paper was in good agreement with the limit supporting force derived from existing research,with convenient and accurate calculations.The limit supporting force decreased nonlinearly with the increase of the internal friction angle,and was more sensitive to changes in the friction angle when the angle was small.The limit supporting force decreased approximately linearly with the increase in cohesion.When the burial depth was small,it had a more significant impact on the limit supporting force.When the C/D ratio exceeded 1.0,the increase of the burial depth of the tunnel had no obvious effect on the limit supporting force,and the friction angle had a very significant effect on the failure area.With the increase of internal friction angle,the failure area decreased significantly.Cohesion had little impact on the failure area,i.e.,the size of the energy dissipation surface remained nearly unchanged under different cohesion values.For the shield tunnel in Beijing,the calculation based on the limit analysis method optimized the collapse range and shape,making the failure mode more reasonable while increasing the failure range,achieving excellent engineering application results.