基于上限定理的砂卵石地层盾构隧道开挖面稳定性分析

目前对砂卵石地层开挖面稳定理论模型的研究相对较少，施工过程中盾构机支护力的施加多凭借施工经验进行。为研究砂卵石地层开挖面失稳问题，运用极限分析法上限定理，结合椭球体放矿理论，建立盾构隧道开挖面极限分析模型的计算方法，研究开挖面前方土体变形未发展至地表与发展至地的表两种工况，得到了极限支护力的上限解析解。并选取五种典型的理论分析方法验证了计算结果的正确性。结果表明：所提出的对数螺线椭球体机制得到的开挖面极限支护力受地层内摩擦角、隧道直径以及土体重度的影响较大，埋深和黏聚力的影响较小，地表超载的影响最小；其中开挖面极限支护力均随着土体重度和隧道直径的增大而线性增大，随着摩擦角增大呈现非线性减小趋势；通过与旋转破坏机制、3D对数螺线机制、FLAC^3D数值模拟得到的开挖面前方塌落区域的对比，所提出的开挖面前方塌落机制与数值模拟能接近地层的失效形状。

Study on excavation Surface Stability of Shield Tunnel in Sandy Cobble Stratum based on Upper limit Analysis

In view of the instability of the excavation face of the sandy cobble stratum, the research on the theoretical model at the present stage is relatively less, and the application of the supporting force of the shield machine in the construction mainly depends on the construction experience. In order to study the instability of excavation face in sandy cobble stratum, the calculation method of limit analysis model of excavation face of shield tunnel is established by using the upper bound theorem of limit analysis method and ellipsoid drawing theory. In this paper, the two working conditions of the deformation of the square stratum before the excavation were studied, and the upper limit analytical solution of the ultimate supporting force was obtained. Five typical theoretical analysis methods were selected to verify the correctness of the calculation results. The results show that the ultimate supporting force of the excavation face obtained by the logarithmic spiral ellipsoid mechanism proposed in this paper is greatly affected by the friction angle in the stratum, the diameter of the tunnel and the weight of the stratum, while the influence of buried depth and cohesion is small, and the influence of surface overloading is the least. Among them, the ultimate supporting force of excavation face increases linearly with the increase of stratum weight and tunnel diameter, and decreases nonlinearly with the increase of friction angle. Compared with the rotational failure mechanism, 3D logarithmic spiral mechanism and the collapse area in front of the excavation face obtained by FLAC3D numerical simulation, the collapse mechanism and numerical simulation in front of the excavation face can approach the failure shape of the stratum.