Abstract One of the main factors that affect the tunnel face stability is the free or unsupported span (i.e., the unlined length adjacent to the tunnel face). In this work, a 2D failure mechanism is developed to compute, in the context of Limit Analysis, the collapse pressure for tunnel faces in Mohr-Coulomb materials, considering the free span. The new mechanism comprises three non-deformable blocks (two translational and one rotational) in such a way that the interface between one of the translational blocks and the rotational one is constructed by an iterative process that fulfills the associated flow rule imposed by Limit Analysis. A numerical model is employed to validate the proposed mechanism, demonstrating that it provides good predictions of the critical pressure and of the failure geometry, especially for tunnels in materials with higher friction angles (i.e., φ ≥ 35 ° ). Results confirm the expected increase of the collapse pressure with the free span; however, the increase is noticeably higher when no pressure is applied on the free span than when the support pressure is applied on the tunnel face and on the free span, especially for cases with lower cohesion (i.e., c ≤ 15 k P a ). In addition, the effect of a forepole umbrella is incorporated into the Limit Analysis mechanism, and a new methodology is proposed to estimate the collapse pressure when a forepole umbrella is installed at the face. Results of the analytical solution in this situation are compared with those of the numerical model, with results confirming that the proposed mechanism is able to capture the stability improvement (i.e., the reduction of the collapse pressure) produced by the umbrella, as well as the shape changes of the failure mechanism; in particular, it can predict a local failure of the face below heavy umbrellas.

中文翻译：

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考虑自由跨度的掌子面稳定性分析上界解

摘要 影响掌子面稳定性的主要因素之一是自由或无支撑跨度（即与掌子面相邻的无衬砌长度）。在这项工作中，开发了一种 2D 破坏机制，以在极限分析的背景下计算 Mohr-Coulomb 材料中隧道工作面的坍塌压力，同时考虑自由跨度。新机制包括三个不可变形块（两个平移和一个旋转），其中一个平移块和旋转块之间的界面是通过迭代过程构建的，该过程满足极限分析施加的相关流动规则。采用数值模型来验证所提出的机制，证明它提供了对临界压力和失效几何形状的良好预测，特别适用于具有较高摩擦角（即 φ ≥ 35 ° ）的材料中的隧道。结果证实了随着自由跨度的增加，坍塌压力的预期增加；然而，当在自由跨度上不施加压力时，增加明显高于在隧道掌子面和自由跨度上施加支撑压力时，特别是对于较低的粘聚力（即 c ≤ 15 k Pa）。此外，将前杆伞的影响纳入极限分析机制，并提出了一种新的方法来估计前杆伞安装在工作面时的坍塌压力。在这种情况下的解析解的结果与数值模型的结果进行了比较，结果证实所提出的机制能够捕捉稳定性的改进（即，伞产生的坍塌压力的降低，以及破坏机制的形状变化；特别是，它可以预测重型雨伞下方的面部局部故障。