An upper bound solution for tunnel face stability analysis considering the free span: Fid-Bau Portal

An upper bound solution for tunnel face stability analysis considering the free span

Senent, Salvador / Yi, Congke / Jimenez, Rafael

Highlights • Advanced 2D mechanism for tunnel face stability considering the free span. • Limit Analysis mechanism combines rotational and translational blocks. • Validated with an FE limit analysis (OPtumG2) numerical model. • Can consider reinforcement effects provided by a forepole umbrella. • Proposes simple methodology to consider forepole umbrellas in practice.

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., $φ \geq 35^{°}$ ). 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., $c \leq 15 k P a$ ). 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.