Analytical Method for Mechanical Behaviors of Pipe Roof Reinforcement

Pipe roof reinforcement allows safe excavation by creating longitudinal arching parallel to the tunnel axis. The complexity of boundary conditions of this method, however, imposes difficulties to understand the reinforcement mechanism. There are few attempts to analyze the mechanical behaviors of the reinforcing pipes. In this study, considering the delay effect of initial lining and revising the Winkler elastic foundation model, an analytical approach based on Pasternak elastic foundation beam theory for pipe roof reinforcement was put forward. The corresponding deformation equations, internal force formula were deduced, and the solutions of this model were given. This model was then reviewed with an actual case study of the Qiaozhuang tunnel. The results prove that reinforcing pipes act as a lever, which increases longitudinal load transfer to an unexcavated area, and consequently decrease deformation and increases face stability.