A Theoretical Model for Pipe Roof Support Considering the Micro-arch Effect between Pipes in Shallow Buried Tunnels under Biased Pressure Conditions

Pipe roof support is widely employed in shallow-buried tunnels under biased pressure conditions. However, the influence of the micro-arch effect between pipes has received little attention, particularly under such biased pressure conditions, making it difficult to accurately reflect the true mechanical response of the pipe roof. To address this, a theoretical model based on Pasternak theory has been developed to analyze the longitudinal internal forces and deformation of the pipe roof, explicitly accounting for the micro-arch effect. This effect is incorporated by introducing the calculation formula for surrounding rock pressure under biased pressure conditions from established design codes. The model is validated against data from existing literature, showing that the variation trends predicted by the theoretical model align with those from other relevant models, while the maximum deformation of the pipe roof corresponds more closely to field monitoring data. Parametric analysis reveals that as the bias angle increases, the micro-arch effect between pipes decays, leading to a significant reduction in internal force and deformation at the crown of the pipe roof. Compared with traditional models, the proposed approach not only analytically accounts for the influence of topographic bias angle on the micro-arch effect, but also enables more accurate prediction of the mechanical behavior of the pipe roof.