Analytical Solution for Lined Circular Water Conveyance Tunnels under the Action of Internal and External Hydraulic Pressure

The interaction between the surrounding rock and the support structure in a circular water conveyance tunnel with lining comprises two main aspects: internal and external hydraulic pressures, and the contact load between the post-excavation lining and the surrounding rock. There is currently no reasonable calculation method to consider both factors simultaneously. Therefore, by utilizing the assumption of smooth contact between the surrounding rock and the lining, an analytical model for a circular water conveyance tunnel with lining is developed through the complex function method. Smooth contact indicates continuity of radial contact stress, coordination of radial displacement, and the absence of shear stress transmission. Considering the inner and outer boundary stress conditions of the lining, two sets of undetermined analytical functions are established, corresponding to internal and external water pressure, as well as the contact stress between the surrounding rock and the lining. Ultimately, the stress and displacement components at any point within the surrounding rock and lining can be derived under the conditions outlined in this study. The analytical model elucidates the mechanism of load transfer within the circular water conveyance tunnel with lining, considering the combined effects of internal and external water pressure and excavation loads. Of particular note, it quantifies the restrictive impact of external water pressure on lining hydrofracturing when subjected to high internal water pressure. Additionally, the model offers a theoretical foundation for designing and assessing support structures for use in long-distance water conveyance projects.