Formation estimation and evolution mechanism of the pressure arch for non-circular tunnels under asymmetrical stress field

The tunneling-induced stress redistribution is dependent on the tunnel shape and the in-situ stress field, and the previous arch characterization method based on the circumferential or maximum principal stresses is only suitable for the circular tunnels under the hydrostatic stress field. In this study, a unified characterization method of the pressure arch for non-circular tunnels under the arbitrary stress field is proposed. By comparing the variations of compressive stress in different directions due to excavation, the ratio of the most significant increase in compressive stress is presented to characterize the arch effect, and the corresponding numerical algorithm is given. Since the proposed method takes the stress element as the basic analytical model, it can be easily applied to various complex excavation situations. Thereafter, combined with the established folding catastrophic model, an objective and unified quantitative method of the pressure arch boundaries is given. Using the proposed method, the longitudinal evolution of the pressure arch is analyzed. According to the expansion rate of the arch boundaries, three evolution stages including the initial formation, rapid expansion and stabilization are categorized. Parametric studies are conducted to illustrate the effect of ground properties and support stiffness on the pressure arch formation. It is found that the ground strength parameters and burial depth affect the arch range at a decreasing rate, while they have little effect on the arch shape. The lateral pressure coefficient has a significant effect on both the shape and range of the pressure arch. Increasing the support stiffness helps reduce the pressure arch range with a decreasing rate, while the synchronous variation of the elastic moduli of the surrounding rock and support does not affect the arch range under a certain relative elastic modulus. Finally, field monitoring is conducted to validate the proposed method in actual support design.