Analytical modeling of complex contact behavior between rock mass and lining structure

Based on the nondestructive test data of operating railway tunnels in China, this paper summarizes the basic characteristics of the complex contact behavior between the rock mass and lining structure. The contact modes are classified into dense contact, local non-contact, and loose contact. Subsequently, the corresponding mechanical model for each contact mode is developed according to its mechanical characteristics using the complex variable method. In the proposed mechanical model, a special algorithm is introduced to detect whether the local non-contact zone is re-contacted. Besides, a novel conformal mapping method is also proposed to accurately calculate the mechanical response of the concrete lining. Finally, the accuracy of the proposed method is verified by comparing it with the finite element method (FEM). Several parameter investigations are conducted to analyze the effects of different contact modes on the rock–lining interaction. The results show that: (i) the height of the local non-contact area does not have a significant effect on the contact stress distribution if no re-contact occurs; (ii) backfill grouting can reduce the local stress concentration caused by poor contact modes; and (iii) reducing the friction coefficient of the interface can lead to a more uniform distribution of internal forces in the concrete lining.