Abstract: This paper aims to investigate the calculation theory for roof stability in small section arch tunnels with deep horizontal layered surrounding rock. Based on summary and analysis of existing theory, we studied the calculation methods for the vertical relative deformation of the mid-span (vault) of layered roofs with both equal section and variable section by using the equivalent stiffness method. The results demonstrate that during the excavation of a small cross-section tunnel with horizontal layered surrounding rock, the layered roof primarily exhibits a simply supported beam model as the main stress mode. Therefore, predicting the displacement stability with a simply supported beam model is suitable for the layered roof. Additionally, when theoretically predicting the displacement stability of the layered roof, we should select the simply supported beam model with either equal section or variable section based on the actual situation. The rationality and applicability of the proposed calculation theory are verified through engineering examples and numerical simulations. Overall, the calculation theory presented in this paper effectively determines the stability of the roof in small section arch tunnels with deep buried horizontal layered surrounding rock.

Key words: horizontal layered surrounding rock, equivalent stiffness method, vertical relative deformation, simply supported beam model, layered roof with variable section