Sheltering effect induced by established station to the new station excavation in Zhengzhou

This study focuses on the interaction between the excavating pit and the adjacent established station, which was defined as sheltering effect and the inverse sheltering effect. A comprehensive conceptual framework and mathematical-physical expression were developed to define these effects, with the sheltering effect coefficient serving as an evaluation metric. The 0–1 boundary was defined to delineate the influence range of sheltering effect, and the sheltering circle family is thus established to describe the distribution of sheltering effect in the spatial range. Field monitoring data and numerical analysis was employed to investigate the multivariate nature of the sheltering effect. The results indicated a larger influence range for horizontal displacement while a greater influence degree for vertical displacement. The sheltering effect decreased with the increasing of spacing, while it increased with the excavation depth, having a jump mutation at a certain depth. In the Zhengzhou case study, the 0–1 boundaries for horizontal displacement are 30.24 m (1.2He) and 5.04 m (0.2He), for vertical displacement are 9.4 m (0.37He) and 18.9 m (0.75He), and for the rigid rotation of the station floor are 13.86 m (0.55He) and 5.04 m (0.2He). The critical points for jump mutations in horizontal displacement occur between 20 m and 22.1 m, for vertical displacement between 15.2 m and 22.1 m, and for the rigid rotation of the station floor between 16.4 m and 22.1 m. Constructing sheltering maps can effectively guide the project to leverage the sheltering effect and mitigate the inverse sheltering effect.