Insights into Water Inflow Mechanisms from Roof Aquifers: Analytical Solution of the Ditch Inflow Model

Water inflow from roof aquifers is a critical parameter in longwall mining, which greatly affects mine safety. Existing analytical methods, such as the large well method, can only provide single-value predictions and fail to reveal the underlying mechanisms of inflow variations. To address this, a time-dependent water inflow model named ditch inflow model is proposed. The model integrates fractal theory for fracture quantification, unsteady flow theory for flow modeling, and voussoir beam theory to link inflow dynamics to strata instability. Validation with field monitoring data from the Menkeqing coal mine demonstrates that the model accurately captures the increasing trend of water inflow, and greatly outperforms the large well method. As the rock strata undergo periodic fracturing, the water inflow exhibits a stepwise increase, accompanied by fluctuations during plateau periods. The analysis reveals that more than 70% of the water inflow occurs through the top of the conceptualized ditch, highlighting the importance of the vertical flow paths. This study theoretically reveals the underlying mechanisms controlling water inflow, which involve the dynamic co-evolution of the fracture network and hydraulic properties in response to mining activities over time. The findings are expected to provide valuable insights for water inflow assessment under similar hydrogeological conditions.