Abstract: This paper presents a theoretical prediction model for the surface movement duration in coal mining, which takes into account various factors such as coal seam mining height, average mining depth, loose layer thickness, bedrock layer thickness, and mining speed. The model is based on the improved Knothe time model and incorporates the definition of surface movement duration. Additionally, a method for determining the model parameters using the probability integration method is provided. To validate the rationality and accuracy of the prediction model, monitoring data from 24 deep working faces are utilized. The results demonstrate that the predicted surface movement duration aligns well with the monitoring results from the working faces. The mean absolute error is only 38 days, the root mean square error is only 47 days, and the mean absolute percentage error is only 9%. These values indicate a significantly lower prediction error compared to existing empirical models. The accuracy of the surface movement duration prediction model is confirmed. The study further reveals that the duration is influenced by coal seam mining height, average mining depth, loose layer thickness, bedrock layer thickness, and mining speed. Specifically, it increases nonlinearly with coal seam mining height, linearly with average mining depth, loose layer thickness, and bedrock layer thickness, but decreases nonlinearly with mining speed. This research provides theoretical guidance for evaluating the stability of surface movement and deformation in coal mining and formulating scientifically sound mining plans.

Key words: surface movement duration, improved Knothe time model, prediction, dynamic subsidence, mining speed