Prediction of mining-induced surface movement duration based on an improved Knothe time model

The surface movement duration is a key parameter for the evaluation of the stability of surface movement and deformation, and accurately predicting the surface movement duration under different geological conditions and mining intensity is crucial for the stability assessment of the surface and ground facilities. Firstly, a new model assumption is proposed based on the classical Knothe time model assumption, and an improved Knothe time model, which only contains one model parameter and can accurately describe the dynamic subsidence law of the surface, has been developed. Then, based on the improved Knothe time model, a surface movement duration prediction model that can comprehensively consider the mining depth, coal seam thickness and mining speed of the working face is established, and the determination method of model parameters is provided according to the probability integral method. Finally, the accuracy and rationality of the surface movement duration prediction model were verified by using monitoring data of the surface movement duration in 20 mining areas. The results showed that the predicted value of the surface movement duration prediction model based on the improved Knothe time model is highly consistent with the monitoring values in 20 mining areas, and their root mean square error (E_RMS) is only 64 days, which is far less than 882 days of the Specifications of Coal Mining and Pillar Retention Under Buildings, Water and Railways and 152 days of the Knothe time model, which verifies the accuracy and rationality of the prediction model of surface movement duration. The surface movement duration is affected by coal seam mining height, average mining depth and coal seam mining speed, and increases nonlinearly with the increase of coal seam mining height, increases linearly with the increase of average mining depth, but decreases nonlinearly with the increase of coal seam mining speed; When the mining speed of coal seam is less than 5 m/d, the surface movement duration can be shortened by appropriately increasing the mining speed of coal seam. The study can provide some reference for the prediction of the stable time of surface movement and deformation in coal mining.