Objectives and Methods Presently, there remains a lack of theoretical models for predicting the coal mining-induced surface subsidence during the initial, active, and decline stages. Given this, this study derived the time-varying exponential function of the ratio of maximum to dynamic surface subsidence first using measured data from seven coal mines. Accordingly, an improved Knothe time function model was established. Then, the impacts of the model parameters on dynamic surface subsidence W(t), subsidence velocity v(t), and subsidence acceleration a(t) were analyzed. Subsequently, based on the improved Knothe model and the critical subsidence velocity v₀ used to determine the three surface subsidence stages, this study constructed models for predicting the subsidence during the three stages and determined the expressions for calculating the model parameters. Finally, the accuracy and applicability of the improved Knothe model were verified using data from a certain mine in the Huainan mining area, Anhui Province, including global navigation satellite system (GNSS)-derived real-time surface subsidence monitoring data and measured data from four conventional subsidence monitoring points. Additionally, the rationality and accuracy of the surface subsidence prediction models for the three stages were verified using the measured dynamic surface subsidence data from 20 coal mines.

Results and Conclusions When fitting to the GNSS-derived real-time surface subsidence monitoring data, the improved Knothe model showed significantly higher accuracy than the classical Knothe model while also outperforming the Weibull and Hill models. When fitting to the measured data from four conventional monitoring points, the improved Knothe model yielded relative standard deviations of all less than 4%, verifying the accuracy of the model. Furthermore, the measured dynamic surface subsidence data from 20 coal mines were roughly consistent with the predictions of the surface subsidence prediction models for the initial, active, and decline stages, with root mean square errors corresponding to the three stages determined at merely 0.039 m, 0.105 m, and 0.076 m, respectively. These results also verify the accuracy and rationality of the prediction models. This study provides models and a theoretical basis for analyzing and predicting dynamic surface subsidence regularity.