• As coal mining subsidence areas increasingly require remediation and reuse, accurately determining the surface movement duration caused by underground mining becomes crucial for evaluating surface stability and guiding engineering construction. In this paper, based on the dynamic subsidence characteristics (S-shaped curve) of surface points, a Hill time function model was established. Combining this model with the formal definition of surface movement duration yielded a robust theoretical prediction model. Validation with the 30 measured cases indicated relatively good agreement between the predicted and observed durations. Specifically, the mean absolute error was 23 days, the root mean square error stood at 30 days, and the mean absolute percentage error was 5.9%, values that reflect favorable prediction performance. Verification based on actual cases indicates that compared with existing empirical models, the proposed model exhibits notable improvements in prediction accuracy and applicability. As such, it may be considered a feasible approach for predicting the duration of surface movement. As coal mining subsidence areas increasingly require remediation and reuse, accurately determining the surface movement duration caused by underground mining becomes crucial for evaluating surface stability and guiding engineering construction. However, an increasing number of cases show that the existing prediction models of surface movement duration have large errors and are difficult to meet the requirements of actual engineering. This study analyzes the dynamic subsidence characteristics of surface points to establish a Hill time function model that accurately reflects the spatiotemporal variation of surface dynamic subsidence. Building upon this model and the definition of surface movement duration, we develop a theoretical prediction model. Validation using 30 sets of measured surface movement duration cases demonstrates strong agreement between predicted and observed values. The model achieves a mean error ( MAE ) of 23 days, root mean square error ( RMSE ) of 30 days, mean absolute percentage error ( MAPE ) of 5.9%, and normalized RMSE of 0.076. Both prediction accuracy and applicability surpass those of existing empirical models, establishing this approach as an effective method for precisely predicting surface movement duration.
Jiang et al. (Sun,) studied this question.