Dynamic prediction of surface subsidence at any point based on Boltzmann time function model

The underground extraction of coal resources can induce surface subsidence, posing a potential threat to both the ecological environment and the structural stability of buildings. Anticipating the dynamic subsidence values prior to mining is crucial for establishing a foundation for dynamic restoration designs in mining subsidence areas. This represents a pressing concern within the field. In order to precisely predict the dynamic progression of surface subsidence resulting from underground coal mining, an optimal time function model is synthesized based on the dynamic principles governing surface subsidence. Subsequently, the Boltzmann time function model is introduced to comprehensively analyze the model in terms of subsidence value, subsidence velocity, and subsidence acceleration. The analysis reveals that the model aligns with the dynamic trends of surface subsidence. Through an exploration of the influence of various parameters on the model’s representation, their physical significance is determined, and defined as the final subsidence value A, the time of maximum subsidence rate t₀, and the coefficient of the degree of urgency of subsidence B, leading to the establishment of a dynamic prediction model parameter system based on the Boltzmann time function. Fitting the measured subsidence values at a singular point demonstrates that the accuracy of this model surpasses that of traditional dynamic prediction models, achieving a fitting disturbance R² of 0.998 8. Parameter inversion is conducted on the measured subsidence values at monitoring points within the mining area. Based on the inversion results, correlations are established between the dynamic predicted parameters of any point in the subsidence basin and the maximum subsidence value on the surface, mining speed, and overlying rock lithology coefficient. A calculation method for determining the dynamic predicted parameters of the model at any surface point is provided, and its accuracy is verified to be reliable by utilizing the data collected from six working faces. A dynamic prediction model for surface subsidence, integrating the Boltzmann time function and probability integration method, is formulated, enabling predictions at any point and time within the subsidence basin. The model is employed to obtain subsidence values for multiple periods, and its accuracy is validated. Results indicate that the dynamic prediction relative error during the mining process is less than 6.0%, the minimum is 2.7%.