Research on surface dynamic subsidence prediction model for western mining areas based on GNSS time series data

Compared to conventional observation stations, continuous GNSS monitoring stations in mining areas can better capture dynamic subsidence characteristics of the ground surface. However, the practical application is constrained by the excessive number of GNSS stations required and the high associated costs. To explore the feasibility of constructing surface dynamic subsidence models using continuous GNSS observations from a limited number of stations, the surface subsidence monitoring project in the Loess Plateau mining area was used as a case study. By plotting dynamic subsidence curves and their corresponding velocity and acceleration variation curves, it was found that their distribution characteristics closely matched those of the Boltzmann angular function and its first-order and second-order derivatives. Therefore, the Boltzmann angular function with its “S-shaped” distribution characteristic was selected to construct the surface dynamic subsidence model. Two parameters−the relative position angle x and eccentricity angle y−were introduced to describe the relative positional relationship between monitoring stations and the dynamic boundary of the working face. The four parameters of the Boltzmann model (A₁, A_2, a, b) were inverted using GNSS time-series observation data, and the physical significance and variation characteristics of each parameter were elucidated. Based on this, a Boltzmann model for surface dynamic subsidence was constructed using GNSS time-series observation data acquired during the working face advancement. Analysis of how model parameters vary with the working face advancement position (parameter x) revealed that these parameters' temporal changes tend toward stable values as surface subsidence increases. This model enables precise prediction of subsequent subsidence. Further analysis revealed that the spatial variation of Boltzmann model parameters across GNSS stations on the main fault plane conforms to Gaussian distribution characteristics. Observation data from no fewer than five GNSS stations can stably fit Gaussian function parameters, enabling the establishment of a Boltzmann prediction model for dynamic subsidence at any surface point. Field data validation demonstrates that the Boltzmann model constructed from time-series observations at a small number of stations (no fewer than five) exhibits excellent parameter determinacy and prediction accuracy. This provides an effective approach for dynamic monitoring and prediction of surface subsidence in western mining areas.