Study on the calculation of surface residual deformation in goaf based on the Gudermann time function

Under the strict differential limit requirements related to post construction subsidence of high-speed railway subgrade, the residual deformation of the surface is susceptible to a lasting and serious threat to the preliminary standardized construction and later safe operation of high-speed railway in goaf site. In order to comprehensively and effectively grasp the dynamic evolution process of surface movement and deformation, and realize the scientific and accurate residual deformation calculation of each key point of the surface in goaf, the Gudermann time function for dynamic anticipation is established by introducing the Gudermann function and optimizing it, the spatial and temporal characteristics of this function in the subsidence prediction are analyzed, and the influence law of parameter changes on the surface subsidence, subsidence velocity and subsidence acceleration curve patterns of the Gudermann time function is discussed, and the method of extracting the optimal values of the function parameters by Simulated Annealing Algorithm (SAA) is presented. Combined with the probability integral method, the calculation method of the residual subsidence at any point of the ground surface is proposed. Finally, 1176 east working face is adopted for verification, and the results show that the mean absolute error (MAE) and mean absolute percentage error (MAPE) of using the Gudermann time function for maximum subsidence point estimation are 40.23 and 0.17 respectively, and the determinable coefficient is 0.993, and the estimated value matches with the measured value. The Gudermann time function can be effectively adopted for the calculation of the residual deformation of the surface in goaf, while SAA is calculated at different times, the contour diagrams clearly show that residual subsidence increases gradually along the mining direction and reaches the maximum value at the surface near the stopping line, which is consistent with the actual mining process of the working face and proves the feasibility of the model calculation method. The accurate calculation of residual deformation provides an essential basis for judging the stability of goaf site.