Subsidence Prediction Method Based on Elastic Foundation Beam and Equivalent Mining Height Theory and Its Application

Grouting technology in overburden separation is recognized as an effective method to prevent surface subsidence and reuse solid waste. This study used mechanical analysis to explore deflection characteristics of key strata and accurately predict and control surface subsidence. Conceptualizing the coal–rock mass beneath the key strata as an elastic foundation, we developed a method to calculate the elastic foundation coefficients for various regions and established an equation for key strata deflection, validated through discrete element numerical simulations. This simulation also examined subsidence behavior under different grout injection–extraction ratios. Additionally, combining the equivalent mining height theory with the probability integral method, we formulated a predictive model for surface subsidence during grouting. Applied to the 8006 working face of the Wuyang Coal Mine, this model was supported by numerical simulations and field data, which showed a maximum surface subsidence of 546 mm at a 33% injection–extraction ratio, closely matching the theoretical value of 557 mm and demonstrating a nominal error of 2%. Post-grouting, the surface tilt was reduced to below 3 mm/m, meeting regulatory standards and eliminating the need for ongoing surface structure maintenance. These results confirm the model’s effectiveness in forecasting and controlling surface subsidence with grouting. The study can provide a basis for determining the grouting injection–extraction ratios and evaluating the effectiveness of surface subsidence control in grouting into overburden separation projects.