Application of the Time Function Model for Dynamic Deformation Prediction in Mining Areas under Characteristic Constraints

The fundamental model for dynamically predicting surface subsidence is the time influence function. However, current research and the application of time functions often neglect the comprehensive characteristics of the entire surface deformation process, leading to a less systematic representation of the actual deformation law. To rectify this, we explore ground point deformation along the strike line from two perspectives: dynamic subsidence and dynamic horizontal movement. Moreover, we develop prediction models for dynamic subsidence and dynamic horizontal movement at any point along the strike line, utilizing the probability integral method (PIM) and considering the surface deformation features. We then use characteristic constraints based on the prediction models to constrain the time influence function. For this purpose, we employ the Richards time function which has strong universality to establish the time functions for dynamic subsidence and horizontal movement under these constraints. We provide an illustrative example of its application in the 12,401 working face. Additionally, we explore the suitability of interferometric synthetic aperture radar (InSAR) technology for acquiring dynamic subsidence data on the surface. The experimental findings reveal the following key observations: the Richards model, when applied for dynamic subsidence prediction under constraints, exhibits high accuracy with an R-squared (R 2 ) value of 0.997 and a root mean squared error (RMSE) of 94.6 mm, along with a relative mean square error of 1.9%. Meanwhile, the dynamic horizontal movement prediction model exhibits an accuracy in fully mined areas with an R 2 of 0.986, an RMSE of 46.2 mm, and a relative mean square error of 2.6%.