Research on prediction model of surface dynamic subsidence of mined-out region based on Usher time function

The surface dynamic subsidence prediction of the goaf is one of the key problems in the field of mining subsidence，which plays an important role in the prevention and control of the subsidence disaster. In view of the problems existing in the prediction model of surface subsidence in goaf at present，through analyzing the law of surface subsidence and deformation caused by coal mining systematically，it is considered that the surface subsidence in goaf is a S shaped subsidence process with accelerating first and decelerating after，which can be roughly divided into three stages:initial subsidence，severe subsidence and declining subsidence. It is concluded that the ideal prediction model of surface subsidence in goaf should have a curve which can better fit the time relationship of surface subsidence，and the subsidence speed and acceleration should conform to the basic characteristics of the surface subsidence physical process. The Usher mathematical model，which is used to describe the change of growth information with time，is introduced into the surface dynamic subsidence prediction of the goaf. Through the in-depth analysis of the model structure and related parameters，it is considered that the Logistic model，Gompertz model，Knother model，Mitscherlich Brody model and Von Bertalanffy model are all special cases of the Usher model. Usher model，whose parameters can be solved by genetic algorithm，accords with the basic requirements of the ideal subsidence prediction model，and can better simulate the surface dynamic subsidence process of the goaf. On the basis of the above research，the Usher model is combined with the section function on the main section of the strike or dip of the subsidence basin after the stable subsidence，and the settlement calculation model at any point and at any time in the whole subsidence basin is constructed. The results show that Usher time function model，which can provide some reference for mining subsidence prediction，has stronger adaptability，higher fitting accuracy and better prediction effect than Knoth model，normal time function model，Logistic model and Gompertz model.