Theoretical model and verification of 'analogous hyperbola (hyperboloid)' for the overall movement of mining rock strata: From two-dimensional 'analogous hyperbola' to three-dimensional 'analogous hyperboloid' models

Coal mining can cause the deformation, fracture, and movement of overlying strata from bottom to top, leading to surface subsidence and other problems. This is a mechanical process, so it is urgent to develop a movement theoretical model based on the mechanical mechanism of rock fracture. Firstly, this paper reviews some theoretical models of rock movement worldwide, and then focuses on our research progress in the field of overall rock movement theoretical models in recent years. Based on the mechanical analysis of the fracture morphology of different layers of rock and the results of similar simulation tests, an “analogous hyperbola” model for the overall movement of mining induced overlying strata was proposed, the focus of the model was approximately located in the layer of the main key stratum of the overlying strata. Furthermore, the overall model of “analogous hyperbola” inside and outside the strata movement was established, and the expression and physical significance parameter system for the internal and external movement of mining overlying rocks were provided. The evolution law of the “hyperbolic like” model for the overall movement of rock layers was analyzed based on different occurrence conditions of overlying rocks and coal seams. On this basis, further extending the two-dimensional “analogous hyperbola” model to the three-dimensional “analogous hyperboloid” model, the three-dimensional movement model of “analogous hyperboloid” in the whole space of mining overburden was established, which includes “quasi-single-leaf” and “quasi-double-leaf” hyperboloids. This theoretical model is based on the research of many predecessors and scholars in China, from the perspective of systems science, it considers the overall movement law of rock layers. A preliminary theoretical model framework of the “analogous hyperbola (hyperboloid)” theory for the overall movement of mining overburden has been formed, hoping to provide a theoretical guidance for scientific coal mining in China.