Continuous curved beam formation and strata control theory in coal backfill mining

Based on a large number of engineering practice and physical similarity experiments,a theoretical model of continuous curved shape beam has been proposed to describe the mechanical behavior of overlying strata in backfill mining. Before the filling rate reaches a critical value,the roof will not fracture. And there are only bending deforma- tion and no penetrating cracks in overlying strata. These conditions result in forming a continuous bending shape beam structure at overlying strata. The structure can prevent the subsidence deformation of key rock stratum. In this paper, the geometric features and mechanical characteristics of the continuous curved beam are proposed. And the continuity conditions of the continuous curved beam are also provided. Through establishing the mechanical model,the authors have obtained the theoretical solution and simple engineering solution of the continuous curved beam deformation. The quantitative relationship between the continuous curved beam and the key layer is also analyzed,which can provide a theoretical basis for the filling rate design. A 3D model of continuous curved beam is discussed in detail. And its theo- retical solution and numerical solution are also obtained. The control mechanism of rock deformation is revealed for backfill mining.