Semi-analytical Solution For Deformation Of Thin Rectangular Plate On Non-uniform Elastic Foundation And Its Application In Roadway Driving Along Goaf

Along with the development of China’s economy, construction projects continuously increasing and the scale constantly expanding, plate structures on non-uniform elastic foundation have been more and more widely applied in civil, foundation and mining engineering, so study on the bending deformation of the thin plate on non-uniform elastic foundation has important engineering practical significance. This thesis study mainly adopted the methods of theoretical analysis, numerical calculation and numerical simulation. It put forward a new semi-analytical solution for the deformation of thin rectangular plate on non-uniform elastic foundation, and the solution was applied in the deformation calculation of basic roof on working face with roadway driving along goaf in actual mining. The cycle evolvement of the basic roof deformation was analyzed. Study results and conclusions are summarized as follows:(1) By assuming arbitrary shape region distributions of the elastic foundations, this thesis established the bending deformation mechanics model of the thin plate on non-uniform elastic foundation and deduced the differential equation of the plate bending deformation. It proposed a new semi-analytical solution of solving ideas and methods for the problem that the unified form of trial deflection function were unable to find due to the difference of the loads, boundary conditions and elastic foundation coefficients of each area. First, the whole piece of rectangular thin plate was divided into small rectangular areas and numbered them. Than the trial deflection functions of each areas were set to the form that met the known boundary conditions and contained undetermined parameters, and their coefficients were solve out in the form of undetermined parameter by the commonly methods of the thin plate bending deformation. At last, the parameters values were determined by using the continuity conditions of public boundary deformation of each rectangular areas, and all the plate deflection distribution functions of solving domain were obtained.(2) Considering the basic roof periodic breakage and the twice mining influence, the basic roof mechanics model of rectangular thin plate on non-uniform elastic foundation is established on the basis of the failure characteristics and stress distribution of on working face with roadway driving along goaf in actual mining. The numerical results of the basic roof bending deformation were calculated by applying the theory of semi-analytical solution for the deformation of thin rectangular plate on non-uniform elastic foundation and the MATLAB programs. And the basic roof bending deformation law was analyzed as a result.(3) Combined with engineering example, the bending deformation of basic roof on working face with roadway driving along goaf in actual mining were simulated based on FLAC3D. The evolution law of the basic roof deformation values as the working face advancing was analyzed, which summarized the period of the most serious roof deformation and the most dangerous roadway drived along goaf in actual mining and put forward some suggestions of roadway surrounding rock control on the basis. And contrastive analysizing the results of numerical simulation and theoretical calculation, it was found that the two were almost consistent, which verified the reliability and validity of the theoretical calculation and provided a theoretical basis for the control of the surrounding rock deformation of roadway driving along goaf.