Fracture regularity of thin plate model of main roof with elastic foundation boundary for backfill mining

Under the condition of filling coal mining,a thin plate mechanics model of main roof on elastic foundation with elastic foundation boundary was established. According to the difference theory and the fracture principle of pri- mary bending moment,the effects of the elastic foundation coefficient kf of filling body,the thickness h and elastic modulus E of the main roof and the elastic foundation coefficient km of boundary on the primary bending moment and fracture regularity of the main roof were studied. It is concluded that when the kf increases,the absolute maximum prin- cipal bending moment of the short side and long side ahead of the coal wall and the filling area Mb ,Md and Mo all de- crease,while the Mo decreases most,and the distance b of Mb ahead of the coal wall increases. When E or h decreases, the b and the Mo ,Mb and Md all decrease. When the km decreases,the b decreases,whlie the Mb ,Md and Mo increase. In the filling area,the principal bending moment of main roof has differentiation phenomenon. The larger the kf ,or the smaller the h and E,the maximum principal bending moment of the filling area is gradually transferred to the surround- ing area. The principal bending moment in the non-midpoint region is more than Mo . The km has little effect on the differentiation phenomenon. Under the filling conditions,when the principal bending moments of main roof is greater than the ultimate moment of main roof,the initial fracture position is the upper surface of the long side leading coal wall or the middle lower surface of main roof. When the kf is small,the filling rate is low and the overlying load is large,there are three types of main roof fracture sequence:① upper surface of long side→upper surface of short side→lower sur- face of the middle;② upper surface of long side→lower surface of the middle→upper surface of short side; ③ lower surface of the middle→upper surface of long side→upper surface of short side.