Mechanical model and application of mixed boundary protection roof
For mines with poor stability of direct roof,it is usually necessary to reserve protective roof to prevent collapse of direct roof.In order to ensure safe mining,it is very important to determine reasonable thickness of protective roof.According to the structural mechanics analysis of goaf roof of room pillar mining,protective roof was regarded as thin plate fixed by the free rest of four sides in the middle,that is,mixed boundary thin plate.Using reciprocal theorem,deflection surface equation of thin plate with mixed boundary was derived,and the mechanical model of protective roof with mixed boundary was constructed.On this basis,calculation formula of safe thickness of top protective roof was obtained.The results show that,by comparing deformation of thin plate with mixed boundary and thin plate with four fixed edges,the deflection of the mixed-boundary thin plate is larger than that of the four-sided fixed thin plate,and the length of the free section of the mixed boundary is positively correlated with the maximum deflection.The results of theoretical analysis and numerical simulation have been applied to No.9 stope of a bauxite mine,and the safety thickness of protective roof is determined to be 1 m,which verifies the accuracy of the mechanical model.