Study on the Thin Plate Model with Elastic Foundation Boundary of Overlying Strata for Backfill Mining

In order to better study the movement principles of overlying strata during backfill mining, we established a thin plate model on an elastic foundation with elastic foundation boundary of the main roof. And by the finite difference method, the variation principles of the main roof’s principal moments and maximum subsidence ω 0 with the elastic foundation coefficient k 1 of the coal seam, the elastic foundation coefficient k 2 of backfill body, the thickness h , Young’s modulus E , and Poisson’s ratio μ of main roof are calculated and studied. Using these calculations, we were able to determine that the main roof had three principal bending moment extreme points, including M zz in backfill areas, M c of the long side area, and M d of the short side area. The distance L c of M c advancing coal wall continuously increased with the increase in k 2 , while the principal moment of main roof’s middle area decreased with an increase in k 2 ; when k 2 became larger, the maximum principal moment in the midpoint of main roof transferred to the surrounding and the maximum principal moments was in four-corner area; M c and M d decreased with an increase in k 2 , and M d was more sensitive to k 2 than M c ; and M d decreased significantly with the increase in k 2 . L c continuously decreased with the increase in k 1 , while M c , M d and M zz increased with the increase in k 1 and the reduced amplitude of M zz was the minimum. The effect of μ on principal bending moments and ω 0 was very small; The growth rate of M zz was the largest when E or h increased. M d , M zz , and L c remained unchanged when k 1 , k 2 , and Young’s modulus E of the main roof increased while the ratio value remained constant ( k 1 / k 2 / E ). Finally, the theoretical calculations were applied to the I26 backfill working face in the Xingdong mine to calculate the final subsidence amounts of the main roof. Field observations and theoretical calculations were about 48 mm, verifying the method’s applicability.