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 ω0 with the elastic foundation coefficient k1 of the coal seam, the elastic foundation coefficient k2 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 Mzz in backfill areas, Mc of the long side area, and Md of the short side area. The distance Lc of Mc advancing coal wall continuously increased with the increase in k2, while the principal moment of main roof’s middle area decreased with an increase in k2; when k2 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; Mc and Md decreased with an increase in k2, and Md was more sensitive to k2 than Mc; and Md decreased significantly with the increase in k2. Lc continuously decreased with the increase in k1, while Mc, Md and Mzz increased with the increase in k1 and the reduced amplitude of Mzz was the minimum. The effect of μ on principal bending moments and ω0 was very small; The growth rate of Mzz was the largest when E or h increased. Md, Mzz, and Lc remained unchanged when k1, k2, and Young’s modulus E of the main roof increased while the ratio value remained constant (k1/k2/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.
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