Coal serves as the primary energy source in China

playing a crucial role in maintaining national economic stability. Due to the characteristic of high thick-and-hard overburden strata

strong mine tremors occur frequently in Shilawusu coal mine in Inner Mongolia

which seriously restricts the safe mining of coal. The primary cause of strong mine tremors is the fracture of high thick-and-hard overburden strata

making it imperative to investigate the mechanical mechanism of such fractures under adverse geological conditions. The study is conducted using the 1206A and 1208 panels of the Shilawusu coal mine as the research context. On the basis of Reissner theory and considering the influence of gravity stress field

the analytical formulas of deflection

rotational angle

shear force

bending moment

and maximum tensile stress of the thick plate with fixed supports on four sides are derived. Considering the influence of horizontal ground stress field and its transfer

the breaking criterion of the high thick-and-hard overburden strata is established

and a MATLAB-based calculation program for determining the initial fracture step distance of such strata is developed. Finally

the program was used to systematically study the influence of the panel width

overburden strata thickness and overburden load on the initial fracture step distance of the thick-and-hard overburden strata.