Space-time distribution model of ground fracture ratio caused by mining-induced underground coal fire

A space-time unified distribution model of ground fracture ratio caused by mining-induced underground coal fire was proposed based on the theory of random medium movement. The distribution and dynamic change laws of ground line (tension) fracture ratio, areal fracture ratio and shear fracture ratio were revealed through the analysis of an example. The maximum values of these three categories of ground fracture ratio respectively distribute in the ground surface region corresponding to the 20-m inner side from the surrounding boundary, the 4 midpoints of the surrounding boundary, and the 4 marginal endpoints of goaf. With combustion of the coal seam, the line fracture ratio perpendicular to the fire development direction and the areal fracture ratio corresponding to the boundary of goal change according to the half normal curve and stable at the maximum, while the shear fracture ratio, line fracture ratio along the fire development direction and the areal fracture ratio corresponding to the interior of goaf change according to the normal curve.