Constitutive relation and particle size distribution model of rock fragments in the goaf

Permeability is considered a key parameter used in goaf flow simulation. Particle size of caved rock fragments is an important factor that affects permeability. Current literature treats the particle sizes of rock fragments as a constant, which is something that will inevitably lead to great errors. The sigmoid function is introduced, based on the existing main roof subsidence displacement model, to establish a new main roof subsidence displacement model, which will reflect the characteristics of the natural accumulation zone, load-affected zone, and compacted zone in the goaf. The constitutive relationship of the rock fragments meanwhile is established from a mechanical perspective. Particle sizes of the rock fragments in the goaf are controlled by the maximum median particle size, with the minimum particle size calculated as 69.25% of the maximum median particle size. In addition, with the same mining height, the stronger the overlying strata is, the larger the particle size, while under the same geological conditions, the larger the mining height, the smaller the particle size of the rock fragments. This paper provides a constitutive relation and particle size distribution model of rock fragments which is more consistent with the actual coal mine's characteristics.