It is difficult to accurately calculate the lump coal rate in a fully mechanized mining face.Therefore,a numerical simulation of the coal wall cutting process,which revealed the crack expansion,development,evolution in the coal body and the corresponding lump coal formation mechanism,was performed in PFC2D.Moreover,a correlation was established between the cutting force and lump coal formation,and a statistical analysis method was proposed to determine the lump coal rate.The following conclusions are drawn from the results:(1) Based on a soft ball model,a coal wall cutting model is established.By setting the roller parameters based on linear bonding and simulating the roller cutting process of the coal body,the coal wall cutting process is effectively simulated,and accurate lump coal rate statistics are provided.(2) Under the cutting stress,the coal body in the working face underwent three stages—microfracture generation,fracture expansion,and fracture penetration—to form lump coal,in which the fracture direction is orthogonal to the cutting pressure chain.Within a certain range from the roller,as the cutting depth of the roller increased,the number of new fractures in the coal body first increases and then stabilizes.(3) Under the cutting stress,the fractured coal body is locally compressed,thereby forming a compact core.The formation and destruction of the compact core causes fluctuations in the cutting force.The fluctuation amplitude is positively related to the coal mass.(4) Because the simulation does not consider secondary damage in the coal,the simulated lump coal rate is larger than the actual lump coal rate in the working face;this deviation is mainly concentrated in large lump coal with a diameter greater than 300 mm.