1.Hunan University of Science and Technology，School of Resource，Environment and Safety Engineering，Xiangtan ，China；2.CCTEG Shenyang Research Institute，Fushun ，China；3.Work Safety Key Lab on Prevention and Control of Gas and Roof Disasters for Southern Coal Mines，Hunan University of Science and Technology，Xiangtan ，China

Foam fluid is an effective technical means for prevention and control of leakage of roof cracks and spontaneous combustion of coal due to its excellent construction characteristics and application characteristics.Based on the engineering background of foam fluid injection in recycled roof cracks，the analysis of the force and flow of foam fluid in cracks are carried out.The mathematical model of the flow and diffusion of foam fluid in the cracks with arbitrary occurrences containing the retardation of the original medium was derived.The numerical model of foam fluid diffusion in regenerated roof cracks was constructed by ANSYS FLUENT software，and the rationality of the mathematical solution was verified by comparison.The effects of construction parameters (including grouting pressure and grouting hole radius) and fracture parameters (including fracture opening，dip angle，inclination and original medium pressure) on the diffusion law during the foam grouting diffusion process of foamed roof regeneration were carried out.The sensitivity of the parameters to the diffusion process was calculated quantitatively and it wasfound that the fracture opening degree had the greatest influence on the diffusion distance，followed by the grouting pressure，and the inclination angle and the original medium pressure had the least influence.

国家自然科学基金资助项目（51974119，51604110，51774135，51874131）；中国博士后科学基金资助项目（2017M612558，2018T110831）；教育部高等学校特色专业建设点资助项目（TS11624）