Abstract: In order to identify the influence of stress on the porosity of broken coal in goaf,based on the compacted environment of residual coal in gob,the influence of goaf porosity on air leakage intensity,oxygen concentration distribution and thermal storage environment in coal spontaneous combustion was analyzed from the point of stress recovery in goaf and the effect of porosity on coal spontaneous combustion. Through the compaction experiment of broken coal samples of Hengsheng goaf,the change characteristics of stress-strain and porosity were tested. Combining with fractal theory,the porosity fractal model of the compacted coal particles was established,the initial parameters of the fractal model were determined,and the theoretical calculation and the experimental data were compared. The results show that:① under the action of stress,the compaction deformation of granular coal occurs,resulting in the change of particle gradation,the increase of fractal dimension and the variation of porosity. It indicates that with the advance of the working face and the action of the stress recovery,the porosity of the broken coal body in the goaf presents a dynamic change. ② With the test of the particle size distribution and gradation changes of original coal sample and broken coal sample,the fractal dimension of the coal sample is obtained. The increase of the fractal dimension of the broken coal indicates that the loaded coal sample is more broken,the porosity decreases gradually under the stress loading.③ Based on the fractal theory and the stress-strain relationship of crushed coal under pressure,the fractal porosity theoretical model of granular coal under pressure is established. The porosity error of the theoretical calculation and experimental results is between 0.028 and 0.106 by the relationship between fractal theory and the stress-strain of pressure bearing broken coal body,which meet the requirements of engineering,and the model is relatively reliable. ④ The application conditions of the model are analyzed,the model can predict the porosity change dependent on the premise of mastering the stress-strain function and stress loading path of broken coal and rock.