Abstract: In order to study the stability of the roof-pillar system in the goaf and determine its stability time， the rheological model of roof-pillar system in goaf was established by using Hooke-Kelvin-kelvin model， the thin plate theory， and the rheological mechanics theory. Based on this model， the differential equation of goaf roof mining subsidence was deduced， and according to the damage conditions of roof boundary， the stability time of goaf roof pillar system was calculated. By comparison of calculated results with the actual monitoring data， the rationality and reliability of the model were verified. The research shows that the rheological deformation of pillar is an important reason for the instability of roof-pillar system in the goaf. The rheological mechanical model can be applied to predict the stability time of the mined-out area， and also can be used to realize the timely and effective supporting and filling for goaf.

Key words: Goaf, Thin plate theory, Rheological model, Stability time