A three-dimensional (3D) roof-pillars model was established to prevent disasters caused by the sudden release of high strain energy of goaf group system in the underground mine. The stability and mutational tendency of this model were analysed qualitatively and quantitatively based on the catastrophe theory and rheological mechanics theory. The mathematical criterion and mechanical conditions of the mutation and energy release at different moments were also derived. Moreover

an analytical algorithm for the stability of goaf group system was proposed

and its validity and practicability were verified. The effect of each factor on the stability of this system was further discussed on this basis. The results showed that

with the rheological process of pillars

the tendency of system mutation decreased. However

the integrity of roof was destroyed gradually

and its boundary condition successively the following three stages: the fixed end

simple support and free end. The critical value of the effective load bearing area ratio of pillars which maintained the system stability decreased at each stage

but jumped at the starting point of the stage of simple support and free end. In addition

the average reduction rates of at three stages decreased in turn. The system stability was dominated by the numerical relationship among the roof stiffness (D)

overlying strata load

the effective load bearing area ratio of pillars and the size of goaf group. Therefore

the study results provide a new idea and method for the safe excavation of mine as well as the evaluation and control of goaf group system stability.