Abstract: A plastic hinge area was formed before the empty area in the roof corner lost its stability and the three-hinged arch bearing mechanism was formed due to stress redistribution. Based on this characteristic， the roof was approximately regarded as three-hinged arch axis curve structure with a half span， the mechanical model including span (L)， arch loss (f) and roof rock load (q(x)) was established to solve the caving line equation (y(x)) and arch axis equation (N(x))， the roof stability and the caving line form were analyzed， and the critical span and the critical exposure area were calculated. Taking Paishanlou Gold Mine for example， the conclusion of sub stable goaf was drawn with the critical span being 70m in transverse， 140m in the vertical dimension and the critical exposure area 7 693m² by using the mechanical model. Therefore， the pillar mining is prohibited and the rapidly filling area is proposed so as to guarantee underground safety.

Key words: tilted roof, three-hinged arch axis, stability analysis, critical span, goaf treatment