Stability analysis of large-span roadway roof based on cusp catastrophe theory

Instability criterion of large-span roadway roof is established based on cusp catastrophe theory and mechanical model of roof composite beam. The criterion shows: critical state of instability about roadway roof depends on combination of roadway width, roadway roof vertical stress and horizontal stress. When the roof side pressure is greater than 5MPa,the roof top pressure causing instability is from large to small with roadway width increasing; When the roof side pressure is smaller than 5MPa the roof top pressure is all most same with any roadway width. When the roadway span than 5m,the roof top pressure causing instability is from large to small with roof side pressure increasing. When the top pressure is a constant, the roof of large-span roadway maybe occur instability with smaller or larger roof side pressure.