Instability behaviors of main roof in gentle dipping seam longwall mining

By applying the initial post-buckling theory and the cusp catastrophic model, the instability behaviors of gentle dipping key roof stratum during the first weighting are studied. By using the bifurcation set of key roof stratum and the critical equilibrium condition in a state of bifurcation state, the formulae for breaking convergence and breaking span of main roof are derived, and the criteria for step convergence and instability due to rotation after breaking of the main roof are established. It is pointed that the rock blocks are in a state of either stable equilibrium or unstable equilibrium after breaking of the main roof, that is, the breaking convergence has determinate relation with the breaking span in a state of stable equilibrium, and either step convergence or instability due to rotation for rock blocks may occur in a state of unstable equilibrium after breaking of the main roof. In accordance with the occurrence behaviors of roof structures, rock materials and thick unconsolidated layers above the roof, the integrated application of the initial post-buckling theory and the catastrophe theory can be adopted to determine catastrophic forms of the main roof structures during the first weighting.