Application of Cusp Catastrophe Theory in the Research of Periodic Weighting Step in Shallow Seams

Taking Northern Shaanxi shallow seams as the background,using cusp catastrophe theory to analyze the stope bedrock periodic weighting step.The first bedrock cyclical pressure is treated as the cantilever periodic breaking.Potential function has been obtained to characterize the fracture process through the establishment of a mechanical model of the bedrock breaking.The bedrock cycle pressure limit span necessary condition is quantitatively obtained. Finally,comparatively analyzing the measured results with the engineering example,it shows that using catastrophe theory to analyze the shallow coal imrt span seam cycle pressure limit span is reasonable.