Study on the instability mechanism of interbedded rock strata and remaining coal pillar groups based on cusp catastrophe theory

• Explored instability of interbedded strata and coal pillars via cusp catastrophe theory. • Found advanced pressure transfer and coal pillar modulus reduction cause chain instability. • Determined shear stiffness-thickness ratio <0.206 triggers interbedded strata catastrophic failure. • Simulated max coal pillar stress (8.26 MPa) at 4-6 m ahead of face, inducing dynamic mine pressure. To investigate the instability mechanism of interbedded rock strata and remaining coal pillar groups during close-distance coal seam mining, this study takes the 3301 working face of Hanjiawan Coal Mine as the research object. Combining theoretical analysis with numerical simulation, a mechanical model of the "remaining coal pillar group-overburden" system was constructed. Using cusp catastrophe theory, the stability criterion for interbedded rock strata was derived, explicitly proposing that a cusp catastrophe occurs when the ratio of shear stiffness to thickness product between key and non-key strata is less than 0.206, triggering catastrophic instability. The results indicate that the load on remaining coal pillars is related to the roof flexural rigidity, overlying load, pillar spacing, and the elastic coefficient of concentrated coal pillars. The transfer of advanced abutment pressure and the reduction of k are identified as the primary causes of chain instability in coal pillar groups, leading to shear-sliding failure of interbedded rock strata. Numerical simulations confirm that the maximum vertical stress on coal pillars (8.26 MPa, stress concentration factor 2.95) occurs 4-6 m ahead of the working face when exiting concentrated coal pillars, triggering chain instability and dynamic mine pressure. This research provides a novel theoretical framework for safety control in close-distance coal seam mining.