Dynamic failure analysis and support optimization for web pillars under static and dynamic loading using catastrophe theory

• A dynamic failure criterion for web pillars under non-uniform loading was established using catastrophe theory, defining instability when the bifurcation set D<0. • Vertical displacements of web pillars exhibit exponential-trigonometric variation under static loads and multi-variable power-law behavior under dynamic blasting. • Instability risks arise when the roof’s tensile strength-to-stress ratio drops below 1, and failure occurs when the unstable web pillar section length exceeds the roof’s critical collapse distance. • An optimal web pillar width of 4.6 m was determined through case studies and simulations, enhancing safety and resource recovery in highwall mining.