Energy evolution and catastrophic instability of excavated consequent slopes: A cusp catastrophe-based criterion and gradient-anchoring reinforcement strategy

Understanding energy evolution and associated entropy production during slope excavation is crucial for predicting catastrophic failures in geomechanical systems. This study, from the perspective of energy conservation, investigated the stability of a phosphorus mine tailings dam in Guizhou. By integrating cusp catastrophe theory, we establish a novel energy catastrophe instability criterion, defining the characteristic value Δ as a dynamic indicator of system stability, where Δ > 0 denotes a stable state and Δ < 0 indicates an unstable state. The reliability of this criterion is rigorously validated by comparing the evolution of Δ with the development patterns of the plastic zone across sequential excavation stages (0-50 m depth). Results demonstrate a critical transition: slopes remain stable (Δ > 0) during excavation to 40 m depth but become unstable (Δ < 0) upon reaching 50 m. Crucially, leveraging insights from the energy catastrophe analysis (specifically the spatial and temporal evolution characteristics of system instability precursors), a gradient prestressed anchor cable support strategy was designed and implemented. Field monitoring data confirms the efficacy of this energy-informed reinforcement, showing significantly enhanced slope stability with Δ values persistently maintained in the positive regime.