Research on prediction of instability-induced disasters in deep sandstone based on cusp catastrophe theory
摘要
The long-term stability of sandstone roadways is essential for the safe and efficient exploitation of deep coal resources, as their sudden instability can readily cause major disasters. To address the critical challenge of instability warning for deep sandstone, an effective method for identifying precursors is established to achieve precise early warning of its pre-failure critical state. Based on the cusp catastrophe theory, a sandstone model was built using the numerical simulation software RFPA2D (Realistic Failure Process Analysis). Complete loading process numerical simulations under uniaxial and confining pressures of 5, 10, 15 and 20 MPa were conducted, with acoustic emission (AE) data acquired synchronously. The evolution characteristics of elastic strain energy during loading were analyzed from the complete stress-strain curves. A cusp catastrophe model with elastic strain energy as the key state variable and a time-series potential function were constructed. The bifurcation set characteristics of the elastic strain energy were then used to quantify early warning signals. The results show that the bifurcation set function value exhibits two distinct negative phases during loading. The starting moment of the second negative phase is defined as the instability warning moment, and the corresponding axial stress at this moment is defined as the warning stress. The warning moment derived from the cusp catastrophe model provides sufficient lead time, with its ratio to the final failure moment generally exceeding 80%, and the ratio of the warning stress to the peak strength also consistently above 80%. The temporal characteristics of AE precursors are not consistent with those of the elastic strain energy mutation; the onset of AE activity always precedes the warning moment indicated by the elastic strain energy mutation. This objectively reflects the accumulation and activity of micro-damage, whereas the elastic strain energy mutation signifies the loss of macro