A CALCULATION MODEL OF SAFETY FACTOR OF SHEAR FRACTURED FALLING DANGEROUS ROCK MASS BASED ON NATURAL FREQUENCY

The safety and stability of shear fractured falling dangerous rock mass is controlled by the depth of trailing edge fracture. The critical value of the depth of trailing edge fracture can be obtained by calculating the stability factor based on statics, but the statics calculation method cannot obtain the real-time change of the fracture depth. Based on the modified Timoshenko Beam theory, the dynamic equation of rock beam was established. Combined with the half-space theory of dynamic foundation, the constraint stiffness and boundary conditions of rock beam were analyzed in depth, and theoretical analysis of natural frequency of dangerous rock mass under different fracture depths was conducted. The correctness of the natural frequency algorithm was verified through numerical calculation. It was concluded that the natural frequency decreases with the increase of crack depth, and the natural frequency is sensitive to the change of fracture depth at trailing edge of dangerous rock mass. According to the natural frequency value of dangerous rock mass, the fracture depth at trailing edge of dangerous rock mass can be inversely calculated. Based on the relationship between the natural frequency and the fracture depth of the trailing edge of dangerous rock mass, the calculation model of the stability coefficient of the dangerous rock mass was established, and the indoor test was used to verify it. It was concluded that the natural frequency of the dangerous rock mass is approximately negative-linearly correlated with the crack depth of the trailing edge. The calculation model of stability factor of shear fractured falling dangerous rock mass based on natural frequency can provide useful reference for automatic monitoring of dangerous rock mass.