Abstract: The collapse of tension-splitting rock mass on slopes often occurs instantaneously, and traditional displacement time series analysis is difficult to predict the collapse time. Using vibration mechanics theory, the tension-splitting rock mass is generalized as a vertical swing vibration system, and the relationship equation between the natural frequency and the depth of the controlled fissure is solved. Combined with the method of fracture mechanics, the collapse evolution process of tension-splitting rock mass under the gravity is generalized as a subcritical fissure expansion process under stress corrosion, and a time-varying evolution equation of natural frequency with expansion of the controlled fissure is established. Theoretical calculation analysis shows that the natural frequency of the vertical swing vibration mode of a tension-splitting rock mass exhibits signs of accelerated reduction before collapse, and that there is a significant linear relationship between the natural frequency and the collapse residual time in logarithmic coordinates. A "frequency trend" collapse time prediction model is established. In addition, a series of physical model monitoring experiment is designed and implemented to investigate the frequency response of micro vibrations during the natural collapse process of a fractured rock mass. The results shows that the X/Z resonance peak frequency can characterize the trend change of the natural frequency of vertical swing vibration of the rock mass, thereby verifying the correctness of the prediction model. Real time error analysis shows that the prediction equation can produce an average relative error rate of 7.1% with an average lead time of 32.6 hours. The research results can provide a new idea for predicting the collapse time of tension-splitting rock mass on slopes.