Perilous rock instability on the soil slope brings a substantial threat to project operation and even people’s lives. The buried depth of the perilous rock is a challenge to deal with and primarily determines its stability, and the indirect rapid identification of its buried depth is the key to its stability evaluation. The paper aims to find a new and quick method to measure the buried depth of perilous rock on the soil slope and to solve the hard-to-measure buried depth stability evaluation. When the damping ratio is less than one, and the deformation is linear elastic throughout the amplitude range, the potentially perilous rock vibration model may reduce to a multi-degree-of-freedom vibration one. By theoretical deduction, a quantitative relationship is established among the perilous rock mass, the basement response coefficient, the buried depth of the perilous rock, and the natural horizontal vibration frequency. In addition, the accuracy of this relationship is confirmed via numerous indoor experiments, showing that the horizontal vibration frequency of the perilous rock model in one dimension increases as the buried depth increases. Finally, based on the natural vibration frequency and guided by the limit balance model, a stability evaluation model of the perilous rock on the soil slope is constructed. Hence, the example shows that the method is feasible. The research findings are of vital significance for the stability evaluation of the perilous rock on the soil slope and give a novel approach and theoretical foundation for quick identification and monitoring.

The dynamics parameters cause sudden change during the damage of the structural plane of landslide perilous rocks, and these can be easily accessed. Therefore the changes in dynamics parameters can effectively achieve early identification, stability evaluation, and monitoring and pre-alarming of the perilous rocks. Seven kinds of dynamic indexes, such as pulse indicator, margin index, the center of gravity frequency, root mean square frequency, impact energy, relative energy of the first frequency band, and damping ratio, are introduced and the early identification of landslide perilous rock is achieved based on the support vector machines (SVM) model, improved by particle swarm optimization algorithm. A laser vibrometer collected seven dynamic indexes of two rock masses on the reservoir bank slope in Baihebao Reservoir, China. Based on the particle group optimization algorithm optimization support vector (PSO–SVM) perilous rocks recognition model, and seven dynamic indicators, the stability of two rock masses was recognized with high efficiency and accuracy. The identification results were consistent with the landslide perilous rock identification results based on natural vibration frequency, and the results verify the accuracy of the PSO–SVM perilous rocks identification model. The results show that the sensitivity order of each identification index is: root mean square frequency > margin index > relative energy of the first frequency band > center of gravity frequency > impact energy > pulse indicator > damping ratio. The accuracy of the multi-dynamics parameters landslide perilous rock mass identification model can be improved by selecting appropriate dynamic indexes with good sensitivity. The research results have high theoretical significance and application value for early identification of landslide perilous rocks, stability evaluation, and safety monitoring, and early warning.