The instability of the slope of the unstable rock poses a great threat to the safety of engineering and people’s lives and properties. The buried depth of an unstable rock is a key factor affecting its stability. It is difficult to directly measure the buried depth of the unstable rock. Therefore, it is of vital importance to indirectly and quickly identify the buried depth of the unstable rock. Assuming that the foundation soil is homogeneous and isotropic, the damping ratio is less than 1; it can be found that the deformation is linear elastic deformation within the amplitude range, and the unstable rock vibration model is simplified to a multi-degree-of-freedom vibration model. Through theoretical derivation, the quantitative relationship between the rock mass, foundation reaction force coefficient, rock burial depth, and the natural vibration frequency in the horizontal direction is established. The quantitative relationship was verified to be correct by laboratory tests. From the tests, the relationship is verified and shows that with the increasing buried depth of the unstable rock, its natural vibration frequency increases nonlinearly in the horizontal direction and also acts in a weakening growing trend; the mass of the unstable rock is a monotonically decreasing function of the natural vibration frequency, and it decreases by a one-half square with the increasing mass of the unstable rock. The research results can calculate the buried depth by measuring the vibration frequency of the unstable rock, which provides a new idea and theoretical basis for the stability evaluation of the slope of the unstable rock and the rapid identification and monitoring of the unstable rock.

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 instability of perilous rock is mostly manifested as sudden collapse and failure without obvious displacement characteristics. Therefore, it is difficult to achieve the purpose of monitoring and early warning by conventional displacement monitoring. But the existing stability monitoring indicators are mostly deformation, stress, and strain. There is a problem that the stability evaluation parameters are inconsistent with the monitoring parameters. Taking sliding-type perilous rock as the research object, the structural plane is assumed to be homogeneous and isotropic, and linear elastic deformation in the amplitude range. Based on the dynamic theory and limit equilibrium model, the quantitative relationship model can be established involving safety factors, natural vibration frequency, structural surface bonding area, elastic modulus, and mass. The remote laser vibrometer is used to monitor the natural vibration frequency of the sliding-type perilous rock on the slope of the Huangzangsi Hydrojunction, and the stability evaluation of the perilous rock is achieved based on the quantitative relationship model between the safety factor and the natural vibration frequency. In this way, the frequency of slipping perilous rock stability evaluation and safety factor can be monitored. The results are basically the same with the safety factor calculated by the limit equilibrium method, indicating that the method is correct and feasible. The research has high theoretical significance and practical value for the safety monitoring and advanced warning of sliding perilous rock.

Rock block tilting is one of the most common types of dangerous rock block failures with no clear indicator of displacement prior to failure. Existing stability evaluation methods remain limited in their ability to constrain the non-penetrating section area, which is closely related to rock stability, and stability evaluations are therefore associated with large uncertainties. The dynamic characteristic parameters of toppling dangerous rock are closely related to structural plane strength. Under vibration loading, rainfall, and/or excavation unloading conditions, the structural plane becomes damaged and the dynamic characteristic parameters change. In this study, we present a dynamic characteristic model of rock tilting and identify the quantitative and qualitative relationship between dynamic characteristic parameters and the bonded area of the structural plane. The model accuracy is verified by experiments. The experimental results show that the damping ratio decreases linearly with structural plane damage, whereas the maximum vibration speed and particle trajectory increases nonlinearly and the natural vibration frequency decreases nonlinearly. The dynamic characteristic model and experimental results can be used to evaluate the degree of structural surface damage of toppling dangerous rock.

Altered rocks widely exist in rock mass engineering. Alteration has an obvious deterioration effect on the physical and mechanical properties of rocks, which may cause engineering geological prob-lems or geological hazards. The main method to obtain the uniaxial compressive strength of altered rocks is indoor uniaxial compression test, which has the reality of long period, high cost, difficult sampling, and limited transportation. In this paper, the uniaxial compression test and short wavelength infrared spectral test analysis are performed on the altered rocks of a hydropower station in Southeast China to study the relationship between the strength and the short wavelength infrared spectral curve of altered rocks. The results show that, there is a correlation between the number of absorption peaks of short wavelength infrared spectral curve and the uniaxial compressive strength of altered rocks. In the wavelength ranges of 1880–1950 nm and 2170–2230 nm, the uniaxial compressive strength of altered rocks with two absorption peaks in the short wavelength infrared spectral curves are generally higher than 150 MPa. In the wavelength ranges of 1380–1430 nm, 1880–1950 nm, and 2170–2230 nm, the uniaxial compressive strength of altered rocks with three absorption peaks in the short wavelength infrared spectral curves are generally lower than 100 MPa. In the wavelength ranges of 1380–1430 nm, 1630–1660 nm, 1880–1950 nm, 2170–2230 nm, 2230–2380 nm, the uniaxial compressive strength of altered rocks with four absorption peaks in the short wavelength infrared spectral curves are generally between 100–150 MPa. This research will provide a new method for rapid evaluation of strength of altered rocks in the field.