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Since the instability of dangerous rock mass exhibits as the sudden collapse of destruction, no obvious displacement characteristics can be identified. Thus, the application of conventional displacement monitoring techniques is difficult to achieve the purpose of monitoring and early warning. In addition, the stability of dangerous rock mass is influenced by the bonded area between dangerous rock block and bedrock, which is considered as one of the critical parameters. However, this bonded area is hard to obtain, which makes it difficult to evaluate the stability of the dangerous rock block. In this study, we assume that the rock block is homogeneous and isotropic, the main control structural plane is a single plane, the damping ratio of the system is less than 1 and the deformation is linear elastic deformation within the amplitude range. As a result, the vibration model of the dangerous rock mass can be simplified as a spring oscillator model. Then, the relationships among the natural vibration frequency of dangerous rock mass, the bonding area, the elastic modulus and the quality of dangerous rock mass were established by the theoretical derivation. Considering the limit equilibrium model, a new model based on natural vibration frequency was derived to evaluate the stability of dangerous rock mass. A dangerous rock block on the right bank of Baihebao reservoir was selected as the case study. A wireless vibration sensor (micro core) was fixed on the dangerous rock block to acquire data, which was converted to natural vibration frequency by the Fourier transform and other mathematical methods. Furthermore, the bonded area was determined according to the relationship among natural vibration frequency, rock block bonding area and elastic modulus. Finally, the stability evaluation of dangerous rock mass was completed using the new model. This case study verifies the feasibility of the proposed procedure with a faster rate and more accuracy than traditional methods.

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... ey found that the fundamental natural frequency decreased when the cohesion of the potential sliding plane gradually weakened. Jia et al. [25] monitored the fundamental natural frequency of hazardous rock onsite and calculated the actual safety factor of the rock mass by the mass-spring model. us, frequency response monitoring is a practical and reasonable method to evaluate the stability of hazardous rock block. ...

... During progression from state 1 to state 5, the block stability has a significant negative correlation with P1 and P5, which shows that the magnitude and constringency of the vibration frequency domain increase; the block stability has a significant positive correlation with P2-P4, which shows that the main frequencies gradually decrease. In addition, the data show that using a single parameter for assessment is susceptible to erroneous evaluation, such as the peak frequency commonly used by researchers [23][24][25], which has an abnormal trend change in state 3. For this reason, we use multiple parameters to assess the stability evolution trend. ...

This paper explores a new approach for assessing the stability of a hazardous rock block on a slope using vibration feature parameters. A physical model experiment is designed in which a thermally sensitive material is incorporated into the potential failure plane of the hazardous rock, and the complete process of hazardous rock collapse caused by strength deterioration is simulated by means of constant-temperature heat transfer. Moreover, the vibration response of the hazardous rock is monitored in real time by laser vibrometry. The experimental results show that five vibration feature parameters, including the mean frequency, the center frequency, the peak frequency, the mean frequency standard deviation, and the root mean square frequency, are well-correlated with rock stability. Furthermore, through principal component analysis, the five vibration feature parameters are synthesized into a principal component factor (PCF) as a representative assessment parameter. The results of the analysis demonstrate that the variation in the PCF exhibits three characteristic stages, i.e., “stationary-deviation-acceleration,” and can effectively identify the stability evolution trend and collapse precursor behavior of hazardous rock block.

... Xie et al. (2021) established a three-dimensional (3-D) analysis method for the rock vibration, and they proved the effectiveness for the rock stability analysis based on the natural frequency. At present, investigations on the natural frequency of rock primarily concentrate on the field or laboratory scales, such as seismic failure of rock slopes (Song et al. 2019a) and rock block's instability (Jia et al. 2017(Jia et al. , 2019(Jia et al. , 2023b, which are characterized by much smaller pores relative to the size of a rock to be studied. Rock is a typical porous medium, and the presence of weak structural surfaces in rocks such as beddings, joints and faults will strengthen the complexity on mechanical behaviors of the fissured rock (Zhao et al. 2022;Ivars et al. 2011). ...

Not confined to static effects such as permeability, the effect of porosity on the natural frequency of a rock is crucial to explore its dynamic behaviors. In the present work, a cylinder vibration model governed by the Lame-Navier equation is developed to clarify the mechanism of porosity-effect on the natural frequency of a rock. Focusing on the structural difference of the pore, the porosity-effect on the natural frequency for a cylinder model is preliminarily investigated by finite element (FE) simulations, in consideration of ideal straight and conical hole structures. To probe the distribution of real pores, the micro-computed tomography (micro-CT) technique is used to extract the accurate geometry of pores of the digital core, and the results are imported into the FE model for simulation. By introducing the Nur’s model and Krief’s model, the improved cylinder vibration model is able to predict multiple orders of the natural frequency of real rock samples with various porosities, and therefore overcomes the defects of the conventional spring-dashpot model. Verified by the resonant experiment on various rock samples, the results of the FE model and the improved cylinder vibration model show a basically consistent trend, i.e. the natural frequency decreases with the increase of porosity. These findings are beneficial to a wide range of engineering applications such as resonance enhanced drilling (RED) of rocks, high-speed processing of novel porous materials, and oil or gas explorations.

... Du Yan [21] and other rock mass collapse disaster early warning ideas based on the identification of damage precursors in the separation stage have obtained an early monitoring and early warning index system based on a trinity of dynamic indicators, static indicators, and environmental quantity indicators. Jia Yanchang [22] and others calculated the bonding area between the perilous rock block and the parent rock by real-time monitoring of the natural vibration frequency of the perilous rock block and realized its stability accurately and quickly. Zhao Chen [23] and others introduced the concept of mutual approximation entropy and extended it to three dimensions, and realized the quantitative analysis of particle trajectories, which provided a new research idea for the early warning of perilous rock damage identification and collapse. ...

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.

... They found that the penetration rate was inversely proportional to the dominant frequency and damping ratio under the same excitation setting. Through theoretical derivation, Jia et al. (2017) demonstrated the relationship between the intrinsic vibration frequency of dangerous rock blocks, bond areas of dangerous rock blocks and parent rocks, elastic modulus, and mass of dangerous rock blocks. Furthermore, they developed a stability evaluation model of dangerous rock blocks based on natural frequency using a limit equilibrium model. ...

Block collapse is a common disaster in the jointed rock mass of tunnels and usually involves two typical evolution stages: rock bridge breakage and rock block instability. The evolutionary characteristics of mutation induced by the gradual failure of rock mass are the mechanical basis for monitoring and assessing disasters. In this study, an acoustic emission (AE)-vibration joint monitoring method is proposed to fully investigate the two failure stages based on the disaster mechanism. It is critical to reveal the evolution law of AE and natural frequency information in block collapse. Small-scale shear tests on rock specimens are conducted to investigate the rock bridge breakage stage, while large-scale physical simulation tests are performed to investigate the block instability stage. During rock bridge breakage, AE exhibits a clearer signal response to the internal rock fracture than the natural frequency and captures brittle failure under low-and medium-stress conditions. The natural frequency exhibits a significant signal response under low-stress conditions during the block instability stage. Under medium and high-stress conditions, the signal becomes less sensitive. Under low-stress conditions, the natural frequency of the block gradually decreases with increasing free surface, implying that the stability of the block declines. The natural frequency decreases with the decreasing stiffness of the block, which is a vital precursor to the early warning of block collapse disasters. Additionally, AE is the primary indicator in the rock bridge breakage stage, while natural frequency is the primary indicator in the rock block instability stage. From the perspective of technological innovation in underground tunneling, AE-Vibration joint monitoring prompts a new idea to evaluate the stability of key blocks in tunnel construction safety applications.

... Based on the vibration monitoring technology, Bottelin et al. [16] studied the dynamic response of four unstable rock masses in the Alps, and according to the measurements, there was a distinct energy peak at the resonance frequency of the perilous rock mass's vibration spectrum; Ma et al. [17], by comparing the safety factors of the test blocks, found that the vibration characteristic parameters, such as frequency, have a certain indication effect on the stability of the rock block. After analyzing the mechanical indicators, such as friction force, it was concluded that rock mass safety monitoring based on the vibration mode will play an important role in practical engineering [18][19][20]; then, Jia Yanchang et al. [21][22][23][24][25][26][27] obtained the change rule of the dynamic characteristic parameters of perilous rock with structural damage through tests and a theoretical analysis and realized the quantitative stability evaluation based on the vibration frequency. Numerous investigations have shown that for the stability assessment of the rock blocks it is reliable to use dynamic indicators. ...

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.

... Assuming that the distance from the origin at a certain moment Frontiers in Earth Science frontiersin.org 03 is x, the horizontal stiffness of the soil layer is K x , and according to Newton's second law, the mechanical balance Eqs 1, 2 of the horizontal direction of the unstable rock are obtained (Jia et al., 2017): ...

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.

... e model proposed by Ma et al. [15] and Xie et al. [25,26] for calculating the natural frequency of the rock is shown in Figure 2(a). is model simplifies the rock as a single-degree-of-freedom block and the rock-slope connection as a tension-compression spring K 0 . ...

The limit equilibrium method’s analysis index cannot be measured by on-site monitoring equipment and cannot be used for monitoring and early warning of rock instability. The existing rock stability evaluation methods based on vibration information cannot evaluate the stability of rocks quantitatively. In this paper, the slope’s constraints on the rock were simplified to springs and a three-dimensional analysis model of rock vibration was established. The equation for calculating the natural frequency of rock that includes the spring stiffness as an indicator was derived. The rock stability calculation function containing the index of natural frequency was brought into the traditional rock stability coefficient calculation equation, and a new rock stability analysis method based on natural frequency was established. The experiment proved the measurability of the index of the natural frequency of rock and the method’s effectiveness for the stability analysis of the rock based on natural frequency.

The declaration on the “natural frequency of rock” exists in many engineering areas, and it has caused many misunderstandings. Different from the mass-spring model usually used, the circular plate and cylinder models are respectively established to clarify the relationship between the vibration characteristics (including the natural frequency and vibration mode) and their influencing factors of rock by modal analysis. The effect of the dimension, geometric shape and boundary condition on the vibration characteristics of rock with plate structure is investigated, in which the semi-analytical solutions agree well with the simulation results. By using the cylinder model based upon the Lamé–Navier equation, the effect of such influencing factors on the vibration characteristics of the block rock sample is further studied and verified by numerical simulation and experimental results. The results suggest that the natural frequency of “rock” (including the experimental rock sample) is strongly dependent on the dimension, geometric shape and boundary condition. The resonance frequency observed in the excitation experiment is not only closely associated with the natural frequency of a specific order but also dependent on the dominance of the particular vibration mode. These findings contribute to a better understanding of the rock-breaking mechanism under dynamic loads with a certain excitation frequency.

Rock collapse is a type of fast-moving mass wasting process common in mountainous areas worldwide, and it is hard to predict when collapse will occur. In the experiment, we monitored vibration parameters to predict the time of rock collapse. The results show that the vibration amplitude and fundamental vibration frequency had obvious variations before rock failure, which was consistent with the predicted results of the theoretical model. As the rock became unstable, the vibration amplitude increased by more than 5 times, and the fundamental vibration frequency decreased to less than 41%. Therefore, the monitoring method based on the vibration parameters can record obvious failure precursors for unstable rocks. Our results further develop and refine ambient vibration methods used for implementing the early warning of rock collapse.

A large model testing system was developed to simulate the rockfall impacting the slope of tunnel exit of Chengdu-Lanzhou railway which is under construction in the southwest area of China. The system is composed of the model testing bench, three-dimensional rockfall release device and high-speed photographic system. This system with high structural strength can meet the visual requirements in the testing process. Based on the measured physical and mechanical parameters of rock specimens, similar materials to phyllite and sandstone were developed to simulate slopes and rockfall by mixing with different proportions of vaseline, silicone oil, cement, fine sand, barite powder, gypsum and talcum powder. The effects of the initial slip angle, shape and mass of cuboid rockfall on the coefficients of restitution were studied through the physical model tests. Besides, a high-speed camera and coordinate callipers were adopted to record the complete trajectories of rock blocks during the rockfall process. At last, a video processing software was employed to analyze the variation of velocity before and after the collision between the rockfall and the slope, and the normal and tangential restitution coefficients of the rockfall were calculated by formulas. The testing results showed that with the increase of the initial slip angle, the normal restitution coefficient of the plate specimen increased, whereas the tangential restitution coefficient decreased and its variation was more obvious. The normal restitution coefficient had a remarkable decreasing trend with an increase of rock mass, but the tangential restitution coefficient seldom changed. For cuboid rock blocks, the normal and tangential restitution coefficients of cuboid specimens are larger than those of thick plate specimens. The normal and tangential restitution coefficients of strip specimens exhibited a polarisation trend due to different contact forms. Finally, the impact mechanism of rockfall was explored according to testing results and previous research results.

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