# Experimental Study on the Vibration Characteristics of Dangerous Rock Mass under Constant Micromotion

Authors: Xiaoyong Zhang; Mowen Xie; Zhengjun Huang; Yan Du; Lei Zhang; Zhixiang Wu; Zhuang Fan
Journal: Advances in Civil Engineering
 (2023)

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## Abstract

In mountainous areas, dangerous rock mass collapse is a serious threat to human life and property safety. However, how to effectively prevent and control the instability of dangerous rock mass is still an urgent unsolved problem. In this study, the dynamic characteristics of dangerous rock mass under constant micromotion were analysed from the perspective of elastic wave propagation. When the slip plane of the dangerous rock mass is damaged, many micropores and cracks will appear in the medium composed of the slip surface. With constant micromotion as the vibration source, the elastic wave propagates to the dangerous rock mass through the damaged slip plane. The high-frequency components of elastic waves scatter in pores and fissures, where energy dissipates. According to this characteristic, a laboratory simulation experiment was designed. In the experiment, the damage process of the slip plane was simulated by the freeze‒thaw process of frozen hydrosol. The experimental analysis showed that the centre frequency of the high-frequency part of the dangerous rock mass model and bedrock mass model decreased as the frozen surface continued to melt. As the dangerous rock mass model and the bedrock mass model continued to fit, the centre frequency of the high-frequency part of the two rock mass models rebounded. This phenomenon showed that the damage degree of the slip plane between the dangerous rock mass and the bed rock mass can be effectively reflected by the centre frequency of the high-frequency part of the two rock mass models. During the experiment, the dangerous rock mass did not slide in the whole process, indicating that the deformation index has difficulty reflecting the stability of the hidden dangerous rock mass. In addition, the application conditions of using the natural frequency characteristics of dangerous rock mass and the scattering characteristics of elastic wave in the damage identification of structural plane were analysed: (1) when the structural plane has macrofracture, the change of natural frequency of dangerous rock mass should be used to analyse the damage degree of structural plane; (2) when there is no macrofracture of the structural plane, the characteristics of elastic wave scattering should be used to analyse the damage degree of the structural plane. This study provided a new idea for the prevention and control of dangerous rock masses and is expected to provide a useful reference for the automation of dangerous rock mass prevention and control.


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## Body

## 1. Introduction

The collapse of a dangerous rock mass is one of the three common geological disasters (collapse, landslide, and debris flow) in mountainous areas. The instability and collapse of dangerous rock masses often bring serious threats to human life and property safety [1]. There have been many studies on the mechanism of dangerous rock mass collapse. Through research, Strom et al. pointed out that the failure and fracture of rock bridges is the main reason for the instability of dangerous rock masses [2]. In fact, there are many external factors that lead to rock collapse, including earthquakes, rainstorms, plant root splitting, weathering, or blasting, and these activities lead to rock bridge damage and the degradation of rock bridge strength, so that the original structural plane falls through, resulting in rock collapse disasters [3]. Ishikawa et al. concluded that freeze‒thaw damage affects crack propagation by analysing the correlation between crack width and temperature [4]. Marzorati et al. analysed the influence of earthquakes on the stability of unstable rock masses and used statistical theory to analyse the influence of earthquakes on the stability of unstable rock masses [5]. In practical engineering, some rock bridges that hinder the movement of dangerous rock masses may be destroyed, causing the sliding of immovable blocks. When the scale of the block is relatively large, the possibility of the local rock bridge being destroyed under the action of gravity will increase, which is manifested as composite brittle fracture failure composed of the original structural plane and the extended rock bridge section at the end of the self-structural plane. [6] A large number of studies have shown that the stability of unstable rock slopes is directly controlled by the degree of structural plane damage. A dangerous rock mass environment determines to a certain extent that the instability forms of dangerous rock mass are divided into sudden and progressive types [7]. Compared with the former, the latter has strong concealment, a long incubation period, greater harm, and more serious economic losses and casualties. The deformation and failure of dangerous rock mass is a nonlinear process of multifactor coupling [8]. The change process of dangerous rock mass stability is difficult to calculate directly by theoretical means, which leads to the following characteristics: randomness of spatial position, uncertainty of time, and suddenness of instability. The transition of dangerous rock mass from stable to unstable is a process due to damage accumulation. Based on the theory of damage structure dynamics, many scholars have analysed rock mechanics from the view of dynamics [9–13]. Zhang et al. proved that the natural vibration frequency of a dangerous rock mass can reflect the stability of dangerous rock mass through theoretical calculations and experiments [14, 15]. Du et al. simulated the process of landslides through experiments and found that the natural frequency and damping ratio of unstable rock decrease with the decrease in the contact area between unstable rock and bedrock mass [16]. Xie et al. proposed a method to calculate the stability coefficient of unstable rock mass based on natural frequencies [17]. Tanaka et al. pointed out that the difference in vibration modes of a dangerous rock mass can reflect its stability [18]. Ma et al. found a direct data correlation between the stability of dangerous rock mass and dynamic characteristic parameters based on remote laser vibration measurement experiments [19].At present, most studies approach rock dynamics using theoretical and experimental methods, deriving the relationship between the degree of damage and dynamic characteristics of dangerous rock mass from a qualitative or quantitative point of view. Laboratory tests often use artificial excitation to obtain the dynamic characteristic parameters of dangerous rock mass. In practice, dangerous rock mass is often on a high and steep slope. Human climbing to the location of a dangerous rock mass may be hazardous, and the volume of the dangerous rock mass is often very large. It is difficult to determine the intensity of human incentives. Therefore, human tapping incentives do not have much practical significance. In practice, there are always microvibrations in any area of the Earth’s surface that cannot be detected. This microvibration is called constant micromotion [20]. Constant micromotion data contain a large amount of stratum information and rich random noise frequency bands. Studies of constant micromotion are mainly applied to the site classification and calculation of seismic intensity increments [21, 22]. Relative to the natural rock mass, constant micromotion is the natural dynamic excitation source. The microvibration propagates continuously in the form of an elastic wave to the unstable rock mass. Based on laboratory experiments, this paper used this natural elastic wave excitation source to analyse the dynamic characteristics of dangerous rock masses to provide a useful reference for the automatic prevention and control of dangerous rock masses.


## 2. Analysis of the Elastic Wave Propagation Characteristics in Damaged Media

The stability of dangerous rock mass is affected by the damage degree of the slip plane. Therefore, this paper focused on the analysis of the propagation characteristics of elastic waves at the damaged slip plane, as shown in Figure1.Figure 1
Elastic wave propagation diagram.When the slip plane is damaged, many pore cracks appear in the composition medium of the slip plane. The microvibration propagates from the bedrock mass to the dangerous rock mass in the form of an elastic wave, and the propagation process of the elastic wave at the micropore cracks changes. To illustrate the propagation characteristics of elastic waves in tiny pores and fissures, the S wave was taken as an example to analyse the scattering of the S wave in pores. The porosity of the medium was simplified into a cylindrical cavity, and the elastic wave propagation problem was simplified into an antiplane strain problem.The incident wave functionWi is shown as follows:(1)Wi=W0eikx−ωt,where W0 is the amplitude of the incident wave, k is the wavenumber of the elastic wave, and ω is the vibration frequency.Suppose the pore is a cylindrical cavity with a radius ofa, then the boundary condition of the cavity position in the cylindrical coordinate system r,θ can be shown as follows:(2)r=a,μ∂Wr,θ,t∂r=0.Elastic wave propagation satisfies the Helmholtz equation in a cylindrical coordinate systemr,θ:(3)∂2∂r2+1r∂∂r+1r2∂∂θ2+k2W=0.To briefly analyse the elastic wave propagation process, the steady wave was analysed. The incident wave is represented byWi, and the scattered wave is represented by Ws. Equation (3) was solved by the method of separation of variables to obtain the general solution satisfying the characteristics of a scattered wave:(4)Ws=Hncosnθe−iωt=W0∑n=0∞AnHnkrcosnθe−iωt,where Hn1 is the first kind Hankel function, and n is the eigenvalue.Based on the boundary condition (2), the unknown coefficient An can be determined:(5)An=−εninJn′kaHn′ka,where Jnka is the first kind Bessel function, and εn=1,n=02,n=1,2,3,….Therefore, the expression of the scattered wave is(6)Ws=Hncosnθe−iωt=W0∑n=0∞−εninJn′kaHn′kaHnkrcosnθe−iωt.According to the scattered wave expression (4), the average energy flow at the cavity position can be calculated as follows:(7)AVE=−14iπμωW02∑n=0∞2εnAnAn∗kR⋅Hn′kRH′n∗kR−HnkRH′n∗kR,where An∗ denotes the conjugate of An, R is the radius of the medium outside the cavity, and AVE represents the average energy flow.Relative to the radiusa of the tiny cavity, the radius R of the medium outside the cavity is almost infinite. According to the asymptotic properties of the Hankel function, when kR⟶∞, the limit of the Hankel function is(8)HnkR⟶2πR1/2⋅expkR−n−12π2i,and when ka⟶0,(9)A0⟶iπka2;An⟶2in+1πn!n−1!−1⋅ka22n,n≥1.Takingn=0,1 and omitting the higher order small quantity, the average energy flow is expressed as follows:(10)AVE=kμcsW038π2ka4>0,where cs is the wave velocity, and μ is the shear modulus.It can be seen from equation (10) that the scattering energy AVE of the elastic wave at the cavity position is proportional to the fourth power of the cavity diameter a, indicating that the larger the void is, the greater the scattering energy. In addition, AVE is proportional to the fourth power of the wavenumber k. The higher the elastic wave band frequency is, the stronger the scattering. Through the analysis of the scattering properties of the S wave in the pore position, it can be shown that the larger the slip plane medium pores are, the more serious the energy scattering of the high-frequency part of the S wave. Scattered waves are gradually dissipated by material friction. The analysis shows that with the damage of the slip plane medium, there are many pores and fissures generated in the medium, and scattering and energy dissipation occur when the S wave passes through the slip plane, especially the high-frequency part of the elastic wave. In fact, not only the S wave, other types of elastic waves also obey the following properties: for any shape of microscopic pores in solid medium, the larger the equivalent radius and the more the number, the more obvious the elastic wave scattering phenomenon, especially the high-frequency part of the elastic wave [23–25].There are many high-frequency and low-frequency vibrations in frequent microtremors. During the propagation of the elastic wave from the bedrock mass to the dangerous rock mass, the high-frequency wave has more energy dissipation. The elastic wave is reflected at the boundary of the dangerous rock mass, and the high-frequency wave energy dissipation occurs again when the reflected wave passes through the slip plane. The high-frequency component in the elastic wave is greatly reduced, as shown in Figure2.Figure 2
Diagram of the frequency distribution change of the elastic wave.


## 3. Laboratory Simulation Experiment

### 3.1. Introduction of the Experimental Process

To simulate the propagation law of elastic waves in rock masses under the condition of frequent microtremors, laboratory experiments were carried out. The dangerous rock mass and slip plane of real rock mass materials are difficult to build. Considering that the basic laws of elastic wave scattering in porous media of different materials are consistent, this test used other materials to simulate the sliding dangerous rock mass model. As shown in Figure3, the white plastic steel material was used as the dangerous rock mass model in the experiment, and the wood block was used as the bedrock mass model. Viscous hydrosol was used to bond the dangerous rock mass model to the bedrock mass model, and the whole model was placed in a refrigerator. The minimum temperature of the refrigerator was set to −10°C to freeze the hydrosol between the dangerous rock mass model and the bedrock mass model. After 24 hours of freezing, the whole model was removed, and the ice plane was used to simulate the slip plane between the dangerous rock mass model and the bedrock mass model. The melting of the ice plane was compared to the process of the slip plane changing from integrity to damage. Two acceleration collectors were pasted on the dangerous rock mass model and the bedrock mass model. The sampling frequency of the acceleration collector was set to 4000 Hz, and the vibration acceleration data were collected at 1 min intervals. A total of 30 sets of data were collected to obtain the vibration data of the dangerous rock mass model and bedrock mass model during the thawing process of the bonding plane. During the experiment, no human excitation was applied to the experimental model, and only the microvibration caused by the constant micromotion was considered.Figure 3
Model of the laboratory test.The equipment used in the experiment was a DASP modal testing system, which included an INV3062C signal processor and an INV9832-50 acceleration sensor. The signal processor and acceleration sensor are shown in Figure4. The device parameters are shown in Tables 1 and 2.Figure 4
Testing equipment. (a) Signal acquisition instrument. (b) Acceleration sensors.
(a)(b)Table 1
Technical parameters of the signal acquisition instrument.
Technical specificationsParameter valuesAccuracy24 bit∆−∑ADFrequency range (Hz)0.6∼216 kRange (g)50Resonant frequency (Hz)40 kTable 2
Technical parameters of the acceleration sensor.
Technical specificationsParameter valuesSensitivity (mv⋅g−1)2100Frequency range (Hz)20∼10 kRange (g)50Resonance frequency (Hz)40 k


### 3.2. Experimental Data Processing Method

In essence, the formation of any structural vibration mode is the result of the standing wave formed by the incident wave and the reflected wave of the elastic wave. Since this paper focused on the one-way propagation law of elastic waves in damaged media, it is necessary to avoid the frequency band where resonance occurs. With the increase of the damage degree of the slip plane between the dangerous rock mass and the bedrock mass, the resonance frequency of the dangerous rock mass decreases continuously [26, 27]. The damage of the slip surface is irreversible. Therefore, it is only necessary to identify the resonance frequency of the dangerous rock mass at the initial stage and select the frequency band higher than the resonance frequency for analysis, so as to avoid the influence of resonance. The empirical mode decomposition method can effectively divide the original vibration data into intrinsic mode sequences of different time scales. In this paper, the empirical mode decomposition method used was CEEMD [28], focusing on the analysis of the first- and second-order intrinsic mode sequences and calculating the marginal spectrum [29]of the first two-order intrinsic mode sequences. Taking as an example, the vibration data collected when the melting time of the frozen plane is 1 min, the time domain data are shown in Figure 5, and the marginal spectrum of the first two eigenmode sequences of the bedrock mass and dangerous rock mass model vibration sequence is shown in Figure 6.Figure 5
Vibration time domain sequence.Figure 6
Marginal spectrum of the first two intrinsic modal sequences of the dangerous rock mass and bedrock mass model. (a) Marginal spectrum of the first two intrinsic modal sequences of the dangerous rock mass model. (b) Marginal spectrum of the first two intrinsic modal sequences of the bedrock mass model.
(a)(b)Since this paper focused on the properties of high-frequency elastic waves, vibration data with a frequency greater than 777 Hz were selected, as shown in Figure6. A Butterworth high-pass filter with a threshold of 777 Hz was used to filter the data, and then, FFT was performed on the filtered data. The spectrum was calculated, as shown in Figure 7.Figure 7
777–2000 Hz spectrum diagram of the dangerous rock mass and bedrock mass model. (a) Spectrum of the dangerous rock mass model. (b) Spectrum of the bedrock mass model.
(a)(b)As shown in Figure7, there were no obvious peaks in the frequency band of 777–2000 Hz, and there was no resonance frequency in this frequency band. Since this paper focused on the high-frequency component of the elastic wave, any frequency band greater than 777 Hz can be selected. The minimum frequency selected was 1000 Hz.The Butterworth high-pass filter was used to filter the data of each period, and the threshold of the high-pass filter was set to 1000 Hz. The marginal spectrum of the filtered data in each period was calculated, and the central frequency was calculated based on the marginal spectrum. The calculation method of the central frequency is(11)F=∑10002000fkAk∑10002000Ak,where F is the central frequency, fk is the frequency, and Ak is the amplitude corresponding to fk.Based on equation (11), the central frequencies of the dangerous rock mass model and bedrock mass model in different time periods can be calculated in the frequency range of 1000–2000 Hz, as shown in Figure 8.Figure 8
Central frequency variation curve of the dangerous rock mass model.


### 3.3. Experimental Result Analysis

As shown in Figure9, the variation curve of the central frequency of the dangerous rock mass model and bedrock mass model with time can be obtained by calculation. In the time interval of 0–10 min, the central frequencies of the bedrock mass model and dangerous rock mass model decreased with the increased melting of the frozen plane. The reasons for this phenomenon were as follows: (1) the elastic wave passed through the damage freezing plane during the propagation of the elastic wave from the bedrock mass model to the dangerous rock mass model. The melting of the damage freezing plane led to a large number of pores in the local area, and the high-frequency elastic wave energy was lost, resulting in the central frequency of the dangerous rock mass moving from high frequency to low frequency. (2) The elastic wave passed through the damage freezing plane during the propagation from the bedrock mass model to the dangerous rock mass model, and the energy of the high-frequency wave was lost. The elastic wave propagated to the bedrock mass model after reflecting at the boundary of the dangerous rock mass model. The elastic wave passes through the damage freezing plane again during propagation to the bedrock mass model, and the energy of the high-frequency wave is lost again. At this time, the proportion of the high-frequency wave in the elastic wave decreased, while the proportion of the low-frequency wave increased, which led to an increase in the relative proportion of the low-frequency component in the vibration sequence of the bedrock mass model, resulting in its central frequency moving to the low frequency, and the amplitude of the movement was larger than that of the dangerous rock mass model. The curve of the ratio of the central frequency of the dangerous rock mass model to the bedrock mass model is shown in Figure 10.Figure 9
Central frequency variation curve of the dangerous rock mass model and bedrock mass model.Figure 10
Ratio of the central frequency variation curve.As the frozen plane continued to melt and damage, the dangerous rock mass model tended to fit the bedrock mass model. The pore size between the two was continuously adjusted with the degree of melting of the frozen plane, and the central frequency of the two fluctuated in the 10–20 min period. In the 20–30 min period, the frozen plane continued to melt, the dangerous rock mass model and the bedrock mass model gradually fitted, and the pores between the two models continued to decrease, resulting in a continuous decrease in the energy loss of high-frequency elastic waves. The central frequency of the bedrock mass model and the dangerous rock mass model began to rise until the frozen plane completely melted.Because the slope of the bedrock mass model was relatively small and the hydrosol was sticky, the sliding model did not slip after the frozen plane completely melted, and there was no displacement in this process. However, the vibration central frequency of the sliding body model in the 1000–2000 Hz frequency band changed significantly with the thawing damage of the frozen plane. It can be seen from this phenomenon that the displacement of the dangerous rock mass cannot fully reflect the change in the damage degree of the sliding plane. In engineering applications, displacement monitoring for slipping dangerous rock masses often has difficulty achieving good prevention and control effects. The work presented here is a new method that reflects the damage degree of slip planes by monitoring the vibration characteristics of slip-type dangerous rock mass and bedrock mass.


## 3.1. Introduction of the Experimental Process

To simulate the propagation law of elastic waves in rock masses under the condition of frequent microtremors, laboratory experiments were carried out. The dangerous rock mass and slip plane of real rock mass materials are difficult to build. Considering that the basic laws of elastic wave scattering in porous media of different materials are consistent, this test used other materials to simulate the sliding dangerous rock mass model. As shown in Figure3, the white plastic steel material was used as the dangerous rock mass model in the experiment, and the wood block was used as the bedrock mass model. Viscous hydrosol was used to bond the dangerous rock mass model to the bedrock mass model, and the whole model was placed in a refrigerator. The minimum temperature of the refrigerator was set to −10°C to freeze the hydrosol between the dangerous rock mass model and the bedrock mass model. After 24 hours of freezing, the whole model was removed, and the ice plane was used to simulate the slip plane between the dangerous rock mass model and the bedrock mass model. The melting of the ice plane was compared to the process of the slip plane changing from integrity to damage. Two acceleration collectors were pasted on the dangerous rock mass model and the bedrock mass model. The sampling frequency of the acceleration collector was set to 4000 Hz, and the vibration acceleration data were collected at 1 min intervals. A total of 30 sets of data were collected to obtain the vibration data of the dangerous rock mass model and bedrock mass model during the thawing process of the bonding plane. During the experiment, no human excitation was applied to the experimental model, and only the microvibration caused by the constant micromotion was considered.Figure 3
Model of the laboratory test.The equipment used in the experiment was a DASP modal testing system, which included an INV3062C signal processor and an INV9832-50 acceleration sensor. The signal processor and acceleration sensor are shown in Figure4. The device parameters are shown in Tables 1 and 2.Figure 4
Testing equipment. (a) Signal acquisition instrument. (b) Acceleration sensors.
(a)(b)Table 1
Technical parameters of the signal acquisition instrument.
Technical specificationsParameter valuesAccuracy24 bit∆−∑ADFrequency range (Hz)0.6∼216 kRange (g)50Resonant frequency (Hz)40 kTable 2
Technical parameters of the acceleration sensor.
Technical specificationsParameter valuesSensitivity (mv⋅g−1)2100Frequency range (Hz)20∼10 kRange (g)50Resonance frequency (Hz)40 k


## 3.2. Experimental Data Processing Method

In essence, the formation of any structural vibration mode is the result of the standing wave formed by the incident wave and the reflected wave of the elastic wave. Since this paper focused on the one-way propagation law of elastic waves in damaged media, it is necessary to avoid the frequency band where resonance occurs. With the increase of the damage degree of the slip plane between the dangerous rock mass and the bedrock mass, the resonance frequency of the dangerous rock mass decreases continuously [26, 27]. The damage of the slip surface is irreversible. Therefore, it is only necessary to identify the resonance frequency of the dangerous rock mass at the initial stage and select the frequency band higher than the resonance frequency for analysis, so as to avoid the influence of resonance. The empirical mode decomposition method can effectively divide the original vibration data into intrinsic mode sequences of different time scales. In this paper, the empirical mode decomposition method used was CEEMD [28], focusing on the analysis of the first- and second-order intrinsic mode sequences and calculating the marginal spectrum [29]of the first two-order intrinsic mode sequences. Taking as an example, the vibration data collected when the melting time of the frozen plane is 1 min, the time domain data are shown in Figure 5, and the marginal spectrum of the first two eigenmode sequences of the bedrock mass and dangerous rock mass model vibration sequence is shown in Figure 6.Figure 5
Vibration time domain sequence.Figure 6
Marginal spectrum of the first two intrinsic modal sequences of the dangerous rock mass and bedrock mass model. (a) Marginal spectrum of the first two intrinsic modal sequences of the dangerous rock mass model. (b) Marginal spectrum of the first two intrinsic modal sequences of the bedrock mass model.
(a)(b)Since this paper focused on the properties of high-frequency elastic waves, vibration data with a frequency greater than 777 Hz were selected, as shown in Figure6. A Butterworth high-pass filter with a threshold of 777 Hz was used to filter the data, and then, FFT was performed on the filtered data. The spectrum was calculated, as shown in Figure 7.Figure 7
777–2000 Hz spectrum diagram of the dangerous rock mass and bedrock mass model. (a) Spectrum of the dangerous rock mass model. (b) Spectrum of the bedrock mass model.
(a)(b)As shown in Figure7, there were no obvious peaks in the frequency band of 777–2000 Hz, and there was no resonance frequency in this frequency band. Since this paper focused on the high-frequency component of the elastic wave, any frequency band greater than 777 Hz can be selected. The minimum frequency selected was 1000 Hz.The Butterworth high-pass filter was used to filter the data of each period, and the threshold of the high-pass filter was set to 1000 Hz. The marginal spectrum of the filtered data in each period was calculated, and the central frequency was calculated based on the marginal spectrum. The calculation method of the central frequency is(11)F=∑10002000fkAk∑10002000Ak,where F is the central frequency, fk is the frequency, and Ak is the amplitude corresponding to fk.Based on equation (11), the central frequencies of the dangerous rock mass model and bedrock mass model in different time periods can be calculated in the frequency range of 1000–2000 Hz, as shown in Figure 8.Figure 8
Central frequency variation curve of the dangerous rock mass model.


## 3.3. Experimental Result Analysis

As shown in Figure9, the variation curve of the central frequency of the dangerous rock mass model and bedrock mass model with time can be obtained by calculation. In the time interval of 0–10 min, the central frequencies of the bedrock mass model and dangerous rock mass model decreased with the increased melting of the frozen plane. The reasons for this phenomenon were as follows: (1) the elastic wave passed through the damage freezing plane during the propagation of the elastic wave from the bedrock mass model to the dangerous rock mass model. The melting of the damage freezing plane led to a large number of pores in the local area, and the high-frequency elastic wave energy was lost, resulting in the central frequency of the dangerous rock mass moving from high frequency to low frequency. (2) The elastic wave passed through the damage freezing plane during the propagation from the bedrock mass model to the dangerous rock mass model, and the energy of the high-frequency wave was lost. The elastic wave propagated to the bedrock mass model after reflecting at the boundary of the dangerous rock mass model. The elastic wave passes through the damage freezing plane again during propagation to the bedrock mass model, and the energy of the high-frequency wave is lost again. At this time, the proportion of the high-frequency wave in the elastic wave decreased, while the proportion of the low-frequency wave increased, which led to an increase in the relative proportion of the low-frequency component in the vibration sequence of the bedrock mass model, resulting in its central frequency moving to the low frequency, and the amplitude of the movement was larger than that of the dangerous rock mass model. The curve of the ratio of the central frequency of the dangerous rock mass model to the bedrock mass model is shown in Figure 10.Figure 9
Central frequency variation curve of the dangerous rock mass model and bedrock mass model.Figure 10
Ratio of the central frequency variation curve.As the frozen plane continued to melt and damage, the dangerous rock mass model tended to fit the bedrock mass model. The pore size between the two was continuously adjusted with the degree of melting of the frozen plane, and the central frequency of the two fluctuated in the 10–20 min period. In the 20–30 min period, the frozen plane continued to melt, the dangerous rock mass model and the bedrock mass model gradually fitted, and the pores between the two models continued to decrease, resulting in a continuous decrease in the energy loss of high-frequency elastic waves. The central frequency of the bedrock mass model and the dangerous rock mass model began to rise until the frozen plane completely melted.Because the slope of the bedrock mass model was relatively small and the hydrosol was sticky, the sliding model did not slip after the frozen plane completely melted, and there was no displacement in this process. However, the vibration central frequency of the sliding body model in the 1000–2000 Hz frequency band changed significantly with the thawing damage of the frozen plane. It can be seen from this phenomenon that the displacement of the dangerous rock mass cannot fully reflect the change in the damage degree of the sliding plane. In engineering applications, displacement monitoring for slipping dangerous rock masses often has difficulty achieving good prevention and control effects. The work presented here is a new method that reflects the damage degree of slip planes by monitoring the vibration characteristics of slip-type dangerous rock mass and bedrock mass.


## 4. Discussion

### 4.1. Application Method of Dynamic Index of Dangerous Rock Mass

The typical single structural plane dangerous rock mass includes cantilever dangerous rock mass, shear fractured dangerous rock mass [14, 15], and sliding dangerous rock mass. The cantilever dangerous rock mass and the shear fractured dangerous rock mass are shown in Figures 11 and 12.Figure 11
Cantilever dangerous rock mass.Figure 12
Shear fractured dangerous rock mass.Cantilever dangerous rock mass and shear fractured dangerous rock mass can be approximately simplified as a cantilever beam, and the failure mode of the structural plane is fractured under the condition of tension-shear composite action. With the increase of the depth of the fracture, the geometric characteristics and boundary conditions of the dangerous rock mass change (1) for the cantilever dangerous rock mass, with the increase of the depth of the fracture, the constraint area of the bedrock mass to the dangerous rock mass decreases, and the constraint position of the structural plane to the dangerous rock mass changes; (2) for the shear fractured dangerous rock mass, the part not subject to lateral constraints is compared to a cantilever beam. As the depth of the fracture increases, the length of the cantilever beam increases, the geometric characteristics change, and the constraint area of the structure on the dangerous rock mass decreases. The resonance frequencies of the two types of dangerous rock mass decrease obviously with the increase of the fracture depth of the structural plane [14, 15]. For the slip-type dangerous rock mass, before the instability of the dangerous rock mass, the dangerous rock mass and the bedrock are in a bonding state, and the structural plane does not necessarily show a macroscopic fracture. The constraint area and constraint position of the structural plane to the dangerous rock mass do not change greatly, and the variation of the resonance frequency may be very small. Taking the data measured in this experiment as an example, the calculation steps are as follows:(1)
FFT transform was performed on the vibration data of the dangerous rock mass model and the bedrock mass model collected every minute. The ratio of the amplitude in the spectrum of the dangerous rock mass model to the amplitude in the spectrum of the bedrock mass model was defined as the relative amplitude, and the relative amplitude spectrum diagram was obtained to find the resonance frequency of the dangerous rock mass model, as shown in Figure13.(2)
According to the relative amplitude spectrum per minute, the resonance frequency-time curve of the dangerous rock mass model is obtained, as shown in Figure14.(3)
According to the calculation results of steps (1) and (2), the time-frequency spectrum of relative amplitude (as shown in Figure15) and the curve of the relative amplitude corresponding to the resonance frequency with time were obtained (as shown in Figure 16).Figure 13
Calculation process of resonance frequency of dangerous rock mass model. (a) Spectrum of dangerous rock mass model. (b) Spectrum of bedrock mass model. (c) Relative amplitude spectrum.
(a)(b)(c)Figure 14
Resonance frequency-time curve of dangerous rock mass model.Figure 15
Relative amplitude time-frequency spectrum.Figure 16
The relative amplitude-time curve corresponding to the resonance frequency.It can be seen from Figures14 and 15 that the resonance frequency of the dangerous rock mass model remained at about 187 Hz during the whole test, and the resonance frequency did not change significantly. It can be seen from Figures 15 and 16 that the relative amplitude corresponding to the resonance frequency of the dangerous rock mass model decreased with time, which also illustrated that the more serious the damage of the slip plane is, the more the energy dissipation of the elastic wave is, but the corresponding resonance frequency of the dangerous rock mass model did not change significantly.In fact, structural plane damage often includes two forms: macrofracture and microfracture. If there is microfracture in the structural plane medium but no macrofracture occurs, the elastic wave scatters at the microcracks; if there is a macrofracture in the structural plane, the elastic wave is mainly reflected at the macrofracture interface, and it is difficult to diffract or scatter. Macrofracture and microfracture are not opposite. The expansion and connection of microfracture will eventually develop into macrofracture, while macrofracture further aggravates the expansion and connection of microfracture. Therefore, the single use of elastic wave scattering theory or vibration mechanics theory to analyse the damage of the structural plane has limitations, and it is necessary to combine the two to judge the damage state of the structural plane.


### 4.2. Correlation between Dynamic Characteristics of Dangerous Rock Mass and Site Characteristics

The site condition information is included in the constant microvibration data. The predominant period can reflect overburden thickness and the dynamic characteristics of the site [30]. In theory, constant micromotion data can reveal the strata characteristic. However, due to the inhomogeneity of the geological body, the complexity of the geometry of the formation system, the unknown and randomness of the physical and mechanical properties of the rock and soil, the predominant frequency can only roughly reflect the dynamic characteristics of the site. It is difficult to determine the local characteristics of the site according to the propagation law of elastic waves in the stratum [31]. Compared with the site, the natural frequency of the dangerous rock mass is often inconsistent with the predominant frequency of the site. Therefore, the predominant frequency of the site cannot reflect the dynamic characteristics of the dangerous rock mass. Due to the complexity and uncertainty of the stratum, the propagation law of elastic waves in different sites is inconsistent, and the energy distribution of microvibration in different frequency bands is different. Therefore, in different sites, with the increase of structural plane damage, the change of energy distribution of microvibration of dangerous rock mass in different frequency bands is not completely consistent. Therefore, the change of energy distribution of vibration of dangerous rock mass in different frequency bands can only qualitatively reflect the damage of structural plane.In addition, the damage form of the structural plane is affected by its geological environment and external environment. The damage of the structural plane shows diversity at the microlevel, and different types of elastic wave scattering properties are different. The author will conduct more in-depth research on the scattering properties of various elastic waves at various pores and fracture and explore methods that can accurately reflect the damage of structural planes.


## 4.1. Application Method of Dynamic Index of Dangerous Rock Mass

The typical single structural plane dangerous rock mass includes cantilever dangerous rock mass, shear fractured dangerous rock mass [14, 15], and sliding dangerous rock mass. The cantilever dangerous rock mass and the shear fractured dangerous rock mass are shown in Figures 11 and 12.Figure 11
Cantilever dangerous rock mass.Figure 12
Shear fractured dangerous rock mass.Cantilever dangerous rock mass and shear fractured dangerous rock mass can be approximately simplified as a cantilever beam, and the failure mode of the structural plane is fractured under the condition of tension-shear composite action. With the increase of the depth of the fracture, the geometric characteristics and boundary conditions of the dangerous rock mass change (1) for the cantilever dangerous rock mass, with the increase of the depth of the fracture, the constraint area of the bedrock mass to the dangerous rock mass decreases, and the constraint position of the structural plane to the dangerous rock mass changes; (2) for the shear fractured dangerous rock mass, the part not subject to lateral constraints is compared to a cantilever beam. As the depth of the fracture increases, the length of the cantilever beam increases, the geometric characteristics change, and the constraint area of the structure on the dangerous rock mass decreases. The resonance frequencies of the two types of dangerous rock mass decrease obviously with the increase of the fracture depth of the structural plane [14, 15]. For the slip-type dangerous rock mass, before the instability of the dangerous rock mass, the dangerous rock mass and the bedrock are in a bonding state, and the structural plane does not necessarily show a macroscopic fracture. The constraint area and constraint position of the structural plane to the dangerous rock mass do not change greatly, and the variation of the resonance frequency may be very small. Taking the data measured in this experiment as an example, the calculation steps are as follows:(1)
FFT transform was performed on the vibration data of the dangerous rock mass model and the bedrock mass model collected every minute. The ratio of the amplitude in the spectrum of the dangerous rock mass model to the amplitude in the spectrum of the bedrock mass model was defined as the relative amplitude, and the relative amplitude spectrum diagram was obtained to find the resonance frequency of the dangerous rock mass model, as shown in Figure13.(2)
According to the relative amplitude spectrum per minute, the resonance frequency-time curve of the dangerous rock mass model is obtained, as shown in Figure14.(3)
According to the calculation results of steps (1) and (2), the time-frequency spectrum of relative amplitude (as shown in Figure15) and the curve of the relative amplitude corresponding to the resonance frequency with time were obtained (as shown in Figure 16).Figure 13
Calculation process of resonance frequency of dangerous rock mass model. (a) Spectrum of dangerous rock mass model. (b) Spectrum of bedrock mass model. (c) Relative amplitude spectrum.
(a)(b)(c)Figure 14
Resonance frequency-time curve of dangerous rock mass model.Figure 15
Relative amplitude time-frequency spectrum.Figure 16
The relative amplitude-time curve corresponding to the resonance frequency.It can be seen from Figures14 and 15 that the resonance frequency of the dangerous rock mass model remained at about 187 Hz during the whole test, and the resonance frequency did not change significantly. It can be seen from Figures 15 and 16 that the relative amplitude corresponding to the resonance frequency of the dangerous rock mass model decreased with time, which also illustrated that the more serious the damage of the slip plane is, the more the energy dissipation of the elastic wave is, but the corresponding resonance frequency of the dangerous rock mass model did not change significantly.In fact, structural plane damage often includes two forms: macrofracture and microfracture. If there is microfracture in the structural plane medium but no macrofracture occurs, the elastic wave scatters at the microcracks; if there is a macrofracture in the structural plane, the elastic wave is mainly reflected at the macrofracture interface, and it is difficult to diffract or scatter. Macrofracture and microfracture are not opposite. The expansion and connection of microfracture will eventually develop into macrofracture, while macrofracture further aggravates the expansion and connection of microfracture. Therefore, the single use of elastic wave scattering theory or vibration mechanics theory to analyse the damage of the structural plane has limitations, and it is necessary to combine the two to judge the damage state of the structural plane.


## 4.2. Correlation between Dynamic Characteristics of Dangerous Rock Mass and Site Characteristics

The site condition information is included in the constant microvibration data. The predominant period can reflect overburden thickness and the dynamic characteristics of the site [30]. In theory, constant micromotion data can reveal the strata characteristic. However, due to the inhomogeneity of the geological body, the complexity of the geometry of the formation system, the unknown and randomness of the physical and mechanical properties of the rock and soil, the predominant frequency can only roughly reflect the dynamic characteristics of the site. It is difficult to determine the local characteristics of the site according to the propagation law of elastic waves in the stratum [31]. Compared with the site, the natural frequency of the dangerous rock mass is often inconsistent with the predominant frequency of the site. Therefore, the predominant frequency of the site cannot reflect the dynamic characteristics of the dangerous rock mass. Due to the complexity and uncertainty of the stratum, the propagation law of elastic waves in different sites is inconsistent, and the energy distribution of microvibration in different frequency bands is different. Therefore, in different sites, with the increase of structural plane damage, the change of energy distribution of microvibration of dangerous rock mass in different frequency bands is not completely consistent. Therefore, the change of energy distribution of vibration of dangerous rock mass in different frequency bands can only qualitatively reflect the damage of structural plane.In addition, the damage form of the structural plane is affected by its geological environment and external environment. The damage of the structural plane shows diversity at the microlevel, and different types of elastic wave scattering properties are different. The author will conduct more in-depth research on the scattering properties of various elastic waves at various pores and fracture and explore methods that can accurately reflect the damage of structural planes.


## 5. Conclusion

(1)
The stability of sliding dangerous rock mass is affected by the damage degree of the sliding plane. When the sliding plane is damaged, many pores and fissures will appear in the medium around the sliding plane. The pores and fissures directly affect the propagation law of the elastic wave. When the elastic wave passes through the damaged medium, the characteristics of high-frequency wave dissipation will appear, which leads to a decrease in the central frequency of the high-frequency band of the sliding body.(2)
Under the condition of constant micromotion, the elastic wave propagates from the bedrock mass to dangerous rock mass, and the elastic wave propagates to the bedrock mass again after reflecting at the boundary of the sliding dangerous mass. In this process, the elastic wave passes through the damage slip plane twice, the high-frequency component of the elastic wave propagating to the bedrock mass decreases, and the proportion of the low-frequency component contained in the bedrock mass vibration data increases, which leads to a decrease in the central frequency of the bedrock mass in the high-frequency band.(3)
The experimental results showed that the high-frequency vibration data of the sliding dangerous rock mass and the bedrock mass are sensitive to the change in the damage degree of the sliding plane, which can directly reflect whether the damage degree of the sliding plane in which the current sliding body is located changes. This method can be applied in the prevention and control of sliding dangerous rock mass.(4)
When the structural plane has macrofracture, the change of natural frequency of dangerous rock mass should be used to analyse the damage degree of structural plane; (2) when there is no macrofracture of the structural plane, the characteristics of elastic wave scattering should be used to analyse the damage degree of the structural plane. The structural plane often has both macro- and microfractures. Therefore, the two methods should be used to analyse the damage of the structural plane comprehensively.



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*Source: 6323929-2023-03-07.xml*