Study on the inuence of stress wave disturbance on ultra-low friction effect of broken blocks

With the increase of mine mining depth, deep rock mass tends to be broken into block medium. The roof-rock layer-floor can be regarded as block system fractured rock mass. Under the condition of high ground stress and mining disturbance, the ultra-low friction effect of block system fractured rock mass is easy to occur, and then induce rock burst and other disasters. Taking the block rock mass as the research object, the self-developed ultra-low friction test system is used to carry out the experimental research on the ultra-low friction effect of the broken block under the condition of stress wave disturbance. Taking the horizontal displacement of the working block as the characteristic parameter reflecting the ultra-low friction effect, by changing the stress wave disturbance frequency and amplitude, the characteristic law of the horizontal displacement, acceleration and energy of the working block during the occurrence of the ultra-low friction effect is analyzed. The research results show that the stress wave disturbance frequency is related to the generation of ultra-low friction of the broken block. The disturbance frequency of the stress wave is within 1~3Hz, and the maximum acceleration and horizontal displacement of different broken degree blocks increase significantly. This frequency range is prone to ultra-low friction effect. The greater the intensity of the stress wave disturbance, the higher the degree of block fragmentation, and the more likely to have ultra-low friction effects between the blocks. The greater the intensity of the horizontal impact load, the higher the degree of rock mass fragmentation, the easier it is for ultra-low friction effects to occur. Stress wave disturbance and horizontal impact are the main reasons for the sliding instability of broken blocks. When the dominant frequency of the kinetic energy of the broken block is within 20 Hz, the ultra-low friction effect is more likely to occur.


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Zhao An-ping et al. (2018) established a one-dimensional analysis model of jointed rock mass and carried out dimensional analysis to discuss the influence of joint characteristics on the law of stress wave propagation.
Based on the above research results, in the theoretical models of block rock mass established by domestic and foreign scholars, only the dynamic response under vertical impact load and horizontal static force is analyzed. On this basis, there is a lack of further analysis on the influence of parameters such as the degree of block fragmentation and the disturbance frequency and amplitude of stress wave on the ultra-low friction effect of block rock mass. In this paper, on the basis of the direction of research scholars, the ultra-low friction effect was designed and developed to load test device, in under the action of stress wave disturbance crushing block of ultra-low friction effect test, to work for the parameter block horizontal displacement and horizontal acceleration, the study of the stress wave disturbance frequency and intensity of disturbance of the broken block of ultra-low friction effect. The obtained research results are compared with the related results of predecessors, and provide a scientific basis for the prediction and prevention of disasters caused by the ultra-low friction effect.

Establishment of theoretical model of ultra-low friction effect of block rock mass
In the process of establishing the theoretical model of the ultra-low friction effect, springs or spring damping are often used to simulate the mechanical characteristics of the weak interlayer, and the overall model is established by connecting the mass points. In recent years, some mechanical models have been put forward in the study of block system rock mass dynamics Wu Hao et al.2009;Wu and Fang 2010), which provide a theoretical basis for studying the ultra-low friction effect of block system broken rock mass.

Model establishment
The deep rock mass is divided by geological structures such as fissures and joints. The mechanism of the ultra-low friction effect is closely related to the dynamic deformation characteristics of the block interface and the stability of the block system. To study the deformation characteristics of deep block media, we must first reveal the normal and tangential dynamic characteristics of the block interface. Therefore, on the basis of previous research, the block is regarded as a rigid body, and the theoretical model of ultra-low friction effect as shown in Figure 1 is established. In Figure 1, the size of the block is the same, and the mass is Axial pressure H  , Acting on the surface of block 1. Springs and dampers are set between the blocks to describe the energy transfer and retardation of the weak connecting medium between the blocks. The stiffness coefficient is k i and the damping coefficient is c i . The movement of the block consists of two stages. The first stage is forced vibration under the action of a vertical impact, and the second stage is the free vibration of the block starting from the moment t 0 with the state of that moment as the initial condition.
n n n n n n n n mz k z z l c z z mg P ωt F mz k z z l c z z k z z l c z z mg mz k z z l c z z k z z l c z z mg mz k z l c z k z z l c z Where m i -Block mass; z i-Ordinate of block i ; l-Free length of spring; g-Acceleration of gravity; F v-The resultant force of ground stress in the vertical direction of the model.
Simplify the above formula into a matrix form, and get: Where u-Block horizontal movement displacement, m; d  -Dynamic friction coefficient between blocks; () Nt -Normal force on the block, N. Set z=z 0 +y, the vertical balance position has: Solve the initial coordinates of each block in the z-axis direction as: Substituting z=z 0 +y, 0 z = Kb into the matrix equation, we get: Set k 1 =k 2 =…=k n ， c 1 =c 2 =…=c n ， m 1 =m 2 =…=m n ， the approximate solution of the block acceleration in the model is:

Comparative analysis of test theory
Since the correctness of the above theoretical model has been verified (Li Li-ping et al. 2019). In order to study the effect law of stress wave disturbance on ultra-low friction effect of fractured rock mass under axial compression and facilitate comparative analysis, ultra-low friction tests under the combined action of axial compression and stress wave disturbance were conducted. The size of the block is 100 mm×100 mm ×100 mm, and the mass of the block is 2.56 kg. The test model consists of five rock blocks stacked in the vertical direction without weak interlayers. A 4MPa axial pressure is applied to block 1 to simulate the pressure effect of the overlying rock layer, and the stress wave disturbance function is applied, and the stress wave disturbance amplitude is applied, it is 40kN, and the disturbance frequency is 1Hz, 3Hz, 5Hz, 10Hz, 20Hz. Acceleration sensor (attached to the center of the block), the data acquisition instrument is used to collect test data. The calculation in the theoretical formula is consistent with the test parameters: c=60 N·s/m, k=4.0×10 6 N/m, l=0.005m, m i =2.56 kg. The working block is the third block and takes its acceleration as a parameter, sorts out the test data, and compares the result with the acceleration derived from the theoretical model, as shown in Figure 3. It can be seen from Figure 3: The maximum acceleration of the test block and the theoretical block both decrease with the increase of frequency. The acceleration amplitude of the working block can be divided into three stages, which are the steep decline stage, the slow decline stage and the steady stage. When the perturbation frequency is in the range of 1~5Hz, the amplitude of acceleration change is larger, indicating that low-frequency perturbation has a significant impact on the movement of the block. When the disturbance frequency is 1Hz, a maximum acceleration of respectively 14.13m/s 2 and 49.52m/s 2 . With the increase of the disturbance frequency, the change trend of the block acceleration amplitude slows down and stabilizes. Due to the difference between the theoretical model and the experimental conditions, the maximum acceleration is different, but the change trend is consistent with the frequency of the stress wave disturbance. Therefore, the rationality of this experiment is verified.

Ultra-low friction test system
The equipment used in the test can realize the three-dimensional stress loading of the broken rock mass, and better simulate the real stress condition of the broken rock mass when the ultra-low friction rock burst occurs. The loading equipment is composed of four main parts: axial pressure loading mechanism, confining pressure loading  mechanism, impact loading mechanism and disturbance loading mechanism. This design mainly adopts hydraulic transmission and control system. The model size of the test block can be adjusted according to different test requirements. The length range is 0~200mm, the width range is 0~200mm, and the height range is 0~600mm.
Confining pressure can be applied to the front and back of the test body, in the range of 0 ~ 30MPa; horizontal impact is applied to the left side, in the range of 0 ~ 30MPa. The axial pressure and vertical disturbance can be applied in the vertical direction at the same time, the axial pressure range is 0～30MPa; the vertical disturbance range is 0～3MPa, and the frequency can be adjusted within 0～50Hz, as shown in Figure 4. The horizontal displacement of the block is measured by the Panasonic mini laser sensor.
(The red solid line in the picture is the pipe connection, and the blue solid line is the wire) Fig.4 Ultra-low friction test system

Preparation of test pieces
Red sandstone has uniform grain size and is widespread underground. Therefore, the rock sample used in the test was selected as red sandstone. In order to make the test results comparable, all samples are required to be taken from the same sandstone with good integrity and homogeneity. The samples used in the test are all processed into cylinders with a diameter of 50 mm and a height of 100 mm, and the samples are polished to ensure that the parallelism of the surfaces at both ends is within 0.05 mm and the surface flatness is within 0.02 mm. The uniaxial compression test of the rock sample is carried out in the mechanics laboratory. All the tests adopt the displacement-controlled loading method, and the loading rate is required to be constant at 0.15 mm/min. the vertical direction. The stress wave disturbance form is a sine wave. This paper does not consider the delay time effect, and applies a horizontal impact to the rock block at t 0 .
The specific experimental steps are as follows: (1)Put the Intact sandstone block in the testing machine from top to bottom in the vertical direction, apply 4 MPa axial pressure in the vertical direction, and set the confining pressure to 15 MPa.
(2)The stress wave disturbance is applied in the vertical direction, the initial stress wave disturbance amplitude is 0.3MPa, and the vibration frequency is 1Hz.
(3) A horizontal impact is applied to the No. 3 working block, and the horizontal displacement of the working block is measured by the optical fiber non-contact displacement sensor, the acceleration is measured by the acceleration sensor.
(4)Change the stress wave disturbance frequency, disturbance amplitude and horizontal impact in turn, and carry out the test.
(5)Replace the working block with two sandstone rock blocks and four sandstone rock blocks, repeat the steps (1) (2) (3) (4) respectively, and record the data.

Stress wave disturbance frequency influence analysis
(1) Analysis of the influence of the horizontal displacement of the broken block As the frequency of stress wave disturbance increases, the horizontal displacements of blocks of different fragmentation levels all show the fluctuation characteristics of increasing first and then decreasing. When the stress wave disturbance frequency is 1~3Hz, there is a high displacement area of the working block. Under the same level of impact and stress wave frequency, the horizontal displacement of the four sandstone rock blocks is the largest, followed by the two sandstone rock blocks, and the intact sandstone block is the last. As shown in Figure 7, as the frequency of stress wave disturbance increases, blocks with different fragmentation levels have high displacement areas. Under the same disturbance frequency, the residual displacement of the four sandstone rock blocks is the largest, followed by the two sandstone rock blocks, and finally the intact sandstone block. In the high displacement area, when the frequency is 2.5 Hz, the horizontal displacement of the block is the largest, indicating that the ultra-low friction effect of the block is the strongest at this frequency during the entire dynamic disturbance process. Taking the horizontal impact of 1.5MPa as an example, when the disturbance frequency is increased from 1Hz to 1.5Hz, 2Hz, 2.5Hz, 3Hz, the residual displacement of the four sandstone rock blocks and the residual displacement of the intact sandstone block are respectively 0.0302mm, 0.0702mm, 0.0618mm, 0.0983mm, 0.037mm, the above shows that under low-frequency disturbance, the degree of fragmentation of the block affects the strength of the ultra-low friction effect of the block during the impact. The more the block system rock mass tends to be broken, the greater the horizontal displacement of the block is, the easier it is to cause engineering disasters. As the mining depth increases, the rock blocks tend to be more broken, so stronger support methods should be used in actual projects to increase the strength of the rocks around the roadway to avoid engineering disasters.
(2) Analysis of the influence of the acceleration of broken blocks When the blocks are disturbed by the stress wave, the working block oscillates back and forth in the vertical direction at the equilibrium position. At this time, a horizontal impact is applied, and the acceleration of the working block increases suddenly and is greater than the acceleration without stress wave disturbance. It can be seen from Figure 7 that when the stress wave disturbance frequency is in the range of 1 to 3 Hz, the working block has an obvious ultra-low friction effect under the action of horizontal impact. The greater the horizontal impact energy of the working block is, the greater the extreme value of its acceleration and the stronger the ultra-low friction effect. Under the same level of impact and stress wave frequency, the horizontal displacement of the four sandstone rock blocks is the largest, followed by the two sandstone rock blocks, and the intact sandstone block is the last. With the gradual increase of the disturbance frequency from 3 Hz, the maximum acceleration of the broken block gradually decreases, and gradually returns to the level when there is no disturbance, and the ultra-low friction effect of the broken block is weakened. During the propagation of the stress wave, the accumulated energy of the block increases, and when the block tends to be more broken, the stability of the entire block rock mass decreases during the disturbance process, and the phenomenon of "separation" between the blocks frequently occurs. Therefore, when the block is subjected to strong impact and disturbance, the friction between the blocks is weakened, the acceleration of the block increases, and the strength of the ultra-low friction

Analysis of the influence of stress wave disturbance intensity
(1) Analysis of the influence of the horizontal displacement of the broken block It can be seen from Figure 8 that with the increase of the disturbance intensity, the horizontal displacement of the working blocks of different fragmentation degrees all increase almost linearly, and the fitting degree is higher.
Enhanced ultra-low friction effect. Under the same level of impact and stress wave disturbance intensity, the horizontal displacement of the four sandstone rock blocks is the largest, followed by the two sandstone rock blocks, and the intact sandstone block is the last. When the horizontal impact is 1.5MPa, the horizontal displacement of the four sandstone rock blocks under the disturbance strength of 1 MPa is increased by 16.6% compared to the horizontal displacement without disturbance, the two sandstone rock blocks is increased by 15.4%, and the intact sandstone block is increased by 15.1%. When the horizontal impact is 2.5MPa, the horizontal displacement of the four sandstone rock blocks under the disturbance strength of 1 MPa is increased by 31.6% compared to the horizontal displacement without disturbance, the two sandstone rock blocks is increased by 25.6%, and the intact sandstone block is increased by 23%. By comparison, it is found that the increase of the disturbance intensity makes the horizontal displacement of the working block slightly increase, and the increase of the horizontal impact will make this phenomenon obvious. (2) Analysis of the influence of the acceleration of broken blocks It can be seen from Fig. 9 that with the increase of the disturbance intensity, the maximum acceleration of the working block of different broken degrees increases to different degrees. Enhanced ultra-low friction effect. Under the same level of impact and stress wave disturbance intensity, the maximum acceleration of the four sandstone rock blocks is the largest, followed by the two sandstone rock blocks, and the intact sandstone block is the last.
When the horizontal impact is 1.5MPa, the maximum acceleration of the four sandstone rock blocks under the disturbance strength of 1 MPa is increased by 19.3% compared to the horizontal displacement without disturbance, the two sandstone rock blocks is increased by 38.1%, and the intact sandstone block is increased by 35%. When the horizontal impact is 2.5MPa, the maximum acceleration of the four sandstone rock blocks under the disturbance strength of 1 MPa is increased by 42.3% compared to the horizontal displacement without disturbance, the two sandstone rock blocks is increased by 55.8%, and the intact sandstone block is increased by 48.5%. By comparison, it is found that the increase of the disturbance intensity makes the maximum acceleration of the working block increase more obviously, and the increase of the horizontal impact will make this phenomenon more obvious. The more the blocks tend to be broken, when the intensity of the stress wave disturbance increases, the stability of the blocks decreases, and the separation between the blocks is more obvious, so the intensity of the ultra-low friction effect is also greater. the more rock mass tends to be broken and the roadway damaged by stress is more prone to ultra-low friction effect. This is the same as the actual field observation result. With the increase of mining depth, the rock mass tends to be broken and intermittently formed into a block structure. Under the combined action of ground stress and mining disturbance, the broken block is more prone to dislocation, resulting in ultra-low friction effect. In turn, disasters such as rock bursts occurred.

Research on energy characteristics of ultra-low friction effect
The occurrence process of rock burst is the instantaneous release of energy (Wang Gui-feng et al. 2018). In the case of dynamic disturbance, according to the research results of Wang Ming-yang et al.(2015), the effect of disturbance makes the rock block vibrate, and the equivalent vibration generated by the disturbed block Kinetic energy W is: Where v -Equivalent vibration velocity, write formula (5-1) as Set W m -Kinetic energy per unit mass.
The horizontal displacement of the working block obtained from the experiment is derived to obtain the block velocity, and then the block kinetic energy per unit mass in the time domain is obtained, and the unit mass kinetic energy is Fourier transformed to obtain its power spectral density curve, which can be known for each frequency The strength of the energy contained. (1) It can be seen from the time domain change curve of unit mass kinetic energy in Figure 10 and Figure 11, Under the horizontal impact of 1.5MPa and 2.5MPa, the maximum kinetic energy of the working block is reached in 125ms, that is, when the working block is subjected to horizontal impact for a short time, due to the impact and ultra-low friction effect, the working block's the kinetic energy quickly increases to its maximum value. The smaller the friction between the blocks, the greater the kinetic energy of the working blocks. Due to the constraint of axial pressure and the energy consumption of horizontal impact, the energy of the block is greatly attenuated within 4ms of impact. After that, the working block returns to a stable vibration state, and the kinetic energy of the block increases with the increase of the horizontal impact load. Therefore, when rock masses with different fracture levels are disturbed by vertical stress waves and have an ultra-low friction effect, their kinetic energy will experience transient accumulation and transient peak effects. Under the same level of impact load, the kinetic energy of the four sandstone rock blocks is the largest, and the kinetic energy of the intact sandstone block is the smallest. At this time, the ultra-low friction effect of the block is the strongest.

Energy characteristics of ultra-low friction effect of different broken blocks
(2) The test simulates the occurrence and development process of rock burst well. The study found that the ultra-low friction effect of the broken rock mass is caused by the stress wave disturbance. During this process, the power spectral density amplitude increases instantaneously and fluctuates significantly. The frequency corresponding to the maximum power spectral density of the working block is called the extreme frequency, the more the working block tends to be broken, the closer its extreme frequency is to the low frequency. When ultra-low friction type rock impact occurs, the kinetic energy of the working block has the characteristics of transferring from high frequency to low frequency. The more the working block tends to be broken, the greater the maximum power spectral density. The energy is concentrated in the low frequency area and attenuates in the transition area. The energy value in the high frequency area is small, and it is not easy to produce ultra-low friction effect. When the working block is subjected to a large impact load, the energy increases significantly, and it is easier to produce an ultra-low friction effect under the action of the stress wave. (1) Analyzing the data on the kinetic energy per unit mass in Table 3, it is obtained that the kinetic energy of different broken degree blocks increases with the increase of the horizontal impact load, and the energy of the four sandstone rock blocks reaches the maximum during the ultra-low friction effect, intact sandstone block has the least. Under the horizontal impact of 1.5MPa, the energy of the four sandstone rock blocks and the two sandstone rock blocks are respectively 2.90 times and 1.68 times that of the intact sandstone block under the same impact. Under a horizontal impact of 2.5 MPa, the energy of the four sandstone rock blocks and the two sandstone rock blocks are respectively 2.12 times and 1.62 times that of the intact sandstone block under the same impact. After blocks of different fracture levels are subjected to horizontal impacts in the stress wave disturbance process, the energy accumulation situation is different. The blocks tend to be broken, the roadways have stress defects, and the rock blocks with lower strength and stability are affected by the impact.

Comparative analysis of related parameters of ultra-low friction effect energy
The block energy can accumulate to the maximum in a short period of time, and it is very easy to have ultra-low friction effect, which in turn induces natural disasters such as rock impact. Therefore, the degree of rock fragmentation is the main controlling factor that affects the ultra-low friction strength of the block.
(2) Analyzing the data on the extreme frequency in Table 3, it is obtained that the more the block tends to be broken, the lower the dominant frequency when ultra-low friction occurs. The higher the horizontal impact load of the block is, the lower the dominant frequency when ultra-low friction occurs. When the horizontal impact is 1.5 MPa, the main frequency of the block is within 20 Hz, and when the horizontal impact is 2.5 MPa, the main frequency of the block is within 10 Hz. This is consistent with the conclusion that the actual underground ultra-low friction effect occurs in the low frequency range.
(3) Analyzing the data on the power spectrum density in Table 3, it is obtained that the more the block tends to be broken, the higher the power spectrum density is when the ultra-low friction occurs. The higher the horizontal impact load of the block is, the higher the power spectral density when ultra-low friction occurs. The more the block tends to be broken, the stronger it is subjected to horizontal impact, the more obvious the dynamic response, and the more prone to ultra-low friction effect, which will cause rock burst disasters.

Discussion
With the gradual reduction and depletion of shallow resources, mines in various countries around the world have with previous studies and found that the experimental research of Su Guo-shao et al. (2016) found that in the frequency range of 0～3 Hz, as the frequency of axial disturbance load increases, the kinetic energy of rock burst ejection first increases and then decreases. Pan Yi-shan (2014) and other studies found that the frequency of external disturbances will change the maximum stretch value between rock blocks. When the disturbance frequency is close to the quasi-resonant frequency of the block system rock mass, the maximum stretch value increases sharply. Compared with the above experiments, due to differences in loading conditions, physical and mechanical properties and dimensions of the specimens, this paper finds that ultra-low friction is prone to occur when the perturbation frequency is 1 ~ 3Hz. Limited to the only research object, the conclusions of this article have yet to be verified by a large number of experiments. In the future, ultra-low friction tests under field conditions will be carried out to make theoretical and practical application values for the prediction and prevention of deep rock bursts.

Conclusion
(1) The stress wave disturbance frequency has a wave effect on the ultra-low friction effect of broken rock mass.
The stress wave disturbance frequency is in the range of 1~3 Hz. The horizontal displacement and acceleration maximum value of the block subjected to dynamic response increase significantly, and the ultra-low friction effect is the strongest. As the disturbance frequency of the stress wave increases again, the maximum horizontal displacement and acceleration of the block gradually fall back to the state without disturbance. The more broken the block, the greater the dynamic response.
(2) The influence of the intensity of the stress wave disturbance on the ultra-low friction effect of the crushed block changes linearly. The more the block is broken, the greater the intensity of the stress wave disturbance is, and the more obvious the ultra-low friction effect of the block is.
(3) Under the same level of impact, the ultra-low friction effect of the block is four combined blocks, two combined blocks and complete sandstone blocks in order from strong to weak. The horizontal impact load strength is also an important factor for the enhancement of the ultra-low friction effect of the block.
(4) Under the combined action of axial compression, horizontal impact, and stress wave disturbance, the kinetic energy of the block has the characteristics of agglomeration and short-term peak value. When the strength of the ultra-low friction effect is the largest, it is manifested in the block unit mass kinetic energy, power spectral density, and kinetic energy extreme value The frequency shifts from high frequency to low frequency, and the waveform tends to be low frequency waves, and the main frequency of the block has an ultra-low friction effect within 20 Hz.
Acknowledgments: This research was financially supported by the National Science Foundation of China (51974148) and Liaoning Xingliao Talent Program (XLYC1807130).
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