2. 1
Research on spatial-temporal response law of seismic
wave generated by rock mass fracture under load
Feng Shena,b Shengquan Hea*,b··Xueqiu Hea Dazhao Songa,b Jialin Donga Yang Liua
Majid Khanb
aSchool of Civil and Resources Engineering, University of Science & Technology Beijing, Beijing
100083, China
bKey Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mine, University
of Science and Technology Beijing, Beijing 100083, China
*Corresponding author. E-mail address: shenqhe@163.com
Highlights
·The parameters of seismic wave and fracture source have a highly linear functional
relationship.
·The spatial distribution of amplitude and frequency of seismic wave has obvious
directivity.
·The spatial response characteristics of seismic wave signal are consistent with the
displacement field theoretical model.
Abstract:
The increased intensity of dynamic disasters due to overlying burden in deep
mining has become a global issue. Understanding the spatial characteristics and
governing principles of seismic waves propagation resulted due to dynamic load hold
imperative meaning, however, it remained challenging. In this paper, the characteristics
of fracture source and spatiotemporal response law of seismic wave generated by rock
fracture are studied through uniaxial loading, high-resolution X-ray scanning and 3D
visual reconstruction technology. The obtained results show that with the increase in
stress, the peak amplitude of seismic wave signal exponentially increases whereas the
3. 2
dominant frequency decreases. The characteristic parameter of the seismic wave
displays a linear functional relationship with fracture source. The amplitude and energy
of seismic wave signal are linearly related to fracture size, while the dominant
frequency linearly decreases. The spatial distribution of seismic amplitude and
frequency possess prominent directivity. The spatial seismic characteristics are
fundamentally consistent with the theoretical field radiation model of seismic wave
displacement. The research results further elucidate the spatial propagation
characteristics of seismic wave which would be helpful in understanding the dynamics
of disturbances caused in worldwide deep mining.
Key words: Rock fracture; Source morphology; Seismic wave; Frequency spectrum;
Response law
0 Introduction
With the continuous increase of the mining depth of coal mines in China, the scale
and intensity of rockburst are increasing. In order to prevent rockburst more accurately,
it is necessary to have a deeper understanding of the mechanism of rockburst occurrence
and reveal the essence of rockburst occurrence from the root. The seismic wave
produced by the fracture of rock mass under high stress is one of the main sources of
dynamic load, which has an important influence on the induced rockburst.
The characteristics of rock fracture source under load are important factors to
reveal the mechanism of rockburst. Relevant researchers used acoustic emission and
digital image technology combined with CT imaging to explore the characteristics of
crack propagation, revealing the fracture and propagation of fracture under different
sizes and angles of prefabricated cracks, coupled effects of dynamic and static load,
different water content, different porosity and other conditions, which greatly enriched
the research on the characteristics of rock crack evolution[1-4]. Zhang et al.[5] conducted
uniaxial experiments and combined with numerical simulation to study the crack
development characteristics in the process of uniaxial fracture and instability of coal
rock combinations. The results showed that shear crack was the main mechanical
behavior of sample damage. Sun et al. [6] quantitatively studied the progressive crack
evolution process of materials by using CT technology, and found that small invisible
fracture began to appear soon after loading, gradually accumulated in the elastic
deformation stage, and finally formed through damage in the plastic stage. Zhu et al.[7],
Ji et al.[8] revealed the evolution of internal fracture in rocks using acoustic emission
characteristic parameters during rock deformation. Zhang et al.[9] proposed a method of
4. 3
classification criteria for tensile fracture and shear fracture based on the dominant
frequency characteristics of acoustic emission waveform, and verified the accuracy of
this method through four rock loading failure experiments. Wang et al.[10] studied the
response characteristics of artificial layered rock with different bedding dip angles
under uniaxial compression fracturing, identified 9 independent crack types, and
analyzed the influence of bedding dip angle on damage propagation. Gao et al.[11] and
Chen et al.[12] and Zhu et al.[13] revealed the mechanism of rock fracture propagation
from the perspective of energy, and determined the fracture propagation threshold.
Before and after the crack damage threshold, the energy release rate and dissipation rate
have opposite changes. Bouchaala et al.[14] pointed out significant seismic dissipation
in a medium with high concentration of natural discontinues such as fractures and
cracks.
The seismic signal generated in the process of coal and rock fracture can make an
early warning to the occurrence of coal and rock dynamic disasters. Therefore, many
scholars have been made based on the characteristics of seismic wave signals of rock
fracture. Su et al.[15] simulated the static and dynamic fracture process of hard rock
through compression test, and found that a kind of seismic wave with "high energy and
low frequency" characteristics will appear before rock instability damage. Shcherbakov
and Chmel '[16] studied the amplitude frequency characteristics of seismic wave
generated by granite damage in high temperature environment, and concluded that the
corresponding damage size can be evaluated according to the amplitude frequency
characteristics. Dong et al.[17] studied the precursory characteristics of rock instability
based on the variation law of wave velocity in rock acoustic emission experiment. The
results showed that the difference of damage type and morphology was the main reason
for the anisotropy of wave velocity variation of acoustic emission. Zhao et al.[18], Zhang
et al.[19] statistically analyzed the distribution characteristics of seismic wave signals
with different frequency bands and amplitudes in the process of rock deformation and
damage. The results show that the signal frequency is relatively dispersed in the linear
deformation stage, and the dominant frequency of acoustic emission signal is relatively
concentrated in the nonlinear deformation stage. Du et al.[20] studied the AE
characteristics and fracture classification during rock damage. Their results showed that
the elastic strain energy released by shear fracture was greater than that released by
tensile fracture, and the frequency of seismic wave signal released by the two fracture
was lower than 100 kHz. Lu et al.[21] studied the original seismic waveform in the
5. 4
process of coal and rock fracture and found that when rock burst occurred, the dominant
frequency of the main seismic signal moved significantly to the lower frequency band,
and the corresponding energy of the main frequency band rose sharply and reached the
maximum value. Bouchaala et al.[22] explained the lowering of seismic dominant
frequency, by the stronger attenuation of high frequencies than lower frequencies.
Belikov et al.[23] studied the seismic wave signals temporal variation law during uniaxial
loading of rock samples, constructed the amplitude spectrum of seismic wave signals
at four consecutive times, and quantitatively studied the evolution mode of rock
structural parameters fracture process. Li et al.[24] used HHT method to analyze the
characteristics of seismic wave waveform in different loading stages, and concluded
that hilbert instantaneous energy reflects the energy of seismic wave shape in different
stages, and found that waveform frequency and amplitude are the main factors affecting
hilbert instantaneous energy.
The predecessors mainly studied the fracture morphology and expansion
characteristics under load or the change characteristics of acoustic emission parameters
of rock mass fracture respectively. The research on the characteristics of invisible
fracture in rock mass under uniaxial loading, the amplitude frequency evolution of
seismic wave signals under different fracture sizes, and the response characteristics of
seismic wave signals in different directions in the fracture source space are rarely
studied. Therefore, based on the uniaxial loading system, using X-ray scanning and 3D
reconstruction technology, this paper quantitatively establishes the relationship
between seismic wave properties and the internal fracture source of rock. The research
results further clarify the spatial propagation characteristics of seismic waves and lay a
theoretical foundation for the response characteristics of rock to dynamic disturbance.
1 Experimental system and experimental scheme
1.1Experimental system
The uniaxial loading damage experiment system, including the loading control
system, the acoustic emission monitoring system, the data collecting system, the 3D
scanning imaging system, and other subsystems, was designed for this study, as shown
in Fig. 1. Additionally, a high-speed camera was used to record the loading of samples
in real time. The YAW-600 pressure testing machine was employed as the loading
control instrument in the experiment. An acoustic emission sensor and an acoustic
emission preamplifier make up the acoustic emission monitoring system. The response
6. 5
frequency of the acoustic emission sensor is 50~400kHz, the amplification factor of the
preamplifier is adjustable in three gears of 20, 40 and 60dB, and the frequency band of
the built-in filter is 20kHz~1.5MHz. The data acquisition and processing device adopts
DS5-16B full information acoustic emission signal analysis system. The nano Voxel
3502E high-resolution X-ray 3D CT scanning imaging system was used in the
experiment, which can carry out large-scale and non-destructive 3D scanning analysis
and imaging of the 3D pore structure in solid rock structural materials.
Fig. 1 Schematic diagram of experimental system structure
1.2Experimental scheme
Following China National Standard GB/T 23561.1-2009 and GB/T 23561.7-2009,
the large size sandstone and shale taken from Sichuan, China, are processed into
standard samples. The specimen size is Φ 50 × 100 mm, and each type of rock contained
eight samples (figure 2(a)). Both types of rock are basically isotropic. During the
loading process, the rock samples were loaded by 2 µm/s displacement control. The
sampling frequency of the acoustic emission signal acquisition system was set to 3MHz,
the hit identification time was set to 100 µs, and the peak identification time and hit
locking time were set to 500 µs. The arrangement of sensors is shown in Fig. 2 (b). In
the uniaxial loading experiment, eight sensors were employed, which were positioned
on the sample's surface to track the seismic wave signal produced by the sample fracture
in various spatial locations in real time.
7. 6
Fig. 2 Physical diagram of partial samples and sensor arrangement scheme
Two shales (YY1, YY2) and two sandstones (CS1, CS2) are loaded firstly until
they are completely destroyed, and their critical damage loads were measured to
analyze the correlation between the seismic signal and the load. The remaining samples
were then loaded to stop at peak stress to ensure that enough micro-fractures were
generated within the sample. Finally, CT scanning was carried out on the samples that
stopped loading when the load reached the peak load to obtain the characteristics of the
internal fracture source of the samples.
2 Time series evolution characteristics of rock damage and
seismic waves during loading of rock samples
The whole process of uniaxial loaded stress-strain curve of a typical rock sample
can be divided into four stages [25,26]. As shown in Fig. 3 (a), the four stages are: I -
Compaction stage, II - Linear elastic stage, III - Accelerated inelastic deformation stage,
and IV - Damage and development stage. The internal pores and original cracks of the
sample in stage Ⅰ are compacted, and the sample keeps accumulating energy in stage
Ⅱ. Then gradually releases from stage Ⅲ, and finally releases all in stage Ⅳ, causing
macro-damage to the sample. In this paper, the stress-strain curve of rock samples
during uniaxial loading is shown in Fig. 3 (b). It can be seen that the sample stress
decreases rapidly after reaching the peak value, and large deformation occurs at this
stage. The duration of the sample in stage III is relatively short, and many fracture in
the sample in this stage connect with each other in a very short time in stage IV leading
to macro-damage.
8. 7
（a）Typical stress-strain diagram （b）Stress-strain curves
Fig. 3 Typical stress-strain diagram and stress curve of the whole process in sample loading
Fig. 4 shows the typical damage characteristics at each stage during the loading of
CS2 sample with time interval of 0.02 s. The red arrows in the figure point to the
damage location, and the numbers are labeled as the damage sequence number. It can
be seen that with the rise of the load, the sample in stage Ⅰ and stage Ⅱ remain intact
and no visible damage is noted. After entering stage III, a damage developed almost
through the whole sample appeared instantly on the right side of the sample. At the
same time, it can be found that at the end of stage III, there are several traces with a
little depression in the middle of the sample. This indicates that there are many fracture
in this position inside the sample, which are about to be connected together. Combining
the surface depression position of the sample in stage III with the three newly appeared
damage positions in stage IV, the surface depression position of the specimen in stage
III is the precursor of the imminent macro-damage and finally formed four penetration
damage. Combined with the stress-strain curve in Fig. 3, it can be found that the sample
gradually fracture with the increasing load. In stage I and II, the specimen mainly
undergoes elastic deformation, which is extremely difficult to damage until the sample
is loaded to stage III when plastic deformation and damage occur. Under the action of
the load, the damage continues to expand and extend. Therefore, as the load continues
to rise, numerous damage extensions gather and instantly release the accumulated
internal elastic energy, finally forming the macro-damage distribution that appears in
stage IV. In summary, the internal structure of the specimen changes because of the
load. With the gradual increase of the load, the degree of structural damage is getting
worse, resulting more fractures, and the damage size become larger.
9. 8
Fig. 4 macro-damage morphology of CS2 rock sample at each stage
In order to more clearly reveal the evolution law of damage time series during
loading, typical seismic wave signals of CS2 sample at each stages are extracted, which
their spectra are shown in Fig. 5-Fig. 8. The blue arrow and red arrow point to the peak
amplitude and dominant frequency of the signal, respectively.
Fig. 5 Characteristics of seismic wave signal in stage I
10. 9
Fig. 6 Characteristics of seismic wave signal in stage Ⅱ
Fig. 7 Characteristics of seismic wave signal in stage Ⅲ
Fig. 8 Characteristics of seismic wave signal in stage Ⅳ
From those figures, it can be seen that the peak values of seismic wave signal
amplitude in each loading stage are 17.1 mV, 24.1 mV, 89.8 mV and 704.3 mV, and
the dominant frequencies of rock samples in each stage are concentrated between 70-
90 kHz. The amplitude of the seismic wave signal varies greatly at different loading
stages. As the load gradually increases, the intensity of the seismic wave signal
gradually increases. The peak value of seismic wave signal amplitude in stage I is the
smallest, which is due to the signal generated in this stage is mainly caused by the
closure of pores in the sample. In stage II, the signal intensity of the seismic wave
increases slowly. The continual increase of external load, the internal elastic potential
energy of the sample continues to accumulate and rise. The peak value of its amplitude
is higher than that of stage I, and the dominant frequency is lower than that of stage I.
Sufficient energy is accumulated in the sample in stage III. With the increasing load,
the deformation of the sample accelerates, and a large number of fracture converge and
connect. Therefore, the peak amplitude of the seismic wave signal generated in this
stage is larger. The damage generated within the sample is interpenetrated in stage Ⅳ.
At this stage, the rock mass is destabilized to produce damage, the peak amplitude of
11. 10
seismic wave signal rises sharply. The intensity reaches the maximum when the
dominant frequency is the minimum. It can be seen that the time-series evolution
characteristics of the seismic waves show consistency with the four stages of uniaxial
loading of the rock mass. With the increasing load, the size of the fracture in the sample
is larger, the amplitude and energy are stronger, and the intensity of the monitored
seismic wave signal is stronger. Meanwhile, the dominant frequency of each stage has
a gradual downward trend.
The amplitude frequency results of seismic wave signals at different loading stages
of different samples are shown in Table 1. From the table, it is noticed that the amplitude
frequency change law of the other three samples was basically consistent with that of
CS2. By increasing load, the peak value of signal amplitude gradually increased, and
the dominant frequency overall showed a downward trend. The high-frequency
component signal generated in the compaction stage reflects the active strength of the
micro-pores in the rock, and then the continuous decreasing trend indicates the
formation and development of fracture in the rock. The low-frequency component of
stage IV represents the appearance and evolution of macro-damage, which is similar to
the research results of Mei et al [27].
Table 1 Amplitude frequency characteristics signal at different stages
stage 1 stage 2 stage 3 stage 4
Amplitude
(mV)
Frequency
(kHz)
Amplitude
(mV)
Frequency
(kHz)
Amplitude
(mV)
Frequency
(kHz)
Amplitude
(mV)
Frequency
(kHz)
CS1 12.7 87.8 34.1 72.5 517.4 54.6 1137.4 42.2
CS2 17.1 86.6 24.1 82.5 89.8 75.8 704.3 71.3
YY1 25.5 43.5 71.6 24.7 188.6 21.8 813.9 51.8
YY2 11.6 68.8 34.7 45.9 52.8 73.2 754.7 33.3
3 Correlation between seismic wave and fracture source
Stage III produced a large number of fractures, and the fracture did not intersect,
laying the foundation for exploring the characteristics of seismic wave response to
fracture inside the sample. Therefore, in order to accurately reveal the correlation
between the seismic wave and the fracture source, the most homogeneous shale (YY3)
is loaded before the peak load (i.e. stage III) and then stopped loading. This is to avoid
12. 11
the complete damage of the sample, which affects the search for the corresponding
relationship between the seismic wave and the fracture source. The full stress-strain
curve and the non-full stress-strain curve are shown in Fig. 9. It can be seen that the
sample YY3 load stops at stage III. The stress remains in a high range at the time of the
last stop of loading, indicating that the sample has not undergone through macro-
damage.
Fig. 9 Stress-strain curves of samples under loading
3.1Temporal and spatial distribution of acoustic emission events
during loading
The acoustic emission system has the function of fracture source positioning and
waveform acquisition, where the corresponding code of this function has been included
in the system. And the system automatically calculates the coordinates and energy of
the location events according to the arrival time difference of each seismic wave from
the eight acoustic emission sensors in different planes. The threshold value of acoustic
emission signal is set as 10 mV, which can be counted as effective signal after
exceeding the threshold value in this study. And besides the equipment accuracy, we
improved the accuracy of location events by arranging all sensors on the surface of the
sample and setting 60db amplifier to realize effective identification of low-intensity
signals of micro-fractures. Finally, the spatial distribution of acoustic emission events
on the sample is shown in Fig. 10, where each dot represents an acoustic emission event,
and different colors represent different energy levels. It can be seen from Fig. 10 that
the sample produced a macro-damage under load. During the loading process in the
sample, the positioning events are mainly concentrated in the upper half of the sample,
while they are concentrated in the macro-damage position. Only sporadic data points
13. 12
appear in the lower half of the sample, indicating that the lower half of the sample is
relatively complete, and the invisible fracture inside the sample are mainly in the upper
half. Analysis of the energy distribution characteristics of the acoustic emission events
shows that more than half of the positioning points over 100 aJ are found in the middle
and upper part of the sample, and less near the macro-damage. Less than 20 aJ
positioning data is far from the location of the macro-damage, which may be due to
damage inside the sample at a location far from the macro-damage or the closure of
small and large pores inside the sample. In contrast, the vast majority of 20-100 aJ
acoustic emission event positioning points are mainly concentrated near macro-damage,
indicating that macro-damage are composed of a large number of fracture extension
penetrations with fracture energies of 20-100 aJ. In summary, the acoustic emission
events generated by the fracture of the sample are concentrated in the upper part of the
sample. And they are not all gathered near the macro-damage, indicating that the macro-
damage is a combination of numerous cracks. At the same time, there are more cracks
that do not penetrate each other inside the sample.
Fig. 10. Failure state of sample and energy diagram of positioning data
Fig 11 shows the distribution law of acoustic emission events inside the sample
when loaded to different proportional peak loads. When loaded to 11.69%, two large
energy events higher than 100 aJ occur inside the sample. Since the specimen is in the
compaction stage at this time, the large energy events are caused by the closure of the
pores inside the sample. When the load reaches 90.21% of the peak load, this is the end
14. 13
of the stage II of the sample, and only a few positioning points appear in the sample,
indicating that there is hardly a large number of fracture in the samples at stage I and
stage II. From the moment of 92.51% peak load, the sample has entered the stage III
where plastic fracture occurs. As can be seen from the figure, the number of acoustic
emission events rises abruptly at this stage as the load increases, and a large number of
positioning events appear at this stage. Simultaneously, the acoustic emission event has
a tendency to expand to a deeper part of the sample away from the macro-damage
direction. This is because the energy accumulated at the macro-fracture location of the
rock has been released, the load continues to increase, so the acoustic emission events
continue to expand inward and cause greater fracture.
Fig. 11 Distribution characteristics of positioning events in different peak load stages
Acoustic emission positioning event is a bridge between the fracture source and
the seismic signal. During data processing, the seismic wave signal collected by the
acoustic emission signal analysis system is extracted. Then the time and space
coordinates of the signal are determined by acoustic emission location technology.
Combined with the three-dimensional coordinates of the fracture in the X-ray scanning
system, the seismic wave signal and the corresponding fracture source can be linked.
Through the temporal and spatial analysis of the above acoustic emission location
events, it can be found that a large number of fracture were generated inside the sample
during the loading process. Although some of the fracture has penetrated to form
macro-damage, a large number of fracture still exists independently. It can lay a
foundation for further exploring the response characteristics of seismic wave signals to
fracture.
3.2Characteristics of rock loaded fracture source
Uniaxial loaded sample in the laboratory have small internal fracture that are not
visible to the naked eye. If one wants to explore the internal conditions of the sample
and quantitatively establish the relationship between acoustic properties and the
15. 14
fracture source characteristics, CT scanning is a better choice. In recent years, CT
scanning has been applied to various fields with good results in exploring the invisible
information inside the sample and reconstructing the source of fracture, which can be
applied to the extraction of invisible fracture inside the sample[28,29]. In this paper, the
sample YY3 was divided into 2400 slices from top to bottom after X-ray scanning, and
all the slices were combined together to become the original sample after reconstruction.
Fig. 12 shows the images of the 5th, 1500th and 2380th slices of sample YY3 and the
corresponding location of the three slices in the sample. The internal fracture of the
sample is clearly visible in the images. Therefore, fracture within the sample that are
not visible to the naked eye can be characterized using CT equipment.
Slice 5th Slice 1500th Slice 2380th
(b) (c) (d)
(a)
Fig. 12 3D scanning of different slice images
In this paper, the interactive threshold segmentation method is used to extract the
internal fracture of the samples scanned by CT after loading. The threshold
segmentation is to select a specific threshold first, and change those greater than the
threshold to the maximum gray 255, and those less than the threshold to the minimum
gray 0. Thus, all pixel points in all graphs after segmentation are shown as[30]:
(1)
dst(x,y) = {𝑚𝑎𝑥𝑉𝐴 𝑠𝑟𝑐(𝑥,𝑦) ≥ 𝑡ℎ𝑟𝑒𝑎𝑑
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Based on equation (1) to extract the fracture inside the sample. In the process of
data processing, remove the fracture that are lower than the maximum original pore
area counted by the X-ray scanning system before uniaxial loading. The typical fracture
results in the sample except for macro-damage is shown in Fig. 13. For better display
effect, macro-damage has been screened out, and each color in the figure only
represents a fracture source. It can be seen that a large number of fracture sources are
generated during the loading process of rock sample, and distributed in various
positions of the sample, not all concentrated around the macro large fracture. That is
consistent with the characteristics of acoustic emission positioning events. The typical
crack source morphology is shown in Fig. 14, and fracture sources 1, 2 and 3 are typical
shear cracks.
16. 15
Fig. 13 The typical damage results
Crack 1 Crack 2 Crack 3
Fig. 14 Typical cracks source morphology caused by loading
3.3Characteristics of seismic wave signal response to fracture source
size
Based on 3.1 positioning events and 3.2 fracture source characteristics analysis,
the typical fracture sources inside the sample and their corresponding seismic wave
signals were extracted. Then the data were further processed to obtain the characteristic
parameters of fracture source width and area, and the characteristic parameters of
seismic amplitude, energy and frequency. All results are shown in Table 2. As can be
seen from Table 2, the size of the fracture produced during loading is small, with an
average width and area of 1.99 mm and 9.28 mm2 respectively. With the increase of
width and area, the amplitude and energy of seismic wave signal gradually increase,
and the dominant frequency has a decreasing trend.
Table 2 statistical results of each parameters of fracture sources and seismic waves with
different sizes
S/N Width/mm Area/mm2 Amplitude 102mV Energy/102V*ms Frequency/102kHz
1 3.15 26.46 7.76 1.15 0.55
2 2.17 12.89 6.67 1.24 0.25
3 2.16 10.31 5.92 1.17 0.76
4 2.07 12.31 5.79 1.91 0.33
17. 16
5 1.91 8.38 5.26 1.18 0.98
6 1.84 7.35 4.74 1.08 0.32
7 1.77 6.17 4.65 0.86 0.31
8 1.76 5.04 4.64 0.73 1.14
9 1.71 7.01 4.63 0.68 0.82
10 1.57 7.96 4.06 1.04 1.06
The width and area are selected as the characteristic parameters of the fracture
source, and the energy, amplitude, frequency are selected as the acoustic characteristic
parameters. Then the fitting analysis of the two parameters is carried out, and the results
are shown in Fig. 15. It can be seen that there is a highly correlated linear function
relationship between the characteristic parameters of the fracture source and the
characteristic parameters of the seismic wave, and the correlation coefficients are all
above 0.88. Among them, amplitude-width, amplitude-area, energy-width and energy-
area are positive correlation changes, and frequency-width and frequency-area are
negative correlation changes. The response of frequency and energy to the width of
fracture source is more obvious, and the amplitude changes more obviously with the
area of fracture source; The width of the fracture source has the greatest influence on
the energy of the seismic wave signal, while the area has the greatest influence on the
amplitude. Through the functional relationship between the characteristic parameters
of the fracture source and the characteristic parameters of the seismic wave, it can be
found that with the continuous increase of the fracture width and area, the
corresponding seismic wave energy will be higher, the amplitude will be larger, and the
signal intensity generated by the fracture source increases, which is consistent with the
results of engineering practice.
Based on the above results, through the analysis of large energy events in the
process of rockburst prevention and control, the size of fracture source can be calculated,
and then the stress concentration degree in the corresponding area can be judged, so as
to carry out targeted protection.
18. 17
Amplitude/10
2
mV
Width/mm
Amplitude/10
2
mV
Area/mm2
(a) Amplitude-width (b) Amplitude-area
Width/mm
Frequency/10
2
kHz
Frequency/10
2
kHz
Area/mm2
(c) Frequency-width (d) Frequency-area
Width/mm
Energy/10
2
V*ms
Energy/10
2
V*ms
Area/mm2
(e) Energy-width (f) Energy-area
Fig. 15 Variation correlation between the parameters of fracture source and the parameters
of seismic wave signal
4 Characteristic law of three-dimensional spatio seismic waves
around typical fracture source
The spatial distribution law of seismic waves generated by rock fracture is also an
important factor affecting the fracture law of seismic waves to rock mass. And the
19. 18
spatial propagation characteristics of seismic waves can provide effective guidance for
accurately guiding the prevention of rockburst at different spatial location. Figure 16
shows the time signal and spectra of the seismic wave generated by the typical fracture
source in the rock mass (i.e., crack 2 of Fig. 14) at each measuring point in the space.
Comparing the amplitude and frequency characteristics of the seismic waves at each
measurement point, it can be seen that the dominant frequency value is concentrated
between 35-45 kHz, and the peak amplitude value is concentrated between 500 mV and
1500 mV. Even though the amplitude and dominant frequency values of seismic waves
signals are concentrated in a certain range at each measurement point in spatio, there
are differences in different spatial locations due to the difference in azimuth angle.
Sensor No.1 has the largest amplitude of 4070 mv, and sensor No.7 has the smallest
amplitude of 540 mv, with a difference of nearly 8 times. At the same time, the
dominant frequency value of sensor No.1 is the lowest, sensor No.8 is the strongest,
and the amplitudes of other measuring points are also different.
Sensor 1#
Time/ms
Amplitude/V
Time/ms
Amplitude/V
Time/ms
Amplitude/V
Time/ms
Amplitude/V
Time/ms
Amplitude/V
Time/ms
Amplitude/V
Time/ms
Amplitude/V
Amplitude/V
Amplitude/V
Time/ms Time/ms
Sensor 2# Sensor 3# Sensor 4#
Sensor 5# Sensor 6# Sensor 7# Sensor 8#
(a) Waveform and amplitude of seismic wave of each sensor
Frequency/102 kHz
Amplitude/mV
Sensor 1#
Frequency/102 kHz
Amplitude/mV
Frequency/102 kHz
Amplitude/mV
Frequency/102 kHz
Amplitude/mV
Frequency/102 kHz
Amplitude/mV
Frequency/102 kHz
Amplitude/mV
Frequency/102 kHz
Amplitude/mV
Frequency/102 kHz
Amplitude/mV
Sensor 4#
Sensor 3#
Sensor 2#
Sensor 5# Sensor 6# Sensor 7# Sensor 8#
(b) Seismic wave spectrum of each sensor
Fig. 16 Characteristic parameters of seismic wave signal at each sensor
20. 19
In order to accurately investigate the distribution law of seismic wave signals with
different spatial azimuth angles, this paper calculates the azimuth angles between
different measurement points and fracture sources in space by vector method. The
three-dimensional spatial vector angle is calculated by the equation：
(2)
cos θ =
a·b
|a||b| =
x1·x2 + y1·y2 + z1·z2
x2
1 + y2
1 + z2
1· x2
2 + y2
2 + z2
2
Taking an extracted fracture source as an example, the central coordinate of the fracture
source is (3.15, 12.02, 35.99) and the boundary coordinate of the fracture source is
(33.15, 12.02, 39.31), so the corresponding spatio of the fracture source is =(0,0,-
𝑎
3.32). The coordinate of sensor No.1 is (45.5, 27, 5), so the spatial vector formed by
sensor No. 1 and the fracture source is =(12.35, 14.98, -30.99). Similarly, the spatial
𝑏
vector and spatial angle between any fracture source and each sensor can be obtained.
The peak value and dominant frequency of seismic wave signal amplitude at different
measuring points in Fig. 15 are counted, and the spatial angle between typical shear
fracture source and each sensor is calculated based on equation (2). The results are
shown in Table 3. It can be seen that sensor location No. 1 with an azimuth angle of
90° produces a much higher amplitude than the remaining locations, while sensor No.
5 with an angle of 165° is greater than sensors No. 3, No. 4, No. 6 and No. 7 with angles
of 34°, 79°, 144° and 125°, respectively. The sensor No. 2 with an angle of 48° is larger
than sensor No. 8 with an angle of 137°, and the intensity of the seismic wave signals
collected at sensor locations No. 3, No. 5 and No. 8 with different angles are similar.
The amplitude of the seismic wave signal at each measurement point is ranked from
largest to smallest as No. 1 > No. 2 > No. 8 > No. 5 > No. 3 > No. 6 > No. 4 > No. 7.
At the same time, the dominant frequency and amplitude of the seismic wave signals
differed among the measurement points. The dominant frequency value of sensor No.
1 with the largest amplitude is the lowest, and the dominant frequency value of sensor
No. 4 with the lower amplitude is much higher than most of the high amplitude
measurement points. The dominant frequency values of measuring points No. 2, No. 3
and No. 4 are similar, and there is little difference between the dominant frequency
values of measuring points No. 1, No. 5, No. 6 and No. 7.
The difference in amplitude and frequency spectrum of each measurement point
in the shear fracture space in Table 3 proves the directional characteristics of seismic
wave propagation. We found the high amplitude and low frequency signals of the
seismic wave are mainly concentrated in the fracture plane and its orthogonal plane,
21. 20
and other directions are characterized by low amplitude and high frequency [31]. This
may be caused by the inconsistency between the particle vibration direction and the
wave propagation direction in the transverse and longitudinal waves of the seismic
wave signal. The difference between the vibration direction and the propagation
direction results in different amplitude frequency characteristics of seismic wave
signals at different locations.
Table 3 Characteristic parameters of seismic wave signals at different measuring points in
three-dimensional spatio of typical shear fracture source of YY3 sample
Sensor Angle/° Amplitude /V Frequency /kHz
1 90 4.07 13.2
2 48 1.48 37.4
3 34 0.94 40.3
4 79 0.74 36.6
5 165 0.96 14.6
6 144 0.75 13.2
7 125 0.54 14.5
8 137 0.99 54.2
The seismic wave generated by rock fracture consists of P-wave and S-wave, and
the spatial propagation characteristics of P wave and S wave are different. Cao[32]
theoretically studied the spatial distribution characteristics of the seismic displacement
field of the seismic wave generated by rock fracture, and obtained the equation of the
seismic displacement field of the sample during shear fracture as:
(3)
{
𝑢𝑃
=
1
4𝜋𝜌𝜐3
𝛼𝑟
𝑓′(𝑡 ―
𝑟
𝜐𝛼
)(𝑐𝑜𝑠2
𝜃 ―
1
2𝑠𝑖𝑛2
𝜃𝑠𝑖𝑛2𝜑)
𝑢𝑆𝑉
=
1
4𝜋𝜌𝜐3
𝛽𝑟
𝑓′(𝑡 ―
𝑟
𝜐𝛽
)𝑠𝑖𝑛2𝜃(1 + 𝑠𝑖𝑛2
𝜑)
𝑢𝑆𝐻
=
1
4𝜋𝜌𝜐3
𝛽𝑟
𝑓′(𝑡 ―
𝑟
𝜐𝛽
)𝑠𝑖𝑛𝜃𝑠𝑖𝑛2𝜑
where, the is the angle between the line from the origin to any point and the
𝜃
positive z-axis, is the angle between the projection line of the line from the origin
𝜑
to any point in the xy-plane and the positive x-axis.
According to equation (3) displacement field expression can be plotted in the case
of shear fracture P wave and S wave displacement radiation pattern [33], as shown in
Fig. 17. Among them, the red arrow is the staggered direction of the rock mass fracture
22. 21
surface. From the figure, it can be seen that the maximum displacement amplitude of P
wave is in the plane of ± 45° with the fracture surface, and the maximum displacement
amplitude of S wave reaches the maximum value on the fracture surface and its normal
plane. Meanwhile, He et al.[34], Lee et al.[35] and TenCate et al.[36] revealed that the main
effect occurs in the seismic wave is the S wave, and the peak amplitude of S wave in
the seismic wave is the maximum value. Therefore, the S-wave radiation pattern is used
as the basis for analyzing the spatial characteristics of fracture sources. We found that
the spatial response characteristics of the seismic wave parameters of the typical shear
fracture source in Table 3 are basically consistent with the theoretical seismic wave
signal radiation mode.
θ=0°
θ=180°
θ=90°
θ=90°
θ=90°
θ=90°
θ=0°
θ=180°
P wave S wave
Fig. 17 Radiation pattern of seismic wave displacement field
In summary, the seismic wave generated by rock fracture propagates differently
in different azimuth angles in spatio, which is mutually verified with the theoretical
analysis results. Therefore, the spatial characteristics of seismic wave propagation
should be fully considered in the prevention and control of rockburst on site, and
targeted guidance and suggestions should be given to the prevention and control of
rockburst.
5 Conclusion
1) With the increase of load, the seismic wave signal is positively correlated with
the change of stress. The strength of the seismic wave signal increases gradually, while
the dominant frequency tends to decrease.
2) The amplitude and energy of seismic wave signal go up linearly with the
increase of the width and area of fracture source. On the contrary, the dominant
frequency decreases linearly.
3) The seismic wave signals at different locations in the fracture source space have
23. 22
significant directional characteristics due to the different expansion speed of the
fracture in each direction. With the increase of fracture expansion speed, the amplitude
of seismic wave signal increases. However, a large number of micro-cracks lead to the
decrease of dominant frequency.
4) The distribution characteristics of the seismic wave signals in different
directions of the fracture source are basically consistent with the displacement field
theoretical model, which can provide guidance for the accurate prevention and control
the rockburst by dynamic load.
Disclosure statement
No potential conflict of interest was reported by the authors.
CRediT authorship contribution statement
Feng Shen: Writing - original draft, Investigation, Conceptualization. Shengquan
He: Validation, Conceptualization, Methodology, Funding acquisition. Xueqiu He:
Methodology, Conceptualization. Dazhao Song: Investigation, Formal analysis. Jialin
Dong: Writing - review &editing, Formal analysis. Yang Liu: Methodology, Formal
analysis.
Declaration of Competing Interest
The authors confirm that there are no conflicts of interest associated with this
publication.
Data availability
Data will be made available on request.
Acknowledgments
This research was financially supported by the Postdoctoral Research Foundation
of China (Project No. 2021M700371) and the Open fund of State Key Laboratory of
Coal Mining and Clean Utilization (Project No. 2021-CMCU-KF013). We thank
anonymous reviewers for their comments and suggestions to improve the manuscripts.
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CRediT authorship contribution statement
Feng Shen: Writing - original draft, Investigation, Conceptualization. Shengquan
He: Validation, Conceptualization, Methodology, Funding acquisition. Xueqiu He:
Methodology, Conceptualization. Dazhao Song: Investigation, Formal analysis. Jialin
Dong: Writing - review &editing, Formal analysis. Yang Liu: Methodology, Formal
analysis. Majid Khan: Writing - review &editing.
Declaration of Interest Statement
The authors confirm that there are no conflicts of interest associated with this publication.
