Study on decomposition of acoustic emission signal and identification of rock mass fracture

Abstract

To study the effect of rock body’s brittleness on rupture, acoustic emission test of rupture of rock body under the action of load has been studied. The character of rock’s rupture has been studied which is bonded with the result of the AE test and based moment tensors method. The study selected a block and the joint determination test of indoor uniaxial compression and acoustic emission is developed through selecting a shale rock of Qingshankou formation of a certain geological structure. The test has tested the change rule between stress strain and acoustic emission parameters of rock body and the rupture model of shale is analyzed through the moment tensors model which is developed by this study. The result shows that: When the brittleness of rock body is relatively low, single rupture face is common and the AE is concentrated around the rupture face. As the brittleness of rock body is enhanced, a lot of rupture faces appeared and some tension fracture and shear fracture and other multiple mixed fracture models existed.

Keywords

Rock fracture acoustic emission signal central moment tensor wavelet analysis

1. Introduction

The rupture of rock body can be measured through AE. And different rupture pattern presents different AE character. Describing the rupture pattern of rock body can be analyzed accurately by studying the analysis of AE character of rupture of rock body.

Gang [1] discussed the disposing character of different wavelet basis. Han and Ma [2] and Zhang et al. [3] studied different distributing rule of different wave band of AE energy under the engineering background of explosion of Meiyangang. Khanduja and Gokhale [4] studied the AE character of rock body rupture by experimental means. Gao et al. [5] did the AE signal’s noise reduction, decomposition and reconstruction of hard coal, hard coal and soft coal in the coal sample by wavelet analysis. Kim et al. [6] and Wu and Liu [7] did the machines’ failure diagnosing through distracting the characteristic value of wavelet by wavelet exchange of AE. Li [8] studied reduction rule of different component gained through vibrant signal of explosion of rock body based on analysis of wavelet. Kang et al. [9] studied acoustic emission signal time delay estimation method based on the time-frequency energy analysis technology through wavelet exchange. Ling et al. [10] summarized the energy distribution and discussed energetic band distributing character by extracting character of energetic AE distribution through analysis of wavelet. Zhang et al. [11] designed a time-delay wavelet network predictor based on sensitivity analysis. Chen et al. [12] studied the HEVC and 3D dual-tree discrete wavelet transformation. Wang et al. [13, 14, 15] calculated and drawn energetic distribution of different band by discomposing and reconstructing the AE signal through wavelet. Tang et al. [16] counted on the characteristics of acoustic emission spectrum difference in the whole process of coal and rock failure, wavelet packet analysis is used to study the acoustic emission signals of coal and rock. Zhao [17] got significant results which are based on the study on acoustic emission signals of coal and rock by multi-wavelet energy band. Zhao et al. [18] carried out rock acoustic emission test of indoor uniaxial compression by using wavelet packet analysis theory, analyzes the different frequency of the acoustic emission signal of sandstone distribution, studied the energy distribution of the failure process of acoustic emission signals of the loss. Rafsanjani et al. [19] studied the chaotic time series prediction. Zhao [20] used the wavelet packet method, and the fracture precursor of water bearing rock is studied. The paper chooses China reservoir structure of Qingshankou formation shale cores as research example, through laboratory tests to study the rock shale fractures and load effect of acoustic emission characteristics, through the method of moment tensor, shale rock with different brittle fracture mode. The results show that when the brittle strength of rock is low, with a single fracture rock mass is mainly concentrated in the acoustic emission rules around the rupture surface. With the increase of the brittleness of rock mass, a number of fracture surfaces have appeared, and there are multiple fracture modes such as tensile and shear fracture. The research results have important guiding significance for the understanding of the shale reservoir reconstruction and fracture rule.

2. Theory of acoustic emission signal wavelet transform

2.1 The selection criterion of wavelet basis function

(1) (1)
In the project site monitoring, the sampling time of the acoustic emission instrument is often long to collect the acoustic emission signal. So the data quantity of the signal is huge, and the calculation of the continuous wavelet transform is bigger than the discrete wavelet transform. Therefore, discrete wavelet transform is needed.
(2)
The natural rock material contains all kinds of defects from the microcosmic to the macroscopic scale, and the existence of the defect has a decisive influence on the destabilization and destruction of the rock, the existence of the rock mass structure not only destroys the integrity of the rock mass, but also directly affects the mechanical properties and the stress field distribution of the rock mass, and affects the failure mode of the rock mass to a great extent. Therefore, the selection of wavelet basis should also take into account these defects.
(3)
The actual rock acoustic emission signal is extremely susceptible to noise interference. However, the wavelet basis function with some vanishing moments can highlight the characteristics of the signal. Therefore, we must choose such wavelet basis functions.
(4)
In order to eliminate or reduce the distortion of the signal in wavelet decomposition and reconstruction, the selected wavelet basis function must have symmetry.
(5)
In order to ensure the smoothness of the curve after wavelet decomposition, the wavelet basis function with regularity can be given priority.

2.2 Continuous wavelet transform

If any function $\Psi\left(\omega\right)$ and the quadratically integrable function $f(t)$ in the $L^{2}\left(R\right)$ space satisfy the condition of the Fourier transform as shown in Eq. (1):

$\Psi\left(\omega\right)=\int\limits_{-\infty}^{+\infty}{\frac{\left|{f\left(% \omega\right)}\right|^{2}}{\left|\omega\right|}}d\omega<+\infty$ (1)

Then the function $\Psi(\omega)$ can be characterized by $f(t)$ decomposition, $f(t)$ is called a wavelet basis of the function $\Psi(\omega)$ .

The wavelet base $f(t)$ is scaled and translated to obtain the wavelet function sequence $f_{(a,b)}(t)$ :

$f_{\left({a,b}\right)}(t)=\frac{1}{\sqrt{\left|a\right|}}f\left({\frac{t-b}{a}% }\right)$ (2)

where $f_{\left({a,b}\right)}(t)$ is also called wavelet, where $a,b\in R,a\neq 0$ ; The scale parameter or scaling factor and the translation parameter or translation factor are called $a, b$ for $\psi_{\left({a,h}\right)}(t)$ . Where $f(t)$ satisfies the following equation:

$\begin{cases}\displaystyle{\int\limits_{-\infty}^{+\infty}{f(t)dt=0}}\\ \displaystyle{\left|{f(t)}\right|\leqslant\frac{c}{\left({1+\left|t\right|}% \right)^{1+d}},∼{}c,d={\rm const}>0}\\ \end{cases}$ (3)

For any given function $g(t)\in L^{2}\left(R\right)$ continuous wavelet transform, the wavelet transform of $g(t)$ is:

$W_{g}\left({a,b}\right)=\left\langle{g,f_{\left({a,b}\right)}}\right\rangle=% \frac{1}{\sqrt{\left|a\right|}}\int\limits_{R}{g\left(t\right)}f\left({\frac{t% -b}{a}}\right)dt$ (4)

3. Location method of acoustic emission sources based on wavelet analysis

Assuming there are $n$ sensors respectively denoted by $T_{0},T_{1},T_{2}\ldots T_{n-1}$ , where $T_{0}$ is the reference sensor, measuring the time difference between the other sensor and the reference signal. The acoustic emission signals of the ruptured rock mass propagate at a constant velocity in the rock mass, with relative spatial coordinates (as shown in Fig. 1).

Figure 1.

The position of sensor and sound source in three-dimensional coordinates.

Set $T_{0}$ as the origin of the spatial coordinates, other points of the relevant coordinates: $T_{i}\left({x_{i},y_{i},z_{i}}\right)$ , $i=1,2,\ldots n-1$ , acoustic emission sound source position coordinates of $S\left({x,y,z}\right)$ , then we can list the sound source position signal and the distance between any point difference is:

$\left|{ST_{i}}\right|-\left|{ST_{0}}\right|=d_{0i},∼{}i=1,2,\ldots n-1$ (5)

Substituting coordinates in order to obtain:

$2\left({x_{i}x+y_{i}y+z_{i}z}\right)+2d_{0i}\sqrt{x^{2}+y^{2}+z^{2}}=x_{i}^{2}% +y_{i}^{2}+z_{i}^{2}-d_{0i}^{2},∼{}i=1,2,\ldots n-1$ (6)

Assuming that the relevant coordinates are all on the $y$ plane, we obtain:

$\displaystyle x=\frac{\left({d_{j}-c_{jk_{1}}d_{k_{1}}}\right)\left({z_{j}-c_{% jk_{2}}z_{k_{2}}}\right)-\left({d_{j}-c_{jk_{2}}d_{k_{2}}}\right)\left({z_{j}-% c_{jk_{1}}z_{k_{1}}}\right)}{\left({x_{j}-c_{jk_{1}}x_{k_{1}}}\right)\left({z_% {j}-c_{jk_{2}}z_{k_{2}}}\right)-\left({x_{j}-c_{jk_{2}}x_{k_{2}}}\right)\left(% {z_{j}-c_{jk_{1}}z_{k_{1}}}\right)}$ (7) $\displaystyle y=\sqrt{\left[{\frac{d_{j}-\left({x_{j}x+z_{j}z}\right)}{d_{0j}}% }\right]^{2}-\left({x^{2}+z^{2}}\right)}$ (8) $\displaystyle z=\frac{\left({d_{j}-c_{jk_{1}}d_{k_{1}}}\right)\left({x_{1}-c_{% jk_{2}}x_{k_{2}}}\right)-\left({d_{j}-c_{jk_{2}}d_{k_{2}}}\right)\left({x_{j}-% c_{jk_{1}}x_{k_{1}}}\right)}{\left({z_{j}-c_{jk_{1}}z_{k_{1}}}\right)\left({x_% {j}-c_{jk_{2}}x_{k_{2}}}\right)-\left({z_{j}-c_{jk_{2}}z_{k_{2}}}\right)\left(% {x_{j}-c_{jk_{1}}x_{k_{1}}}\right)}$ (9)

It is assumed that the calculation result of the difference between any two sensor distances satisfies the following relationship with the observation result:

$e_{jk}=\left({d_{j}-d_{k}}\right)-v_{p}\cdot\Delta t_{jk}$ (10)

where:

$\displaystyle d_{j}=\sqrt{\left({x-x_{j}}\right)^{2}+\left({y-y_{j}}\right)^{2% }+\left({z-z_{j}}\right)^{2}}$ (11) $\displaystyle d_{k}=\sqrt{\left({x-x_{k}}\right)^{2}+\left({y-y_{k}}\right)^{2% }+\left({z-z_{k}}\right)^{2}}$ (12)

Where $e_{jk}$ is the theoretical calculation result and the actual observation result error; $d_{j}$ is the $j$ th measurement point to the acoustic emission source calculation distance; $d_{k}$ is the $k$ th measurement point to the acoustic emission source calculation distance; $v_{p}$ is the acoustic velocity of the acoustic emission signal in the rock, and $\Delta t_{jk}$ is the time difference between the two points.

The signal cross-correlation function of any two channels is defined as:

$\lambda_{jk}\left({\Delta t_{jk}}\right){\rm=}\frac{1}{n}\sum\limits_{i=0}^{n-% 1}{X_{j}(t)}X_{k}\left({t+\Delta t_{jk}}\right)$ (13)

In Eq. (13), $X_{j}(t)$ is the signal received by the $j$ th sensor, and $X_{k}$ is the signal received by the $k$ th sensor.

The correlation coefficient between any two-channel signals is expressed as:

$\xi_{jk}=\frac{\displaystyle\sum\limits_{i=0}^{n-1}{X_{j}(t)}X_{k}\left({t+% \Delta t_{jk}}\right)}{\displaystyle\sqrt{\sum\limits_{i=0}^{n-1}{\left[{X_{j}% (t)}\right]^{2}}\sum\limits_{i=0}^{n-1}{\left[{X_{k}\left({t+\Delta t_{jk}}% \right)}\right]^{2}}}}$ (14)

Correlation coefficient of $\rho_{ij}$ indicates a similarity between signal $X_{j}(t)$ and signal $X_{k}(t)$ , and when the two waveforms are identical, $\xi_{jk}=1$ . In the process of signal transmission, the signal is decomposed by wavelet transform, and then the time difference of the received signal is determined according to the time corresponding to the maximum value of the correlation coefficient.

Sum the square of error Eq. (10) and from Eq. (14), we can get:

$e=\sum\limits_{k=1,i\neq j}^{n}{\left({e_{jk}}\right)^{2}}$ (15)

Using the least squares method, we can take the minimum value of Eq. (15) $x, y, z$ as the coordinates of the acoustic emission source point.

4. Moment tensor analysis of rock fracture

4.1 Wave equation of acoustic emission signal

If the rock mass contains different clay minerals, it is assumed that the acoustic emission propagation in the rock mass satisfies the elastic wave equation. If the influence of the bulk force is neglected, the wave equation of the acoustic emission signal can be expressed as follows according to Darlan’s basic theory:

$u_{i,jj}({s,t})+\frac{({\bar{{\lambda}}+\bar{{\mu}}})}{\bar{{\mu}}}u_{j,ji}({s% ,t})=\frac{\rho}{\bar{{\mu}}}\frac{d^{2}u_{i}\left({s,t}\right)}{\partial t^{2}}$ (16)

where:

$\displaystyle\bar{{\lambda}}=\left({1+\frac{\partial^{\chi}s}{\partial t^{\chi% }}}\right)\cdot\lambda$ (17) $\displaystyle\bar{{\mu}}=\left({1+\frac{\partial^{\chi}s}{\partial t^{\chi}}}% \right)\cdot\mu$ (18)

Where $u\left({s,t}\right)$ is the starting point of any rupture point at the $s$ point of $t$ displacement, it can be understood as $s$ points at a certain moment the amplitude of the acoustic emission signal.

Assuming that the boundary of the rock mass region is a plane, according to Breckenridge (1975) and others, the fracture propagation at any point is considered as the point source of acoustic emission. The wave equation can be expressed as the form of Green’s function:

$u_{i}\left({s,t}\right)=\int\limits_{S}{\left[{G_{ik}\left({s,q,t}\right)\ast t% _{k}\left({y,t}\right)-C_{sqkl}G_{is,q}\left({s,q,t}\right)\ast u_{k}\left({q,% t}\right)n_{l}}\right]}ds$ (19)

In the formula: $G_{ip,q}\left({s,q,t}\right)$ is the spatial derivative of the Green function, $t_{k}\left({q,t}\right)$ and $u_{k}\left({q,t}\right)$ are the stress vector and displacement vector respectively, $C_{sqkl}$ is the constant and $n_{l}$ is the normal vector on the boundary surface.

It is assumed that shale is isotropic rock mass, $C_{sqkl}$ can be expressed as:

$C_{sqkl}=\bar{{\lambda}}\delta_{sq}\delta_{kl}+\bar{{\mu}}\left({\delta_{sq}% \delta_{kl}+\delta_{sl}\delta_{qk}}\right)$ (20)

It is assumed that there is a micro-fracture at any point $x$ in the region to form a rupture surface. The acoustic emission wave equation at this point is:

$\displaystyle u_{i}\left({s,t}\right)=\int\limits_{f}{C_{sqkf}G_{ip,q}\left({s% ,q,t}\right)\ast b_{k}\left({q,t}\right)}df$ $\displaystyle\quad∼{}+\int\limits_{S}{\left[{G_{ik}\left({s,q,t}\right)\ast t_% {k}\left({q,t}\right)-C_{sqkf}G_{ip,q}\left({s,q,t}\right)\ast u_{k}\left({q,t% }\right)n_{l}}\right]}dS$

If the influence of external force on the displacement of rock mass is not taken into account, the amplitude fluctuation of the boundary surface can be neglected, so we have the following formula:

$u_{i}\left({s,t}\right)=\int\limits_{f}{C_{sqkl}G_{ip,q}\left({s,q,t}\right)n_% {l}\ast b_{k}\left({q,t}\right)}df$ (22)

Seek differentiation for the Eq. (22), and written in tensor form as:

$u_{i}\left({s,t}\right)=\int\limits_{f}{G_{ip,q}\left({s,q,t}\right)}\ast b_{k% }\left({q,t}\right)df=G_{is,q}\left({s,q,t}\right)\ast S(t)C_{sqkl}n_{l}l_{k}\Delta V$ (23)

Insides, fracture complex or $b_{k}\left({s,t}\right)=b\left({s,t}\right)l_{k}$ , the source time function is $S(t)$ , fracture volume is $\Delta V$ .

The moment tensor is defined as:

$M_{sq}=C_{sqkl}\Delta Vn_{l}l_{k}$ (24)

The amplitude of the acoustic emission wave caused by the fracture can be obtained, It can be expressed as:

$u_{i}\left({s,t}\right)=G_{is,q}\left({s,q,t}\right)M_{sq}\ast S(t)$ (25)

Equation (25) is the basic model of acoustic emission wave propagation

Consider the influence of noise on acoustic emission signal during fracturing, the mathematical model of acoustic emission signal is:

$X_{i}=\sum\limits_{s=1}^{N}{u_{i}\left({s,t}\right)e^{-\xi_{s}\left({t-t_{s}}% \right)}}\sin\left({2\pi\varpi_{s}\left({t-t_{s}}\right)}\right)+\Phi$ (26)

Where, $X_{i}$ is different acoustic emission signal in different frequency channel; $N$ is the total number of acoustic emission signal, $\varpi_{s}$ is the frequency of acoustic emission signals; $t_{s}$ is the times for acoustic emission signal get to the receivers; $\xi_{s}$ is the attenuation coefficient of acoustic emission signal; $\Phi$ is the external interference noise generated by external equipment in the fracturing process.

According to the theory of Ohtsu [21], acoustic emission signal of the initial amplitude of $A(x)$ can be written as:

$A(x)=C_{s}\frac{2k^{2}a\left({k^{2}-2\left[{1-a^{2}}\right]}\right)}{L\left({k% ^{2}-2\left[{1-a^{2}}\right]}\right)^{2}+4a\left[{1-a^{2}}\right]\sqrt{k^{2}-1% +a^{2}}}\textit{RMR}^{T}$ (27)

Where, $R=({r_{1}}∼{}∼{}{r_{2}}∼{}∼{}{r_{3}})$ , $C_{s}$ is the sensitivity of the probe, can be obtained by calibration; $L$ crack initiation point and receiving point distance respectively; ${\begin{array}[]{*{20}c}{r_{1}}&∼{}{r_{2}}&∼{}{r_{3}}\\ \end{array}}$ is the point to point detection direction cosine separately; $t$ is the sensor sensitivity direction vector; $k$ is the acoustic emission of longitudinal and transverse ratio, $k=\frac{v_{p}}{v_{s}}$ ; $a$ is the inner product of vector $r$ and vector $t$ .

Figure 2.

AE signals observation.

4.2 Moment tensor identification of rock mass fracture mode

The moment tensor is expressed as:

$\displaystyle\left({{\begin{array}[]{*{20}c}{M_{1}}\\ {M_{2}}\\ {M_{3}}\\ \end{array}}}\right)=\frac{M_{1}+M_{2}+M_{3}}{3}I+\left({{\begin{array}[]{*{20% }c}{M_{1}^{\prime}}\\ {M_{2}^{\prime}}\\ {M_{3}^{\prime}}\\ \end{array}}}\right)$ (28) $\displaystyle M_{sq}=C_{sqkl}\Delta Vn_{l}l_{k}$ (29)

Assume the shale as isotropic materials, the moment tensor is decomposed into: Double couple (DC), compensated linear vector dipole (CLVD) and isotropic part (isotropic). As shown in Fig. 3.

Figure 3.

Decompose the characteristic values into DC, CLVD and isotropic.

According to the moment Zhang Aki and Richard proposed halo shear fracture and tension fracture eigenvalue expressions, considered the principal moments of the magnitude and direction of certain conditions in the process of rock fracture, a maximum shear wave component is $X$ , part of the DC group was divided into $\left({X,0,-X}\right)$ . The largest component of CLVD is $Y$ , for the CLVD part, divided into $\left({Y,-0.5Y,-0.5Y}\right)$ . The components of all directions of the isotropic part are $Z$ . The three characteristic values obtained by the matrix are standardized:

Maximum eigenvalue:

$\frac{\lambda_{\max}}{\lambda_{\max}}=X+Y+Z$ (30)

Minimum eigenvalue:

$\frac{\lambda_{\min}}{\lambda_{\max}}=-X-0.5Y+Z$ (31)

Intermediate eigenvalue:

$\frac{\lambda_{int}}{\lambda_{\max}}=0-0.5Y+Z$ (32)

The Ohtsu method is used to identify the micro fracture source: $X>$ 60% is a shear fracture; $Y+Z>$ 60% is an open fracture; 40% $<X<$ 60% is a mixed type fracture. The direction of motion of crack I, the normal direction $N$ and the moment tensor eigenvector are as follows.

Maximum feature vector:

$e_{1}=I+n$ (33)

Intermediate feature vector:

$e_{2}=I\times n$ (34)

Minimum feature vector:

$e_{3}=I-n$ (35)

Where $e_{1},e_{2},e_{3}$ are the eigenvectors corresponding to the eigenvalues, which can be used to obtain the fracture direction and normal direction $n$ . Figure 4 is the vector annotation of the three different fracture types.

Figure 4.

The vector markup diagrams of different fracture types.

Figure 5.

Stress-strain curves of 4 kinds of test samples.

5. Experimental results and analysis

This paper combined with the physical property of the reservoir in Liaohe oil field, carried out the acoustic emission damage monitoring experiment which under the condition of uniaxial compression loading. The relevant parameters are shown in Tables 1 and 2. Through the uniaxial compression test, the stress-strain curves of rock mass and the energy of acoustic emission and the number of acoustic emission are shown in Fig. 4.

Table 1
Mineral composition table of the block

Core	Mineral content (%)
	Clay	Quartz	Feldspar	Anticline	Calcite	Dolomite	Siderite	Others
1# core sample	22.9	23.1	9.3	3.1	8.6	29.8	0.6	2.6
2# core sample	25.2	19.2	20.8	9.2	5.0	14.2	2.4	4.0

Table 2

Fracture development characteristics of the block

Well	Core	Total	Number	Number	Crack	Fracture	Fracture	Fracture	Crack	Crack
name	number	length	of crack	of crack	penetration	penetration	line	relative	opening	dip angle
		(m)	segments	branches	length (m)	rate (%)	density	line density	(mm)
1# well	2	9.91	16	25	1.39	14.0	18	2.5	0.1–2.0 mm	60 ${}^{\circ}$ –80 ${}^{\circ}$
2# well	2	12.9	33	47	1.81	14.1	26	3.6

The Fig. 5 shows that with the continuous rock loading, rock acoustic emission signal counting changing in loaded rock compaction stage, the AE counts were less in the elastic phase, have produced less acoustic emission signals. When entering into the plastic region, the quantity of acoustic emission of rock mass increases obviously, and the brittle characteristic of rock mass is weaker, and the acoustic emission counts increased more slower, the brittleness of rock mass is stronger, the acoustic emission quantity increased faster. The brittleness of rock mass is more stronger, the rupture time of the main body is shorter, the more the acoustic emission signal is, the larger the number of acoustic emission and the greater the energy of acoustic emission. With the increase of the brittle mineral content of the rock mass, the threshold width of the strain produced by the acoustic emission signal is smaller, the more the strain is concentrated in the 0.6%–0.8% area. The results show that the brittleness of rock mass is stronger, and the fracture behavior is abrupt.

Figure 6.

Four kinds of fracture mode and uniaxial compression rock sample.

Sample 1# $\sim$ sample 4# in Fig. 6 show that: when the rock brittle minerals is lower relatively, the rock rupture occurred along with a rule rupture surface, the type of rupture is shear fracture mode mainly, signals are centralized in the rupture of the surrounding which the sound produced in other non rupture area of the acoustic emission signal number. With the increase of brittle mineral content, rock burst has become diverse, the emergence of a number of fracture surfaces around the original natural fractures also generate acoustic emission signals, the failure mode of rock mass becomes complicated, and there a mixed fracture mode of shear fracture, and the distribution of fractured rock body is not along a rupture surface, but in the region formed a rupture behavior of rock mass.

6. Conclusion

(1) (1)

Based on the wavelet packet theory, the method of acoustic emission signal waveform analysis is proposed to analyze the evolution of acoustic emission signal.

(2)

Considering the characteristics of shale reservoir, the wave equation of acoustic emission signal propagation is established. Based on the combination of wavelet analysis and correlation coefficient, the 3D localization of acoustic emission source of rock mass is studied.

(3)

The results show that: when the elastic deformation stage of the rock mass is loaded, there are fewer acoustic emission signals. When entering the plastic area, rock acoustic emission volume increased significantly, and the brittle characteristics of weaker, AE counts increased speed is slower and more brittle rock mass, the number of acoustic emission increased faster, the main rock rupture time shorter, more focused acoustic emission signal, the maximum acoustic emission count more, the maximum sound the emission energy also increases, fracture behavior presents more abrupt rupture.

(4)

The results show that: when the brittle minerals of rock mass are low, the fracture of rock mass occurs along a regular fracture surface. With the increase of brittle mineral content, rock burst has become diverse, the emergence of a number of fracture surface, fracture pattern of rock is complicated, and there a mixed fracture mode of shear fracture, fracture surface and the distribution of rock mass is not along a fracture plane, but in the region formed a rupture behavior rock mass.

Conflict of interest

The authors confirm that this article content has no conflicts of interest.

Footnotes

Acknowledgments

This work is supported by The National Natural Science Foundation of China (51574088, 51404073), Natural Science Foundation of Heilongjiang Province of China (Young Scientists) (QC2017043), Heilongjiang General Undergraduate Colleges and Universities Young Innovative Talents Training Plan (UNPYSCT-2016084), The 9th Special China Postdoctoral Science Foundation Projects (2016T90268), China Postdoctoral Foundation (2014M550180), HeiLongJiang Postdoctoral Foundation (LBH-TZ-0503), Northeast Petroleum University Innovation Foundation For Postgraduate (YJSCX2017-028NEPU).

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Study on decomposition of acoustic emission signal and identification of rock mass fracture

Abstract

Keywords

1. Introduction

2. Theory of acoustic emission signal wavelet transform

2.1 The selection criterion of wavelet basis function

4.1 Wave equation of acoustic emission signal

Table 1 Mineral composition table of the block

Conflict of interest

Footnotes

Acknowledgments

References

Table 1
Mineral composition table of the block