Investigation of the influence of pre-crack number on acoustic emission characterization of red-sandstone short-term creep damage and failure precursors

Abstract

Rock crack is one of the main factors responsible for rock failure. Uniaxial compression creep tests are performed using acoustic emission techniques, a high-sensitivity, non-radiative, non-destructive testing method to understand the influence of crack number on the precursor characteristics of short-term creep damage in the fractured rock mass. Based on the Grassberger-Procaccia (G-P) algorithm, the calculation step size for the correlation dimension value (D ₂) of the acoustic emission ringing count rate is consistent with that for the acoustic emission b-value. The influence of the number of pre-cracks on the Acoustic emission precursor characteristics of red sandstone creep is analyzed. The results show that near the destabilization of the specimen, the Acoustic emission accumulative ringing count surges in a stepwise manner, the Acoustic emission b-value decreases, the D ₂-value increases, the Acoustic emission amplitude shows high intensity and high frequency, and the ringing count increases sharply, all with the characteristics of failure precursors. During the accelerated creep stage of the specimens, with the increase of pre-cracks number, the precursory time points of acoustic emission b-value and D ₂-value advance, and their acoustic emission ringing counts increase sharply.

Keywords

Acoustic emission precursor information pre-cracks

1 Introduction

Under the influence of long-term tectonic stress, different types of fractured rock mass composed of joints, cracks, and weak interlayers will be formed. Xu [1] used rock-like materials to simulate the crack evolution expansion mechanism during the stepwise failure of rocks by varying the number of cracks, crack dip, and crack spacing. To investigate the influence of the geometric distribution position of open pre-cut cracks on the failure mechanism of the rock, Huang [2] made two open non-overlapping pre-cut cracks for triaxial compression tests on the confining pressure surface of the rock specimen. To determine the fracture mechanism of the initial crack, Yu [3] conducted Brazilian splitting tests on single prefabricated crack sandstone with different crack dip angles and established five fracture modes. The inclination, number, and distribution position of fractured rock mass has a significant impact on the actual engineering. Therefore, disaster prediction and structural damage monitoring of fractured rock mass engineering are particularly important. Xue [4] constructed a theoretical quantitative correlation between the crack damage stress (σ_cd) and the uniaxial compressive strength (σ_ucs), suggesting that it is an intrinsic property of low-porosity rocks that can be used as a potential predictor of rock failure. Wei [5] used the low attenuation property of infrasound to predict rock damage, and found that the phase change of infrasound energy in different frequency bands is consistent with the phase of rock deformation damage. Based on the stability of energy dissipation and invariance of fracture energy, He [6] proposed a new prediction model of accumulated energy dissipation in salt rock. Yang [7] found that the energy ratio (EL/EH) showed a trend of “increase-transient quiescence-increase” through microseismic monitoring of coal rocks, and the fracture of coal rocks can be effectively monitored and warned when EL/EH is greater than 10. Yang [8] analyzed the time-frequency characteristics of EMR in the failure process of coal and rock material and believed that the time-frequency characteristic parameters of EMR had the precursor of failure and could indirectly reflect the damage evolution process of coal and rock. Shukla [9] analyzed three well-known meta-heuristic methods to predict rock-burst phenomena in hard rock engineering and found that the decision tree model can accurately predict and evaluate the rock-burst phenomenon. As an NDT technique, acoustic emission (AE) can be recorded in real-time and continuously as a result of the evolution of cracks within the rock. Lockner [10], Thompson [11], and Cai and Kaiser [12, 13] found that the whole process of crack evolution can be quantitatively analyzed by processing AE data. Falmagne [14] believed that AE events are closely related to rock damage or fracture, and thus rock degradation or damage can be measured. In addition, Xie [15] quantified the acoustic emission energy dissipated during rock failure. Therefore, AE monitoring technology can be used as a method to predict rock failure. Xu [16] used the ESMD method to de-noise and reconstruct acoustic emission data and found that acoustic emission has a quiet period when the rock is close to failure, and the quiet period of acoustic emission becomes more obvious with the increase in confining pressure. Zhai [17] found that the failure process of brittle rocks can be accurately characterized by the AE event rate, and the AE energy can accurately predict the energy failure. Lee [18] proposed to establish a quantitative rock damage prediction model based on machine learning (ML) by combining various acoustic emission parameters and found that accumulated absolute energy and initiation frequency are sensitive to rock damage changes. In AE signal processing, AE characteristic parameter b-value and fractal dimension (D), both of which are precursory. The change in AE b-value can reflect the evolution of micro-fractures within the material [19]. The variation of the AE b-value at different creep stages can, to a certain extent, predict the creep damage of red sandstone rocks [20]. Aki and Turcotte [21, 22] found that the b-value is closely related to the AE fractal dimension (D). It is considered that the b-value also has fractal characteristics, and both of them can reflect the process of crack evolution and expansion inside the specimen. It is proposed that the theoretical value of D is twice that of b, but it cannot be verified in the actual test. Lu [23] proposed that a sudden drop in fractal dimension may be a precursor to catastrophic failures in disordered media. Fu [24] regarded the continuous decline of the correlation dimension value (D₂) and the b-value as a precursor signal of impending rock failure and instability. While Gao [25] concluded that the larger the correlation dimension value (D₂), the more severe the destructive damage in the rock interior. Different scholars have different views on the fractal dimension, which may be caused by different calculation methods. However, numerous studies now collectively point to abrupt changes in the b-value and the fractal dimension (D) as the rock approaches damage and instability. The calculation of the correlation dimension value (D₂) is mainly based on the G-P algorithm [26] and analyzed according to the variation of damage variables and strain ratios [27]. However, the temporal characteristics of rock destabilization precursors are less studied based on the analysis of the amount of temporal variation at present, and the relevant studies remain at the stage of qualitative analysis, with less consideration of the influence of pre-crack factors on the precursor characteristics and the temporal variability of each acoustic emission precursor characteristic parameter. Therefore, it is necessary to analyze the precursor time characteristics of the AE b-value and the correlation dimension value (D₂).

In the review of the above, this paper focuses on the failure and instability of discontinuous fractured rock mass, which is common in geological disasters. Based on the creep test of uniaxial compression under step loading, this paper analyses the three-dimensional spatial dynamic evolution of AE of crack expansion and penetration in pre-crack rock masses, and the influence of the number of pre-crack on the variation patterns of AE b-value and correlation dimension value (D₂) of rock masses in the three creep stages is investigated. The differences in the precursor time characteristics of the AE accumulative ringing count, AE b-value, and correlation dimension value (D₂) and the influence of the number of pre-crack on the precursor characteristics of instability are explored when instability damage occurs in rock masses during the tertiary creep stage. The precursory information characteristics of creep failure of discontinuous fractured rock mass are revealed, which provides a key scientific basis for rock mass disaster warning and prevention.

2 Test procedure and method

2.1 Specimen preparation

A total of 12 specimens were prepared from a red sandstone block of Triassic sandstone formation in Shandong, China. The tested red sandstone was macroscopic homogeneous with an average bulk density of 2.64×10³kg/m³. The size of the rectangular specimen was 70 mm in length, 70 mm in width, and 140 mm in height, the deviation of end face unevenness was controlled within±0.05 mm, and the deviation of the end face perpendicularity to the axis was controlled within±0.25°, which was in accordance with the tested specimen size suggested by the International Society for Rock Mechanics (ISRM, Fairhurst and Hudson 1999). The average uniaxial compressive strength (σ_ucs) of the tested intact sandstone was 120.5 MPa, and the average elastic modulus was 31.88 Gpa. In this test, specimens containing one penetration crack, two penetration cracks, and three penetration cracks were made respectively based on complete specimens. The main geometrical parameters of single through pre-crack specimens were crack length (2a=30 mm), crack inclination angle (α=45°), and crack width(2 mm). The main geometrical parameters of double through pre-cracks specimens and three through pre-cracks specimens were crack length (2a=30 mm), crack inclination angle (α=45°), crack width (2 mm), and crack spacing (b = 15 mm), as shown in Fig. 1.

Fig. 1

Pre-crack specimens.

2.2 Step loading uniaxial creep tests

The test system consisted of SAM-3000 microcomputer-controlled electrohydraulic servo rock test system developed by the China University of Mining and Technology (Beijing), PCI-2 AE system, and ZT8320 multifunctional static strain gauge. The AE system consists of PCI-2 AE tester and AE-win software (developed by American Physical Acoustic Corporation), which simultaneously collected basic parameters such as amplitude, number, energy, and peak frequency. The threshold of the AE channel was set to 45 dB, the pre-signal gain was set to 40 dB, the frequency band of the analog filter was set to 1kHz∼1 MHz, waveform flow acquisition was allowed, and the sampling rate was set to 1 MSPS. The test system is shown in Fig. 2.

Fig. 2

Creep acoustic emission test system.

Eight AE probes were used in this test. Each group of two AE probes was placed on the opposite side of the sample, ensuring that they were at the same height. Four groups of AE probes were placed alternately on each side of the sample. The AE probes were coupled to the specimen surface with Vaseline and reinforced with a rubber band. The strain gauges were attached to the center of the specimen on both sides and fixed in place with a special adhesive. The layout of the AE probes and the strain gauges is shown in Fig. 3.

Fig. 3

The layout of the acoustic emission probe.

Signal acquisition settings: eight acoustic emission channels are defined as a single channel group; positioning type: three-dimensional positioning; event definition value: maximum distance between adjacent sensor probes; wave speed value setting: actual wave speed value; event blocking value: 1.5-2 times the event definition value; over-location value: 0.1 times the event definition value; positioning display distance unit: mm. subsequently, the material, shape, size and acoustic emission After the AE software is set up on the PC side, the acoustic emission probe coupling is detected and the event coordinates are calibrated. The details are as follows: (1) The lead core of HB with a diameter of 0.5 mm is placed 30 mm away from the probe, the extension length is 2.5 mm, and the lead breaking test is carried out repeatedly at the position of the sample surface Angle of 30°. If the lead break amplitude of the channel exceeds 95db, it indicates that the acoustic emission probe sensor is highly coupled. (2) The wave velocity test is carried out on the sample. First, the acoustic emission system automatically measures an initial wave velocity value, and combined with the lead breaking test of the acoustic emission probe, it observes whether there is any error between the lead breaking position and the event point of lead breaking. The wave velocity is adjusted in a small range to make the lead breaking position consistent with the event point of lead breaking, to obtain the optimal wave velocity, and the wave velocity is the actual wave velocity in this test, as shown in Fig. 4. Due to the length limitations of this paper, only the acoustic emission 3D localization map of the single pre-crack specimen is shown for comparison with the actual damage map to verify the validity of the wave velocity. The results show that the acoustic emission three-dimensional localization process is consistent with the actual rupture form, which ensures the authenticity of this test data collection, as shown in Fig. 5.

Fig. 4

Wave velocity location diagram.

Fig. 5

Single pre-crack specimen failure map. Note: Due to the limitation of three-dimensional positioning principle, the acoustic emission monitoring range of the specimen is only the blue box area.

The creep test of uniaxial compression under step loading was carried out on the four kinds of specimens respectively. The force-controlled loading method was used in this experiment. In order to reduce stress concentration and combine with the performance of the equipment, the stress loading rate was 400 N/s. According to the uniaxial compression test results of the four kinds of specimens, the axial stress difference of each stage was set at 10MPa and the dead-load time was set at 10 minutes. In order to ensure the failure of the pre-crack specimens in the dead-load stage, the axial stress difference was appropriately reduced in the late test period, according to the results of the uniaxial compressive test of the pre-crack specimens. The creep test was monitored by an AE instrument throughout.

The purpose of this test was to investigate the axial strain characteristics and the variation of the AE signal during constant load creep and to analyze the effect of the number of pre-crack on the creep AE characteristics of the specimens.

3 Test results and analyses

3.1 Uniaxial creep mechanical behavior of rock masses with different numbers of pre-crack

According to the test results, select one group of specimens for comparison. The creep curves of the intact specimen, single pre-crack specimen, double pre-cracks specimen, and three pre-cracks specimen under step loading are shown in Fig. 6.

Fig. 6

Creep curves of specimens under fractional loading.

Compared with the intact specimen, the creep failure strength of pre-specimen with different numbers of cracks is reduced that the failure strength of the single pre-crack specimen, double pre-cracks specimen, and three pre-cracks specimen decreased by 44.0%, 56.0%, and, 60.0% respectively (in Table 1). The results indicate that with the increase in the number of pre-crack, the overall stability of the specimen decreases and it is more prone to instability failure.

Table 1

Creep failure strength of specimens

Number of pre-crack	Failure strength /Mpa	Degree of failure strength reduction/%
0	125	/
1	70	44.0
2	55	56.0
3	50	60.0

In Fig. 6, at the end of each level of loading, the slope of the axial strain curve of the specimen decreases significantly and levels off, indicating that the specimen enters the initial creep stage. As the creep rate gradually decreases, the axial deformation curve of the specimen grows slowly in a nearly horizontal straight-line state, indicating that the specimen enters the steady-state creep stage. As the stress level continues to increase, when the stress level breaks through a certain threshold, the specimen axial strain increases rapidly with time, indicating that the specimen enters the tertiary creep stage, which eventually leads to deformation instability of the specimen until failure, as shown in Fig. 6(d).

At the same stress level, compared with the creep curve of the intact specimen, the axial strain gradually increases with the increase in the number of pre-crack, and the creep characteristics become more and more obvious. Taking the three pre-cracks specimen as an example, under the final stress level, the specimen sequentially undergoes the initial creep stage (I), the steady creep stage (II), and the tertiary creep stage (III), as shown in Fig. 6(e). In the initial creep stage (I), the strain rate increases rapidly, and the curve rises quickly during this stage. This indicates that the specimen experiences a rapid deformation process at this stage, gradually slowing down and entering the stable creep stage. The strain rate increases slowly in the steady creep stage (II). Finally, the specimen enters the tertiary creep stage (III), where the strain rate increases again, significantly higher than the rate in the initial creep stage, until the specimen failure. This stage usually lasts for a short time and is characterized by suddenness.

The axial strain curves of the intact specimen are approximately horizontal during the constant load stage, as shown in Fig. 6(a). During the 40 MPa constant load stage, the axial strain curve of the single-crack specimen experiences a transient increase, as shown in Fig. 6(b). During the 30 MPa constant load stage, the axial strain curve of the double-crack specimen experiences a transient increase as shown in Fig. 6(c). During the 20 MPa constant load stage, the axial strain curve of the three pre-cracks specimen experiences a transient increase as shown in Fig. 6(d). The results indicate that under the constant load stage, there are many micro-fractures in the specimen due to stress. During compression of the specimen, the micro-fractures within the specimen develop and connect with the pre-crack, resulting in local large-scale failure. As a result, there is an ‘abrupt change’ in the axial strain curve. The results indicate that as the number of pre-crack increases, the lower the stress required for a local large-scale failure to occur within the specimen, the earlier an “abrupt change” in the axial strain curve occurs.

4 Acoustic emission signal parameters

In the rock compression test, the acoustic emission signal parameters are directly collected by the acoustic emission instrument, called acoustic emission basic parameters, mainly ringing counts, amplitude, etc.

4.1 Acoustic emission amplitude

The acoustic emission amplitude is typically the maximum amplitude value (dB) of the acoustic emission signal waveform. It can be used to identify the type of acoustic emission source and to analyze the variation in signal strength attenuation.

In Fig. 7, at each level of the stress loading stage, the acoustic emission amplitude of all specimens increases significantly, generating a large acoustic emission signal due to the release of energy from the compression-dense closure of microcracks inside the loaded stress level specimens. In the constant stress stage, the specimen’s internal microcrack closes and expands steadily, and the acoustic emission amplitude decays. At all levels of the stress loading and constant stage, the specimen acoustic emission amplitude generally shows a rising-decreasing change pattern. It shows that the amplitude of the acoustic emission of the specimen is proportional to the creep of the specimen.

Fig. 7

The AE amplitude of different pre-crack specimens.

With the pre-crack number of specimens increasing, the acoustic emission amplitude of the specimen with the same stress level increases gradually, mainly concentrated in the range of amplitude 60–70 dB, which shows “medium intensity, high frequency”. It shows that with the increase of the pre-crack number, the specimen acoustic emission signal is intensive and strong, the acoustic emission high amplitude signal is more, and the specimen internal microcrack evolution expands rapidly with the speed of crack penetration. When the specimens are near the damage stress stage, the acoustic emission amplitude of all specimens is “high intensity and high frequency”. After the specimen axial deformation increases sharply, destabilization damage occurs along with a large number of acoustic emission high amplitude signals. It means that when the specimen acoustic emission amplitude appears “high intensity, high frequency”, the rock is about to be destabilized.

4.2 Acoustic emission ringing count

The acoustic emission ringing count is the number of times the acoustic emission signal waveform crosses the threshold voltage, that is, the number of oscillations exceeding the set threshold voltage.

In the loading stress stage, the microcracks inside the specimen are closed and generate high acoustic emission ringing count signals. In the constant stress stage, the internal microcrack closure ends and expands, and the acoustic emission ringing count signal decrease. The acoustic emission ringing counts of all specimens have a rising-declining trend in all levels of stress loading and constant stages and have the same trend as the acoustic emission amplitude signal, which are all proportional to the creep of the specimens. At the last stress level, the specimen enters the accelerated creep stage, destabilization damage occurs, and the acoustic emission ringing counts rise intensively and reach the maximum values of 4652, 5026, 5345, and 5982, respectively. Therefore, the acoustic emission ringing count can be a basis for the precursor of rock damage, and the maximum ringing count of the specimen increases with the increase of the pre-crack number when creep damage occurs, as shown in Fig. 8.

Fig. 8

The AE ringing count of different pre-crack specimens.

5 Acoustic emission derived parameters

The emission basic parameters are processed by mathematical algorithms to derive new acoustic emission parameters, which are called AE-derived parameters, mainly b-value, D-value, etc.

5.1 Acoustic emission b-value

The magnitude-frequency relationship proposed by Gutenberg and Richter [28] is expressed as:

{log}_{10}^{N} = a - bM

(1)

where, M is the earthquake magnitude, N is the cumulative number of earthquakes with a magnitude not less than M, a is the seismic activity constant, and b is the b-value in seismology. In the calculation of the AE b-value, the AE amplitude (A) is generally divided by 20 to obtain the equivalent earthquake magnitude, i.e.

M_{L} = \frac{A}{20}

(2)

where, M_L is AE magnitude; A is acoustic emission amplitude, in dB; In AE, N represents the cumulative frequency of AE events greater than or equal to M_L. This paper adopts the least square method to calculate the b-value. The spacing of this AE b-value calculation is set to 1000.

5.2 Acoustic emission correlation dimension value (D₂)

The correlation dimension value (D₂) takes time series as the research object, and the AE time series (AE ringing count rate) is selected for calculation in this paper. Set this time series as the set of time series {x₁, x₂, x₃, x₄..., x_n - 1, x_n} with a sample size of n to compute. Then, a phase space is constructed with this sample data and the dimension is set as m. Take the first m data x₁, x₂, ... , x_m in turn, as the first phase point in the m-dimensional space, denoted as X₁. Then, starting with x₂, take m data until x_m +1, as the second phase point, denoted as X₂. Constructing N phase points backward, denoted as X_{(n - m +1)}, the function expression is as follows:

C (r) = \frac{1}{N^{2}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} H (r - | X_{i} - X_{j} |) (i \neq j)

(3)

where, |X_i-X_j| refers to the position of the two-phase points, and H(x) is the Heavjsive function.

H (x) = {\begin{matrix} 1, x \geq 0 \\ 0, x \leq 0 \end{matrix}

(4)

Set the observation scale to r = kr₀ and the observation coefficient to k to reduce the dispersion.

r_{0} = \frac{1}{N^{2}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} | X_{i} = X_{j} | (i \neq j)

(5)

If there is a correlation function C(r)∝r^D2, the correlation dimension value (D₂) is as follows:

D_{2} = lim_{r \to 0} \frac{ln C (r)}{ln r}

(6)

where, r₀ is the average distance of the phase points in the attractor phase space R^m. C(r) is the probability that the distances of all phase points in the phase space R^m do not exceed the observation scale r. Under any observation scale, when the value of the observation coefficient k is different, there will be different C(r) values. The correlation dimension value (D₂) of AE time series (AE ringing count rate) refers to the slope of the linear regression line corresponding to point (r, C(r)) in the case of linear correlation between lnr and lnC(r) in double logarithmic coordinates, as shown in Fig. 9.

Fig. 9

lnC(r)-lnr curve.

The correlation dimension value (D₂) generally reference the strain ratio and damage ratio [27], while calculating acoustic emission b-value is based on time. In this paper, we maintain a consistent step length in calculating both acoustic emission b-value and the correlation dimension value (D₂) to explore whether there are similarities and differences between these two types of damage derivation parameters. Therefore, we set the calculation distance for the correlation dimension value (D₂) to 1000. Taking the intact specimen as a standard, the observation scale is set to r = 500 and the phase space dimension m of the specimen is calculated on a trial basis. The slope of the univariate linear regression equation of the curve corresponding to different m values is the D₂-value. With the increase of m, the curve moves downward to the right, and mobility gradually decreases. When the value of m is larger, the linear range becomes smaller, and the fractal range becomes smaller, indicating that the value of m is too large and there is no fractal feature. As shown in Fig. 10, as the m value increases, the D₂-value gradually increases, but after the convergence point of the D₂ (m) curve, the growth rate of the D₂ decreases, and the D₂ (m) curve begins to stabilize. Therefore, take the point m = 7 before the convergence point of the D₂ (m) curve for calculation. To ensure the consistency of the calculation, the four kinds of specimens all take the same phase space dimension m value.

Fig. 10

D₂ (m) curve.

5.3 Characteristic analysis of the AE b-value and correlation dimension value (D₂) with different numbers of pre-crack

The AE b-value and the correlation dimension value (D₂) are obtained by mathematical calculation of the AE basic parameters. The evolution of the material damage can be reflected by the change in AE b-value and the correlation dimension value (D₂).

As shown in Fig. 11(a), taking the single pre-crack specimen as an example, in the initial creep stage, due to the redistribution of stress, with the increase of axial strain, the micro-fractures inside the specimen continue to propagate and the micro-fracture activities are frequent, resulting in more AE events. The small-scale intensive fluctuation of the b-value decreases, and the small-scale intensive fluctuation of the D₂-value increases. It shows that the interior of the specimen is dominated by large-scale fractures at this stage. In the steady-state creep stage, the axial strain ascents very slowly, and the b-value and the D₂-value maintain a stable cyclic state within a certain range. It can be seen that the micro-fracture inside the specimen shows a small-scale disordered change at this stage, and the crack propagation is relatively stable and slow. In the steady-state creep stage, when the b-value of the specimen decreases sharply, the D₂-value increases sharply, indicating that the specimen is a local large-scale failure at this stage, as shown in Fig. 11(b).

Fig. 11

Axial strain-b value-D₂ value curve of single-stage stress level of specimens.

As shown in Fig. 11(c), in the process of initial creep and steady-state creep, the b-value first decreases and then increases, and the D₂-value first increases and then decreases. In the tertiary creep stage, when the axial strain suddenly increases, the b-value drops sharply to a minimum value, and then the b-value ascents, the D₂-value ascents sharply to a maximum value, and then the D₂-value drops and ascents again. The minimum values of the b-value for the four kinds of specimens are 0.6921, 0.6431, 0.5531 and 0.2502, respectively, and the maximum values of the D₂-value are 3.1498, 3.1945, 3.7941 and 4.3347, respectively. It shows that the micro-fractures in the specimen rapidly and unstable propagate and produce plenty of large-scale fractures during the tertiary creep stage. The micro-fractures created at the pre-crack tip interpenetrate and gradually extend outwards to form a macroscopic fracture surface, leading to specimen failure. Micro-fracture activity within the specimen changes from disordered expansion to ordered extension. With the increase in the number of pre-crack, the crack activity scale of the specimen increases in the creep failure stage, the minimum value of the b-value decreases, the maximum value of the D₂-value increases, and the specimen is more prone to instability failure.

With the increase in the number of pre-crack, the $\bar{b}$ -value of the four specimens were 2.0868, 1.8605, 1.7277, and 1.6573, increasing by 10.84%, 17.21% and 20.58% in turn, the Δb-value of the four specimens were 2.3150, 2.3515, 2.3978 and 2.7046, increasing by 1.58%, 3.58% and 16.83% in turn (in Table 2). The ${\bar{D}}_{2}$ -value of the four specimens were 1.0105, 1.1577, 1.1797 and1.3089, and the ΔD-values of the four specimens were 2.9842, 3.1389, 3.4995, and 4.4013; increasing by 5.18%, 17.27% and 47.49% in turn (in Table 3). The decreasing trend of the b-value increases and the increasing trend of the D₂-value increases. In the creep failure stage, the b-value is at the lowest level, and the D₂-value is at the highest level. As shown in Fig. 12, under the same stress level, with the increase in the number of pre-crack, the $\bar{b}$ -value decreases, and the ${\bar{D}}_{2}$ -value increases. It shows that when the specimen increases with the stress level, the specimen axial strain gradually increases, the micro-fracture inside the specimen gradually propagates and the scale of micro-fracture activity gradually increases. At the same stress level, the scale of micro-fracture activity within the specimen increases as the number of pre-crack increases.

Table 2

The $\bar{b}$ -value and Δb-value of the specimens with different numbers of pre-crack

Number of pre-crack	$\bar{b}$	Increase ratio	Δ b	Increase ratio
0	2.0868	/	2.3150	/
1	1.8605	10.84%	2.3515	1.58%
2	1.7277	17.21%	2.3978	3.58%
3	1.6573	20.58%	2.7046	16.83%

Table 3

The ${\bar{D}}_{2}$ -value and ΔD₂-value of the specimens with different numbers of pre-crack

Number of pre-crack	${\bar{D}}_{2}$	increase ratio	Δ D ₂	increase ratio
0	1.0105	/	2.9842	/
1	1.1577	14.57%	3.1389	5.18%
2	1.1797	16.74%	3.4995	17.27%
3	1.3089	29.53%	4.4013	47.49%

Fig. 12

The $\bar{b}$ -value and $\bar{D}$ ₂-value curves of specimens with different numbers of pre-cracks under the same stress level.

During the rock creep process, the AE b-value and the correlation dimension value (D₂) of the rock change from disorder to order, corresponding to the initiation of internal micro-fractures and the evolution of micro-fractures propagation of the rock. The b-value shows the overall change trend of decreasing-rising-stable-decreasing-rising, and the D₂-value shows the overall changing trend of rising-decreasing-stable-rising-decreasing. They show the opposite trend.

5.4 Analysis of the information characteristics of red sandstone acoustic emission failure precursors

In the process of rock failure, the AE accumulative ringing count, b-value, and correlation dimension value (D₂) can be used as precursor information for rock failure. When the axial strain of the specimen is vertical ascent without any other change, it means that the specimen fails at the point where the vertical ascent in axial strain begins. The mutation starting point of its characteristic curve is taken as the precursor time point to ensure the consistency of the data, and their differences are analyzed, as shown in Fig. 13.

Fig. 13

Characteristics of AE precursor parameters of specimens with different numbers of pre-crack at the last stress level.

As shown in Fig. 13, the time-dependent features of the accumulated ringing count are similar to those of the axial strain. During the initial creep stage of the specimen, the creep rate gradually decreases, the axial strain gradually increases, and the accumulated ringing count increases at a stable rate. In this stage, the internal micro-fractures of the specimens are mainly large-scale failures, and the fractures propagate erratically by the generation of new fractures, the b-value decline of fluctuation, and the D₂-value rising volatility. In the steady-state stage of the specimen, the creep rate is relatively stable, the axial strain increases slowly and steadily, the accumulated ringing count increases steadily, and the b-value and D₂-value are relatively stable. It shows that the micro-fractures inside the specimen propagate stably on a small scale. In the tertiary creep stage of the specimen, the creep rate increases, the axial strain increases rapidly, the accumulated ringing count surge in a step-like manner, the b-value begins to plummet to a minimum value, and the D₂-value begins to surge to a maximum value. It indicates that the micro-fractures inside the specimen will propagate and penetrate each other, producing a macro-fracture surface. Then the accumulated ringing counts tend to be stable after a sharp increase, the b-value increases slightly after a sharp decline, and the D₂- value increases sharply and then drops, indicating that the specimen has been a failure at this time.

The plummeting rates of the specimen minimum AE b-value are 0.1533, 0.1669, 0.2445, and 0.2891, respectively (in Table 4). Compared with the intact specimen, the plummeting rate of the single-crack specimen increased by 8.87%, the plummeting rate of the double-cracks specimen increased by 59.50%, and the plummeting rate of the three-cracks specimen increased by 88.58% . The surging rates of the maximum value of the D₂-value of the specimen acoustic emission are 0.7292, 0.7549, 0.7576, and 1.2395, respectively (in Table 5). Compared with the intact specimen, the surging rate of the single-crack specimen increased by 3.52%, the surging rate of the double-crack specimen increased by 3.89%, and the surging rate of the three-crack specimen increased by 69.99%, as shown in Table 5. When the specimen is about to destabilize, as the number of pre-crack increases, the decreasing rate of the AE b-value is accelerated, and the rising rate of the D₂-value is accelerated, indicating faster failure of the specimen.

Table 4

Plummet rate of AE b-value before specimen failure

Number of pre-crack	Before the plummet	After the plummet	Plummet time /s	Plummet rate /s	increase ratio /%
0	0.9987	0.6921	2	0.1533	/
1	1.3106	0.6431	4	0.1669	8.87%
2	1.2867	0.5531	3	0.2445	59.50%
3	1.4085	0.2520	4	0.2891	88.58%

Table 5

Surge rate of AE D₂-value before specimen failure

Number of pre-crack	Before the surge	After the surge	Surge time/s	Surge rate/s	increase ratio /%
0	1.6915	3.1498	2	0.7292	/
1	0.9301	3.1945	3	0.7549	3.52%
2	0.7634	3.7941	4	0.7576	3.89%
3	0.6161	4.3347	3	1.2395	69.99%

The axial strain of the intact specimen increases sharply at 581 s, and the accumulative ringing count, b-value, and D₂-value precursor time points at 580 s, 578 s, and 578 s, respectively (in Table 6). The AE b-value and D₂-value predict the creep failure of the intact specimen 3 s ahead of time, which is 2 s ahead of the accumulative ringing count. The axial strain of the single-crack specimen increases sharply at 109 s, and the accumulative ringing count, b-value, and D₂-value precursor time points at 107 s, 103 s, and 100 s, respectively. The AE b-value predicts the creep failure of the single-crack specimen 6 s earlier, and the D₂-value predicts the creep failure of the single-crack specimen 9 s earlier, which is 4 s and 7 s earlier than the cumulative ringing count. The axial strain of the double-crack specimen increases sharply at 551 s, and the accumulative ringing count, b-value, and D₂-value precursor time points at 545 s, 542 s, and 537 s, respectively. The AE b-value predicts the creep failure of the double-crack specimen 9 s earlier, and the D₂-value predicts the creep failure of the double-crack specimen 14 s earlier, which is 3 s and 8 s earlier than the cumulative ringing count respectively. The axial strain of the three-crack specimen increases sharply at 645 s, and the accumulative ringing count, b-value, and D₂-value precursor time points at 639 s, 636 s, and 630 s, respectively. The AE b-value predicts the creep failure of the three-crack specimen 9 s earlier, and the D₂-value predicts the creep failure of the three-crack specimen 15 s earlier, which is 3 s and 9 s earlier than the cumulative ringing count. The results show that as the number of pre-crack increases, the accumulative ringing count, b-value, and D₂-value precursor time of the specimen advance. The precursor time for both the AE b-value and the D₂-value appear earlier than the accumulative ringing count precursor time.

Table 6

The accumulative ringing count–b-value–D₂-value precursor time for different numbers of pre-crack specimens

Number of pre-crack	Axial strain	AE accumulative ringing count	b	D ₂
0	581s	580s	578s	578s
1	109s	107s	103s	100s
2	551s	545s	542s	537s
3	645s	639s	636s	630s

6 Conclusions

In this paper, the creep test of uniaxial compression under step loading was carried out on red sandstone specimens. The effect of the number of pre-crack on the creep mechanical properties and AE precursor information of the rock mass is investigated. (1)

Under a stress level that does not exceed a certain threshold, the specimen only undergoes initial creep and steady-state creep. When the axial stress exceeds a certain threshold, the specimen undergoes initial creep, steady-state creep, and tertiary creep in sequence. The creep failure strength of the intact specimen, single pre-crack specimen, double pre-cracks specimen, and three pre-cracks specimen are 125MPa, 70MPa, 55MPa, and 50MPa. Compared to the intact specimens, the creep damage strength of the pre-crack specimens decreased by 44.00%, 56.00%, and 60.00% .

(2)

In this test, the acoustic emission amplitude and ringing count of specimens with different pre-crack numbers have a rising-declining trend, both proportional to the creep of the specimens. Under the same stress level, as the number of pre-crack increases, the acoustic emission amplitude of the specimens gradually increased, mainly concentrated in the range of amplitude 60-70 dB, which showed “medium intensity, high frequency”, the AE $\bar{b}$ -value and D₂ -value shows a decreasing and increasing trend, respectively, and the Δ b-value and Δ D₂-value both increase. Under the last level of stress, as the number of pre-crack increases, the maximum value of the acoustic emission ring count increased sequentially, which was 4652, 5026, 5345, and 5982, and the minimum value of the AE b-value of the specimen decreases successively and the plummet rate increases, the maximum value of the D₂-value of the specimen increases successively and the surge rate increases. In the process of rock creep failure, the AE b-value and the D₂-value show an opposite trend.

(3)

In the creep failure stage, when the specimen is close to failure, the acoustic emission amplitude of all specimens showed “high intensity, high frequency” the acoustic emission ringing counts increased sharply, the acoustic emission b-value decreases sharply to the minimum value, the D₂-value sharply increases to the maximum value and the accumulated ringing count surge in a step-like manner. As the number of pre-crack increases, the precursory time points of the accumulative ringing count, b-value, and D₂-value of AE advance. And the precursor time points of the b-value and the D₂-value are earlier than the accumulated ringing count. Therefore, combining the AE signal parameter and the AE-derived parameters can provide a reliable theoretical basis for rock deformation prediction in practical engineering.

Footnotes

Acknowledgments

We acknowledge the funding support from the National Natural Science Foundation of China (Project No. 51508556), the National Key Research and Development Program of the 13th Five-Year Plan of China (Grant No. 2016YFC080250504), the Fundamental Research Fund for the Central Universities (Project No. 2020YJSLJ14). The authors sincerely thank the anonymous reviewers for their significant contribution to the improvement of this paper.

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