An experimental study on the precursory characteristics of EP before sandstone failure based on critical slowing down

Journal of Applied Geophysics 170 (2019) 103818

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An experimental study on the precursory characteristics of EP before sandstone failure based on critical slowing down Xin Zhang a,c, Zhonghui Li a,b,c,⁎, Yue Niu a,c, Fuqi Cheng a,c, Muhammad Ali c,e, Sher Bacha d,e a

Key Laboratory of Coal Mine Gas and Fire Prevention and Control of the Ministry of Education, China University of Mining and Technology, Xu Zhou, Jiangsu 221116, China State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China, School of Safety Engineering, China University of Mining and Technology, Xu Zhou, Jiangsu 221116, China d School of Mines, China University of Mining and Technology, Xu Zhou, Jiangsu 221116, China e Department of Mining Engineering, Balochistan University of Information Technology, Engineering and Management Sciences, Quetta, Pakistan. b c

a r t i c l e

i n f o

Article history: Received 6 April 2019 Received in revised form 2 July 2019 Accepted 10 July 2019 Available online 15 July 2019 Keywords: Sandstone Electric potential Precursor characteristics Critical slowing down

a b s t r a c t The electric potential (EP) generated during coal rock deformation and fracture reflects coal rock mass stress and damage states. However, identifying the EP signal precursory signs that characterize a coal rock mass tending toward instability and failure is difficult. In this paper, we established an acoustic-electric multiparameter test experimental system, synchronously tested and collected acoustic emission (AE), surface potential (SP), and axial strain (AS) and observed surface crack propagation during the sandstone sample failure process. Meanwhile, by introducing the critical slowing down theory, the EP signal precursory characteristics before the sandstone sample unstable failure were explored. The results showed that EP signal time series autocorrelation coefficients and variances increased abruptly and continuously before the main fracture of the sandstone samples, which could be used as sandstone failure precursory information. Compared with the autocorrelation coefficient, the variance mutation point was easy to identify and was not affected by lag length selection, which was an effective precursory point to predict sandstone sample failure. From the precursory point to the main fracture of the sandstone samples, the AE events gradually gathered at the fracture damage location, high-energy AE events gradually increased, and the crack propagation rate gradually accelerated. Compared with the AE count time series, the variance mutation point (precursory point) of the EP signal time series appeared earlier. The research results were of theoretical significance for the monitoring and early warning of coal rock mass instability and failure and for identifying precursory characteristics using the EP response. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Coal and rock dynamic disasters are the processes of rapid, unstable failure of a mine rock mass under the combined action of ground stress and mining stress. With increasing mine exploitation depth, coal and rock dynamic disasters are occurring more frequently, which seriously threatens safe mine production (Jiang et al., 2014; Xie et al., 2015). Static methods, such as the drill cutting method, are usually adopted in traditional coal and rock dynamic disaster monitoring (Dou et al., 2018). These methods cannot dynamically reflect the development and evolution process of disasters and cannot be used as real-time monitoring methods for coal and rock dynamic disasters. Studies have shown that during the process of rapid instability and failure of coal

⁎ Corresponding author at: Key Laboratory of Coal Mine Gas and Fire Prevention and Control of the Ministry of Education, China University of Mining and Technology, Xu Zhou, Jiangsu 221116, China E-mail addresses: [email protected] (X. Zhang), [email protected] (Z. Li).

https://doi.org/10.1016/j.jappgeo.2019.103818 0926-9851/© 2019 Elsevier B.V. All rights reserved.

and rock, the energy existing inside the coal and rock masses will be released in the form of elastic energy, sound energy, electromagnetic energy, etc. (Kong et al., 2018a; Wang et al., 2018a). To a certain extent, these forms of energy can reflect the loading state and damage process of coal rock (Feng et al., 2018). The acquisition and analysis of these energies provides some new geophysical methods for monitoring coal and rock dynamic disasters (Kong et al., 2018b), these methods include the AE method, electromagnetic radiation (EMR) method and infrared radiation (IR) method (Carpinteri et al., 2012; Rabinovitch et al., 2017; Song et al., 2018; Wang et al., 2015). During the dynamic failure process of coal and rock, there are free charge generation and transfer due to the piezoelectric effect, electrokinetic effect, motion of charged dislocations, crack propagation and other mechanisms (Aydin et al., 2013; Eccles et al., 2005). Therefore, EP signals are generated on the surface of coal. Niu et al. (Niu et al., 2018) built a similar physical model of coal rock and showed the change of EP signals are periodic and can well correspond to the change of stress in the mining process. Pan et al. (2012) studied the application of charge sensing technology in impact ground pressure predictions and

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conducted field tests in a mine with a developed charge sensor. Archer et al. (2016) showed the good correlation between AE and pressure stimulated current and demonstrated that EP signal can be applied to a number of fields including monitoring and predicting earthquakes and landslides. Other studies also indicated EP signal has immense potential for structural health monitoring of cement-based structures (Kyriazopoulos et al., 2011; Stergiopoulos et al., 2013). So EP signal can be used to assess damage state and provide an indication prior to catastrophic failure of coal and rock (Cartwright-Taylor et al., 2014). Therefore, this method is expected to be used for monitoring and early warnings in coal and rock dynamic disasters in mines (Niu et al., 2018; Triantis et al., 2012). Most previous studies have focused on the characteristics and regularity of EP in the process of coal and rock instability and failure under different experimental conditions, but the validity of EP as a precursory signal of coal and rock instability and failure has not been verified. The general sequence signals of EP cannot directly reflect the precursors of failure, so the precursory characteristics of the EP signal of coal rock failure requires further study. Recently, the critical slowing down theory has shown great potential in revealing whether a complex, dynamic system tends toward a critical catastrophe (Dakos and Bascompte, 2014; Dakos et al., 2008; Drake and Griffen, 2010; Hsieh et al., 2006; Kefi et al., 2007; Scheffer et al., 2001; Van Nes and Scheffer, 2007). Van Nes and Scheffer (2007) studied the critical slowing down phenomenon in six ecological models. Chisholm and Filotas (2009) showed that critical slowing down could be an indicator of transitions in two species predator-prey and competition models. Dakos et al. (2008) suggested that slowing down can be a useful indicator of impending climate change. Gao et al. (2013) and Yan et al. (2011) applied the theory of critical slowing down to the study of earthquake precursor data and found that critical slowing down phenomena existed in some deformation and hydrochemistry measurement items before earthquakes, which could be used as early signals of earthquake occurrence. The critical slowing phenomenon of complex, dynamic systems has attracted widespread attention in different disciplines and has shown great potential in explaining sudden catastrophic events and determining precursory information before catastrophic events (Carpenter and Brock, 2006; Ovaskainen and Hanski, 2002). This phenomenon provides the research foundation and inspiration for studying the precursory characteristics of EP before coal and rock failure. As the main component of engineering excavated rock masses, sandstone usually exhibits sufficient brittleness and similarity under external forces and is one of the brittle materials commonly used in basic experimental research (Cheng et al., 2015). In this paper, failure tests of sandstone specimens under load are conducted, and AE, EP and AS are synchronously tested. Macroscopic crack propagation on the observation surface of the sandstone specimens is recorded by an industrial

camera. The critical slowing down theory is applied to the analysis of the autocorrelation coefficients and variances of EP signal time series. Additionally, an attempt is made to explore the response characteristics and variation rules of the two parameters to determine an effective precursory point to characterize the failure of sandstone. 2. Materials and methods 2.1. Experimental system The acoustic and electric multiparameter test experimental system includes a load control system, an EP data acquisition system, an AS data acquisition system, an AE data acquisition system, and a highspeed camera system (see Fig. 1). The test system can measure and store the load, AS, AE and EP data of sandstone samples during the loading and fracture process in real time. The stress is provided and recorded by the YAW4306 microcomputer-controlled electrohydraulic servo pressure tester. The EP signal is received by the electrode slices, transmitted through an amplification circuit, converted from analog to digital, and obtained by a high-speed collector. The maximum acquisition frequency of the EP data can reach 1 kHz. AE signals are collected and stored by a Micro-II Express Digital AE system, which is paired with R3a and NANO-30 GC08 AE probes. Dynamic failure images of the sandstone samples were captured by a high resolution industrial camera (Prosilica Gc2450 produced by AVT Germany), which is paired with a KOWA ultrahigh precision 10-megapixel lens (LM5JC10M). 2.2. Sample preparation The sandstone samples used in this experiment were processed in the laboratory into standard cubic specimens of 100 mm × 100 mm × 100 mm, and the surface of the specimens was smoothed with fine sandpaper to attain a flatness error of less than 0.02 mm. The sandstone samples were wiped with alcohol and then placed indoors to dry naturally. 2.3. Experimental scheme Sandstone samples with no apparent defects in appearance were selected for testing. The strain gauges, copper electrode slices and AE probes were arranged on the specimens with conductive paint, adhesive tape and hot melt adhesive (the positions and coordinates of the measuring points are shown in Fig. 2 and Table 1, respectively). After the experimental system was arranged and debugged normally, the load control system was started. The press was raised to the upper press head just touching the upper end of the sample. The gaskets were insulated on both ends, at the top and bottom of the sample, and the electromagnetic shielding net was arranged around the press.

Fig. 1. Acoustic and electric multiparameter test experimental system.

X. Zhang et al. / Journal of Applied Geophysics 170 (2019) 103818

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Fig. 2. Schematic diagram of the AE, EP and AS measurement locations.

Simultaneously, the loading control system, LB-IV multichannel EP data acquisition system, AS data acquisition system and AE data acquisition system were started to collect the stress, strain, EP and AE data during the sandstone sample loading process, and the sandstone sample failure process under loading was simultaneously recorded by an industrial camera. After the complete destruction of the sandstone samples, loading and data acquisition were stopped, and the failure characteristics of the samples were recorded. Then, the experiment was finished. 3. Results In this experiment, 8 sample groups were loaded for successive fracturing by displacement controlled loading of 0.01 mm/min. The results of the EP and AE responses of four representative specimen groups are shown in Fig. 3. Notably, the EP, AS and AE signal trends over time are obtained from the data measured by electrode slice Ch6, strain gauge Ch2 and AE probe 5#, respectively. We selected sandstone sample 1 for analysis. The entire loading process for sample 1 can be divided into five stages: compaction stage, linear elastic stage, damage stable development stage, accelerated damage development stage and post-peak stage. At the initial stage of loading, all kinds of original cracks and defects in the sandstone samples gradually close, and slip and dislocation occur between particles and cements, resulting in friction electrification (Li et al., 2009; Song et al., 2016; Wang et al., 2009). This process occurs in the sandstone interior, so the damage and deformation of the sandstone is small. The development of microfractures is slower, so the EP value is small, the fluctuation is gentle, and the AE activity is lower. During the linear elastic stage, the AE counting is relatively stable, the AS increases steadily, and the EP increases slowly. After entering the stable damage development stage, the AE counts increase sharply, the AS curves decrease slightly, and the EP signal fluctuates sharply but increases slowly overall. During the accelerated damage development stage, the AE activity is intense, and the AE counts show a maximum value of approximately 225 s. With the sudden strain curve decrease, Table 1 Coordinates of AE probes, strain gauges and electrode slices measurement locations. AE probes locations/mm

Strain gauges locations/mm

Coordinates

Electrode slices locations/mm

Coordinates

Coordinates

Numbers

x

y

z

Numbers

x

y

z

Numbers

x

y

z

1# 2# 3# 4# 5# 6# 7#

75 25 0 0 0 25 75

25 75 25 50 75 25 75

100 100 75 50 25 0 0

Ch1 Ch2 Ch3 Ch4

50 30 50 90

60 50 20 50

100 100 100 100

Ch5 Ch6 Ch7 Ch8 Ch9 Ch10

50 60 50 20 50 70

50 50 30 50 90 30

0 0 0 0 0 0

the EP signal rises sharply and fluctuates sharply. The EP signal rises to a maximum value of 14 mV at the main rupture. After sandstone failure, the AS remains unchanged, and the AE signal and EP signal are rapidly reduced at a low level. Through the above analysis, it can be concluded that the change in the EP signal shows a periodic characteristic during the different sandstone failure stages and can better respond to the sandstone specimen fracture. In addition, the EP signal trend corresponds well with the AE counts and AS changes. Therefore, the EP signal can be effectively used to study the damage evolution and instability failure process of materials and to evaluate the damage and stress state of rock specimens (Wang et al., 2009). However, during the loading process, the entire EP signal fluctuates sharply and is subject to many external disturbances. It is inaccurate to consider the sudden change in EP signal to be precursory information when predicting the unstable failure of sandstone samples. Further analysis and processing of the EP signal is needed to find the precursory point that can truly predict the impending unstable failure of sandstones. 4. Discussion 4.1. Basic theory of critical slowing down Critical slowing is a concept in statistical physics. This concept refers to the fluctuation phenomenon that is favorable for the formation of new phases when the dynamic system approaches the critical point (especially at the critical point) before changing from one phase to another. This kind of fluctuation shows not only the increase in amplitude but also the prolongation of fluctuation duration, the slowing of the disturbed recovery rate, and the lesser ability to restore the old phase. When the scale involved in the fluctuation extends to the whole system, the new phase of the entire phase transition can no longer be restored to the old phase (Guttal and Jayaprakash, 2008; Scheffer et al., 2009; Van Nes and Scheffer, 2007). This phenomenon of time lengthening, slower recovery rate and smaller recovery ability is called slowing down. Critical slowing down leads to three possible early warning signals in dynamics: slow recovery of disturbance, increase in autocorrelation coefficient and increase in variance (Carpenter and Brock, 2006; Kleinen et al., 2003). For the failure process of sandstone under load, the load accumulation before the main fracture can be understood as the old phase, and the stress unloading during the instability failure can be regarded as the phase transformation. At the initial stage of loading, the sandstone specimen is in the elastic deformation stage. The strain of the sandstone gradually increases at a stable rate and presents a good periodic change. Although the strain will change slightly due to some local ruptures during loading, due to the fast recovery rate of sandstone specimens subjected to small amplitude disturbance, the system will return to the

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Fig. 3. EP and AE responses during the loading process.

original loading state for a short time, and the load and strain continue to increase at the original rate (Gao et al., 2013). When the loading process enters the accelerated damage development stage, the stable increase characteristics of strain gradually disappear, and the quasiperiodic characteristics gradually disappear. Then, the characteristics of exponential change are shown, and there is a significant increase in the change amplitude and a significant increase in the deformation extent within the same time period. The deformation recovery obviously slows down when the rock is loaded near the critical fracture point (Gao et al., 2013). Theoretically, when the sandstone samples tend toward the critical point of instability failure, the ability of the sandstone to be restored to its original state will tend toward zero. The sandstones' internal crack propagation and penetration rate will be accelerated, and the transfer and accumulation of free charge per unit time will increase sharply. The EP signals measured on the surface of the sandstone samples should also show a series of critical slowing down characteristics, such as the increased fluctuation, prolonged duration in unit time and reduction in the ability to be restored to the original state. Therefore, the critical slowing down principle can be applied to the analysis of EP signal characteristics during the process of coal instability and failure. 4.2. The relation among critical slowing down, increased autocorrelation and increased variance Variance is a characteristic quantity that describes the data degree of deviation from the mean in a dataset. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the

squares by the number of values in the set. The calculation formulas are as follows: s2 ¼

n 1X ðx −xÞ2 n i¼1 i

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X ðx −xÞ2 σ ¼t n i¼1 i

ð1Þ

ð2Þ

where s2 represents the variance, and σ represents the standard deviation. The autocorrelation coefficient is a statistic describing the data correlation at different moments for the same variable. The autocorrelation coefficient of variable x with lag length j is recorded as α(j): α ð jÞ ¼

  n− j  X xi −x xiþ j −x σ σ i¼1

ð3Þ

It is assumed that the stated variable has a forced perturbation with a period of Δt, which is approximately exponential during the disturbance process, and the recovery speed is λ. In the autoregressive model, this can be described as follows: xnþ1 −x ¼ eλΔt ðxn −xÞ þ σεn

ð4Þ

ynþ1 ¼ eλΔt yn þ σ εn

ð5Þ

where yn is the deviation from the system variable to the equilibrium

X. Zhang et al. / Journal of Applied Geophysics 170 (2019) 103818

5

state, and εn is a random quantity that conforms to a normal distribution. If λ and Δt do not depend on yn, the process can be simplified to a first-order autoregressive model: ynþ1 ¼ αyn þ σεn

ð6Þ

Among the variables, the autocorrelation coefficient is α = eλΔt, and eq. (5) is analyzed by the variance:     Var ynþ1 ¼ E yn 2 þ ½Eðyn Þ2 ¼

s2 1−α 2

ð7Þ

When the system approaches the critical point, the recovery rate of small amplitude disturbance will be increasingly slower. The recovery rate will approach zero, the autocorrelation coefficient will approach 1, and the variance will approach infinity. Therefore, the increase in the variance and autocorrelation coefficient can be regarded as the precursor signal of the system approaching the critical point (Carpenter and Brock, 2006). 4.3. The relationship between window length, lag length, variance and autocorrelation coefficient Window length refers to the selected sequence containing a specific amount of data, and the lag step refers to the lag length from the sequence containing a specific amount of data to another new sequence containing the same amount of data. For example, there is a data sequence with 100,000 data volumes, the window length is 5000, and the lag length is 7500, indicating that a sequence of 5000 data is taken from the first data of the total data sequence, and then a new sequence of 5000 data is taken from the 7501 data (shown in Fig.4). The variance is of the new data sequence obtained by the selected window length lagging fixed step, and the autocorrelation coefficient is the correlation between the data sequence of the selected window length and the new data sequence obtained by the lagging fixed step (Kong et al., 2015). 4.4. Critical slowing down characteristics of EP signal time series In the analysis of a complex dynamic system based on the critical slowing down theory, it is very important to choose the appropriate window length and lag length. We analyzed variances and autocorrelation coefficients of the EP signal by a 2000 window length and 6000 lag length based on the amount of collected EP signal data. Fig. 5 shows that the overall change trend of the EP signal autocorrelation coefficients fluctuate, and there is no obvious change trend during the early stage of loading. The EP signal autocorrelation coefficients increase sharply and continuously at the 264 s loading (point D shown in Fig. 5), gradually approaching 1. Point D occurs 12.4 s earlier than the main fracture time, and the corresponding load is 98% of the peak load. In addition, the overall trend of the EP signal variance curve is relatively intuitive. The variance before 222.7 s (point A shown in Fig. 5) remains unchanged overall. After 222.7 s, the variance suddenly

Fig. 5. The index of critical slowing down under specific window length and lag length.

increases and continues to increase. After 242 s (point B shown in Fig. 5), the variance increases at a faster rate. After 273.3 s (point C shown in Fig. 5), the variance increased sharply until sandstone sample 1 was destroyed. The occurrence time of point A is 52.3 s ahead of the main fracture, and the corresponding load accounts for 70% of the peak load. Therefore, there is a critical slowing down of the EP signal during the sandstone sample loading process. The autocorrelation coefficient and variance of the EP signal time series increase suddenly and continuously before the unstable failure of the sandstone samples. The sudden changing points of variances and autocorrelation coefficients both occur during the accelerated damage development stage of sandstone sample 1, but the occurrence times are different, appearing 12.4 s and 52.3 s, respectively, ahead of the main fracture. 4.5. The influence of different window lengths and lag lengths on the analysis results When the EP signal time series is analyzed by the critical slowing down theory, the choice of window lengths and lag lengths will affect the stability of the analysis results. The larger the selected window length, the better the stability of the autocorrelation coefficients and variances, and the smaller the fluctuation. The lag lengths should be selected according to the selected window length. Fig. 6 shows an analysis of the autocorrelation coefficients and variances of EP signals with the same lag step and different window lengths. The lag length is taken as 6000, and the window lengths are taken as 2000, 3000, and 4000. The autocorrelation coefficients of the EP signals at different window lengths increase suddenly and continue to increase at 264 s, gradually approaching 1. The overall change in the autocorrelation coefficient is more fluctuation, and the larger the window lengths, the smoother the autocorrelation coefficient fluctuation. The variance remains basically unchanged before the sudden increase point and suddenly increases at 222.7 s. After the sudden increase point, the larger the window length, the smaller the range of variance increase. Therefore, the window length has little effect on the critical slowing precursor

Fig. 4. Schematic diagram of window length and lag length.

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Fig. 6. The index of critical slowing down under different window lengths.

points of the EP signal time series, and different window lengths only affect the fluctuation stability of the variances and autocorrelation coefficients curve. Fig. 7 shows an analysis of the autocorrelation coefficients and variances of EP signals with the same window length and different lag lengths. The window length is 2000, and the lag lengths are 6000, 6500 and 7000. The variation trend of the variances is the same under different lag steps; the sudden increase point is 222.7 s, which is 52.3 s ahead of the main fracture. In addition, under different lag steps, the autocorrelation coefficients fluctuate sharply, and the change does not show a certain trend. The precursory points that suddenly increase and continue to increase are not easy to capture. Therefore, the lag length has a great influence on the change in the autocorrelation coefficient. This is because the larger the selected lag lengths, the weaker the correlation between the front and back sequence data. Therefore, the autocorrelation coefficient variation trend of the EP signal time series will be different under different lag lengths, and the precursor appearance times that characterize the sandstone sample failures will differ. According to previous studies, the indicators of critical moderation also differ for different systems. For example, in climate change and ecosystem analysis, the autocorrelation coefficients are the main reference, while in epileptic seizures and fishery exploitation analyses, the variance increases are the main references (Scheffer et al., 2009). By comparison, the sudden variance increase point is more suitable as the precursory point of rock sample failure when the critical slowing theory is used to analyze the EP signal. The critical slowing down theory is applicable to EP signal processing during the failure process of sandstone specimens. When the sandstone sample tends to break, the EP signal variance and autocorrelation

coefficient increase suddenly and continuously in advance, which can be used as the precursor information to predict the failure process of the sandstone sample. Among the two parameters used to characterize the critical slowing of potential signals, the variances produce fewer pseudo signals than the autocorrelation coefficients, and the change trend is more intuitive and obvious. The precursory points are easier to identify and do not change with lag length selection. Therefore, the sudden variance increase point is more suitable as a precursor point to predict the unstable failure of sandstone samples when the critical slowing theory is used to analyze the EP signal, which may be because the detection of increased autocorrelation may require a long time series (Bence, 1995).

4.6. Crack propagation and AE location from precursory point to failure The temporal variation of AE parameters (pulse number, energy, etc.) represents the evolution characteristics and internal damage severity at different loading stages (Wang et al., 2017). The three-dimensional spatial orientation of AE can visually reflect the damage location and the evolution of internal microcracks and micropores (Wang et al., 2018b; Wang et al., 2014). Based on the P-wave relative arrival time and simplex positioning iterative algorithm of AE sensors at different positions, we can achieve AE event localization (Pei et al., 2013). During the loading of sandstone, internal microcracks converge, penetrate, connect and join to form macroscopic cracks and macroscopic main cracks (Chen et al., 2017; Li et al., 2018). Industrial cameras can be used to observe the crack development on the sandstone specimens (Liu et al., 2018; Wang et al., 2017).

Fig. 7. The index of critical slowing down under different lag lengths.

X. Zhang et al. / Journal of Applied Geophysics 170 (2019) 103818

Fig. 8. Macroscopic crack propagation and AE location of sandstone samples.

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Fig. 9. The critical slowing down index of AE.

As shown in Fig. 5, the variation trend of the EP signal time series prior to the main fracture of the sandstone sample can be divided into four stages: basically unchanged stage, sudden increase and slow increase stage, rapid increase stage, and sharp increase stage. The different rising trends of the variance indicate the different, changing characteristics of EP signals and indicate the slowing down of deformation recovery in the later stage of loading. Fig. 8 shows the crack propagation and AE localization of sandstone sample 1 at different times. There were no obvious primary cracks and defects on the observation surface of sandstone sample 1 before loading. As shown in Fig. 8(a), at 213 s, which is the end of the stable development stage of damage, two small cracks appear in the upper-left corner of the observation surface of sandstone sample 1, and there is a tendency to continue to expand. At this time, the AE localization events in the middle-left position of the sandstone sample are denser, indicating that the crack inside the sample increases significantly in this direction. As shown in Fig. 8(b), as the load increases at 222.7 s, the stress at the tip of the vertical crack near the left increases, the crack continues to develop downward, the width becomes larger, and the crack tip on the right splits into small cracks. At this time, high-energy AE localization events occur in the densely concentrated area of the AE (middle-left position of sandstone sample 1), indicating that the internal damage of sandstone sample 1 at this location is serious, but there is no obvious crack in this area. At 242 s, as shown in Fig. 8(c), strip spalling occurs at the left boundary of sandstone sample 1, and a crack at the left end of the observation surface penetrates the bottom end. At this time, the AE localization events in the middle of sandstone sample 1 are denser, and high-energy AE localization events have increased. The AE counts are relatively dense and show an ascending state, which proves that under the external load disturbance, the internal fissure expands rapidly and gradually loses the ability to recover to the old phase. At 264 s, as shown in Fig. 8(d), there is a large partial spalling on the left side of the sandstone sample 1 observation surface, and some crack widths are obviously increased. A large number of morphologically complicated microcracks are generated at the red dotted circle, indicating that the damage will occur here. Simultaneously, the AE localization event on the upper right side of the sample is denser, and a small amount of high-energy events appear, indicating that the damage development process on the right side of the sample is accelerated. At 273.3 s, as shown in Fig. 8(e), a significant macroscopic fracture surface can be observed in the middle and left side of sandstone sample 1, and a large caving phenomenon occurs. Two intersecting macroscopic cracks appear on the right side of the observation surface. The large energy AE events are mainly concentrated in the middle of the sample. At 275 s, sandstone sample 1 reached peak stress and instability occurred, and the observation surface appearance was basically the same as the appearance at 273.3 s. However, the number of AE events and amount of AE energy reached a maximum value at 273.3 s.

Generally, the AE event accumulation area corresponds well with the fracture location of sandstone samples. From the precursor point of sudden variance increase at 222.7 s to the final instability failure of sandstone samples, AE events gradually increased, and high-energy AE events gradually increased and accumulated in the serious damage development position. The crack propagation rate and effective penetration gradually increase. For the observation surface, the crack propagation process has experienced the following process. First, the cracks initiate in the upper-left corner. Then, the cracks propagate, penetrate, converge and form local spalling. Next, the cracks with complex shapes expand rapidly, and the crack width expands sharply until the macroscopic fracture surface finally appears. Last, large caving occurs. This process indicates that the damage rate of the sandstone specimen increases gradually under the external load, and sample 1 gradually loses the ability to be restored to the original state, which reflects the critical slowing down principle. 4.7. Comparative analysis of EP and AE precursory characteristics As shown in Fig. 5, the critical slowing theory is introduced to analyze the EP signal time series. The variation of the EP signal time series shows a sharp increasing trend 52.3 s ahead of the main fracture in the sandstone sample. This trend can be used as precursory information for predicting sandstone sample failure. In this paper, the critical slowing down theory is also applied to analyze the AE count time series. As shown in Fig. 9, the entire trend of the AE count time autocorrelation coefficient is disorderly and does not show certain regularity. There are no obvious precursory characteristics prior to sandstone failure. Compared with the EP signal time series, the autocorrelation coefficient of the AE count time series has a small change range, and the difference between the maximum and minimum is only 0.25. The red arrow points to the location where the variance of the AE count time series suddenly increases and continues to increase, and the AE cumulative energy presents a rapid rising trend. The corresponding time of the sudden variance increase point of AE count time series is 230 s, which is 45 s earlier than the sandstone sample failure and 7.3 s later than the precursor point time, as indicated by the EP signal time series variance. The load at the variance mutation point of AE count time series is 75% of the peak load, which is closer to the sandstone sample failure time than the EP signal variance mutation time. However, from the early Table 2 Comparison of EP and AE precursory points. Precursory point appearance time EP 222.7 s AE 230 s

Load at precursory point

Load ratio

Advance time

405.7 kN 437.9 kN

70% 75%

52.3 s 45 s

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warning point of view, the precursory point of the EP signal time series is earlier in time, which can predict that the sandstone sample is in the accelerated damage development stage and is about to destabilize. Therefore, compared with the variance mutation of AE count time series and EP signal time series, the two precursory signals also appear in the accelerated development stage of sandstone damage, with a time difference of 7.3 s and a load difference of 5% (see Table 2). In summary, the precursor points represented by the variance of the EP signal and AE signal are easy to identify and can be used as effective precursor points to predict the failure of sandstone samples. As a precursor of the unstable failure of sandstone samples, the variance mutation point of the EP signal time series occurs earlier and has more advantages in terms of early warning. 5. Conclusions (1) In different failure stages of sandstone specimens, the EP signal shows a periodic change characteristic, which has a good corresponding relationship with AE counts and AS, and the EP signal responds well to the sandstone specimen failure under load. Throughout the loading process, the sandstone sample shows a critical slowing phenomenon. The autocorrelation coefficients of the potential signal time series increase abruptly at 12.4 s before the main fracture of the sandstone sample and continue increasing until nearly reaching 1. The change in the variance undergoes four stages, which are the basically unchanged stage, slow rising stage, rapid increasing stage and rapid increasing stage. The variance increases sharply and continuously 52.3 s ahead of the main fracture of the sandstone samples. This characteristic can be used as precursory information regarding the unstable failure of sandstone samples. (2) Compared with the autocorrelation coefficient, the variance trend of the EP signal time series is more intuitive, the mutation point (precursory point) is easy to identify, and the occurrence time is not affected by the lag length choices. Thus, the EP signal time series variance trend is more suitable as the precursory point for predicting the failure of sandstone samples. (3) During the process from precursory point to unstable failure, the AE events accumulation area corresponds well with the macrofractures position of the observation surface, high-energy AE location events increase rapidly, and the propagation rate and effective penetration flux of the fracture on the observation surface gradually increase. This finding shows that the sandstone sample damage rate increases gradually. (4) Compared with the EP signal time series, the precursory point of the AE count time series also appears during the accelerated damage development stage of sandstone samples, with a lag time of 7.3 s. In terms of monitoring and early warning, the EP precursory point has more advantages.

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