Introduction

As mining and rock engineering migrates to deeper grounds, rockburst, a typical dynamical failure of rocks near the excavation boundary accompanied by violent ejection of rock fragments, frequently occurs and severely threatens mining and construction safety (Cook 1965b; Hedley 1992; Ortlepp and Stacey 1994; Ortlepp 2001; Zhang et al. 2012; Cai and Kaiser 2018; Feng et al. 2018). It has been widely recognized that rockburst is a complex phenomenon associated with multiple factors and multiscale fractures and that the fracture evolution and failure mechanism of rockburst should be further detected to proactively and scientifically predict and prevent rockburst. Over the years, many research works on rockburst failure investigation (Cook 1965a; Zubelewicz and Mróz 1983; Vardoulakis 1984; Linkov 1996; He et al. 2010; Jiang et al. 2010; Manouchehrian and Cai 2015; Xiao et al. 2016; Li et al. 2017; Su et al. 2017a, b; Gong et al. 2018, 2019) have demonstrated that the controlled laboratory experiments that can reproduce and monitor in situ rockbursts safely and economically are essential.

Since the 1960s, following the pioneering acoustic emission (AE) studies on rocks by (Mogi 1962) and (Scholz 1968), AE techniques have been widely used in laboratory studies of fracturing inside the rock volume (Lockner 1993; Lei et al. 2000; Thompson et al. 2006; Ishida et al. 2017; Rück et al. 2017; McLaskey and Lockner 2018; Wong and Xiong 2018). Generally, AE hits/events and AE energy are proportional to the number and magnitude of cracking events, and further, the size, location, and mode of fractures can be estimated by AE source analysis. Using the variation of AE hits, counts or energy, or coupling that with the stress-strain behaviors, researchers have quantitatively evaluated the damage process and detected different stress and cracking thresholds (Martin and Chandler 1994; Eberhardt et al. 1999; Zhao et al. 2013; Kim et al. 2015; Zhao et al. 2015; Moradian et al. 2016). The temporal-spatial evolution of AE source locations or combined with the microscopic examination (CT or SEM) of specimen sections has been widely employed to investigate the microscopic crack initiation, growth, and final coalescence (Lockner et al. 1992; Lei et al. 2000; Chang and Lee 2004; Thompson et al. 2006; Graham et al. 2010; King et al. 2012; Aker et al. 2014; Peng et al. 2019). Particularly, AE source mechanisms, namely the fracture modes of the cracking events, have been investigated by moment tensor inversion, polarity analysis, and parameter-based methods (e.g., Lei et al. 2000; Chang and Lee 2004; Graham et al. 2010). In recent years, many experimental investigations of rockbursts have adopted acoustic emission techniques, improving the understanding of the rockburst mechanism. He and Zhao et al. (He et al. 2010, 2015; Zhao et al. 2014; Zhao and He 2017) have studied the rockburst process under true-triaxial conditions with AE monitoring and found that near the bursting failure, the AE accumulated energy increases rapidly and the frequency–amplitude distribution changes significantly, accompanied by large numbers of higher amplitude and lower frequency events emitted. Researchers (Lu et al. 2013; Gong et al. 2017; Su et al. 2018) have also analyzed the frequency-spectrum and waveform characteristic during rockburst based on AE/MS investigations, which helps identify the immediate precursors to rockburst and facilitate the prediction and prevention of rockburst. The acoustic emission analysis in these rockburst studies, however, mainly focused on the parametric variations or magnitude–frequency characteristics, and the comprehensive characterization of fractures during rockburst requires a detailed analysis of acoustic emission activities.

The free boundary and redistributed stresses resulting from excavation are mainly responsible for the occurrence of rockburst (Kaiser and Cai 2012). One-face-free true-triaxial loading (or unloading) tests can well simulate the in situ stress state and boundary conditions of rockburst and have been widely conducted (He et al. 2010; Zhao et al. 2014; Su et al. 2017a, b; Akdag et al. 2018). In the previous experimental study (Zhai et al. 2020), we investigated the rockburst characteristics of six types of hard brittle rocks under one-face-free true-triaxial loading. In that study, the fracture and failure mode in the rockbursts of different rock types and the differences between them were focused. The experimental results showed that the failure characteristics were reasonably similar in the same lithology, despite the intrinsic variability of rock materials. More importantly, the rockburst failure of the six rocks roughly exhibited two different regimes/modes, and granodiorite and basalt appeared to be representatives of them. In this study, AE monitoring results are focused during the rockbursts of granodiorite and basalt reproduced under a similar loading condition. Fracture evolution during the (two modes of) rockbursts is detected and discussed in detail by acoustic emission analysis in terms of intensity, temporal-spatial distribution, and mechanism. The present work can contribute to the understanding on the rockburst mechanism and the prediction and prevention of rockburst.

Experimental procedures

Rock specimens

The tested granodiorite and basalt were taken from a quarry in Guangdong Province, China, and the underground powerhouse of the Baihetan hydropower station, China. Rectangular prismatic specimens with nominal dimensions of 100 × 100 × 200 mm3 were cut from the same block, as shown in Fig. 1.

Fig. 1
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Photo of rectangular prismatic specimens

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The granodiorite is a medium-grained rock with mineral sizes ranging from 0.6 to 5 mm. The mineral content mainly consists of plagioclase (39%), quartz (28%), k-feldspar (18%), biotite (7%), and hornblende (3%). These mineral grains are unevenly embedded and distributed in the rock, displaying a granitic texture and massive structure. The basalt is fine-grained with a general size range of 0.1–1 mm. The major minerals are plagioclase (40%), pyroxene (28%), chlorite (10%), actinolite (10%), glass (5%), and a small amount of opaque mineral (3%) and epidote (2%). The pyroxene and plagioclase are unevenly embedded and distributed, coupled with the other minerals non-uniformly distributed in the rock, displaying a blastodiabasic and blastopoecilitic texture and a massive structure. The optical cross-polarized micrograph and the three-dimensional hyper-focal distance microscopic image of the two rocks are shown in Fig. 2. The physical and mechanical properties are presented in Table 1.

Fig. 2
figure 2

Optical cross-polarized micrograph (left) and three-dimensional hyper-focal distance microscopic image (right) of a granodiorite and b basalt

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Table 1 Basic physical and mechanical properties of tested rocks
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Rockburst test

Rockburst induced by the gradual concentration of the tangential stress rather than by the sudden unloading of the radial stress (immediately after excavation) was investigated (Su et al. 2017b, c; Akdag et al. 2018; Zhai et al. 2020). Besides, certain radial stress gradient was considered since the rock specimen was taken as a representative element of rocks near the excavation boundary (Su et al. 2017c). In this test, one-face-free true-triaxial loading was conducted to experimentally reproduce rockburst using a true-triaxial rockburst testing system (Fig. 3a, see details in Su et al. (2017b, c)). The loading scheme and stress path are shown in Fig. 3 b and c, in which σx, σy2, and σz mimic axial stress σa, radial stress σr, and tangential stress σθ, respectively. In the tests, σx and σy2 were set to 30 and 5 MPa, respectively, and the loading rate was set to 0.2 MPa/s, which is a relatively regular situation with reference to the settings in previous research (Su et al. 2017b, c).

Fig. 3
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Illustration of testing apparatus and program: a true-triaxial rockburst testing system, b loading scheme, and c stress path

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AE monitoring and processing

AE setup

A multi-channel AE measurement system, SENOR HIGIHWAY II from Physical Acoustics Corporation was employed in the tests. The installed AEwin software can acquire the AE parameters, record the AE waveforms, and locate AE sources in real time. Six Nano30 sensors with a diameter of 8 mm and an operation range from 125 to 750 kHz, and two R6α sensors with a diameter of 19 mm and an operation range from 35 to 100 kHz were used for the source location and parameter/waveform analysis, respectively. The AE transducers were glued to the loading plates with tape using grease as a couplant, and tested by breaking lead before the loading. As displayed in Fig. 4, the AE transducers (of locating group) were installed as symmetrically as possible to provide good coverage of the specimen volume. It is also seen that No. 7 sensor was specially fixed on the free face of the specimen in G-1 test. Originally, this sensor was expected to better monitor the temporal evolution of fracturing. However, it was found that the accumulation of fractures, particularly the splitting failure near the free face could significantly influence the signal monitoring of this sensor. Thus, it was glued back to the loading plates in other tests.

Fig. 4
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Arrangement of AE sensors

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AE signals were amplified by 40-dB preamplifiers. AE acquisition system was set up with a trigger threshold of 40 dB, a band-pass filtration of 1 kHz–1 MHz, sampling rate of 1 MSPS, sample length of 8 K (i.e., 8192 samples in each waveform, corresponding to a duration of 8.192 ms for a sampling rate of 1 MSPS). The time parameters for the AE signals definition, called peak definition time (PDT), hit definition time (HDT), and hit lockout time (HLT), were set to 50, 100, and 200 μs, respectively.

AE source location

P-wave arrival times and amplitudes of AE waveforms were picked automatically at each sensor during loading. AE source locations were estimated by minimizing the sum of the square of differences between the observed and calculated time differences in the array of six Nano30 sensors using a Simplex method (Nelder and Mead 1965):

$$ {\chi}^2=\Sigma {\left(\Delta {t}_{i, obs}-\Delta {t}_{i, calc}\right)}^2 $$
(1)

where Δti, obs = ti − t1 is the difference of observed P-wave arrival times in the array of sensors, \( \Delta {t}_{i, calc}=\left[\sqrt{{\left({x}_i-{x}_S\right)}^2+{\left({y}_i-{y}_S\right)}^2}-\sqrt{{\left({x}_1-{x}_S\right)}^2+{\left({y}_1-{y}_S\right)}^2}\right]/v \) is the difference of calculated P-wave arrival times, and (xs, ys) is the location of AE sources. For the 3D location, a minimum of four sensors/hits are required, and with five or more sensors/hits, the regression analysis will produce the best fit location that averages out errors in the data. Here, an isotropic velocity field was assumed. However, it should be noted that there must be some errors in AE source location for the influence of accumulation of oriented cracks and refraction at interfaces of loading plates on AE propagation in the true-triaxial test (see the “Limitations on AE monitoring and locating” section). By applying an electrical pulse to a sensor, the resulting arrival times were then recorded at other sensors in the array, allowing P-wave velocities along different trajectories to be determined within the sample. In this manner, the mean velocity field was measured, approximately 2108 m/s and 2174 m/s in the granodiorite and basalt tests.

AE waveform analysis

It is well known that the AE signal contains complex frequency components, which should be attributed to the simultaneous occurrence of multiple fracture modes. After the AE signal is decomposed by waveform analysis, the frequency band with a large energy ratio should correspond to important fracture mode. In this way, we can further reveal the evolution law of fractures during rockburst.

In this study, the fast Fourier transform (FFT) was conducted to obtain the frequency spectrum of AE signals. The frequency corresponding to the maximum amplitude is generally regarded as the dominant frequency (Fig. 5).

Fig. 5
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A typical waveform and its frequency spectrum via FFT

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As illustrated in Fig. 6, the wavelet transform was used to decompose the AE signal. In Fig. 6, CA1, CA2, CA3, …, CAn are the low-frequency sub-signal of the first, second, third, …, nth layer of the wavelet decomposition, respectively; CD1, CD2, CD3, …, CDn are the high-frequency sub-signals. Specifically, using the toolbox in MATLAB and taking db3 as the wavelet base, the wavelet decomposition was performed for five layers. Sub-signals of six different frequency bands that are CA5 (0–15.625 kHz), CD5 (15.625–31.25 kHz), CD4 (31.25–62.5 kHz), CD3 (62.5–125 kHz), CD2 (125–250 kHz), and CD1 (250–500 kHz), were obtained.

Fig. 6
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Schematic of decomposition of AE signal by wavelet transform

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Then, the energy of the sub-signals Ei (i = 1, 2, …, 6) could be calculated (by squaring and integrating the voltage within the duration time of the sub-signals), and the energy distribution coefficient of different frequency bands Ki (i = 1, 2, …, 6) was calculated as follows:

$$ {K}_i=\frac{E_i}{\sum \limits_{i=1}^6{E}_i}\times 100\% $$
(2)

The frequency band with the largest energy distribution coefficient was regarded as the advantage frequency band of AE signals/hits. Dividing the loading process into numbers of periods, in the period of t, with the number of AE signals characterized with i-dominant frequency band denoted as Bti, the proportion of the ith advantage frequency band Ati was thus defined as follows:

$$ {A}_{ti}=\frac{B_{ti}}{\sum \limits_{i=1}^6{B}_{ti}}\times 100\% $$
(3)

In this way, the proportion of the advantage frequency band throughout the rockburst test could be checked.

Tensile-shear fracture recognition

A parameter-based method was chosen to carry out crack classification considering the limitation of signal-based methods (such as moment tensor inversion, polarity analysis) for the small number of AE sensors and the complex propagation medium in this true-triaxial experimental study. The parameter-based method has been widely used in the fracture mechanism identification during the damage of rock, concrete, etc., showing strong robustness (e.g., Ohno and Ohtsu 2010; Aggelis 2011; Carpinteri et al. 2013; Sabri et al. 2016). It was conducted by employing two parameters of the RA (the rise angle value = the rise time/the maximum amplitude) and the AF (the average frequency value = AE ring-down count/the duration time). The critical proportion of these two parameters, i.e., AF/RA which can differentiate the tensile fracture and the shear fracture, was determined by conducting three-point bending tests and direct shear tests on the tested rocks. It was recognized that the tensile fracture and the shear fracture dominate the three-point bending test and the direct shear test, respectively. Specifically, for the three-point bending test, rectangular prismatic specimens were prepared with dimensions of 400 mm × 100 mm × 100 mm and a rectangular fluted of 30 mm depth in the middle of the specimen. In the test (see Fig. 7a), the specimen was placed on two bearings points with a distance of 300 mm and loaded in the middle with a rate of 0.0005 mm/s after preloading. In the direct shear test, cubic specimens with dimensions of 100 mm × 100 mm × 100 mm were loaded using a direct shear device (see Fig. 7a). First, load the normal stress to 1 MPa, and then load the upper part of the direct shear device horizontally at a rate of 0.008 mm/s after preloading until the specimen was destroyed. As shown in Fig. 7, an AF/RA of 55 was determined for granodiorite, and an AF/RA of 35 for basalt. Consequently, AE hits/signals with an AF/RA less than the determined proportion were considered from shear fracturing, and tensile fracturing otherwise.

Fig. 7
figure 7

Critical AF/RA values determined by the three-point bending test and direct shear test: a granodiorite and b basalt

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Results and analysis

Test results

During the tests, with σz continually increased, all the specimens, including three specimens for each rock type had violent rockburst ejections. Generally, the fracture and failure modes of the rockbursts in granodiorite and basalt were similar to the previous experimental results (Zhai et al. 2020) as mentioned in the introduction. Thus, the visually observed fracture and failure characteristics of the rockbursts as well as the possible inconsistency caused by the intrinsic variability of rock materials were not focused in this study. The results of the representative specimens G-2 and B-1 will be shown and the general fracture evolution during the two modes of rockbursts will be analyzed in detail.

Figure 8 presents the critical moments captured by the high-speed camera (Fig. 3a) during the rockburst failure of G-2 and B-1, and the corresponding failure results are also shown in Fig. 9. By these visual observations, the failure process and fracture mode of granodiorite and basalt can be identified, which are different from each other.

Fig. 8
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Ejection failure processes of two typical specimens: a G-2 (granodiorite) and b B-1 (basalt); the text in the bottom left corner of images indicates the time in h:m:s and frame number (the magnitude of the frame number is related to the duration of saved segments and the imaging rate is 500 frames per second)

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Fig. 9
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Images of failed specimen (G-2 and B-1) and schematic of corresponding failure mode for a granodiorite and b basalt

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For granodiorite (G-2 in Figs. 8a and 9a), when σz increased to a relatively high level, ejections of small fragments or grains occurred randomly on the free face. With further increasing in σz approximately to the capacity of the specimen, the rock near the free face was split into several sub-parallel slabs and these rock slabs expanded and bent outward. Finally, as σz continued to increase, the slabs buckled and broke off, the specimen collapsed and a large number of fragments were ejected violently. As shown on the failed specimen, the tension splitting occurred near the free face and was characterized by several macro-cracks or slabs subparallel to the σz direction with smooth surfaces covered with a small amount of powder or small grains; the shear rupture or faulting occurred further away from the free face and was associated with several macro-cracks dipping in the σy direction with coarse surfaces mixed with a large amount of white powder or small grains; the rockburst pit formed near the free face and appeared to be resulting from the fragmentation and ejection of the splitting slabs.

For basalt (B-1 in Figs. 8b and 9b), no significant macroscopic fractures appeared on the free face until close to the end of the test. Finally, local ruptures occurred on the free face, and immediately the local broken rocks and a few fragments behind them were ejected. As presented on the failed specimen, the ruptures or macro-fractures that were characterized by an uneven surface, covered by white powder and dipping in the σy direction occurred throughout the specimen, without tension splitting of rocks near the free face. That indicates that the shear or tensile-shear rupture dominated rockburst occurrence. The rockburst pit on the top corner close to the free face was relatively small and regular, which resulted from the local compression-shear or tensile-shear rupture.

Fractures during the rockburst process will be discussed in detail below by acoustic emission analysis to obtain further insights into the nucleation and evolution of the rockburst failure. Given that the rockbursts reported both in the field and laboratory are mostly associated with the splitting or slabbing and buckling failure of rocks, the rockburst mode of granodiorite is thus more typical and will be mainly analyzed.

Fracture developing from AE hits, counts, and energy analysis

Figure 10 shows the changes of AE hits for G-2 and B-1 together with the loading process of σz and the variation of εz, in which the duration of each histogram is 1.28 s. As reviewed in the introduction, the number of AE hits is related (proportional) to the number of fractures, and the AE amplitude and energy are related to the magnitude of fractures (Lockner 1993). During the initial loading stage of 0~300 s, the stress (under 30% σzpeak) should be under the crack initiation stress, and the pre-existing microscopic cracks and flaws were largely compressed and closed, which is also evidenced by the obvious nonlinear strain stress curve that displays an increase in stiffness. In this study, AEs recorded during 0~300 s were thus not considered, to avoid confusion in data analysis. Besides, it is noted that from the variation of AE hits, there appears no special points or features that can be used to exactly differentiate the stages of pre-existing microcrack closure and new microcrack growth.

Fig. 10
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Variation of AE hits for a G-2 and b B-1 together with σz and εz

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For granodiorite (G-2 in Fig. 10a), with the increase of σz in the early loading stages, following the decreasing AE activity from the crack closure, obvious but low AE activity continues indicating insignificant fracturing initiation and development. As σz further increases, a rapid increase of AE hits occurs, which is noted at a stress level of about 80% σzpeak. Thus, this should perhaps be associated with the crack damage stress σcd and unstable fracturing begins with micro- or meso-scale fracturing largely developing and coalescing (Martin and Chandler 1994; Eberhardt et al. 1999; Zhao et al. 2013). Accordingly, with the fracturing accumulation, εz subsequently begins to deviate from linearity and shows an increasing rate. However, shortly before σz increases to the peak level, AE hits sharply drops and shows “quiet periods.” As pointed in Moradian et al. (2016), this phenomenon may happen partially during macro-fracture growth but mostly during macro-fracture coalescence, which may be caused by overlapping of the hits. This will be discussed in more detail in the “Limitations on AE monitoring and locating” section. At the same time, εz shows an obvious nonlinear increase followed by a sudden sharp increase, suggesting the initiation and acceleration of the final rupture or faulting.

For basalt (B-1 in Fig. 10b), there are only a few AE hits except for the early signals in the early loading stages that presumably mainly result from the crack closure. It indicates that small local fractures were significantly suppressed in basalt, probably for the significant decrease in the grain size as well as the increased textural homogeneity and interlocking texture of the minerals in basalt as compared to granodiorite (see Fig. 2 and related text in the “Rock specimens” section and Zhai et al. (2020)). As σz increases close to 90% σzpeak, a notable increase of AE hits occurs and unstable fracturing begins. However, different with granodiorite, there appears to be no continued activity in subsequent AE but several little bursts, and the εz continually increases in linearity. This agrees with the quasi-static nucleation process characterized by dynamic fracturing of asperities, like the evolution of stick-slip behavior (Lei and Satoh 2007; Meng et al. 2016). Then, as σz further increases approaching the peak, AE hits sharply increases, indicating the development of a large number of fractures associated with the macro-cracks. In comparison with granodiorite, AE hits in basalt has a larger peak rate without “quiet periods,” while large fluctuations are observed.

According to the definition for the AE hit/signal, each AE hit may contain a different number of counts, and AE signals can usually present two different forms of waveforms, i.e., burst and continuous, as shown in Fig. 11 (see Grosse and Ohtsu (2008) for more details). Here, the count characteristics of AE hits were thus investigated to relate the duration and intensity of AE signals. The counts and absolute energy and their average variations of AE hits are shown in Fig. 12.

Fig. 11
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Example AE signals: a burst signal and b continuous signal

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Fig. 12
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Variations of counts and absolute energy of AE hits and their averages for a G-2 and b B-1. Size of the sphere indicates the amplitude of AE hits

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From Fig. 12a, it is seen that for granodiorite the counts and absolute energy of AE hits initially continue to maintain relatively low levels for a long time, showing that the AE signals mostly proceed shortly and exhibit burst waveforms. Based on the findings in the literature (e.g., Martin and Chandler 1994; King et al. 2012; Aker et al. 2014; Moradian et al. 2016), it is concluded that these weak and burst signals were presumably emitted by small microfracturing, mostly in tension (see the “Fracture mechanism evolution from AE waveform analysis” section for more details). With the cumulation of fracturing, the counts and absolute energy gradually increase, especially when approaching and during the crack unstable growth stage (beginning from the crack damage stress). As σz continues to increase over 90% σz peak, a number of AE hits with much larger counts and absolute energy that are tens and thousands of times larger than before are detected. The counts, energy (and duration) of the instantaneous AE hits are distributed over a large range more than several orders of magnitude, for the complex and multi-scale fracture developing. At the same time, the averages increase and fluctuate largely, suggesting that the fracturing intensity and scale grow significantly and some large scale fractures may take place in the unstable stage of crack growth. Finally, as σz further increases till rockburst, the counts and absolute energy continue to increase sharply. Simultaneous sharp drops and ‘quiet periods’ in AE hits (see Fig. 10) also indicate that strong and long-lasting continuous AE signals are associated with significant macro-fracturing growth and coalescence. In other words, the sharp drops and “quiet periods” in AE hits and the associated sharp increases or fluctuations of counts and absolute energy provide precursor information of rockburst.

From Fig. 12b, it is observed that for basalt the AE hits proceed with relatively low counts and absolute energy for almost the entire loading process, except that some sudden increases occur when entering the crack unstable growth stage, especially when it is close to the final failure. Probably because the fracturing intensity and scale were indeed not strong for the significant decrease in the grain size, and on the other hand, the signals have not overlapped seriously near the end of the test, the signals from basalt generally proceed shortly and moderately when compared with those from granodiorite. However, from the temporal variations of AE hits (Fig. 11) and their counts and absolute energy (Fig. 12), it is noted that the rockburst failure in basalt occurs more abruptly with fewer precursors.

Fracture temporal-spatial distribution from AE source analysis

The temporal-spatial distributions of AE sources (both staged and accumulated) for G-2 and B-1 that indicates the evolution of significant fracturing events are presented in Fig. 13, along with the stress-strain curve and the image of failed specimens. Several stages were selected randomly with equal intervals during the early loading and specifically from the beginning of plasticity to the initiation of yield platform.

Fig. 13
figure 13figure 13

Temporal-spatial distributions of AE sources (the colored and gray spheres represent the events that are being produced and produced in the past, respectively) for a G-2 and b B-1, along with stress-strain and image of failed specimen. Color and size of the sphere indicate magnitude (color figure online)

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For granodiorite (Fig. 13a), it is seen that at 500 s, AE events are distributed diffusely throughout the specimen but rarely near the ends, with a weak cluster developing in the lower middle of the specimen. Earlier studies have shown that few acoustic emissions were generated near the ends during the early stage of compression, as would be expected if stress constraints owing to end effects were important (Scholz 1968; Ohnaka and Mogi 1982; Lockner et al. 1992). In this study, the specimens were specifically constrained at the ends (and also the sides) to conduct one-face-free true-triaxial loading. In contrast, more freedom would exist, especially outward from the free face at the centre of the specimen, where a relatively weak region appeared. Consequently, a number of AE events with relatively high amplitudes are concentrated at the centre near the free face, where the tension splitting/slabbing would evolve and happen first during the later loading as presented in Fig. 7 and related text. From the above analysis, it seems that these AE events were mainly caused by small tension fracturing and characterized by short duration, which will be discussed further in the following sections. At 700 s, more AE events have been located, showing a progressive change from diffuse to more localized. The cluster in the lower middle of the specimen has expanded and nucleated further, coupled with another new cluster developing in the upper half of the specimen. According to the inclination of dipping in the y-direction, these clusters are presumably evolving shear ruptures or faults, although the fractures may be mostly in a tensile mode. At 900 s, while a few events are still distributed diffusely, most events cluster in the nucleation zone, delineating the rupturing paths. It is should be pointed out that the nucleation of large scale macro-fractures or ruptures attributed to significant development of microfractures does not mean the initiation of rupture or faulting which always occurs with strong self-excitation and fast growth like avalanche or domino upon the final failure and collapse (Lockner et al. 1992; Lei et al. 2000; Thompson et al. 2006; Tarasov 2014; Vu et al. 2019). Besides, it is noted that most of the new events are generated away from the free face rather than near it, indicating the fracturing migrates inwards.

By the time of 1065 s (moment A) when the specimen begins to behave plasticity, it is clear that the event rate has sharply increased for many more events being located in a shorter period than before. The nucleation zones away from the free face significantly develop, expend, and coalesce. Moreover, a cluster can be seen near the free face at the lower part, as well as a strip cluster in the lower right corner, which shows the development and migration of tension splitting/slabbing. It is possible that the fracturing largely develops and turns to evolve unstably on a large scale in the unstable stage of crack growth. Then, at 1197 s (moment B) when the specimen shows obvious plasticity, the event rate continues to maintain relatively high levels. The upper nucleation zone evolves the main rupture and forms first. The lower nucleation zone follows but more diffusely. Besides, it is likely that the shear rupture should first initiate and propagate from the bottom of the upper nucleation zone, accompanied by or triggering the rupture growth of the lower nucleation zone and the rapid fracture and fragmentation of rocks at and near the free face. However, later until 1276 s (moment C) when the specimen initiates yielding platform, because a large amount of fracturing and fragmentation induces the significant signal overlapping and also severely complicates the specimen (the propagation medium) (Lockner et al. 1992; Lei et al. 2000; Thompson et al. 2006; Moradian et al. 2016), few events are located properly. From the image of AE-2 after the test (also in Fig. 9), it can be seen that significant shear ruptures developed inside the specimen away from the free face along the nucleation zones or their branches and extensions and that tension splitting occurred in the nucleation zones near the free face.

For basalt (Fig. 13b), very few AE events have been located during the loading before 1050 s, in agreement with the sparse occurrence of AE hits (from small local fractures). These events appear to be randomly distributed in the sample. As the test approaches the end, both the strain and fracture rapidly develop. At 1227 s (moment A, the beginning of plasticity), a cluster of AE events develops in the upper half of the specimen, showing obviously dipping in the y-direction. Thus, this cluster is presumably evolving shear rupture. Immediately after this, and without a significant increase in the axial load, this cluster expands to the lower part of the specimen, where some events are clustered as shown at 1254 s. In the image of failed B-1 (also in Fig. 9), these nucleation zones roughly match with the final ruptures. Besides, as shown in the image, there is an inflection point on the main rupture, which may be the reason for the successive rather simultaneous evolution and nucleation of the upper and lower parts of the main rupture. Comparing Fig. 13a with Fig. 13b, it is seen that the yield and fracture and rupture of basalt proceed more sudden and rapidly than granodiorite, although AE events detected in basalt are much fewer. Without the small local fracture widely developing in the early loading stages, the final fractures and ruptures in basalt appear to develop more locally on the relatively intact specimen.

Fracture mechanism evolution from AE waveform analysis

Figure 14 shows the evolution of the dominant frequency and the advantage frequency band proportion for G-2 and B-1 from the FFT and the Wavelet transform, respectively.

Fig. 14
figure 14

Evolution of dominant frequency (left) and advantage frequency band proportion (right) for a G-2 and b B-1 (color figure online)

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For granodiorite (Fig. 14a), it is evident that during a long period the AE hits roughly concentrate within five dominant frequency bands, namely 40–50 kHz, 80–100 kHz, 140–142 kHz, 175–180 kHz, and 260–262 kHz, especially the 40–50 kHz and 80–100 kHz. This is probably due to the fracturing preferentially occurring along the specific types of grain boundaries or through the specific types of grains in the crack stable growth stage, and it is also in line with the fact that the tested granodiorite consists of several kinds of minerals, different in grain size, shape and proportion (Tapponnier and Brace 1976; Lei et al. 2004; Rodríguez et al. 2016). Furthermore, the phenomenon that most AE signals are distributed in relatively low dominant frequency bands seems to correspond to the fact that fractures that occur readily or at relatively low applied stresses generally tend to cause AE signals with low frequencies. As σz further increases, the distribution of dominant frequency suddenly turns into a continuous form. This results from the development and coalescence of a large amount of fracturing by more types of intergranular and intragranular failures under relatively high stresses, especially in the crack unstable growth stage. Besides, the fracturing scale significantly increases and fracturing at a large scale could involve fractures at all smaller scales as described as hierarchical properties in (Lei and Satoh 2007). Prior to the rockburst, when AE hits experiences sharp drops and ‘quiet periods’, the AE hits are characterized by high amplitude and low dominant frequency, consistent with experimental observations reported in (He et al. 2010). The majority of these hits concentrate within low dominant frequency bands. This is presumably attributed to the evolution and occurrence of large scale macro-fractures or ruptures.

In terms of the advantage frequency bands, it is clear that during a long period the proportion of advantage frequency bands approximately maintains constant and the AE hits are mainly attributed to the advantage frequency band of 62.5–125 kHz, which basically coincides with the distribution of the dominant frequency. This implies that the majority of AE signals were relatively simple and likely exhibited burst waveforms in which the dominant frequency could be consistent with the energy dominant frequency band. Then, as the fracturing intensity and scale increase, the proportion of advantage frequency bands changes apparently, and proportions of high frequency bands (125–250 kHz and 250–500 kHz, in particular) increase significantly. The major advantage frequency bands are no longer absolutely attributed to one, but approximately to three, for the occurrence of more complicated AE signals. Especially, during the late stage of “quiet periods” and later, the proportion of advantage frequency bands evolves notably inconsistent with the distribution of the dominant frequency. The proportions of advantage frequency bands of 250–500 kHz and 62.5–125 kHz successively increase sharply.

For basalt (Fig. 14b), it is seen most of the AE hits are concentrated within two dominant frequency bands, namely 40–60 kHz and 90–110 kHz, for almost the entire test. There appears a narrow concentration of a small number of hits in dominant frequency around 15 kHz in the late stages. The interpretation for the occurrence of the dominant frequency bands can refer to that mentioned above in granodiorite. Similarly, the advantage frequency bands are mainly concentrated in 31.25–62.5 kHz and 62.5–125 kHz for almost the entire test. Also, the proportion of advantage frequency band of 0–15.625 kHz obviously increases in the late stages, and those of 125–250 kHz and 250–500 kHz close to the end of the test. In general, the distribution of advantage frequency bands coincides with that of the dominant frequency. Comparing Fig. 14a with Fig. 14b, it is clear that the fracture development in basalt is simpler and more regular in mechanism and generates significantly less high frequency component of AE signals, especially in the energy distribution.

Figure 15 presents the variation in proportions of tensile and shear fracturing mechanism for G-2 and B-1 identified by the AF/RA value. In granodiorite (Fig. 15a), the tensile mechanism clearly dominates during the early loading stages, accounting for more than 80% of all fractures. With σz continually elevated, the proportion of shear fractures increases gradually on average, although some fluctuations. As σz approaching and exceeding 90% σzpeak, the shear fracturing largely occurs and dominates substantially with a proportion of over 80%. In basalt (Fig. 15b), while there also appears to be a tendency of shear mechanism increasing as σz loaded, the variation of the T-S proportion is much less than that in granodiorite. During most of the testing, tensile fracturing and shear fracturing develop almost equally. This indicates the increased textural homogeneity and interlocking texture of the minerals in basalt, where the tensile separation of the interlocking grains is closely related to the shear break of them. Thus, it can be seen that the fracture evolution mechanisms interpret the AE phenomena presented in the above sections.

Fig. 15
figure 15

Variation in proportions of tensile and shear fracturing mechanism for a AE-2 and b B-1

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Discussion

Hierarchical fracture evolution of rockburst and prediction

It is widely recognized that rockburst occurs for strain energy continuous accumulation during loading and rapid release upon failure. Also, as indicated by the above AE analyses, the occurrence of rockburst is due to the continuous fracture developing and coalescing in micro- or meso-scale during loading and rapidly or sudden propagating throughout and fragmenting the rock in macro-scale upon failure. Significantly, it is seen that the fracture evolution during rockburst presents hierarchical characteristics.

In granodiorite where a typical rockburst process associated with the splitting and buckling failure occurred, it is seen that the fracture evolution can be roughly divided into three hierarchies or phases, i.e., small local microfractures progressively and stably developing and preliminarily clustering during the early loading; increasing large scale fractures rapidly and unstably developing and coalescing and the nucleation zones of tension splitting and shear rupture significantly developing around and after the crack damage stress σcd; splitting rocks rapidly buckling, fracturing and fragmenting and shear rupture sudden running through upon rockburst failure. Moreover, the fracture developing and clustering in tension splitting zones near the free face proceed slightly ahead of that in shear rupture zones further away from the free face in the first two hierarchies or phases (Fig. 13a), for the more freedom. However, due to the constraints in AE techniques for the sudden and intensive fracturing and fragmenting (see more details in the next section), and the blocking and attenuation of AE signals for significant accumulation of fracturing when rockburst occurs, no enough systematic evidence from AE is available to determine if the sudden buckling and breaking off of external splitting rocks or the shear rupturing of internal rocks primarily dominated the occurrence of rockburst. In other words, further study is needed to determine whether the breaking off of splitting rocks happens first and causes the shear rupturing inside during the typical rockburst or not. This should be of vital importance to the understanding and control of rockburst, and some controlled or slowed down (close to the sudden failure) tests may be helpful and crucial.

In basalt where a shear rupture dominated rockburst occurs without splitting and buckling failure, small local microfractures during the early loading stages were significantly suppressed, and thus the first hierarchy or phase of fracture evolution occurred in granodiorite mentioned above almost did not occur. The last two hierarchies or phases of fracture occurred more suddenly and locally, although the total number of fractures detected was much less than that in granodiorite. Similarly, the final running through of shear ruptures upon rockburst failure in basalt was also not successfully tracked and located.

It is important to understand the fracture evolution mechanism in rockburst for prediction and prevention of rockburst. Field observations and experimental investigations (e.g., He et al. 2010; Xiao et al. 2016; Su et al. 2018) have previously described the fracture process during rockburst in general that is basically consistent with the fracture evolution during the compression failure of most hard-brittle rocks (Lockner et al. 1992; Martin and Chandler 1994; Eberhardt et al. 1999; Lei et al. 2000; Thompson et al. 2006; Graham et al. 2010; Kim et al. 2015; Moradian et al. 2016). Furthermore, several AE precursory anomalies related to the fracturing evolution have been reported for the prediction and evaluation of rockburst or brittle failure, such as the sharp drop and ‘quiet periods’ of the AE hits, sudden increase of the AE counts or energy, significant decrease of the b-value (Lockner 1993; Lei and Satoh 2007; Wang 2014; Kim et al. 2015; Su et al. 2018). However, it seems that these precursory anomalies are mainly based on the sharp changes of fracturing pattern immediately preceding the final failure related to the critical nature of the failure process (Lei and Satoh 2007; Li et al. 2019; Vu et al. 2019), which are generally associated with the sudden initiation and propagation of through-going ruptures or faults. Thus, the forecast and prediction of rockburst or collapse based on these anomalies may fail to provide enough time to avoid damage or take measures in advance, although these anomalies are distinct enough.

Based on the findings reviewed above, the multi-hierarchy or phase fracture evolution of rockburst could be significant and promising for the rockburst prediction to conduct the long-term tracking and forecasting. It is seen that regardless of the rockburst mode (both in granodiorite and basalt), the sudden rupture or faulting of internal rocks should be critical to the occurrence of rockburst, or may be the fundamental mechanism to the occurrence of strong and extremely strong rockburst. And, we note that the distinct nucleation of main ruptures during rockburst, which shows up as clustering and localization of AE events, occurred (before 900 s in granodiorite and around 1100 s in basalt) a relatively long time before the final failure (1285 s in granodiorite and 1258 s in basalt) or even before the beginning of the plasticity (1065 s in granodiorite). Thus, monitoring and detecting the multi-hierarchy or phase fracture nucleation proceeding inside the rocks could be promising as a means of systematically predicting and preventing rockburst, not only for failure warning but also for location and scope forecasting. Nevertheless, it should be aware that the fracturing evolution of rockburst may vary between different rocks and stress conditions.

Limitations on AE monitoring and locating

Hit-based triggering and continuous streaming are two operation modes of AE monitoring. In the continuous method, the system records the continuous waveform over the test. As a result, the monitoring can only span a limited time window due to memory limitations. While in the hit-based method, the system records data that is reasonably required at the time of a fracturing event and needs to re-arm after every hit, and therefore the monitoring is cheaper in cost and in storage space(Li et al. 2015; Moradian and Li 2017). Since rock fractures produce burst (discrete) signals, the hit-based method is commonly used. However, as recently pointed out in the literature (e.g., Moradian et al. 2016; Li et al. 2019), near the final failure, the rock tends to produce a significant amount of emissions in a few seconds. The extremely high rate of cracking coupled with the strong reflections of the signals may cause the overlapping of the hits, that is several hits are registered as one single in the AE system for system saturation. Obviously, this limitation appears to be serious for the monitoring of violent rockburst failure.

Because of overlapping of the hits, blocking of the signal traversing by accumulated cracks and other phenomena, AE hits rate might significantly drop, showing apparent “quiet periods,” whereas the cumulative AE indices such as duration, counts and energy multiply. This is the case in the granodiorite test as described in the “Test results” section. This may influence the accuracy of hit-based analyses and is also the main reason of the inability to locate enough events immediately before the rockburst failure, as well as the strong noise from reflections and reverberations.

In the abovementioned research, to deal with the system saturation close to the failure, a system with hit-based acquisition in the early stages and continuous acquisition near the end of the test was developed (Li et al. 2015; Moradian and Li 2017). In this syncretic system, AE hits were recorded first based on the hit definition time (HDT) and then based on the maximum duration (regularly cutting off the overlapping long-lasting signals). By setting appropriate time parameters, the system can record most of the data in continuous waveforms (84% in Moradian and Li (2017)) close to the failure. However, there are still many questions in the post-processing of the data (close to the failure) such as detecting and dividing the continuous waveform into segments. Even whether the continuous signals are indeed generated correspondingly by large-scale fractures developing near the final failure or whether the simultaneous signals from different fractures that have been mixed together in the continuous waveform indeed can be divided, still needs further study. In this study, the continuous waveforms close to the rockburst failure, particularly in granodiorite were simply regarded as individual AE hits.

True-triaxial compression tests using solid pistons traditionally have issues with installation of AE sensors on the rock specimen directly. Generally, in these true-triaxial tests, the sensors are positioned on the loading plates. In this case, the lack of proper mathematical velocity model, refraction of AE path between interfaces of multi-layer media, and other limitations must result in some errors in the analysis of AE source locations and mechanisms. Thus, in this study, the uncertainty in the AE source locating is inevitable. Recently, as pointed out in the literature (Nasseri et al. 2014; Ren et al. 2019), some efforts have been made to modify the loading plates by installing AE sensors on the rock specimen directly. But there still exist some limitations in the number and layout of AE sensors.

Conclusions

The granodiorite and basalt were tested under one-face-free true-triaxial loading to investigate the fracture evolution during the rockburst process. With, in macroscale, the ejection failure captured by high-speed cameras and the overall failure mode presented from failed specimens, the fracture evolution inside the rock volume was specially monitored by AE techniques and studied in detail using AE analysis. Based on the results, the following conclusions can be reached.

  • The rockbursts of granodiorite and basalt were successfully simulated and reproduced. In granodiorite, a typical rockburst occurred, in which rocks near the free face or excavation boundary in the field split, bent and rapidly broke off, fragmented and ejected, while those further away from the free face evolved several main fractures locally that could expend, coalesce and sudden propagate throughout by shear ruptures. In basalt, a shear rupture dominated rockburst happened without tension splitting and buckling failure of rocks near the free face.

  • The fracture evolution during rockburst exhibits hierarchical characteristics, particularly in granodiorite. That is, during early loading, small local microfractures developed progressively and stably along specific types of grain boundaries mainly by tension and clustered preliminarily; around and after the point of the crack damage stress σcd, large scale fractures developed and coalesced rapidly and unstably, showing increasing shear mechanism, and nucleation zones significantly developed; upon rockburst failure, rocks near the free face rapidly buckled or fractured, fragmented and ejected, and shear ruptures suddenly ran through. In basalt, small local microfractures during the early loading were significantly suppressed, thus the first hierarchy or phase of fracture evolution almost did not occur. However, the last two hierarchies or phases of fracturing occurred more suddenly and locally in several shear ruptures. Overall, the AEs showed obvious responses and precursory phenomena.

  • Based on the fracture evolution in rockburst indicated by AE analysis, short-term prediction using the instantaneous precursors in AE immediately before rockburst can be used to predict and prevent rockburst; long-term tracking and forecast using the hierarchical properties of fracture evolution could be carried out to predict and prevent rockburst as well.

The above findings contribute to better understanding of the evolution and failure mechanism of rockburst and facilitate the rockburst prediction and control.