Introduction

Understanding and predicting the strength and deformation behavior of rocks is an important topic in geomechanics, which can facilitate cost-effective design and long-term stability of engineering structures, such as deep tunnels for mining, boreholes for oil or gas production, tunnels for the storage of radioactive waste, and wells for the injection of carbon dioxides. Numerous laboratory test results have revealed that the deformation (failure) of rocks is, to a large extent, attributed to the closure, initiation, propagation, and coalescence of micro-cracks inside the rock specimens (Bieniawski 1967; Brace et al. 1966; Cai et al. 2004; Diederichs and Martin 2010; Diederichs et al. 2004; Eberhardt et al. 1998; Lajtai and Lajtai 1974; Martin and Chandler 1994; Wong and Einstein 2009a, b; Zhao et al. 2015). The associated micro-cracking processes can divide the rock deformation into several distinct stages from crack closure to crack coalescence (Brace et al. 1966; Martin and Chandler 1994). It is, therefore, of vital importance to study the strength and deformation behavior of rocks from a microscopic view.

In the last several decades, many researchers have studied rock strength and the associated micro-cracking behavior using various microscopic observation techniques. These techniques include scanning electron microscope (SEM) (Tapponnier and Brace 1976), X-ray computed tomography (CT) (Vinegar et al. 1991), acoustic emission (AE) (Lockner et al. 1991), and high-speed camera (Wong and Einstein 2009a, b). Among these techniques, AE is a method which has been proven to be useful particularly for studying the progressive micro-cracking behavior of rock specimens during loading (Chen et al. 2017; Fu et al. 2015; He et al. 2010; Jansen et al. 1993; Lei et al. 2000; Liu et al. 2017; Meng et al. 2017; Slatalla et al. 2010; Yan et al. 2016; Zhao and He 2017; Zhao et al. 2013). Due to its high sensitivity to micro-cracking, AE monitoring has also been used to provide early warning signals with great success in the construction of large-scale engineering structures, such as deep tunnels for hydropower stations or mining (Alcott et al. 1998; Butt et al. 2000; Dai et al. 2016; Goodfellow and Young 2014; Xu et al. 2016, 2017).

AE can be defined as the transient elastic wave generated by the rapid release of energy from a source within a material (Koerner et al. 1981; Mansurov 1994). The AE activity in a rock generally initiates from micro-cracking which is associated with dislocations, grain boundary movement, or the initiation, propagation, and coalescence of micro-cracks through and between mineral grains (Eberhardt et al. 1998). It correlates well with the micro-cracking behavior involved in different stages of the stress–strain relation. A schematic illustration of the AE method used for the examination of micro-crack development in a rock specimen under loading is shown in Fig. 1.

Fig. 1
figure 1

Illustration of transient elastic wave generation and acoustic emission (AE) characteristics during compressive loading of a rock specimen (reproduced from Zhao et al. 2013)

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The AE signal recorded by the AE transducer is first amplified in a pre-amplifier and then transferred to a data logger and subsequently compute for analysis. A threshold value is usually applied to the recorded AE data to filter out the background noises. AE parameters, such as (transient or accumulated) AE count and AE hit, have been widely used to correlate the stress–strain relation with the micro-cracking process in the rock specimen (Eberhardt et al. 1999; Lockner 1993; Scholz 1968a). In addition, some waveform parameters involved in the generation of an AE event, such as ring-down count, energy, peak amplitude, rise-time, and event duration, also provide useful information to further elucidate the micro-cracking mechanisms associated with the macroscopic deformation and failure of rocks (He et al. 2010; Zhao et al. 2014). In general, one signal received by a transducer that exceeds the threshold is termed as one hit. One signal received by at least four transducers is termed as one event. The oscillation number of a pulse signal crossing the threshold is the AE count (short for AE ring-down count). The definitions of these AE parameters illustrated in Fig. 1 can also be referred to in Eberhardt et al. (1998).

The AE monitoring technique has been widely and successfully used in recent years to investigate the brittle failure and the associated micro-cracking behavior of various rock types (see Table 1). For a meaningful comparison of previous studies, the collected test data in Table 1 are exclusively based on compressive loading tests on cylindrical specimens, while test data of other specimen shapes are not included. The reviewed rock specimens generally have a height-to-diameter ratio of 2 to 2.5, with the diameter ranging from 20 to 75 mm. The number of sensors used in these studies ranges from one to 32, while four and eight are the most common. Some advanced analysis methods involving AE monitoring have also been used in rock mechanics, including moment tensor inversion, source location, b-value analysis, and fractal characteristics.

Table 1 Summary of recent acoustic emission (AE) studies on cylindrical rock specimens under compressive loading in laboratory tests
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Thermal damage is a factor which significantly affects the rock strength and deformation behavior (Liu et al. 2017; Peng et al. 2016a, b; Rong et al. 2018a, b; Sirdesai et al. 2017a, b, c, 2018a, b). The mechanical behavior and AE characteristic of rocks are also greatly influenced by the specimen size (Hawkins 1998). The combined influences of thermal damage and specimen size on the physical and macroscopic mechanical behavior of a fine-grained marble have recently been experimentally investigated by Rong et al. (2018c). Their results show that the thermal damage and specimen size greatly influence the physical and mechanical properties, such as P-wave velocity, micro-crack density, stress–strain curves, rock strength, Young’s modulus, and failure mode. The previous experimental studies on the effects of thermal damage and specimen size on the performance of rocks are comprehensively reviewed in their study, which will not be presented here. Interested readers can refer to the paper for more details. In the present study, the AE characteristics of a fine-grained marble with different thermal damages and specimen sizes are investigated. The results of AE parameter, b-value evolution, and source location are examined and analyzed.

Experimental design

Experimental setup

The marble studied in this study is a fine-grained metamorphic rock. It was collected from a mine located in Pingnan City of Fujian Province, China, which is the same as that investigated by Rong et al. (2018c). It is mainly composed of dolomite, accounting for 96.0% of its total volume, with small amounts of calcite and albite. It has a crystalloblastic texture and massive structure. The texture is relatively isotropic. No visible fractures can be found in the rock sample; however, some dark dykes are developed inside the sample. The grain size of the fine-grained dolomitic marble ranges from 0.5 to 1.0 mm and the porosity is about 1.8%.

Cylindrical specimens with a length-to-diameter ratio of 2 were prepared. Four diameters are associated with these prepared specimens, including 25, 50, 75, and 100 mm. The procedure for thermal treatment is the same as that used by Rong et al. (2018c). A furnace was used to heat the specimens to different temperatures (i.e., 25, 200, 400, and 600 °C), with a heating rate of 10 °C/min. After reaching the predetermined temperature, the specimens were kept in the furnace for 4 h and then taken out to cool down to room temperature naturally. When the specimen was heated to a higher temperature, such as 800 °C, the integrity of the specimen was completely destroyed and it could be broken by hand. Hence, the predetermined temperatures in this study have been limited to a maximum value of 600 °C.

In all uniaxial compression tests, the AE information was recorded using AE detection model PCI-2 of the DISP series manufactured by the American Physical Acoustics Corporation. All uniaxial compression tests were loaded using axial displacement-controlled loading at a rate of 0.075 mm/min. Four AE piezoceramic transducers with a resonance frequency range of 100 to 400 kHz were directly mounted onto the circumferential surface of the specimen. As shown in Fig. 2, two AE transducers (1# and 2#, 3# and 4#) were treated as a group and installed symmetrically in a plane at about a quarter of the height of the specimen. An orthogonal layout of the two groups of transducers provided good coverage of the specimen volume. To achieve a satisfactory acoustic coupling, a thin layer of Vaseline was applied at the interface between the specimen surface and the AE transducers (Pei et al. 2013; Guo et al. 2015; Zhang et al. 2015b; Zhao et al. 2013)Two loops of rubber band with width comparable to the AE transducer diameter was used to fix the transducers. To check the coupling between AE transducers and the specimen surface, pencil lead fracture tests were conducted before AE monitoring (Guo et al. 2015; Xiong and Wong 2017). Each AE transducer was calibrated to have a minimum amplitude of 95 dB.

Fig. 2
figure 2

Arrangement of AE transducers (1#, 2#, 3#, and 4#) attached to the cylindrical surface of specimens of various dimensions

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The sensitivity of the AE test is, to a large extent, controlled by the gain and threshold of the system (Eberhardt et al. 1998). The signals are pre-amplified for an effective detection of small AE signals induced from micro-cracking in the rock specimen during loading, and the gain is a measure of the amplification provided by the system. On the other hand, the threshold is used to filter out small signals associated with background noise. Therefore, proper choice of these two parameters is important for analyzing AE characteristics. Based on the literature review shown in Table 1, a gain within the range of 20 to 60 dB is normally used in rock tests. In our study, the gain value is set to 40 dB in the pre-amplifier. Two types of thresholds in the units of dB or V are usually used, as shown in Table 1. The threshold in the unit of V can be converted to that in the unit of dB by using the following equation

$$ tre(dB)=20\log \left(\frac{tre(V)}{10^{-7}}\right)- pre, $$
(1)

where tre(dB) and tre(V) are the thresholds in the units of dB and V, respectively, and pre is the gain value of the pre-amplifier in the unit of dB.

Based on the above, the threshold of 0.1 V in Table 1 corresponds to a threshold value of 60 dB. Therefore, the threshold used in previous AE studies ranges from 30 to 65 dB. In this study, the threshold was set to be 45 dB. As shown in later sections, the assigned gain and threshold values are capable of capturing the AE characteristics of rock specimens of different diameters and treatment temperatures. Full waveform data were sampled at a rate of 2 MHz.

AE data analysis

In this study, the AE parameters, including AE counts, AE hits, AE hit rate, AE energy, and waveform data were recorded during the uniaxial compression tests. To have a better understanding of the combined influences of thermal damage and specimen diameter on the AE characteristics, two analyses based on b-value and source location of AE activities were conducted. In the following sub-sections, the principles of b-value analysis and source location will be introduced.

b-Value

In the field of earthquake seismology, it is generally acknowledged that events of large magnitude occur less frequently as compared with those of small magnitude. Based on the Gutenberg and Richter relationship (Gutenberg and Richter 1942), the b-value can be defined as the log-linear slope of the frequency–magnitude distribution. Because the peak amplitude of AE signals is closely related to the magnitude of the fracture, the b-value is considered as an effective index for evaluation of the fracture process (Mogi 1962; Scholz 1968b). The b-value changes accordingly with the different stages of fracture growth and it has been widely used in recent years to estimate the development of the micro-cracking process in rock mechanics (Kim et al. 2015; Lei et al. 2004). The following equation is generally used to determine the b-value as

$$ logN=a- bM, $$
(2)

where M is the Richter magnitude of events, which is basically proportional to the logarithm of the maximum amplitude Amax recorded in a seismic trace, N is the incremental frequency (i.e., the number of events with magnitudes in the range of M ± ΔM/2), and a and b are empirical constants. The parameter b denotes the widely used b-value.

The b-value can be used, to some extent, to reflect the micro-cracking intensity in the material. In general, a high b-value corresponds to a low micro-cracking rate. On the contrary, a low b-value means that a large amount of micro-cracks is developed at this stage. In this study, the variation of b-value with the normalized axial stress is examined to interpret the micro-cracking process in the rock specimen. An average b-value is calculated using the dataset recorded in the four AE transducers to minimize the error.

Source location

The AE source location is used to retrieve the location of a fracture source through comparing the arrival time of the same P-wave received by different transducers. The evolution of micro-cracks inside a rock specimen can be reflected using the method of source location. The basic principle of the non-linear iterative algorithm in this study is that the location of the fracture source is determined through regressive computation for the time difference of the AE signal arriving at different transducers. The arrival time of each AE event is automatically obtained by the software (AEWIN for PCI-2 software version 1.30). According to the user’s manual, the arrival time is defined as the time when the input signal first exceeds a pre-set threshold and is recorded to have an accuracy of ± 0.05 μs. It is generally assumed that the velocity in the material is uniform. Hence, the P-wave velocity is set to be a constant throughout the entire course of a compression test. In this study, the P-wave velocity was set to be 4.8 km/s (Rong et al. 2018c). However, it should be noted that the velocity field is generally anisotropic, induced from the progressive deformation process. Thus, the constant velocity assumption inevitably produced errors. Based on the least squares method, the AE source residual is minimized by continuously improving the AE source to estimate the AE source position. The iterative process of the AE source location is automatically conducted in the AEWIN software.

The distance between the ith transducer and AE source is estimated as

$$ \sqrt{{\left(\mathrm{x}-{\mathrm{x}}_{\mathrm{i}}\right)}^2+{\left(\mathrm{y}-{\mathrm{y}}_{\mathrm{i}}\right)}^2+{\left(\mathrm{z}-{\mathrm{z}}_{\mathrm{i}}\right)}^2}={\mathrm{v}}_{\mathrm{p}}\left({\mathrm{t}}_{\mathrm{i}}-\mathrm{t}\right), $$
(3)

where (x, y, z) are the estimated coordinates of the AE source, (xi, yi, zi) are coordinates of the ith transducer, t is the estimated initiation time of the AE source, ti is the observed arrival time at the ith transducer, and vp is the P-wave velocity in the rock specimen.

The square of the deviation, Q, is expressed as

$$ \mathrm{Q}=\sum \limits_{\mathrm{i}=1}^{\mathrm{N}}{\left[\sqrt{{\left(\mathrm{x}-{\mathrm{x}}_{\mathrm{i}}\right)}^2+{\left(\mathrm{y}-{\mathrm{y}}_{\mathrm{i}}\right)}^2+{\left(\mathrm{z}-{\mathrm{z}}_{\mathrm{i}}\right)}^2}-{\mathrm{v}}_{\mathrm{p}}\left({\mathrm{t}}_{\mathrm{i}}-\mathrm{t}\right)\right]}^2, $$
(4)

where N is the number of transducers.

The minimum value of the square of the deviation (Q) can be obtained by iterative computations using the least squares method. Three different iteration algorithms, namely the Gaussian method, the modified Gaussian method, and the downhill simplex method, are available for the computation. In general, the minimum number of transducers forming an array is determined by the spatial dimension to be measured. For a cylindrical rock specimen, at least four transducers are required to locate an AE source. As studied by Labuz et al. (1988), four transducers can determine the locations of AE sources with an estimated error of less than 5 mm.

Experimental results

The AE characteristics of rock specimens with different diameters (25, 50, 75, and 100 mm) and different degrees of thermal damage (25, 200, 400, and 600 °C) are compiled and discussed in this section. The obtained AE parameters are first examined, followed by an interpretation of the accumulated AE parameters with temperature. The variation of b-value with the normalized axial stress is then analyzed and discussed. Finally, the micro-cracking evolution using the source location method is examined.

AE characteristics of rock specimens

Specimens with a diameter of 25 mm

The stress–strain relations and the corresponding variations of accumulated AE counts and AE hits with the axial strain for specimens with a diameter of 25 mm are presented in Fig. 3. The results reveal that the evolutions of accumulated AE counts and AE hits can correlate well with the stress–strain relations. For the specimen without thermal damage (25 °C) (see Fig. 3a), almost no AE signals can be recorded in the initial deformation stage. The AE signals initiate at a stress level about 0.4 times the peak strength and multiply at about 0.8 times the peak stress. The accumulated AE counts show a similar trend for specimens with thermal damage (see Fig. 3b–d). However, with the increase in the treatment temperature, the AE signals in the initial stage become more prominent, especially for the specimen thermally treated at 600 °C. This is mainly attributed to more micro-cracks being created at the higher treatment temperature. These initially developed micro-cracks will, hence, become the preferential cracking sites, leading to more dramatic AE activities in the initial deformation stage.

Fig. 3
figure 3

Evolutions of accumulated AE counts and AE hits with axial strain for rock specimens with 25 mm diameter after thermal treatment with different temperatures. a Room temperature (25 °C), b 200 °C, c 400 °C, and d 600 °C

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Occasional stress drops are observed on the stress–strain curves in Fig. 3 (see the red circles). The corresponding AE signals recorded at this stage also show a drastic increase. This phenomenon is generally attributed to the dislocation or breakage of minerals or grain boundary movement in the rock specimen during loading. The sudden slip or breakage of minerals along the grain boundaries will induce a transient stress relaxation, which will result in a sudden stress drop in the stress–strain curve and lead to a large amount of AE activities.

Specimens with a diameter of 50 mm

Figure 4 shows the stress–strain relations and the corresponding variations of accumulated AE counts and AE hits with the axial strain for specimens with a diameter of 50 mm. The results are considerably comparable with those of specimens with a diameter of 25 mm. The evolutions of accumulated AE counts and AE hits show good correlation with the stress–strain behavior. Few AE signals are detected in the initial deformation stage and the accumulated AE counts start to multiply at a stress level about 0.8 times the peak strength. Similarly, the AE signals in the initial stage will become more prominent with the increase in the treatment temperature. In addition, the phenomenon of “sudden stress drop” can also be observed in the pre-peak or post-peak deformation of the specimen, which corresponds to a quick AE signal increase. These points denote the dislocation or breakage of minerals or grain boundary movement in the rock specimen during loading.

Fig. 4
figure 4

Evolutions of accumulated AE counts and AE hits with axial strain for rock specimens with 50 mm diameter after thermal treatment with different temperatures. a Room temperature (25 °C), b 200 °C, c 400 °C, and d 600 °C

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On the other hand, more accumulated AE counts and AE hits of specimens with a diameter of 50 mm can be observed when compared with those of specimens with a diameter of 25 mm. The numbers of these two parameters for specimens with a diameter of 50 mm are about 2 to 3 times greater than those for specimens with a diameter of 25 mm.

Specimens with a diameter of 75 mm

The stress–strain relations and the corresponding variations of accumulated AE counts and AE hits with the axial strain for specimens with a diameter of 75 mm are shown in Fig. 5. The results reveal that, similar to the results of specimens with diameters of 25 and 50 mm, the evolutions of accumulated AE counts and AE hits show good correlation with the micro-cracking process in the rock specimens (i.e., stress–strain behavior). The AE signals initiate at a stress level about 0.3 to 0.4 times the peak stress and multiply at a stress level about 0.7 to 0.8 times the peak stress. A great increase of AE signals in the initial deformation stage is also observed for the rock specimen thermally treated under the temperature of 600 °C. Meanwhile, the “sudden stress drop” phenomenon can also be observed for specimens under the temperatures of 25, 200, and 400 °C, which denotes the dislocation or breakage of minerals or grain boundary movement in the rock specimen.

Fig. 5
figure 5

Evolutions of accumulated AE counts and AE hits with axial strain for rock specimens with 75 mm diameter after thermal treatment with different temperatures. a Room temperature (25 °C), b 200 °C, c 400 °C, and d 600 °C

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When compared with the results of specimens with a diameter of 50 mm, though the number of accumulated AE counts shows a slight decrease for specimens with a diameter of 75 mm, the AE hits increases two- to three-fold. It is also indicated that more AE signals will be generated in large specimens as compared with small specimens.

Specimens with a diameter of 100 mm

Figure 6 presents the stress–strain relations and the corresponding variations of accumulated AE counts and AE hits with the axial strain for specimens with a diameter of 100 mm. It is seen that the recorded AE parameters correlate well with the micro-cracking process in the rock specimen during loading. The evolution of AE parameters can divide the rock deformation into several stages, which is in good agreement with the progressive failure in the stress–strain curve. Similar to the specimens with other diameters, the AE signals in the initial deformation stage will become more prominent with the increase in the treatment temperature for specimens with a diameter of 100 mm. In addition, the “sudden stress drop” phenomenon, which denotes the dislocation or breakage of minerals or grain boundary movement in the rock specimen, can also be observed (see the red circles in Fig. 6). The numbers of accumulated AE counts and AE hits of specimens with a diameter of 100 mm show a significant increase when compared with those of specimens with other diameters. The results reveal that more AE signals will be generated in large specimens as compared with small specimens.

Fig. 6
figure 6

Evolutions of accumulated AE counts and AE hits with axial strain for rock specimens with 100 mm diameter after thermal treatment with different temperatures. a Room temperature (25 °C), b 200 °C, c 400 °C, and d 600 °C

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Relationships between accumulated AE parameters with temperature

This section examines the variations of accumulated AE parameters, such as AE counts, AE hits, and AE energy, in response to the change of treatment temperature. To have a fair comparison of the test results, the AE parameters corresponding to the peak strength point in the stress–strain curve are examined for all the specimens.

Figure 7 presents the variations of accumulated AE counts with the treatment temperature. The details are summarized in Table 2. The results reveal that the accumulated AE counts generally decrease as the treatment temperature gradually increases. This is because more thermally induced micro-cracks will be generated inside the rock specimen with the increase in the treatment temperature. These initially generated micro-cracks will weaken the rock (i.e., lower the rock strength and Young’s modulus) (Rong et al. 2018c). Fewer AE signals (i.e., micro-cracking) will be detected upon failure of the specimen, leading to a decrease of the number of accumulated AE counts with increasing temperature.

Fig. 7
figure 7

Variation of different AE parameters with the treatment temperature

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Table 2 Calculated AE parameters of rock specimens with different diameters and different treatment temperatures
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The variations of accumulated AE hits with the treatment temperature are also shown in Fig. 7. It is seen that, with the increase in the treatment temperature, the accumulated AE hits generally show a decreasing trend, which is mainly associated with the initial thermally induced micro-cracks inside the rock specimen.

It is generally accepted that the energy of an AE signal represents a part of the energy released in the source. The parameter is considered to be representative of the intensity of an AE event and has become widely used to study the brittle failure of rocks (Keshavarz et al. 2010; Kong et al. 2016; Zhang et al. 2015a). In this study, the accumulated AE energy corresponding to the peak stress of rock specimens is investigated. Figure 7 also presents the variations of accumulated AE energy in response to the change of treatment temperature. The results reveal that the accumulated AE energy generally shows a decreasing trend with the increase in the treatment temperature. The results of accumulated AE energy are in good agreement with those of accumulated AE counts and hits as described above.

Variation of b-value along rock deformation

The b-value of rock specimens with different diameters and different degrees of thermal damage is examined in this section. As shown in Fig. 8, the b-value generally shows a decreasing trend with the increase in the normalized axial stress. The b-value can represent the intensity of AE events in the material and a low b-value corresponds to intensive AE activities. It is indicated that the AE signals are not prominent in the initial deformation stage and gradually initiate and propagate upon approaching the peak stress.

Fig. 8
figure 8

Variations of the b-value of specimens possessing different degrees of thermal damages with the normalized axial stress. Specimen diameters of: a 25, b 50, c 75, and d 100 mm

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The results shown in Fig. 8 also reveal that the b-value generally increases with the increase in the treatment temperature. The AE activities in rock specimens with lower treatment temperature are more intensive than those with higher treatment temperature. This phenomenon is mainly due to the greater number of micro-cracks residing inside the rock specimen with higher treatment temperature. These initially developed thermal micro-cracks will weaken the rock specimen and lead to a less intensive micro-cracking (i.e., AE events) when the specimen is mechanically loaded. The results are in good agreement with the observations in uniaxial compression tests (Rong et al. 2018c).

In addition, the b-value is sometimes found to drop suddenly and then recover to a higher value quickly (see the solid circles in Fig. 8), which denotes drastic AE activities at that stage. By comparing the deformation process of rock specimens (i.e., Figs. 3, 4, 5, and 6), it is seen that these events correspond well with these “sudden stress drops” in the stress–strain curve. Hence, the phenomenon is mainly attributed to the dislocation or breakage of minerals or grain boundary movement in the rock specimen.

Micro-cracking evolution

The real-time source location method can be used to determine the micro-cracking evolutions of rock specimens during loading, which provides a better visualization for interpretation of the micro-cracking process. As two examples, Figs. 9 and 10 present the evolutions of accumulated AE events in the rock specimens at different deformation stages for a specimen with a diameter of 50 mm and no thermal damage (25 °C) and for a specimen with a diameter of 100 mm and treated under the temperature of 600 °C, respectively.

Fig. 9
figure 9

Locations of accumulated AE events in a rock specimen (50 mm diameter, no thermal damage) at different deformation stages. a Complete stress−strain curve associated with the evolution of AE counts (the numbers on the stress−strain curve denote different stress levels); b spatial distribution of accumulated AE counts in the specimen (numbers 1 to 8 correspond to stresses at 10.3, 19.7, 30.1, 49.5, 58.6, 55.6, 60.3, and 29.7 MPa, respectively); c experimentally observed splitting fracture approximately parallel to the loading direction

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Fig. 10
figure 10

Locations of accumulated AE events in a rock specimen (100 mm diameter, thermally damaged under the temperature of 600 °C) at different deformation stages. a Complete stress−strain curve associated with the evolution of AE counts (the numbers on the stress−strain curve denote different stress levels); b spatial distribution of accumulated AE counts in the specimen (numbers 1 to 8 correspond to stresses at 5.1, 10.5, 15.2, 17.6, 20.8, 16.4, 13.9, and 10.3 MPa, respectively); c experimentally observed shear fracture in the specimen

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As shown in Fig. 9, the AE counts gradually initiate and multiply as the specimen is loaded to failure. The AE events cloud will finally form a general macroscopic failure plane in the specimen. For the rock specimen with a diameter of 50 mm and without thermal damage, the formed failure plane shown in the AE counts cloud is generally oriented in the axial direction, representing splitting failure (see the blue dashed line). This result is in good agreement with that observed in laboratory tests, as shown in Fig. 9c. It is indicated that the spatial distribution of AE events correlates well with the failure plane observed in uniaxial compression tests.

The results shown in Fig. 10 also reveal that the interpreted failure plane in the AE counts cloud is comparable with that observed in the uniaxial compression test. For the rock specimen with a diameter of 100 mm and treated under the temperature of 600 °C, the failure is found to be associated with a single shear failure plane, which is different from that of the specimen with a diameter of 50 mm and without thermal damage. This observation is similar to previous laboratory test results on thermally damaged rocks (Guo et al. 2015; Kong et al. 2016).

It is also seen from Fig. 10 that the number of located AE counts for the rock specimen with a diameter of 100 mm and treated under the temperature of 600 °C is lower than that for the specimen with a diameter of 50 mm and without thermal damage. This observation is in good agreement with the results from AE parameters studies mentioned above.

It is well known that the results of AE source location is affected by many factors, such as source location algorithm, determination of arrival time, setting of wave velocity, inhomogeneity of the specimen, specimen size, actual position of the transducer, coupling agent, and ambient noise. To minimize the results error of the AE source location, special attention should be paid to the above-mentioned factors. As pointed out by Labuz et al. (1988), at least four AE transducers should be used to determine the locations of AE sources for a cylindrical specimen. When four AE transducers are used, there is no degree of freedom of the AE location system and only a unique set of solutions can be achieved. However, by comparing the located AE counts with the actual failure pattern, a result error of 10 mm is estimated for the AE source location.

Conclusions

This paper experimentally investigates the acoustic emission (AE) characteristics of a fine-grained marble with different thermal damages and specimen sizes. The results in this study reveal that the AE technique provides useful information on the micro-cracking behavior involved in the deformation process of rocks. Based on the test results, the following conclusions can be drawn.

  1. 1.

    It is seen from the variation of AE counts in response to the rock deformation that the stress−strain relation can be divided into several stages. The AE activity is rare in the initial deformation stage, which then multiplies at a stress level about 0.7 to 0.8 times the peak stress. However, the AE activities in the initial deformation stage are found to be more prominent in the rock specimens which have been thermally treated.

  2. 2.

    The AE parameters, such as accumulated AE counts, AE hits, and AE energy, are found to generally decrease with the increase in the treatment temperature. The b-value generally decreases in the deformation process and correlates well with the stress−strain relation. The b-value is also found to generally increase with the increase in the treatment temperature, which is mainly attributed to the initially generated thermal micro-cracks in the rock specimen. The spatial distribution of AE events is in considerable agreement with the failure plane observed in laboratory compressive tests.