The Mechanism of the Kaiser Effect in Phyllite under Indirect Tensile Loading

Determination of in-situ stress serves as an important step in the design and construction of civil and mining projects, among others. Conventional methods of the in-situ stress measurement are timeand cost-intensive. Therefore, the application of low-cost yet rapid methodologies for in-situ stress evaluation has been increasingly regarded by researchers. The Kaiser effect-based acoustic emission method is one of such novel approaches to the in-situ stress evaluation. Not only the point at which the Kaiser effect occurs, but also the mechanism of the Kaiser effect is of paramount importance. In this research, acoustic emission tests were conducted on phyllite rock samples under Brazilian tensile loading to collect a variety of acoustic data, including the amplitude, rise time, count, duration, and energy. Then, the Kaiser effect point was determined using the collected data on acoustic parameters, with its occurrence mechanism investigated. In addition, mathematical transformations were adopted to transform the acoustic signal from the time domain to the frequency domain, where the peak frequency was analyzed. The results of the RA/AF ratio analysis showed that the acoustic emission was sourced from tensile micro-cracks. Moreover, the high level of energy indicated a high intensity of crack formation at the Kaiser effect point. The large number of received hits showed that the count of generated cracks increases abruptly within the range of the Kaiser effect. In addition, the obtained high value of the peak frequency implied that the crack growth rate is high at the Kaiser effect point.


Introduction
Engineering design of structures in rocks is impractical without a knowledge of the stress field. Accordingly, during the past 70 years, many attempts have been made to present proper methods for in-situ stress measurement. Acknowledging the high cost and time-intensiveness of the conventional methods (most of which are insitu methods, including hydraulic fracturing and the overcoring method), the tendency toward the use of lowcost yet fast methods has increased significantly. The acoustic emission method is a low-cost yet rapid methodology for such a purpose. With the help of the acoustic emission method, one can utilize the Kaiser effect to recover the stress memory in such materials as rocks. The Kaiser effect was coined after a German researcher, Joseph Kaiser, when he performed a series of tests on small samples of metal, wood, and sandstone in 1950. Since then, this effect is known under the same title (Kaiser, 1950). In the laboratory, the Kaiser effect is induced by subjecting the rock samples to cyclic loading. The Kaiser effect is defined as lack of acoustic parameters prior to achieving the previously applied level of stress to the sample. As seen on Figure 1, the acoustic parameters follow increasing trends through the first loading cycle. Following the unloading and upon starting the second loading cycle, the acoustic parameters exhibit no increase until the first-cycle maximum load is reached. As that maximum load is reached, the acoustic parameters increase either abruptly or gradually, indicating what we know as the Kaiser effect. These acoustic parameters include the energy level, count, rise time, amplitude, etc.
For a number of years, the Kaiser effect has been studied for evaluating in-situ stresses although no remarkable success was achieved, with different researchers supporting and criticizing the approach. However, recent research works, especially those performed in Ja-Rudarsko-geološko-naftni zbornik i autori (The Mining-Geology-Petroleum Engineering Bulletin and the authors) ©, 2022, pp. 15-31, DOI: 10.17794/rgn.2022.3.2 pan, Australia, Canada, China, and Belgium, have reported promising findings, highlighting the possibility of stress tensor estimation from different samples of oriented core. Results of these studies have boosted the chances of applying this method in estimation in-situ stress, so that a number of projects have used it to estimate the in-situ stress in practice. The application of AE is divided into three groups: prediction and estimation, monitoring and performance assessment, and detection. The use of AE methods, among other laboratory or insitu methods, is very fast and accurate, and by only installing specific sensors with data logging equipment, it has been able to process and analyze data online and remotely (Khoshouei and Bagherpour, 2019).
Montonon and Hardy conducted a comprehensive review of the studies performed on the Kaiser effect in the field of geological materials. They further investigated the effects of sample medium, test method, multiple stress states, etc. Based on their results, they introduced the Kaiser effect as a simple and low-cost approach to measuring the in-situ stress (Montoto and Hardy, 1991). Seto et al. investigated the crack propagation in the rock mass using acoustic emission in the laboratory (Seto et al., 1996). Seto and Villaescua used the acoustic emission method to evaluate the in-situ stress in a mine premise in Australia, and further compared the results to those of the overcoring method (Seto and Villaescusa, 1999). Lavrov stipulated that step-wise loading in three orthogonal direction differs from simultaneous stress application (Lavrov, 2001). Tuncay and Ulusay reported research on the balance between the Kaiser effect and the applied prestresses based on the results of in-lab tests (Tuncay and Ulusay, 2008). Kent and associates compared the acoustic emission method with other methods and showed that, although the rock type and the level of insitu stresses compared to the rock strength affect the success rate of the acoustic emission method, this methodology can still provide proper information about the in-situ stresses, especially where brittle deformation is encountered (Kent et al., 2002). Yuan and Li presented a theoretical and experimental study on the Kaiser effect in brittle rocks. They suggested that conventional experimental methods for Kaiser effect assessment with the help of acoustic emission must be modified to give more accurate results (Yuan and Li, 2008). Li et al. conducted an analytic and experimental study on the estimation of in-situ stress using the Kaiser effect. They showed that a large confining pressure in the rock mass can lead to large differences between the Kaiser effect stress obtained from the uniaxial loading tests in the laboratory and actual in-situ stress (Li et al., 2010). Nikkhah et al. evaluated the Kaiser effect using pattern recognition techniques (Nikkhah et al., 2011). Lehtonen et al. devised the Kaiser effect to estimate the stress. They reported that stress measurement using the acoustic emission method and the Kaiser effect can render successful when the approach is further supported by key geological information and other stress measurement methods (Lehtonen et al., 2012). Hsieh et al. showed that the crack formation and propagation process induces some changes in the stress pattern in the proceeding loading cycles when the pre-stress level reaches a higher level than that at the start of dilation in sandstone and ultramafic rocks, so that the acoustic emission commences way before reaching the previous maximum stress and hence no Kaiser effect is observed (Hsieh et al., 2015). More recently, Chen et al.   view, in brittle rocks, the acoustic emission is usually associated with microcrack propagation, while it is usually attributed to plastic displacement flow mechanism in formable rocks. It has been further confessed that, in geological materials with their multiple-crystal nature, the acoustic emission can be induced due to micro-scale displacements or macro-scale couplings, grain border shifts, or inter-grain and intra-grain fracture initiation and/or propagation (Hardy Jr, 2003).
Based on the theory of acoustic emission testing, a series of the acoustic emission signal parameters (e.g. count, rise time, amplitude, persistence time, and peak frequency) are usually used to describe the damage level of respective materials. Figure 2 depicts the parameters of acoustic emission for a signal.
According to the Japanese standard code of building materials, one can generally classify the sources of acoustic emission under two broad categories, namely tensile and shear cracks. This classification is based on two parameters, namely RA and AF. RA is the ratio of the rise time to peak amplitude of the signal, while average frequency (AF) is defined as the count ratio divided by the persistence time (Ohtsu and Tomoda, 2007).

2021).
Li and Xu checked the rock failure mechanism by monitoring the acoustic emission characteristics and micro-seismic activities (Li and Xu, 2021  The mechanism of the Kaiser effect differs in different rocks and under different tests. Generally speaking, in stressed rocks, the acoustic emission can be induced by microcracks and pore clogging, the development of microcracks, fracture formation in grain structure, shear rupture tension, phase conversions, and electric bursts (Hardy Jr and Leighton, 1984). From another point of   On the other hand, identification of the frequency spectrum of acoustic emission provides some key information regarding the formation of microcracks (Hou et al., 2021). Accordingly, one should transform the received signals from the time domain to the frequency domain -a task that can be handled using mathematical transformations. The b-value provides a measure of the count of weak events to strong events. Different fracture configurations produce different acoustic signals with different amplitude and frequency contents. In general, fracture amplitude and size are controlled by the energy released upon crack opening or displacement. Accordingly, small dis-placements generate low energy levels while large cracks and displacements produce higher energy levels (Liu, 2000). Aki proposed an equation based on statistical principles, where he weighed all recorded earthquakes equally to present a new methodology for determining the distribution of independent frequencies and magnitudes of earthquake events (Sagar et al., 2012). The method proposed by Aki is one of the methods for calculating b-value (Aki, 1965). This method is used to study the fracture process in rocks (Main et al., 1989;Shiotani, 2001). In the acoustic emission technique, the b-value is calculated from Aki's method for independent frequency using Equation (1) (Kyriazopoulos et al.,  2015). The b-value parameter is the logarithmic linear slope of the frequency-amplitude distribution of the acoustic emission. This parameter provides a scale for the distribution of acoustic emission amplitude and is a measure of the relative number of small and large acoustic emissions that indicate local fractures in stressed materials (Rao and Lakshmi, 2005). (1) Where: -the mean amplitude, a c -the threshold amplitude, e -Euler's number. The value of can be obtained from Equation 2: (2) Where: N A -the amplitude of acoustic events, N -the number of acoustic events. In this study, a Brazilian test was used to determine the tensile strength of the samples as well as acoustic diffusion tests. Tensile strength measurements for stone samples are done directly and indirectly, of which the Brazilian method is the most famous. These research studies were conducted in three time phases (Briševac et al., 2015). Carneiro first conducted research on the  Brazilian test (Carneiro, 1943). The formula presented is as follows: Where: -indirect tensile strength determined by the Brazilian test (MPa), F -applied load (kN), D -diameter of the tested sample (mm), t -thickness of the tested sample (mm). Then, in 1978, the International Society of Rock Mechanics presented its proposed method (ISRM, 1978). The research studies were conducted in the second phase between 1979 and 1991. The research was conducted in the second phase between 1979 and 1991, the most important of which were the research conducted by Lajtai, Pandey and Singh, and Newman and Bennett (Lajtai, 1980;Pandey and Singh, 1986;Newman and Bennett, 1990). In the third phase, researchers such as Lavrov et al., Wang et al., Kazareni, Lin and  The tested samples are made of phyllite. Phyllite is a foliated metamorphic rock rich in tiny sheets of sericite mica. It presents gradation in a degree of metamorphism ranging between slate and mica schist. The colour varies between black and gray to greenish-gray. The phyllite forms from pelitic sediments (shale and mudstone) at a slightly higher degree of regional metamorphism from slate (Haldar, 2020). Phyllite has good compressive and tensile strength for acoustic tests, which means that it either does not have a very low resistance to failure at low stresses, or it has such high compressive strength that the utilized apparatus does not have enough capability to induce and recover the stress (Kharghani et al.,  2021).
In this research, we begin by determining the Kaiser effect point through a parametric method followed by investigating all of the mentioned parameters and the mechanism of the Kaiser effect.

Methods
In this research, Brazilian loading tests were performed to measure tensile strength of the samples. The ultimate tensile strength of the samples was evaluated to measure the preloading stress, which is usually considered as a percentage of the ultimate strength. The tested rock samples were Phyllite rock, which has anisotropic behaviour, so the tensile strengths obtained were different. We herein performed the Brazilian tests. The testing apparatus is schematically shown in Figure 3.  Table 1 shows physical and mechanical properties of Phyllite. It should be noted that the experiments were performed according to the ISRM suggested method. Before performing the acoustic emission tests, laboratory tests were performed to determine some of the main mechanical characteristics of the rock sample intended for research.
Rock blocks were collected from the ground that did not experience much stress and the test samples were prepared by core extraction from rock blocks. Samples were collected from western Iran and the Sanandaj-Sirjan Formation. The most important characteristics of rock samples are anisotropic behaviour and brittle rock behaviour. The specification of rock specimens and the results obtained from Brazilian tests are presented in Table 2. Figure 4 shows the observed failure patterns of rock samples after the Brazilian tensile strength test.
The acoustic emission test was herein performed through the following steps: 1. The contact point of the acoustic emission sensor and the rock sample is made of couplant material and the AE sensors are attached to the sample and fixed to the sample with adhesive tape on both sides. Due to the dimensions of the sensors and the rock sample and the appropriate reception of source signals inside the sample, the sensors are embedded in the centre of the disk sample diameter. The sensors were connected to an acoustic data logger. Ensure that the sample surface is thoroughly polished and smooth. 2. Set the data logger configurations including the sampling frequency and other required parameters. 3. Mount the sample inside the Brazilian testing machine. Adjust the jaws of the testing machine on the sample. Use a spacer, if necessary. 4. Start loading and the data logger device simultane- ously. An acoustic emission test begins by subjecting the sample to a first loading cycle (pre-loading). In subsequent experiments, the value of preloading stress was selected at about 70 to 80% of the final strength to create a stress memory in the rock. Next, full unloading is performed and a second loading cycle is triggered immediately until the failure point is reached. In all stages, acoustic data is being collected, for further analyses, through two sensors installed on the disk samples. Based on the results of several tests, the threshold was determined at 45 dB. This threshold was set to attenuate the ambient noise and the noise contents associated with the testing machine itself and the sample-machine contacts, not to mention other possible sources of noise.

Results and Discussion
In this research, the Kaiser effect point was evaluated using the amplitude and rise time. Figure 6 shows the plot of stress, amplitude and rise time versus time for the QP1 sample. As indicated on the figure, no increase is observed in neither the amplitude nor the rise time prior to 31.3 s. At this time, however, abrupt increases occurred in the level of acoustic parameters, indicating the occurrence of the Kaiser effect at this time.
Similar to Figure 6, Figure 7 refers to the sample QP2. Considering Figure 7, it is evident that the acoustic data remained almost unchanged until 123.6 s, at which time an abrupt increase in the data occurred, indicating the occurrence of the Kaiser effect. onstrates the plots of applied stress, amplitude, and rise time versus time for the sample QP3. Based on the figure, the Kaiser effect occurred at 46.5 s for this sample. According to Figure 9 and 10, the Kaiser effect for samples 4 and 5 occurred in 52.8 and 60 seconds, respectively.
According to the Japanese standard code of building materials, a high RA coupled with a low AF describes acoustic emission events sourced from shear microcracks, while a low RA coupled with a high AF characterizes the acoustic emissions generated upon tensile microcracks (Ohtsu and Tomoda, 2007). Therefore, the RA/AF ratio provides a good criterion for characterizing the source of an acoustic emission event. As seen in Figure 11 (referring to the sample QP1), the value of RA/ AF ratio is low at the time of the Kaiser effect (i.e. 31.3 s), implying that the effect is a result of some tensile crack formation. The same state is seen in Figures 12 to 15 where the Kaiser effect occurs at 123.6, 46.5, 52.8 and 60 s, respectively, reflecting the dominant contribution of tensile cracks into the Kaiser effect. The crack pattern from which acoustic emission is originated can be obtained from the characteristics of the distribution of peak frequency of the acoustic emission signals (Hou et al., 2021). Peak frequency is a popular parameter in the analysis of acoustic emission signals. As mentioned earlier, this parameter can be assessed by transforming the signal from the time domain to the fre-quency domain. Once finished with importing the data from the data logger into the software, mathematical transformations were applied to different hits associated with the samples. The peak frequency was considered as a required parameter for analyzing the mechanism of the Kaiser effect, with the relevant data extracted. Figures  16 through 18 to 18 shows the intensity of the corresponding peak frequency. As is evident in Figure 16, in the hit no. 342 for the sample QP1, the maximum intensity occurred at a frequency of 18 kHz. Moreover, Figure 17 and 18 show that the peak frequencies for the hits no. 497 and 802 of the samples QP2 and QP3 are 31 kHz and 22 kHz, respectively. The frequency range of acoustic emission signals varies for different materials and sources. For example, for metals it is between a few kilohertz to several megahertz, for composites it is between a few kilohertz to a few hundred kilohertz, and for rocks it is between a few hertz to a few hundred kilohertz (Hou et al., 2021). The peak frequency distribution provided for the acoustic emission signals of the phyllite specimens varies between 0 and 350 kHz. It is stated that high frequencies are associated with tensile cracks and low frequencies are associated with shear cracks (Shengxiang et al., 2021). As can be seen, due to the high frequencies in the Kaiser effect range, tensile cracks are the main source of the Kaiser effect. Figures 19 through 23 show the obtained peak frequencies for all hits upon the acoustic emission tests on the samples QP1 through QP3, respectively. As the figures indicate, an increase occurs in the number of hits with relatively high (> 200 kHz) peak frequencies within the range of the Kaiser effect. The peak frequency is high at the time of the Kaiser effect. This is related to the increase in crack propagation rate, which means that a higher peak frequency reflects a higher crack propagation rate. It is stated that high frequencies are associated with tensile cracks and low frequencies are associated with shear cracks (Bak et al., 2013;Shengxiang et al., 2021). In this research, high frequency at the time of the Kaiser effect shows that the effect is sourced from tensile cracks. Finally, the increase in the number of hits within the range of the Kaiser effect reflects an increase  in the number of cracks in that range (Moradian et al., 2016).
The energy level is an important parameter for investigating the mechanism of the Kaiser effect (Sause, 2016). In this research, the unit for energy level was eu. Developed by the Vallen Company, an eu is equivalent to 10 -12 J. the energy level is directly related to the intensity of crack formation in the sample (Bak et al., 2013). Figures 24 through 28, the energy level increased significantly at the time of the Kaiser effect, reflecting the high intensity of crack formation at this point, as explained earlier.

As shown in
The value of the b-value parameter is examined to analyze and study the mechanism of occurrence of the Kaiser effect. Regarding the b-value, the higher this parameter, the smaller the magnitude of the acoustic emission, and vice versa (Ohtsu and Tomoda, 2007). Moreover, previous studies have shown that b-values below 1 signify large failure events in the samples (Sagar et al., 2012). Figures 29 through 33 indicate the b-values for the samples QP1 through QP5, respectively. As is evident in Figure 29, at the time of the Kaiser effect, the b-value is 1.15. As detailed previously, the fact that this value exceeds 1 show the occurrence of microcracks, while the relatively low value of this parameter reflects the largeness of the associated acoustic emission and indicates large cracks that are visible to the naked eye. As can be seen, the bvalue related to the failure point of the sample, which includes large cracks, is less than one. Based on Figures 30  through 33, the b-values are 1.05, 1.10, 1.04 and 1.09 at the time of the Kaiser effect, respectively. Therefore, the corresponding samples (i.e. QP2 through QP5) suffer from microcrack-induced acoustic emissions of high intensity. Table 3 summarizes the results of investigating the mechanism of the Kaiser effect. Figure 34 shows the values obtained for different parameters at the Kaiser effect point. As shown in Figure  34, the sample QP1 has low energy, RA/AF, and higher b-value in the Kaiser effect. The sample QP2 has high energy, RA/AF and low b-value, and the sample QP3 has moderate values in all parameters. The sample QP4 has lower magnitude for all parameters than the others and the sample QP5 has low energy and a moderate bvalue and RA/AF ratio.

Conclusions
The following conclusions were drawn based on the acoustic emission tests performed on three samples of phyllite rock.
Different rocks exhibit different mechanisms of the Kaiser effect with different sources. Based on the acoustic emission parameters obtained for the phyllites under the Brazilian tensile tests, the Kaiser effect was found to be a result of tensile stresses.
Regarding the obtained values of peak frequency, it was discovered that the rate of crack propagation is higher in the range of the Kaiser effect. In addition, the relatively high peak frequencies confirmed the tensile nature of the source of Kaiser effect. The increase in the energy level at the Kaiser effect point show that the crack formation intensity is higher at this point rather than other points. The increase in the number of hits in the vicinity of the Kaiser effect point indicated the higher count of cracks formed in this region rather than other ranges.
The low b -value at the Kaiser effect point showed that the acoustic emission intensity is higher at the Kaiser effect point. However, the obtained b-values were above 1, indicating that the acoustic emission was sourced from microcracks.