Investigation on the Effect of Dynamic Frequency on Fracture Evolution in Preflawed Rock under Multistage Cyclic Loads: Insight from Acoustic Emission Monitoring

Key Laboratory of Neotectonic Movement and Geohazard, Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China Beijing Key Laboratory of Urban Underground Space Engineering, Department of Civil Engineering, School of Civil & Resource Engineering, University of Science & Technology Beijing, Beijing 100083, China Architectural Engineering College, Guizhou Minzu University, Guiyang 550025, China


Introduction
Many types of loads applied to rock mass are cyclic essentially, including the human-induced engineering loads and the environmental loads. Cyclic rock mechanical behaviors involve many kinds of rock engineering, such as mining engineering, oil-gas development engineering, underground excavation engineering, pumped storage hydroelectricity engineering, and oil and gas storage engineering [1]. On the stress disturbance on rock damage accumulation, the disturbed loads are usually equivalent to cyclic/fatigue loads. Considerable efforts have been performed to investigate the cyclic loading on rock mechanical properties. Among these studies, the impacts of cyclic loading on rock structure deterioration were widely studied [2][3][4][5][6]. The interactions between the human activities and rock engineering constructions highlight the importance of investigating the cyclic behavior of rock. When rocks experience cyclic and especially fatigue loading, several different kinds of dynamic disaster (e.g., rock blasting, collapse, and landslides) phenomena occur along with the disturbance, which influences the long-time stability of rock structures and rock engineering [2]. Therefore, investigation of the geomechanical properties of rock that are subjected to cyclic and fatigue loading is always important to ensure the long-term reliability of the rock structure in mining and civil engineering.
The rock fatigue characteristics have been revealed in the laboratory by many scholars. As for the fatigue dynamic behaviors of rock mass, the stress amplitude and loading frequency are always the main study inspects [6][7][8][9][10][11]. Singh [12,13] conducted systematic fatigue tests on granite and found that fatigue lifetime decreases with increasing stress amplitude. Ge [14] and Ge et al. [15] found that a fatigue threshold value exists for the rock, and the rock can be damaged and failed when the stress amplitude exceeds the threshold. They also found that the fatigue threshold is close to the crack damage stress on the static stress-strain curve. Bagde and Petroš [9] tested intact sandstone samples from a coal mine under cyclic loading and found that loading frequency and stress amplitude have a great influence on the rock dynamic behavior. They also pointed out that the loading waveforms have a strong influence on the damage accumulation under cyclic loading conditions. Fuenkajorn and Phueakphum [16] conducted a triaxial circulation test and established the relationship between the rock strength and cyclic loading number. In addition, they found that the modulus of elasticity remained almost constant until the specimen failed. Liu and He [10] studied the effect of confining pressure on cyclic mechanical properties of intact rock samples and proposed a residual strain method to describe initial fatigue damage and damage extension. Wang et al. [17] studied the fatigue behavior of granite under triaxial compression and found that the use of axial residual strain can well describe the fatigue behavior of rock. Roberts et al. [18] studied the creep and expansion behavior of salt rock under fatigue load, revealing the deformation characteristics of salt rock. Taheri et al. [19] conducted cyclic loading experiments on lignite and found that the mechanical properties of lignite were not significantly affected by cyclic loading and cumulative irreversible axial strain. Fan et al. [20] conducted discontinuous cyclic loading tests on salt and revealed the differential fatigue life of salt in comparison with continuous cyclic loading tests. Peng et al. [21] investigated the mechanism of loading frequency on sandstone and found that increasing the frequency can improve the strength of rock. Wang et al. [3] revealed the anisotropic fatigue behavior of interbedded marble subjected to constant stress amplitude loading condition; they found that the interbedded structure influences the final fracture morphology of rock. Wang et al. [4] conducted a triaxial fatigue cyclic-confining pressure unloading test on marble; the impact of the rock internal structure on energy evolution and fracture pattern has been investigated.
After the literature review, the influences of dynamic frequency on fatigue mechanical behaviors of rock are limited to constant stress amplitude loading conditions. However, in actual rock engineering, especially in the mining or civil engineering, the rock is subjected to frequent stress disturbance with variable stress amplitudes [17,18]. For example, in underground mining, the cyclic loading generated by blasting also exerts multilevel effects on a certain rock structure; in open pit mining, with the continuous excavation of the rock slope, the applied stress amplitude is varied and not constant [22,23], that is to say, rock accumulative damage resulting from the increasing amplitude cyclic-stress conditions alters the rock structure, and the final failure of rock body; in a hydropower station, the cyclic loads generated by the rise and fall of the water level are multilevel; in a railway or highway, the cyclic loading generated by the increase and decrease of load capacity and also the number of vehicles is multilevel. As a result, to explore the rock fatigue behaviors under varied stress amplitude within the whole fracturing process is necessary. Moreover, the failure morphology of the rock after fatigue loading experiment can only be observed from the rock surface, the internal crack pattern is difficult to detect, and the mesoscopic failure mechanism is not well understood. Moreover, due to the influence of farfield blast vibration and the vehicle loading, the dynamic frequency acted on the rock is varied and not constant. Therefore, investigating the influence of dynamic frequency on a rock subjected to increasing amplitude cyclic loading is necessary and crucial in rock engineering.
In this work, a series of increasing amplitude cyclic loading experiments with different dynamic frequencies have been performed on granite samples that contain two flaws. The approach angle of the two flaws is designed as 50°N

Geofluids
investigation, a dominant joint having an approach angle of 50°to the rock stratum was observed. According to the method recommended by ISRM, the rock mass obtained from the open pit slope was prepared into a cylinder with a diameter (D) of 50 mm and a height (H) of 100 mm. Both ends of the sample were polished to ensure that the nonuniformity error is less than 0.05 mm and the parallelism is less than 0.1 mm. In order to mimic the rock bridge structure in the rock mass, the cylindrical rock cores with two unparallel flaws were prepared using a water jet system (Figure 1(a)). Highpressure water mixed with garnet abrasive ejected from a 0.75 mm diameter nozzle produced a flaw with its aperture of 1 mm [2]. A detailed method to produce the two flaws can be found at Wang et al. [2]. The flaw geometry in a double-flawed sample was a combination of a horizontal flaw with length (2a) and an upper inclined flaw (2a) of 16 mm. The inclined flaw had an approach angle (β) of 50°to the horizontal flaw. The rock bridge length (2b) (i.e., rock bridge length) as defined in Figure 1(b) was set to be 20 mm in order to allow the crack coalescence in the locking section.   Fatigue cycle number (c)   6 Geofluids and a PAC acoustic emission (AE) apparatus made by the Physical Acoustic Corporation Ltd., USA, as shown in Figure 2. The dynamic loading frequency of the rock mechanics machine is 0~10 Hz. The PAC AE system is used to monitor the whole cracking process. Detailed description of the AE system can be found in the literature of Wang et al. [2]. The AE waveform, AE counts, energy, frequency, amplitude, rise time, etc., are recorded during sample deformation.

Geofluids
For the granite samples that have two preexisting flaws, two testing types were conducted, i.e., (1) conventional uniaxial static compression test and (2) uniaxial increasingamplitude stress-cycling tests. For the static loading test, a constant strain rate of 0.06 mm/min (i.e., 1:0 × 10 −5 s −1 ) was applied to granite samples. For the dynamic increasing amplitude stress-cycling experiments, from the monitoring data of blast variation and cyclic tramcar loading, the dynamic frequency is varied and not constant; four kinds of dynamic frequencies were applied to the flawed granite samples, i.e., 0.04, 0.1, 0.5, and 1.0 Hz. First of all, the sample was loaded to a stress of 5 MPa at a constant strain rate 0.06 mm/min (i.e., 1:0 × 10 −5 s −1 ); then, cyclic dynamic loading was loaded with a certain loading frequency (i.e., 0.04, 0.1, 0.5, and 1.0 Hz). During the fatigue loading process, for the first cyclic dynamic loading stage, a stress-controlled sinusoidal cyclic load having a stress amplitude of 10 MPa was applied. In each subsequent cyclic loading stage, the stress amplitude was increased by 10 MPa and also controlled by a sinusoidal cyclic loading type. Stress cycling was continued in this way until the sample eventually failed. For each dynamic cyclic loading stage, 30 stress cycles were applied to the granite sample. Two groups of samples were tested; in group I, they experienced monotonous uniaxial loading; in group II, they are subjected to increasing amplitude stress-cycling conditions, as listed in Table 1.

Typical Cyclic Stress-Strain Responses.
For the samples under different dynamic loading frequencies, the loading paths and the associated completed stress-strain curves are plotted in Figure 3. Figures 3(a), 3(c), 3(e), and 3(g) show that different fatigue loading stages were performed for the samples; they are 5, 6, 6, and 7 stages, respectively. It also shows that the number of loading cycle is different for the four samples due to the difference of loading frequency. The total loading cycle number for the four tested samples is 150, 162, 177, and 190, respectively. The loading cycle number increases with the increasing dynamic loading frequency, which indicates that the frequency impacts the strength, deformation, and the associated fracturing characteristics. The axial stress-strain curves show that obvious brittle failure occurs at the peak stress point; the strain is less than 0.5% for the samples with different dynamic loading frequencies. Plastic deformation occurs inside rock samples with the increase of experimental time; it can be shown that the loading curve was not overlapped with the unloading curve; therefore, hysteresis loop forms. In order to well describe the impact of axial and lateral deformation on the sample volumetric changes, volumetric strain (ε v ) is calculated according to the axial strain (ε 1 ) and lateral strain (ε 3 ) as ε v = ε 1 + 2ε 3   The pattern of the accumulative AE count curve presents a step shape, indicating the sudden increment of the AE event at each fatigue loading stage. From the AE accumulation curve, it can be seen that the AE event increasing rate becomes larger and larger, indicating the accumulative damage in the rock sample, crack initiation, propagation, and coalescence behaviors occuring during the whole loading process. The AE count curve also shows that the generated AE activities are affected by the loading frequency. For the rock sample with a loading frequency of 0.04 and 0.1 Hz, it shows that the AE count response is relatively weak, and the generated AE event is less. However, for the sample with a loading frequency of 0.5 and 1.0 Hz, it can be seen that plenty of AE events generate, especially at the loading stage close to sample failure.
For the changes of AE energy against stress and experimental time are shown in Figures 5(e)-5(h), similar conclusions can also be drawn. The sudden increase of AE energy indicates the increment of accumulative damage. The AE energy curve skips at the onset of one fatigue loading stage.
At each loading stage, the released AE energy continuously increases and the increasing trend become more and more obvious. The AE accumulative energy curves indicate that the loading frequency influences the released energy during sample deformation.
To further reveal the impact of loading frequency on the AE activities, Figure 6 plots the relationship between the accumulative AE count/energy and experimental time. It can be seen that the increment of the AE activities increases with the increases of the loading stage. In addition, loading frequency has an obvious influence on the generation of AE events, and samples subjected to high loading frequency have larger AE activities than those subjected to relatively low loading frequency.
3.4. Analysis of AE Spectrum Frequency. The above sections are focused on observing the AE activity by counting the event rate (or the cumulative numbers) and observing AE energy (or the cumulative energy); these analyses are based on the AE event parameters. The AE signals consisted of a variety of frequency components, and the waveform frequency and amplitude are different for different AE sources [27][28][29][30][31]. The waveform characterization can reflect the crack type, number, and scale; therefore, the spectrum (frequency) information can well reflect the fracture evolution of rock. Some scholars have also found that the AE main frequency characteristics can better reflect the microfracturing of rock, and it is much more sensitive to the AE counts [29,30]. Investigation of the frequency characteristics of emission events, on which our attention will be focused in this section, could be significant and promising as a means of characterizing the effects of dynamic loading frequency on the fracture of rock bridge. The extracted discrete time domain signal can be transferred to the continuous frequency domain signal using Fast Fourier Transform (FFT) Algorithm transformation [30]. Using FFT analysis, the  Figure 6: Depict the AE accumulative counts (a) and AE accumulative energy (b) with the fatigue loading stage. 10 Geofluids frequency distribution is shown in Figure 7. Three frequency band ranges of low, medium, and high can be divided, as listed in Table 2.
From the scatter of the main frequency points, it can be found that the frequency distribution is dense at the onset of each fatigue loading stage. This result is consistent with the result of AE count/energy analysis. The dense characteristic implies the occurrence of plenty of fracturing events. In addition, the number of low-frequency signals is more at the beginning of each fatigue loading stage. The medium-and high-frequency signals gradually generate at the last few of the loading stages, and its distribution is impacted by the loading frequency. The scale of the high-frequency signals increases with increasing loading frequency. This result indicates that the released energy is high when the sample is close to the failure state.
As AE amplitude has certain correction with released energy and also the spectrum frequency characteristics, the division of the AE main amplitude can make us better investigate the impact of dynamic loading frequency on the sample fracturing mechanism. The examination of the AE amplitude distribution makes it possible to monitor the instability of brittle rock [32][33][34]; it has been proved that the fracture energy have correlations with the AE amplitude. In the spectrum figures, the maximum amplitude value is defined as the main frequency amplitude value, which is used to characterize the intensity of the acoustic emission event, and the frequency corresponding to the main amplitude is defined as the main frequency. The effect of the dynamic loading frequency on the AE main amplitude (which  11 Geofluids corresponds to the main frequency in an AE event) distribution is shown in Figure 8. It can be seen that the normalized amplitude can be divided into two parts: one part is more than 0.5, and the other part is less than 0.5. The result indicates that the distribution of AE main frequency in an AE event should introduce the influence of the AE main amplitude to clarify the failure mechanism.
Considering the AE main frequency and main amplitude distribution characteristics in Figures 7 and 8, the AE signals are divided into six types: the low-frequency-low-amplitude (LF-LA) signal, the medium-frequency-low-amplitude (MF-LA) signal, the high-frequency-low-amplitude (HF-LA) signal, the low-frequency-high-amplitude (LF-HA) signal, the high-frequency-medium-amplitude (HF-MA) signal, and the high-frequency-high-amplitude (HF-HA) signal. The AE studies on the fracture process of the rock material have shown the stress waves in the form of an acoustic emission (AE) signals which can give insights into the process of energy dissipation and emission in response to the initiation and propagation of crack. Figure 9 plots the six types of spectrum frequency and the axial stress against axial strain. At the initial loading stage, the type of the AE signals is mainly the low-frequency-low amplitude and the high-frequency-low-amplitude signals. At the initial loading stage, the type of the AE signals is mainly the lowfrequency-low-amplitude and the high-frequency-lowamplitude signals. At the crack initiation and unstable propagation stage, the six kinds of signals coexist, and the AE signals move into the median frequency band; this indicates the occurrence of macroscopic cracks. In addition, the number of low-frequency-low-amplitude and low-frequency-highamplitude signals gradually increase at the crack unstable propagation stage. Furthermore, the emerging lowfrequency-high-amplitude signal gradually decreases at the crack coalescence stage. From the frequency distribution characteristics in Figure 9, main conclusions can be drawn as follows: (1) low-frequency-low-amplitude signals exist through the whole fracturing process; they correspond to the intergranular cracks at the initial loading stage and the microcracks during fracturing. (2) The medium-frequencylow-amplitude AE signals generate during the whole fracturing process; they correspond to microcracks during sample fracturing. (3) The low-frequency-high-amplitude signals occur at the last few fatigue loading stage; they correspond to the occurrence of large cracks. (4) The mediumfrequency-high-amplitude signals occur at the last few loading stages; they correspond to the instable propagation of cracks and the sliding of the fracturing plane. (5) The high-frequency-high-amplitude signals correspond to the medium-scaled crack and the transgranular fracturing crack.
As there is an inverse relationship between the AE frequency and the crack size, generally, large-scaled cracks correspond to low-frequency signals, and small-scaled crack corresponds to high-frequency signals. The main frequency distribution in Figure 9 shows that the high-frequencyhigh-amplitude signals do not exist for samples subjected to 0.5 and 1.0 loading frequency. This result indicates that the number of small-scaled cracks decreases for the rock sample under relatively high loading frequency. To better reflect the influence of dynamic loading frequency on the proportion of the low, medium, and high AE signals, the statistic result is listed in Table 3.

Discussions
Extensive investigations about the mechanical behaviors of rock under cyclic and fatigue loading conditions have been performed [5][6][7][8][9][10]. However, most of the loading condition is the constant stress amplitude; in addition, they are mainly focused on the macroscopic cracking process of intact rock, especially the crack coalescence pattern description on the intact rock after the test. In addition, rock fracturing behavior under cyclic loads is different from the static loading condition [24,[35][36][37][38]. Actually, in rock engineering, the amplitude of the disturbance stress is varied and not constant. Accumulative damage resulting from the increase of stress amplitude    13 Geofluids the sudden increase of axial stress at the onset of each fatigue loading stage results in relatively large damage accumulation in rock. Due to the differential loading frequencies, the AE counts, and AE energy, the main amplitude distribution and the frequency spectrum characteristics present obvious difference. As is known, AE events are the external reflection of the energy dissipation and release during rock deformation; the velocity of energy release is positively related to the loading rate. For rock subjected to high loading frequency, the associated energy release velocity is relatively high, and the AE counts/energy (or accumulative number) is larger than rock subjected to low loading frequency. As the frequency and amplitude of AE events are much more sensitive, frequency spectrum analysis further reveals the crack propagation and rock bridge fracturing characteristics; cracks generated from the fracture process are classified into six kinds. The experimental results show that the highfrequency-high-amplitude signals do not exist for samples subjected to high loading frequency. Because the highamplitude-high-frequency signals correspond to the formation of small-scaled cracks, this result indicates that the number of small-scaled cracks decreases for the rock sample under relatively high loading frequency. This result implies that the rock structure is easily degraded when subjected to high-stress disturbance frequency.

Conclusions
In this work, an acoustic emission monitoring technique was used to investigate the effect of dynamic loading frequency on the rock bridge fracturing of preflawed granite samples. From the above analysis, the following conclusions can be drawn: (1) The deformation, strength, and fatigue lifetime of the preflawed granites are impacted by the applied dynamic loading frequency. Volumetric deformation monitored at the rock bridge area indicates that a sudden rupture occurs at the final cyclic loading stage and the volumetric strain is the maximum for rock subjected to high-frequency loading conditions (2) AE parameters extracted from the AE waveform are strongly influenced by the applied dynamic frequency. The increasing rate of the AE count and AE energy at each loading stage gets faster as the cyclic loading stage increases. The accumulative AE count and energy both increase with the increase of dynamic loading frequency (3) AE spectral analysis reveals different fracturing mechanisms that are impacted by dynamic frequency. It is suggested that the number of highfrequency-high-amplitude signals decreases for rock subjected to high loading frequency, indicating the occurrence of large-scaled cracks. The main frequency is a good index for early warning of instability prediction for rock with geological discontinuities

Data Availability
The experimental data used to support the findings of this study are included within the article.

Conflicts of Interest
The authors declare no conflict of interest.