The Influence of Cyclic Loading-unloading Rates on the Uniaxial Mechanical Anisotropy of Coal

The Influence of Cyclic Loading-unloading Rates on the Uniaxial Mechanical Anisotropy of Coal | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article The Influence of Cyclic Loading-unloading Rates on the Uniaxial Mechanical Anisotropy of Coal Duo Xu, Honghua Song, Like Zhao, Guoqing Tang, Shide Hu, Chenxi Duan, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7522397/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract In this study, the influence of the loading-unloading rate on the uniaxial mechanical anisotropy of coal was investigated via uniaxial compress testaments, acoustic emission (AE) monitor and digital image correlation (DIC), and a series of coal specimens with five anisotropy angles. The results illustrate that the uniaxial compressive stress (UCS) and elastic modulus maintain a U-shaped anisotropic feature under different loading-unloading rates. The anisotropic feature of UCS and axial strain decreases, while the elastic modulus ascends with the increasing loading-unloading rate. The UCS, loading-unloading rate, and anisotropic angle of coal specimens are proved can be described by a cosine function. The impact of bedding plane on the failure characteristics of coal is more significant at anisotropic angles of 0°, 22.5°, and 45°, the penetrating crack mainly propagates along the bedding plane. The increasing loading-unloading rates contribute to a more intact after-failure coal specimen, which makes the anisotropic failure feature of the coal specimen more notable. Meanwhile, the anisotropy of micro-failure characteristics revealed by the AE activity also rises with the loading-unloading rate, which accords with the macro-failure characteristics. The cyclic loading-unloading process generates more damage as specimens with lower UCS, the damage variable caused by it exhibits a parabolic anisotropy feature at anisotropic angle 0º~90º, and the value at 22.5º and 45º is greater than other anisotropy angles, though this anisotropy feature of damage variable decreases as the loading-unloading rate gain. In addition, the dissipated energy density generated during cyclic loading-unloading process also shows a U-shaped variation feature at anisotropy angle 0º~90º, with relatively lower value at 22.5º and 45º, and positively exponential correlation with the UCS. Physical sciences/Energy science and technology Physical sciences/Engineering Earth and environmental sciences/Solid earth sciences coal mechanical anisotropy cyclic loading-unloading rate failure characteristics energy dissipation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Introduction The mechanical property of coal is loading-rate and loading-direction dependent, coal specimens generally exhibit different mechanical responses as the loading direction and the loading rate changes 1 – 7 . During the coal mining process, coal mass around roadway and workingface spaces frequently subjected to various degree of cyclically disturbances that comes from different directions 8 – 12 , which makes the anisotropic coal mass exhibit diverse failure characteristics, due to the varying cyclically loading-unloading rate difference generated by these disturbances complicate the mechanical anisotropy of coal 13 – 15 . Thus, exploring the anisotropic mechanical behavior of coal affected by the cyclic loading-unloading rate is meaningful to coal pillar designing, roadway support assessment, and coal mass failure mechanism analysis. Primary structures are broadly exist in coal mass, which is generated during the sedimentary and geotectonic movement process of the coal formation, including mineral inclusions, pre-existing discontinuities, and weakness interfaces 16 , 17 . These part of primary structures contributes to the mechanical anisotropy of coal via affecting the generation, propagation, and coalescence of failure cracks 18 – 20 . Meanwhile, these primary structures behave a spatially directional distribution characteristics, and the bedding plane is generally chosen as the reference structure in the mechanical anisotropy investigation 21 – 23 , considering the visually recognizable feature of it. Explorations and descriptions of the mechanical anisotropy of coal were broadly carried out based on the inclination variation of the bedding plane to the loading direction 18 , 24 , 25 , viz the anisotropy angle. The influence of cyclically loading-unloading process on the mechanical parameters of coal and rock material is more complicated 26 – 29 . Mechanical parameters and failure characteristics of coal and rock exhibit different variation features as been loaded under different loading rates 30 , 31 , loading path 32 , 33 , fatigue stress level 34 , 35 , and the amount of loading-unloading cycles 8 , 36 . In recent years, the mechanical anisotropy of coal was also proved strengthen when it subjected to the cyclical loading-unloading process 37 . However, the mechanical response of anisotropic coal affected by the cyclical loading-unloading rate still remain unknown, corresponding investigation or experiment are rarely mentioned. Thus, extensive works are needed to implement in this area, and clarify the evolution characteristics of mechanical parameters and failure modes of coal as been cyclically loaded-unloaded under different rates. In this study, a detailed exploration on the mechanical anisotropy of coal affected by the cyclic loading-unloading rate was systematically carried out under the uniaxial compressive condition. Three stress cyclical loading-unloading rates (0.025 MPa/s, 0.025 MPa/s, 0.025 MPa/s) and five anisotropy angles (from 0º to 90º, with interval of 22.5º) were chosen. The microscopic or macroscopic failure characteristics of coal specimens are respectively been monitored by the acoustic emission (AE) and digital image correlation (DIC) monitoring instruments. After that, the mechanical anisotropy of coal affected by the cyclic loading-unloading rate was thoroughly analyzed. 2. Experimental Scheme 2.1 Coal Specimen Preparation To facilitate the observation of strain and fracture propagation on the coal surface, coal specimens were processed with the quadrilateral prism form. It was prepared with a height of 100 mm and a side-to-height length ratio of 1:2. Meanwhile, five anisotropy angles, namely angles between the loading-unloading direction and the inclination of the bedding plane, were chosen from 0º to 90º, with an angle interval of 22.5º, as shown in Fig. 1 (a). Sixty specimens respectively with five anisotropy angles mentioned above were acquired, twelve specimens for each anisotropy angle. For specimens with the same anisotropy angle, they were randomly divided into 4 groups, namely, three specimens for each anisotropy angle per group, part of the specimens used in this study were shown in Fig. 1 (b). 2.2 Experimental Instruments 2.2.1 Uniaxial Testament Facility The servo-controlled stiff uniaxial cyclic loading-unloading equipment was adopted in the experiment, which was produced by the Mechanical Testing & Simulation (MTS) Corporation. It has both the cyclic and the monotonic loading-unloading capabilities. Meanwhile, it also provides two loading-unloading model, respectively, strain and the stress control model. The maximum loading capability of this instrument is 300 kN, with an accuracy of ± 0.3%. 2.2.2 Acoustic Emission Monitoring Equipment A broadly used acoustic emission monitoring device was adopt to detect the AE activity generated during the cyclic loading-unloading process, which was produced by Physical Acoustics Corporation (PAC). This system includes a PIC-2 device, a 6-type preamplifier, and four micro 30 s sensors. It has a bandwidth frequency of 1 kHz ~ 3 MHz, and the maximum signal amplitude of it is 100 dB. Here, the amplification gain was chosen as 40 dB, during the monitoring process. 2.2.3 Digital Speckle Monitoring System A non-contact displacement/strain video measuring instrument was adopted in this experiment (IMETRUM, model ISM-CONTAR-VG5-2D-10G). It consists of a system controller, a dedicated digital camera − 10GigE, with an acquisition of 68 fps and a resolution ratio of 4096×3000, six core cables, a calibration tool, a digital image correlation (DIC) full field measurement module, and LED light source. 2.3 Testament Methodology To acquire a reasonable cyclic loading-unloading threshold, specimens with different anisotropy angles were tested under the monotonic uniaxial compressive condition. A stress loading approach was adopted in this research, with a loading rate of 0.025 MPa/s. The uniaxial compressive strength range was obtained with the maximum value of 9.24 MPa (anisotropy angle 90º), and the minimum value of 1.26 MPa (anisotropy angle 22.5º). Based on the acquired strength range, the begin value and stress increment per cyclic loading cycle were respectively selected as 0.6 MPa and 0.4 MPa, meanwhile, the unloading ended with the axial stress of 0.2 MPa in per cycle. Three loading/unloading rates were chosen, separately 0.025 Mpa/s, 0.050 Mpa/s, and 0.100 Mpa/s. The specimens were cyclically loaded and unloaded until failure, the loading-unloading path is shown in Fig. 2 . 3. Strength and Deformation Anisotropy 3.1 Stress-strain Curves The stress-strain curves of specimens with different anisotropy angles under three cyclic loading-unloading rates were summarized, as shown in Fig. 3 . It indicates the stress and strain varies with the anisotropy angles and cyclic loading-unloading rates. Specimens usually have greater UCS and experience more axial deformation before the specimen failure at anisotropy angles of 90º and 67.5º than that of 22.5º and 45º. Instead, specimens were observed with greater UCS value, while less axial strain at the anisotropy angle 0º. Meanwhile, specimens experience more cyclic loading-unloading cycles in anisotropy angles of 0º, 67.5º, and 90º than that of 22.5º and 45º. The increasing cyclic loading-unloading rate has a more complicated influence on the stress and deformation of coal, mechanical parameters variation such as the UCS and axial strain changes with the anisotropy angle. Thus, calculation and statistical analysis should be made to reveal the mechanical variation affected by the cyclic loading-unloading rate. 3.2 Uniaxial Compressive Strength The mean value of UCS in specimens with different anisotropy angles were summarized in Table 1 . It behaves as a U-shaped characteristics, at the anisotropy angle range of 0º ~ 90º. The UCS usually obtained the maximum value at the anisotropy angle 90º, and with the minimum value at anisotropy angles 22.5º or 45º, as shown in Fig. 4 . This feature accords with the UCS anisotropy characteristics in coal and stratified rocks reported before 38 , 39 , which illustrates the internal structure, especially the bedding plane, still notably impacts the mechanical failure of coal. The UCS exhibits an overall reducing trend as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.10 MPa/s. It reduces from 5.18 MPa to 4.71 MPa, with a reduction of 0.47 MPa, as shown in Table 1 . Meanwhile, this variation is more complicated in coal specimens with different anisotropy angles. An overall reducing feature was observed at anisotropy angles 0º, 22.5º, 67.5º, and 90º, respectively with reductions of 0.02 MPa, 0.60 MPa, 0.62 MPa, 1.34 MPa. While it increases from 1.62 MPa to 1.86 MPa at anisotropy angle 45º, with an increment of 0.24 MPa. The anisotropy feature of the UCS reduces with the increasing cyclic loading-unloading rate, the standard deviation of specimen with different anisotropic angle reduces from 3.45 MPa to 3.13 MPa, as it increases from 0.025 to 0.100 MPa/s. Table 1 The average UCS value in specimens with different anisotropy angles under varies cyclic loading-unloading rates. Anisotropy angle (º) Uniaxial compressive strength (MPa) 0.025 MPa/s 0.050 MPa/s 0.100 MPa/s 0º 7.37 5.46 7.35 22.5º 1.83 1.62 1.23 45º 1.62 1.68 1.86 67.5º 5.57 4.69 4.95 90º 9.52 12.22 8.18 Average value (MPa) 5.18 5.13 4.71 Based on the similarly U-sharped UCS feature observed in the coal and layered rock in specimens with different anisotropy angles 38 , 40 , the UCS anisotropy under the cyclic loading-unloading condition, which is usually represented in forms as where M and N are material-related constants; θ is the anisotropy angle, º; θ min is the anisotropy angle with the minimum UCS, º; σ θ is the UCS with the anisotropy angle θ , MPa. Thus, to have a fundamental understanding on the overall changing characteristics of the UCS with cyclic loading-unloading rate and the anisotropic angle, a unified correlation was developed after numbers attempts, which can be represented in forms as where σ θ,v denotes the UCS of specimen with the anisotropic angle of θ and the cyclically loading-unloading rate of v , A, B , and C are material and loading-unloading rates property related parameters. The fitting curve of the experimental data and the Eq. ( 2 ) exhibits a good correlation and the correlation coefficient is 0.89, as shown in Fig. 5 . Which also indicates the applicable of this correlation in describing the correlation of the UCS, the cyclic loading-unloading rate, and the anisotropic angle, at the cyclic loading-unloading range of 0.025 ~ 0.100 MPa/s. In addition, the variation of the UCS with cyclic loading-unloading rate increases may be contingent upon the UCS of coal. Based on the previous research, the strength thresholds exist in coal 41 , which decides the strength increases or reduces with the increasing loading-unloading rate as the UCS greater or lower than the strength thresholds. 3.3 Axial Strain The peak strain of coal specimens under the cyclic loading-unloading conditions were summarized in Table 2 . Variation feature of these specimens were exhibited in Fig. 6 . In general, the axial strain behaves a firstly reducing and then increasing feature at the anisotropy angle range of 0º ~ 90º, the minimum value is usually observed at the anisotropy angle 22.5º or 45º. This accords with the anisotropy character of UCS, namely specimens with greater UCS generally have a greater value of peak strain, apart from specimens with the anisotropy angle 0º, where specimens have lower axial deformation capability, since the loading-unloading direction is perpendicular to the bedding plane, where the axial deformation depends on the axial deformation of layered coal matrix 16 . Table 2 The axial strain of specimens with different anisotropy angles under varies cyclic loading-unloading rates Anisotropy angle (º) Axial strain (%) 0.025 MPa/s 0.050 MPa/s 0.100 MPa/s 0º 1.57 1.71 2.36 22.5º 1.49 2.54 2.12 45º 2.93 2.45 2.64 67.5º 4.17 3.83 3.57 90º 4.70 4.82 5.41 Average value 2.97 3.07 3.22 The anisotropy feature of the peak strain changes minimal as specimens have been cyclically loaded-unloaded, besides the cyclic loading-unloading rate of 0.050 MPa/s, where the axial strain increases with the anisotropy angle at 0º ~ 22.5º, while reduces at the anisotropy angle range of 22.5º ~ 45º, and then it increases to the maximum at 90º. Unlike the axial strain reduction with the increasing loading-unloading rates in sandstone 42 , the increasing cyclic loading-unloading rate also gains the axial deformation capability, the average value of peak strain increases from 2.97–3.22%, as the loading rate increases from 0.025 MPa/s to 0.100 MPa/s. Meanwhile, the axial strain variation in different anisotropy angles also behaves inconsistently, as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s. It increases with the loading-unloading rate at the anisotropy angle 0º and 90º, while having an overall increasing behavior at 22.5º and an overall reduced trend at 67.5º or 45º. The anisotropy feature of axial strain decreases with the increasing cyclic loading-unloading rate, the standard deviation reduces from 1.46–1.34%, as it increases from 0.025 to 0.100 MPa/s. 3.4 Elastic Modulus To investigate the effect of the cyclic loading-unloading rate on the stress and deformation anisotropy of coal, the tangent elasticity modulus were calculated. The elastic modulus behave a U-shaped anisotropy feature, as the anisotropy angle increase from 0º to 90º, as shown in Fig. 7 . However, it behaves a symmetric anisotropy character with the UCS. The elastic modulus generally has the maximum value at the anisotropy angle 0º, while minimum value at 45º or 22.5º, and the second largest value at 90º. The value of elastic modulus has an overall reducing feature with the increasing cyclic loading-unloading rate, the average elastic modulus increases from 0.39 GPa to 0.41 GPa, and then reduces from 0.41 GPa to 0.37 GPa, as the loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s, as shown in Table 3 . Table 3 The elastic modulus of specimens with different anisotropy angles under varies cyclic loading-unloading rates Anisotropy angle (º) Elastic modulus (GPa) 0.025 MPa/s 0.050 MPa/s 0.100 MPa/s 0º 0.75 0.69 0.78 22.5º 0.25 0.23 0.19 45º 0.17 0.18 0.20 67.5º 0.32 0.30 0.31 90º 0.45 0.64 0.39 Average value 0.39 0.41 0.37 Meanwhile, the elastic modulus has similar anisotropy feature with the UCS as the cyclic loading-unloading rate gain. It exhibits firstly decreasing and then increasing feature at anisotropy angle of 0º and 67.5º, while a firstly increasing and then reducing feature at that of 90º. Meanwhile, it respectively illustrates an overall increasing and decreasing character at 22.5º and 45º, as the cyclic loading-unloading rate increases from 0.025 GPa/s to 0.100 GPa/s. The anisotropy of elastic modulus also increases as the cyclic loading-unloading rate gain, the standard deviation increases from 0.22 GPa to 0.24 GPa, as the cyclic loading-unloading rate increases from 0.025 GPa/s to 0.100 GPa/s. Based on the previous research, the strength thresholds may exist in coal, the strength increases or reduces with the increasing loading-unloading rate as the UCS greater or lower than the strength thresholds 41 . This maybe the reasons that the UCS, the peak strain, and the elastic modulus behave differently as the cyclic loading-unloading rate gains in specimens with different anisotropy angles, as shown in Tables 1 , 2 , and 3 . 4. Anisotropic Failure Characteristics 4.1 Failure Anisotropy Typical failure characteristics of anisotropic coal specimens under different loading-unloading rates were exhibited in Fig. 8 . The failure pattern of the coal specimen changes with the anisotropy angle. The effect of the bedding plane is pronounced at anisotropy angles of 22.5º and 45º, where the major failure crack developed along the bedding plane of the coal specimen, as shown in Fig. 8 . Meanwhile, it also leads to a relatively lower bearing and deformation capacity of specimens at these two anisotropy angles. The influence of the bedding plane gradually reduces at the anisotropy angle 67.5º. The major failure cracks cross and have a greater angle with the inclination of the bedding plane, though coalescence of it with the crack developed along the bedding plane also partially exists, as shown in Fig. 8 . Which makes the mechanical parameters mentioned above has relative greater value. The layered rupture feature is observed and failure cracks developed along the bedding plane at anisotropy angle 0º, due to the lower cohesion that perpendicular to the bedding plane. This may be the reasons that specimens have a relatively lower axial peak strain, greater UCS, and highest elastic modulus, since the bearing and axial deformation capacity of coal are decided by the layered coal matrix. The influence of the bedding plane is less obvious at the anisotropy angle 90º. The major failure cracks are developed cross the bedding plane layers, the deformation and the bearing capacity of coal are mainly subject to the coal matrix, as shown in Fig. 8 . Thus, the greater UCS and axial strain, while lower elastic modulus are observed. 4.2 Failure Anisotropy Affected by Loading-unloading Rates The influence of cyclic loading-unloading rate on the anisotropic failure characteristics of coal is significantly at anisotropy angles 0º and 90º. As the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.10 MPa/s, the failure pattern changes from layered failure pattern to X-shaped shear failure pattern, and the amount of cracks developed along the bedding plane decreases at the anisotropy angle 0º, as shown in Fig. 8 . Meanwhile, the after-failure specimen becomes more intact and the fragments are not cast far away from the damaged specimen at the anisotropy angle 90º, as shown in Figs. 8 (d). Penetrating cracks become mainly propagated along the bedding plane, and the fragmentation behaves more integrated with greater size, at the anisotropy angles of 22.5º and 45º, though the fragment degree at 45º is greater than that of 22.5º, as shown in Figs. 8 (b), (c), and (d). Wider crack bands, more dusty characteristics, and less cracks generated parallel to the loading-unloading direction around the cracks band were observed at the anisotropy angle 67.5º, as shown in Figs. 8 (b), (c), and (d). Before the failure of coal specimens, the horizontal strain concentration zones are more intensively distributed in the main through-crack area, as shown in Fig. 9 . The area of horizontal strain concentration reduces with the increasing loading-unloading rate, especially at that of 0.050 MPa/s. This also may illustrate a relatively less fracture development after specimen failure, which may contribute to the increasing integrity of the damaged coal specimen. 4.3 Anisotropy Revealed by AE Activities 4.3.1 AE Count Acoustic emission is fracture generation and propagation related activity, which also microscopically reflects the failure intensity and characteristics during the cyclic loading-unloading process. Thus, the cumulative AE counts in specimens with different anisotropy angles under varies cyclic loading-unloading conditions was summarized in Table 4 and Fig. 10 . Table 4 The variation of cumulative AE counts with the anisotropy angle of coal specimens under varies cyclic loading-unloading rates Anisotropy angle (º) Cumulative AE counts (×10 5 ) 0.025 MPa/s 0.050 MPa/s 0.100 MPa/s 0º 1.77 2.23 3.54 22.5º 1.18 2.14 1.88 45º 2.95 2.80 3.74 67.5º 5.29 6.36 4.13 90º 8.97 7.25 10.87 Average value 4.03 4.15 4.83 The cumulative AE counts presents a less obvious U-sharped anisotropy feature under the cyclic loading-unloading condition. It generally has minimum values at the anisotropy 22.5º, while the maximum values are obtained at 90º. The cumulative AE counts has similar anisotropic characteristics with that of axial strain, as shown in Figs. 5 and 10 . The positively correlation is due to the axial strain represents the irreversible axial deformation generated during the specimen failure process, greater value of axial strain indicates more cracks, namely, greater amount of AE events, generated during the cyclic loading-unloading process. The increasing cyclic loading-unloading rate strengthens the AE activity, the average cumulative AE counts of specimens with different anisotropy angles gains from 4.03×10 5 to 4.83×10 5 , as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s. However, the variation characteristics of the cumulative AE counts with the loading-unloading rates also changes with anisotropy angles. It exhibits an overall increasing feature at the anisotropy angle 0º, 22.5º, 45º, and 90º, while behaves an overall reducing feature at the anisotropy angle 67.5º. 4.3.2 AE Energy The cumulative absolute AE energy also calculated and summarized in specimens with different anisotropy angles, as shown in Table 5 and Fig. 11 . It behaves similar anisotropic changing characteristics with the cumulative AE counts, as shown in Figs. 10 and 11 . Table 5 The cumulative absolute AE energy of specimens under varies cyclic loading-unloading rates Anisotropy angle (º) Cumulative absolute AE energy (×10 5 aJ) 0.025 MPa/s 0.050 MPa/s 0.100 MPa/s 0º 2.30 3.05 5.95 22.5º 1.31 2.41 1.79 45º 3.04 2.47 3.92 67.5º 4.63 5.82 4.05 90º 9.39 6.44 10.51 Average value 4.13 4.04 5.24 The cumulative absolute AE energy exhibits a U-sharped variation feature, at the anisotropy angle 0º~ 90º, under the cyclic loading-unloading condition. The value of the cumulative absolute AE energy is minimum is at anisotropy angle 22.5º, while maximum at 90º. This indicates that greater amount of cracks generated and AE energy dissipated in specimens with anisotropy angle 90º, where the impact of bedding plane is less obvious. While the crack generation and energy dissipation are less obvious as specimen failure been significantly affected by the bedding plane, namely anisotropy angle 22.5ºand 45º. The cumulative absolute AE energy behaves an overall increasing characteristic, as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s. It has an overall increasing feature at the anisotropy angle 0º, 22.5º, 45º, and 90º, respectively with increments of 3.65×10 5 aJ, 0.48×10 5 aJ, 0.88×10 5 aJ, and 1.12×10 5 aJ, while an overall reduction at the anisotropy angle 67.5º, with a reduction of 0.58×10 5 aJ. The increasing cumulative AE counts and absolute AE energy may be correlate to the greater amount of cracks with longer length generated as the cyclic loading-unloading rate gain. Which accords with the increasing fragmented block size in specimen with greater cyclic loading-unloading rate. Meanwhile, the anisotropy of failure characteristic revealed by the AE activity increases with the cyclic loading-unloading rate, the standard deviation of cumulative AE counts and absolute AE energy separately gains from 3.18×10 5 to 3.29×10 5 , from 3.18×10 5 to 3.48 ×10 5 , as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s. 5. Micro-failure Affected by Cyclic Loading-unloading Rates 5.1 Damage Variable In general, micro-cracks are usually generated in coal and rock material before the emergence of macro-fractures, and the initiation and growth of micro-cracks are defined as damage 26 . The tiny irreversible damage accumulates in each cyclic loading-unloading cycle affects the final failure feature of coal. Thus, the impact of the cyclic loading-unloading rate on the failure process of coal is investigated in this part. In general, the physical quantity used to characterize irreversible damage described above is defined as damage variable. In this research, the residual strain at the last cyclic loading-unloading cycle and peak strain of coal were chosen to evaluate the damage degree as impacted by the cyclical loading-unloading rate. The calculate equation was developed in forms as Eq. ( 3 ) Where ε L and ε p respectively the residual strain in the last cyclic loading-unloading cycle and the peak strain, %, D represents the damage variable of coal. The damage variable in specimens with different anisotropy angles and cyclic loading-unloading rates were exhibited in Fig. 12 . The damage variable behaves a parabolic type variation feature versus the anisotropy angle at the loading-loading rate of 0.025 MPa/s and 0.050 MPa/s. It has the minimum value at the anisotropy angle 0º, the maximum value at anisotropy angle 45º (0.025 MPa/s) or 22.5º (0.100 MPa/s), as shown in Fig. 12 . This anisotropy feature indicates specimens have greater degree of damage at the anisotropy angle 45º and 22.5º during the cyclically loading-unloading process. This accords with the failure feature that the major failure crack mainly developed along the bedding plane, where cracks propagate more easily and contribute to a lower value of UCS, peak strain, elastic modulus. The anisotropy feature of damage variable also changes at the cyclic loading-unloading rate of 0.100 MPa/s. It changes from parabolic type to wave-type variation. The damage variable firstly increases to maximum (0º ~22.5º), then reduces to the minimum (22.5º ~45º), finally gains to second largest (45º ~90º), as shown in Fig. 12 . This indicates more damage generated by the cyclic loading-unloading process in specimens with greater UCS under greater rates, conversely less damage occurred at specimens with lower UCS value. In addition, the damage variable has an overall reducing feature with the increasing loading-unloading rate. It respectively with values of 0.530, 0.507, and 0.528, under the loading-unloading rate of 0.025 MPa/s, 0.050 MPa/s, and the 0.100 MPa/s. 5.2 Dissipated Energy Density In this study, the cumulative dissipated energy density (CDED) before last loading process were adopted to illustrate the damage feature of specimens loading-unloading process, as shown in Fig. 13 . The CDED is unrecoverable deformation and strength increment related energy index. It behaves a U-sharped variation character as the anisotropy angle increases from 0º to 90º. Which indicates plastic deformation and strength increment is maximum at the anisotropy angle of 90º, while is less obviously at that of 22.5ºand 45º. In combining with the parabolic type variation feature of damage variables, greater percentage of plastic strain generated during the cyclic loading-unloading process at anisotropy angles of 22.5ºand 45º. This may be the reasons that contributes to the relatively integrated failure pattern of coal specimens with anisotropy angle of 22.5ºand 45º, since cracks easily developed along the bedding plane, specimen was destructed with less cracks generated, as shown in Fig. 7 . This is consistent with the lower AE activity parameter observed at these two anisotropy angles. The CDED has an overall reducing feature with the increasing loading-unloading rate, it respectively has the average value of 4.88×10 4 J/m 3 , 5.50×10 4 J/m 3 , and 4.70×10 4 J/m 3 , at the loading-unloading rate of 0.025 MPa/s, 0.050 MPa/s, and 0.100 MPa/s. Greater value of CDED represents more deformation, greater stress increments, and more loading-unloading cycles exists in these specimens. Meanwhile, greater value of the UCS observed in specimens with the greater CDED energy density, namely, the UCS and the CDED are positively correlated, as shown in Figs. 4 and 13 . Thus, a power function correlated relationship was proposed after multiple attempts attempts, this correlation can be described by Eq. ( 4 ) Where U d represents the cumulative dissipated energy density, J/m 3 , m is the material related parameter, J/(m 3 •MPa), n is the loading rate correlated parameter, σ is the UCS of specimens with different anisotropy angles, MPa. The regressive analysis result was summarized in Table 6 . Obviously, the experimental data has a good correlation with the Eq. ( 4 ), as shown in Fig. 13 , and respectively with correlation coefficient of 0.85, 0.97, and 0.79 at the loading-unloading rate of 0.025 MPa/s, 0.050 MPa/s and 0.100 MPa/s. Parameters of Eq. ( 4 ) are exhibited in Table 6 . Based on Eq. ( 4 ) and Fig. 14 , this verifies the CDED positively correlated with the UCS in per loading-unloading rates. Table 6 Parameters of Eq. ( 4 ) obtained by regression analysis Loading rate (MPa/s) m n Correlation coefficient 0.025 285.00 2.71 0.85 0.050 285.00 2.62 0.97 0.100 285.00 2.83 0.79 6. Conclusion In this study, the impact of the cyclic loading-unloading rate on the anisotropic mechanical response of coal were experimentally investigated. Research findings and conclusions were summarized as below. a. The UCS and elastic modulus maintain a U-shaped anisotropic characteristics under different cyclic loading-unloading rates. The anisotropy of UCS and axial strain decreases, while the elastic modulus ascends with the increasing loading-unloading rate. The correlation of the UCS, the loading-unloading rate, and the anisotropic angle of coal specimens can be described by a cosine function. b. The failure characteristics of coal are bedding plane related at anisotropy angles of 0°, 22.5°, and 45°, where the penetrating crack mainly propagate along the bedding plane. The after-failure coal specimen is more intact and the anisotropic failure feature of the coal specimen becomes more notable, as the loading-unloading rates increases. c. The anisotropy of micro-failure characteristics revealed by the AE activity rises with the cyclic loading-unloading rate. The cyclic loading-unloading generates more damage as specimens with lower UCS, the damage variable caused by it exhibits a parabolic anisotropy feature at 0º~90º, and the greater value were generally observed at 22.5º or 45º, though this anisotropy decreases as the loading-unloading rate gain. d. The dissipated energy density generated during cyclic loading-unloading process exhibits a U-shaped variation feature at anisotropy angle 0º~90º, with relatively lower value at 22.5º and 45º. Which shows a positively exponential correlation with UCS, namely specimens with greater uniaxial compressive strength has more energy dissipated during the cyclic loading-unloading process. Declarations Acknowledgments The authors acknowledge the State Key Laboratory for Protection and Utilization of Water Resources in Coal Mining, the National Natural Science Foundation of China, the Key Laboratory of Deep Earth Science and Engineering and the China University of Mining and Technology, Beijing for their financial support in completing this paper. Funding Declaration This research is supported by the Open Fund of the State Key Laboratory for Protection and Utilization of Water Resources in Coal Mining (GJNY-21-41-03), the National Natural Science Foundation of China (52004288), the Major Program of the National Natural Science Foundation of China (52394191), Open Fund of the Key Laboratory of Deep Earth Science and Engineering (DUSEYU202302), China University of Mining and Technology (Beijing) Student Innovation Training Program Funding (NICE_RD_2022_135) and Fundamental Research Funds for Central Universities. Data Availability Statements The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. Author Contribution Duo Xu and Honghua Song wrote the main manuscript text ;Like Zhao and Guoqing Tang prepared all the figures;Shide Hu, Chenxi Duan, and Yunting Song analyzed the experimental data. References Wang, G., Qin, X., Han, D. & Liu, Z. 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12:11:44","extension":"png","order_by":38,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1787,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/ea083899ae5d392dd7b14c0f.png"},{"id":91987838,"identity":"c71e8efc-a32e-40ea-b986-f365a73163a9","added_by":"auto","created_at":"2025-09-23 12:11:56","extension":"xml","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":128434,"visible":true,"origin":"","legend":"","description":"","filename":"3be1b7b5d86143d18bdec25f092ebd8f1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/5d8632d268c8d3fae620ae5b.xml"},{"id":91988298,"identity":"88d66297-264e-4e0e-b842-53e94b5e4729","added_by":"auto","created_at":"2025-09-23 12:19:24","extension":"html","order_by":40,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":139424,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/e774c3a9262413835ac60f60.html"},{"id":91987719,"identity":"e3dd4cdf-0ba1-49db-bfc5-b298876259dc","added_by":"auto","created_at":"2025-09-23 12:11:23","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":280853,"visible":true,"origin":"","legend":"\u003cp\u003eThe anisotropy angle and part of specimens used in this study.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/dacf1b5901a427907fb14c2e.png"},{"id":91987810,"identity":"12505802-9df8-40eb-a219-4b569919d5ac","added_by":"auto","created_at":"2025-09-23 12:11:47","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":104971,"visible":true,"origin":"","legend":"\u003cp\u003eThe cyclic loading-unloading paths used in this research.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/fcc011cc34c477930c3fcf3a.png"},{"id":91987755,"identity":"0ed5420a-e91a-4fcf-b391-d2d3384d1d2e","added_by":"auto","created_at":"2025-09-23 12:11:33","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":105842,"visible":true,"origin":"","legend":"\u003cp\u003eThe stress-strain curves of specimens with different anisotropy angles under various loading-unloading rates: (a) 0º, (b) 22.5º, (c) 45º, (d) 67.5º, and (e ) 90º, (f) schematic diagram of loading-unloading stress-strain curves.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/5f7dfb0e0717b2719a9b4b02.png"},{"id":91987586,"identity":"d12140b1-cec4-44d4-8379-715e1ac43b0a","added_by":"auto","created_at":"2025-09-23 12:10:49","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":34123,"visible":true,"origin":"","legend":"\u003cp\u003eThe UCS of specimens with different anisotropy angles under varies loading-unloading rates.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/21baee6185b1c21d6c52c299.png"},{"id":91987814,"identity":"b8aafe3a-ac09-4907-9117-3817dad58b69","added_by":"auto","created_at":"2025-09-23 12:11:48","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":259375,"visible":true,"origin":"","legend":"\u003cp\u003eThe regression analysis result of Eq. (2) of the UCS under different cyclic loading-unloading rates\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/b9ed2357c2b7185daecd14b2.png"},{"id":91987690,"identity":"4f60d4f4-e7e7-450b-a33e-3e0000806f01","added_by":"auto","created_at":"2025-09-23 12:11:08","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":29084,"visible":true,"origin":"","legend":"\u003cp\u003eThe axial strain of specimens with different anisotropy angles under varies loading-unloading rates.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/50d6f1a60a4145fdd52cf600.png"},{"id":91988294,"identity":"4dfc3ed3-93fc-4b2f-bdde-246d4abc1340","added_by":"auto","created_at":"2025-09-23 12:19:08","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":31093,"visible":true,"origin":"","legend":"\u003cp\u003eThe elastic modulus variation with the anisotropy angle under varies cyclical loading-unloading rates.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/0252cc82f198fd5e385b280f.png"},{"id":91987700,"identity":"1dc0ae34-7f02-48cc-aed6-d5f5eef8e6a7","added_by":"auto","created_at":"2025-09-23 12:11:12","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":889545,"visible":true,"origin":"","legend":"\u003cp\u003eTypical failure characteristics of coal specimens with different anisotropy angles and loading-unloading rates: (a) monotonic loading; (b)0.025 MPa/s; (c)0.050 MPa/s; (d)0.100 MPa/s.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/16cd6431a21038c2bbd6f5e9.png"},{"id":91987585,"identity":"64330fa3-d75c-46df-bc32-59943aa07083","added_by":"auto","created_at":"2025-09-23 12:10:49","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":527703,"visible":true,"origin":"","legend":"\u003cp\u003eThe horizontal strain variation in specimens with different anisotropy: (a) monotonic loading; (b) 0.025 MPa/s; (c)0.050 MPa/s; (d)0.100 MPa/s.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/606855ad63c6301ffc4a85fb.png"},{"id":91987726,"identity":"26250e8e-ece1-4827-8ae5-34a6cafc81bf","added_by":"auto","created_at":"2025-09-23 12:11:26","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":34192,"visible":true,"origin":"","legend":"\u003cp\u003eThe cumulative AE counts variation with the anisotropy angle and the cyclic loading-unloading rates\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/69b5731892dba02bb7d85144.png"},{"id":91987587,"identity":"741efdc1-6dc1-4f41-9dd0-7dc2c5f2a0e9","added_by":"auto","created_at":"2025-09-23 12:10:50","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":34574,"visible":true,"origin":"","legend":"\u003cp\u003eThe cumulative absolute AE energy variation with the anisotropy angle and loading approaches\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/bbdbbdd57c4f0cb433d9fd3f.png"},{"id":91987758,"identity":"97f1b78b-51a8-43d6-b024-9c1705b21ef2","added_by":"auto","created_at":"2025-09-23 12:11:35","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":31098,"visible":true,"origin":"","legend":"\u003cp\u003eThe damage variable of the coal specimen under different cyclic loading-unloading rates\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/152d29c29b02de3b032e315a.png"},{"id":91987593,"identity":"7d85f189-a6a2-4ccf-b4fa-df97983fed09","added_by":"auto","created_at":"2025-09-23 12:10:52","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":37742,"visible":true,"origin":"","legend":"\u003cp\u003eCumulative dissipated energy density in specimens with different anisotropy angle and loading rates\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/7863f7eb8ee149f07828e4ab.png"},{"id":91987592,"identity":"427fc953-adc7-4bae-9c58-955f56e6caf5","added_by":"auto","created_at":"2025-09-23 12:10:52","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":45174,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelations between UCS and the CDED in specimens with different loading rates\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/db8272a565352952e72dc9a7.png"},{"id":97178789,"identity":"1b3475bb-83fc-4ae4-b527-1643c969587e","added_by":"auto","created_at":"2025-12-01 16:13:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3610000,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7522397/v1/dd9834c9-51c3-4315-8e7c-aad04b35cf24.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Influence of Cyclic Loading-unloading Rates on the Uniaxial Mechanical Anisotropy of Coal","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe mechanical property of coal is loading-rate and loading-direction dependent, coal specimens generally exhibit different mechanical responses as the loading direction and the loading rate changes\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. During the coal mining process, coal mass around roadway and workingface spaces frequently subjected to various degree of cyclically disturbances that comes from different directions\u003csup\u003e\u003cspan additionalcitationids=\"CR9 CR10 CR11\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, which makes the anisotropic coal mass exhibit diverse failure characteristics, due to the varying cyclically loading-unloading rate difference generated by these disturbances complicate the mechanical anisotropy of coal\u003csup\u003e\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Thus, exploring the anisotropic mechanical behavior of coal affected by the cyclic loading-unloading rate is meaningful to coal pillar designing, roadway support assessment, and coal mass failure mechanism analysis.\u003c/p\u003e\u003cp\u003ePrimary structures are broadly exist in coal mass, which is generated during the sedimentary and geotectonic movement process of the coal formation, including mineral inclusions, pre-existing discontinuities, and weakness interfaces\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. These part of primary structures contributes to the mechanical anisotropy of coal via affecting the generation, propagation, and coalescence of failure cracks\u003csup\u003e\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Meanwhile, these primary structures behave a spatially directional distribution characteristics, and the bedding plane is generally chosen as the reference structure in the mechanical anisotropy investigation\u003csup\u003e\u003cspan additionalcitationids=\"CR22\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, considering the visually recognizable feature of it. Explorations and descriptions of the mechanical anisotropy of coal were broadly carried out based on the inclination variation of the bedding plane to the loading direction\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, viz the anisotropy angle.\u003c/p\u003e\u003cp\u003eThe influence of cyclically loading-unloading process on the mechanical parameters of coal and rock material is more complicated\u003csup\u003e\u003cspan additionalcitationids=\"CR27 CR28\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. Mechanical parameters and failure characteristics of coal and rock exhibit different variation features as been loaded under different loading rates\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e, loading path\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e, fatigue stress level\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e, and the amount of loading-unloading cycles\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. In recent years, the mechanical anisotropy of coal was also proved strengthen when it subjected to the cyclical loading-unloading process\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. However, the mechanical response of anisotropic coal affected by the cyclical loading-unloading rate still remain unknown, corresponding investigation or experiment are rarely mentioned. Thus, extensive works are needed to implement in this area, and clarify the evolution characteristics of mechanical parameters and failure modes of coal as been cyclically loaded-unloaded under different rates.\u003c/p\u003e\u003cp\u003eIn this study, a detailed exploration on the mechanical anisotropy of coal affected by the cyclic loading-unloading rate was systematically carried out under the uniaxial compressive condition. Three stress cyclical loading-unloading rates (0.025 MPa/s, 0.025 MPa/s, 0.025 MPa/s) and five anisotropy angles (from 0\u0026ordm; to 90\u0026ordm;, with interval of 22.5\u0026ordm;) were chosen. The microscopic or macroscopic failure characteristics of coal specimens are respectively been monitored by the acoustic emission (AE) and digital image correlation (DIC) monitoring instruments. After that, the mechanical anisotropy of coal affected by the cyclic loading-unloading rate was thoroughly analyzed.\u003c/p\u003e"},{"header":"2. Experimental Scheme","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Coal Specimen Preparation\u003c/h2\u003e\u003cp\u003eTo facilitate the observation of strain and fracture propagation on the coal surface, coal specimens were processed with the quadrilateral prism form. It was prepared with a height of 100 mm and a side-to-height length ratio of 1:2. Meanwhile, five anisotropy angles, namely angles between the loading-unloading direction and the inclination of the bedding plane, were chosen from 0\u0026ordm; to 90\u0026ordm;, with an angle interval of 22.5\u0026ordm;, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a).\u003c/p\u003e\u003cp\u003eSixty specimens respectively with five anisotropy angles mentioned above were acquired, twelve specimens for each anisotropy angle. For specimens with the same anisotropy angle, they were randomly divided into 4 groups, namely, three specimens for each anisotropy angle per group, part of the specimens used in this study were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Experimental Instruments\u003c/h2\u003e\u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\u003ch2\u003e2.2.1 Uniaxial Testament Facility\u003c/h2\u003e\u003cp\u003eThe servo-controlled stiff uniaxial cyclic loading-unloading equipment was adopted in the experiment, which was produced by the Mechanical Testing \u0026amp; Simulation (MTS) Corporation. It has both the cyclic and the monotonic loading-unloading capabilities. Meanwhile, it also provides two loading-unloading model, respectively, strain and the stress control model. The maximum loading capability of this instrument is 300 kN, with an accuracy of \u0026plusmn;\u0026thinsp;0.3%.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\u003ch2\u003e2.2.2 Acoustic Emission Monitoring Equipment\u003c/h2\u003e\u003cp\u003eA broadly used acoustic emission monitoring device was adopt to detect the AE activity generated during the cyclic loading-unloading process, which was produced by Physical Acoustics Corporation (PAC). This system includes a PIC-2 device, a 6-type preamplifier, and four micro 30 s sensors. It has a bandwidth frequency of 1 kHz\u0026thinsp;~\u0026thinsp;3 MHz, and the maximum signal amplitude of it is 100 dB. Here, the amplification gain was chosen as 40 dB, during the monitoring process.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e2.2.3 Digital Speckle Monitoring System\u003c/h2\u003e\u003cp\u003eA non-contact displacement/strain video measuring instrument was adopted in this experiment (IMETRUM, model ISM-CONTAR-VG5-2D-10G). It consists of a system controller, a dedicated digital camera \u0026minus;\u0026thinsp;10GigE, with an acquisition of 68 fps and a resolution ratio of 4096\u0026times;3000, six core cables, a calibration tool, a digital image correlation (DIC) full field measurement module, and LED light source.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Testament Methodology\u003c/h2\u003e\u003cp\u003eTo acquire a reasonable cyclic loading-unloading threshold, specimens with different anisotropy angles were tested under the monotonic uniaxial compressive condition. A stress loading approach was adopted in this research, with a loading rate of 0.025 MPa/s. The uniaxial compressive strength range was obtained with the maximum value of 9.24 MPa (anisotropy angle 90\u0026ordm;), and the minimum value of 1.26 MPa (anisotropy angle 22.5\u0026ordm;).\u003c/p\u003e\u003cp\u003eBased on the acquired strength range, the begin value and stress increment per cyclic loading cycle were respectively selected as 0.6 MPa and 0.4 MPa, meanwhile, the unloading ended with the axial stress of 0.2 MPa in per cycle. Three loading/unloading rates were chosen, separately 0.025 Mpa/s, 0.050 Mpa/s, and 0.100 Mpa/s. The specimens were cyclically loaded and unloaded until failure, the loading-unloading path is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Strength and Deformation Anisotropy","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Stress-strain Curves\u003c/h2\u003e\u003cp\u003eThe stress-strain curves of specimens with different anisotropy angles under three cyclic loading-unloading rates were summarized, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. It indicates the stress and strain varies with the anisotropy angles and cyclic loading-unloading rates. Specimens usually have greater UCS and experience more axial deformation before the specimen failure at anisotropy angles of 90\u0026ordm; and 67.5\u0026ordm; than that of 22.5\u0026ordm; and 45\u0026ordm;. Instead, specimens were observed with greater UCS value, while less axial strain at the anisotropy angle 0\u0026ordm;.\u003c/p\u003e\u003cp\u003eMeanwhile, specimens experience more cyclic loading-unloading cycles in anisotropy angles of 0\u0026ordm;, 67.5\u0026ordm;, and 90\u0026ordm; than that of 22.5\u0026ordm; and 45\u0026ordm;. The increasing cyclic loading-unloading rate has a more complicated influence on the stress and deformation of coal, mechanical parameters variation such as the UCS and axial strain changes with the anisotropy angle. Thus, calculation and statistical analysis should be made to reveal the mechanical variation affected by the cyclic loading-unloading rate.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Uniaxial Compressive Strength\u003c/h2\u003e\u003cp\u003eThe mean value of UCS in specimens with different anisotropy angles were summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. It behaves as a U-shaped characteristics, at the anisotropy angle range of 0\u0026ordm; ~ 90\u0026ordm;. The UCS usually obtained the maximum value at the anisotropy angle 90\u0026ordm;, and with the minimum value at anisotropy angles 22.5\u0026ordm; or 45\u0026ordm;, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. This feature accords with the UCS anisotropy characteristics in coal and stratified rocks reported before\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e, which illustrates the internal structure, especially the bedding plane, still notably impacts the mechanical failure of coal.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe UCS exhibits an overall reducing trend as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.10 MPa/s. It reduces from 5.18 MPa to 4.71 MPa, with a reduction of 0.47 MPa, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Meanwhile, this variation is more complicated in coal specimens with different anisotropy angles. An overall reducing feature was observed at anisotropy angles 0\u0026ordm;, 22.5\u0026ordm;, 67.5\u0026ordm;, and 90\u0026ordm;, respectively with reductions of 0.02 MPa, 0.60 MPa, 0.62 MPa, 1.34 MPa. While it increases from 1.62 MPa to 1.86 MPa at anisotropy angle 45\u0026ordm;, with an increment of 0.24 MPa. The anisotropy feature of the UCS reduces with the increasing cyclic loading-unloading rate, the standard deviation of specimen with different anisotropic angle reduces from 3.45 MPa to 3.13 MPa, as it increases from 0.025 to 0.100 MPa/s.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe average UCS value in specimens with different anisotropy angles under varies cyclic loading-unloading rates.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eAnisotropy angle (\u0026ordm;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eUniaxial compressive strength (MPa)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.025 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.050 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.100 MPa/s\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.37\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e7.35\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e22.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.23\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e45\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.86\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e67.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.95\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e90\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e9.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e12.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e8.18\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAverage value (MPa)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.71\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eBased on the similarly U-sharped UCS feature observed in the coal and layered rock in specimens with different anisotropy angles\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e, the UCS anisotropy under the cyclic loading-unloading condition, which is usually represented in forms as\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 421px; height: 31.4277px;\" width=\"421\" height=\"31.4277\"\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003eM\u003c/em\u003e and \u003cem\u003eN\u003c/em\u003e are material-related constants; \u003cem\u003eθ\u003c/em\u003e is the anisotropy angle, \u0026ordm;; \u003cem\u003eθ\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e is the anisotropy angle with the minimum UCS, \u0026ordm;; \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ\u003c/em\u003e\u003c/sub\u003e is the UCS with the anisotropy angle \u003cem\u003eθ\u003c/em\u003e, MPa. Thus, to have a fundamental understanding on the overall changing characteristics of the UCS with cyclic loading-unloading rate and the anisotropic angle, a unified correlation was developed after numbers attempts, which can be represented in forms as\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 378px; height: 40.563px;\" width=\"378\" height=\"40.563\"\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ,v\u003c/em\u003e\u003c/sub\u003e denotes the UCS of specimen with the anisotropic angle of \u003cem\u003eθ\u003c/em\u003e and the cyclically loading-unloading rate of \u003cem\u003ev\u003c/em\u003e, \u003cem\u003eA, B\u003c/em\u003e, and \u003cem\u003eC\u003c/em\u003e are material and loading-unloading rates property related parameters. The fitting curve of the experimental data and the Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) exhibits a good correlation and the correlation coefficient is 0.89, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Which also indicates the applicable of this correlation in describing the correlation of the UCS, the cyclic loading-unloading rate, and the anisotropic angle, at the cyclic loading-unloading range of 0.025\u0026thinsp;~\u0026thinsp;0.100 MPa/s.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn addition, the variation of the UCS with cyclic loading-unloading rate increases may be contingent upon the UCS of coal. Based on the previous research, the strength thresholds exist in coal\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, which decides the strength increases or reduces with the increasing loading-unloading rate as the UCS greater or lower than the strength thresholds.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Axial Strain\u003c/h2\u003e\u003cp\u003eThe peak strain of coal specimens under the cyclic loading-unloading conditions were summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Variation feature of these specimens were exhibited in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIn general, the axial strain behaves a firstly reducing and then increasing feature at the anisotropy angle range of 0\u0026ordm; ~ 90\u0026ordm;, the minimum value is usually observed at the anisotropy angle 22.5\u0026ordm; or 45\u0026ordm;. This accords with the anisotropy character of UCS, namely specimens with greater UCS generally have a greater value of peak strain, apart from specimens with the anisotropy angle 0\u0026ordm;, where specimens have lower axial deformation capability, since the loading-unloading direction is perpendicular to the bedding plane, where the axial deformation depends on the axial deformation of layered coal matrix\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe axial strain of specimens with different anisotropy angles under varies cyclic loading-unloading rates\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eAnisotropy angle (\u0026ordm;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eAxial strain (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.025 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.050 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.100 MPa/s\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.36\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e22.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.12\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e45\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.64\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e67.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.57\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e90\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e5.41\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAverage value\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.22\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe anisotropy feature of the peak strain changes minimal as specimens have been cyclically loaded-unloaded, besides the cyclic loading-unloading rate of 0.050 MPa/s, where the axial strain increases with the anisotropy angle at 0\u0026ordm; ~ 22.5\u0026ordm;, while reduces at the anisotropy angle range of 22.5\u0026ordm; ~ 45\u0026ordm;, and then it increases to the maximum at 90\u0026ordm;.\u003c/p\u003e\u003cp\u003eUnlike the axial strain reduction with the increasing loading-unloading rates in sandstone\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, the increasing cyclic loading-unloading rate also gains the axial deformation capability, the average value of peak strain increases from 2.97\u0026ndash;3.22%, as the loading rate increases from 0.025 MPa/s to 0.100 MPa/s. Meanwhile, the axial strain variation in different anisotropy angles also behaves inconsistently, as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s. It increases with the loading-unloading rate at the anisotropy angle 0\u0026ordm; and 90\u0026ordm;, while having an overall increasing behavior at 22.5\u0026ordm; and an overall reduced trend at 67.5\u0026ordm; or 45\u0026ordm;. The anisotropy feature of axial strain decreases with the increasing cyclic loading-unloading rate, the standard deviation reduces from 1.46\u0026ndash;1.34%, as it increases from 0.025 to 0.100 MPa/s.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Elastic Modulus\u003c/h2\u003e\u003cp\u003eTo investigate the effect of the cyclic loading-unloading rate on the stress and deformation anisotropy of coal, the tangent elasticity modulus were calculated. The elastic modulus behave a U-shaped anisotropy feature, as the anisotropy angle increase from 0\u0026ordm; to 90\u0026ordm;, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. However, it behaves a symmetric anisotropy character with the UCS. The elastic modulus generally has the maximum value at the anisotropy angle 0\u0026ordm;, while minimum value at 45\u0026ordm; or 22.5\u0026ordm;, and the second largest value at 90\u0026ordm;.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe value of elastic modulus has an overall reducing feature with the increasing cyclic loading-unloading rate, the average elastic modulus increases from 0.39 GPa to 0.41 GPa, and then reduces from 0.41 GPa to 0.37 GPa, as the loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe elastic modulus of specimens with different anisotropy angles under varies cyclic loading-unloading rates\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eAnisotropy angle (\u0026ordm;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eElastic modulus (GPa)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.025 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.050 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.100 MPa/s\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e22.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.19\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e45\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.20\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e67.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.31\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e90\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.64\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.39\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAverage value\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.37\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eMeanwhile, the elastic modulus has similar anisotropy feature with the UCS as the cyclic loading-unloading rate gain. It exhibits firstly decreasing and then increasing feature at anisotropy angle of 0\u0026ordm; and 67.5\u0026ordm;, while a firstly increasing and then reducing feature at that of 90\u0026ordm;. Meanwhile, it respectively illustrates an overall increasing and decreasing character at 22.5\u0026ordm; and 45\u0026ordm;, as the cyclic loading-unloading rate increases from 0.025 GPa/s to 0.100 GPa/s.\u003c/p\u003e\u003cp\u003eThe anisotropy of elastic modulus also increases as the cyclic loading-unloading rate gain, the standard deviation increases from 0.22 GPa to 0.24 GPa, as the cyclic loading-unloading rate increases from 0.025 GPa/s to 0.100 GPa/s. Based on the previous research, the strength thresholds may exist in coal, the strength increases or reduces with the increasing loading-unloading rate as the UCS greater or lower than the strength thresholds \u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. This maybe the reasons that the UCS, the peak strain, and the elastic modulus behave differently as the cyclic loading-unloading rate gains in specimens with different anisotropy angles, as shown in Tables\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Anisotropic Failure Characteristics","content":"\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Failure Anisotropy\u003c/h2\u003e\u003cp\u003eTypical failure characteristics of anisotropic coal specimens under different loading-unloading rates were exhibited in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. The failure pattern of the coal specimen changes with the anisotropy angle. The effect of the bedding plane is pronounced at anisotropy angles of 22.5\u0026ordm; and 45\u0026ordm;, where the major failure crack developed along the bedding plane of the coal specimen, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Meanwhile, it also leads to a relatively lower bearing and deformation capacity of specimens at these two anisotropy angles.\u003c/p\u003e\u003cp\u003eThe influence of the bedding plane gradually reduces at the anisotropy angle 67.5\u0026ordm;. The major failure cracks cross and have a greater angle with the inclination of the bedding plane, though coalescence of it with the crack developed along the bedding plane also partially exists, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Which makes the mechanical parameters mentioned above has relative greater value.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe layered rupture feature is observed and failure cracks developed along the bedding plane at anisotropy angle 0\u0026ordm;, due to the lower cohesion that perpendicular to the bedding plane. This may be the reasons that specimens have a relatively lower axial peak strain, greater UCS, and highest elastic modulus, since the bearing and axial deformation capacity of coal are decided by the layered coal matrix.\u003c/p\u003e\u003cp\u003eThe influence of the bedding plane is less obvious at the anisotropy angle 90\u0026ordm;. The major failure cracks are developed cross the bedding plane layers, the deformation and the bearing capacity of coal are mainly subject to the coal matrix, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Thus, the greater UCS and axial strain, while lower elastic modulus are observed.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Failure Anisotropy Affected by Loading-unloading Rates\u003c/h2\u003e\u003cp\u003eThe influence of cyclic loading-unloading rate on the anisotropic failure characteristics of coal is significantly at anisotropy angles 0\u0026ordm; and 90\u0026ordm;. As the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.10 MPa/s, the failure pattern changes from layered failure pattern to X-shaped shear failure pattern, and the amount of cracks developed along the bedding plane decreases at the anisotropy angle 0\u0026ordm;, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Meanwhile, the after-failure specimen becomes more intact and the fragments are not cast far away from the damaged specimen at the anisotropy angle 90\u0026ordm;, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e (d).\u003c/p\u003e\u003cp\u003ePenetrating cracks become mainly propagated along the bedding plane, and the fragmentation behaves more integrated with greater size, at the anisotropy angles of 22.5\u0026ordm; and 45\u0026ordm;, though the fragment degree at 45\u0026ordm; is greater than that of 22.5\u0026ordm;, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e (b), (c), and (d). Wider crack bands, more dusty characteristics, and less cracks generated parallel to the loading-unloading direction around the cracks band were observed at the anisotropy angle 67.5\u0026ordm;, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e (b), (c), and (d).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eBefore the failure of coal specimens, the horizontal strain concentration zones are more intensively distributed in the main through-crack area, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. The area of horizontal strain concentration reduces with the increasing loading-unloading rate, especially at that of 0.050 MPa/s. This also may illustrate a relatively less fracture development after specimen failure, which may contribute to the increasing integrity of the damaged coal specimen.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Anisotropy Revealed by AE Activities\u003c/h2\u003e\u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\u003ch2\u003e4.3.1 AE Count\u003c/h2\u003e\u003cp\u003eAcoustic emission is fracture generation and propagation related activity, which also microscopically reflects the failure intensity and characteristics during the cyclic loading-unloading process. Thus, the cumulative AE counts in specimens with different anisotropy angles under varies cyclic loading-unloading conditions was summarized in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe variation of cumulative AE counts with the anisotropy angle of coal specimens under varies cyclic loading-unloading rates\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eAnisotropy angle (\u0026ordm;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eCumulative AE counts (\u0026times;10\u003csup\u003e5\u003c/sup\u003e)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.025 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.050 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.100 MPa/s\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.54\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e22.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.88\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e45\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.74\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e67.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e6.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.13\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e90\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e8.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e10.87\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAverage value\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.83\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe cumulative AE counts presents a less obvious U-sharped anisotropy feature under the cyclic loading-unloading condition. It generally has minimum values at the anisotropy 22.5\u0026ordm;, while the maximum values are obtained at 90\u0026ordm;. The cumulative AE counts has similar anisotropic characteristics with that of axial strain, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The positively correlation is due to the axial strain represents the irreversible axial deformation generated during the specimen failure process, greater value of axial strain indicates more cracks, namely, greater amount of AE events, generated during the cyclic loading-unloading process.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe increasing cyclic loading-unloading rate strengthens the AE activity, the average cumulative AE counts of specimens with different anisotropy angles gains from 4.03\u0026times;10\u003csup\u003e5\u003c/sup\u003e to 4.83\u0026times;10\u003csup\u003e5\u003c/sup\u003e, as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s. However, the variation characteristics of the cumulative AE counts with the loading-unloading rates also changes with anisotropy angles. It exhibits an overall increasing feature at the anisotropy angle 0\u0026ordm;, 22.5\u0026ordm;, 45\u0026ordm;, and 90\u0026ordm;, while behaves an overall reducing feature at the anisotropy angle 67.5\u0026ordm;.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec19\" class=\"Section3\"\u003e\u003ch2\u003e4.3.2 AE Energy\u003c/h2\u003e\u003cp\u003eThe cumulative absolute AE energy also calculated and summarized in specimens with different anisotropy angles, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e. It behaves similar anisotropic changing characteristics with the cumulative AE counts, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e and \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe cumulative absolute AE energy of specimens under varies cyclic loading-unloading rates\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eAnisotropy angle (\u0026ordm;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eCumulative absolute AE energy (\u0026times;10\u003csup\u003e5\u003c/sup\u003e aJ)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.025 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.050 MPa/s\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.100 MPa/s\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e5.95\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e22.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.79\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e45\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.92\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e67.5\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.05\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e90\u0026ordm;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e9.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e6.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e10.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAverage value\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e5.24\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe cumulative absolute AE energy exhibits a U-sharped variation feature, at the anisotropy angle 0\u0026ordm;~ 90\u0026ordm;, under the cyclic loading-unloading condition. The value of the cumulative absolute AE energy is minimum is at anisotropy angle 22.5\u0026ordm;, while maximum at 90\u0026ordm;. This indicates that greater amount of cracks generated and AE energy dissipated in specimens with anisotropy angle 90\u0026ordm;, where the impact of bedding plane is less obvious. While the crack generation and energy dissipation are less obvious as specimen failure been significantly affected by the bedding plane, namely anisotropy angle 22.5\u0026ordm;and 45\u0026ordm;.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe cumulative absolute AE energy behaves an overall increasing characteristic, as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s. It has an overall increasing feature at the anisotropy angle 0\u0026ordm;, 22.5\u0026ordm;, 45\u0026ordm;, and 90\u0026ordm;, respectively with increments of 3.65\u0026times;10\u003csup\u003e5\u003c/sup\u003e aJ, 0.48\u0026times;10\u003csup\u003e5\u003c/sup\u003e aJ, 0.88\u0026times;10\u003csup\u003e5\u003c/sup\u003e aJ, and 1.12\u0026times;10\u003csup\u003e5\u003c/sup\u003e aJ, while an overall reduction at the anisotropy angle 67.5\u0026ordm;, with a reduction of 0.58\u0026times;10\u003csup\u003e5\u003c/sup\u003e aJ. The increasing cumulative AE counts and absolute AE energy may be correlate to the greater amount of cracks with longer length generated as the cyclic loading-unloading rate gain. Which accords with the increasing fragmented block size in specimen with greater cyclic loading-unloading rate.\u003c/p\u003e\u003cp\u003eMeanwhile, the anisotropy of failure characteristic revealed by the AE activity increases with the cyclic loading-unloading rate, the standard deviation of cumulative AE counts and absolute AE energy separately gains from 3.18\u0026times;10\u003csup\u003e5\u003c/sup\u003e to 3.29\u0026times;10\u003csup\u003e5\u003c/sup\u003e, from 3.18\u0026times;10\u003csup\u003e5\u003c/sup\u003e to 3.48 \u0026times;10\u003csup\u003e5\u003c/sup\u003e, as the cyclic loading-unloading rate increases from 0.025 MPa/s to 0.100 MPa/s.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"5. Micro-failure Affected by Cyclic Loading-unloading Rates","content":"\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e5.1 Damage Variable\u003c/h2\u003e\u003cp\u003eIn general, micro-cracks are usually generated in coal and rock material before the emergence of macro-fractures, and the initiation and growth of micro-cracks are defined as damage\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. The tiny irreversible damage accumulates in each cyclic loading-unloading cycle affects the final failure feature of coal. Thus, the impact of the cyclic loading-unloading rate on the failure process of coal is investigated in this part. In general, the physical quantity used to characterize irreversible damage described above is defined as damage variable. In this research, the residual strain at the last cyclic loading-unloading cycle and peak strain of coal were chosen to evaluate the damage degree as impacted by the cyclical loading-unloading rate. The calculate equation was developed in forms as Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e)\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 345px; height: 41.3142px;\" width=\"345\" height=\"41.3142\"\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e respectively the residual strain in the last cyclic loading-unloading cycle and the peak strain, %, \u003cem\u003eD\u003c/em\u003e represents the damage variable of coal. The damage variable in specimens with different anisotropy angles and cyclic loading-unloading rates were exhibited in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe damage variable behaves a parabolic type variation feature versus the anisotropy angle at the loading-loading rate of 0.025 MPa/s and 0.050 MPa/s. It has the minimum value at the anisotropy angle 0\u0026ordm;, the maximum value at anisotropy angle 45\u0026ordm; (0.025 MPa/s) or 22.5\u0026ordm; (0.100 MPa/s), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e. This anisotropy feature indicates specimens have greater degree of damage at the anisotropy angle 45\u0026ordm; and 22.5\u0026ordm; during the cyclically loading-unloading process. This accords with the failure feature that the major failure crack mainly developed along the bedding plane, where cracks propagate more easily and contribute to a lower value of UCS, peak strain, elastic modulus.\u003c/p\u003e\u003cp\u003eThe anisotropy feature of damage variable also changes at the cyclic loading-unloading rate of 0.100 MPa/s. It changes from parabolic type to wave-type variation. The damage variable firstly increases to maximum (0\u0026ordm; ~22.5\u0026ordm;), then reduces to the minimum (22.5\u0026ordm; ~45\u0026ordm;), finally gains to second largest (45\u0026ordm; ~90\u0026ordm;), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e. This indicates more damage generated by the cyclic loading-unloading process in specimens with greater UCS under greater rates, conversely less damage occurred at specimens with lower UCS value.\u003c/p\u003e\u003cp\u003eIn addition, the damage variable has an overall reducing feature with the increasing loading-unloading rate. It respectively with values of 0.530, 0.507, and 0.528, under the loading-unloading rate of 0.025 MPa/s, 0.050 MPa/s, and the 0.100 MPa/s.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003e5.2 Dissipated Energy Density\u003c/h2\u003e\u003cp\u003eIn this study, the cumulative dissipated energy density (CDED) before last loading process were adopted to illustrate the damage feature of specimens loading-unloading process, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e. The CDED is unrecoverable deformation and strength increment related energy index. It behaves a U-sharped variation character as the anisotropy angle increases from 0\u0026ordm; to 90\u0026ordm;. Which indicates plastic deformation and strength increment is maximum at the anisotropy angle of 90\u0026ordm;, while is less obviously at that of 22.5\u0026ordm;and 45\u0026ordm;.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn combining with the parabolic type variation feature of damage variables, greater percentage of plastic strain generated during the cyclic loading-unloading process at anisotropy angles of 22.5\u0026ordm;and 45\u0026ordm;. This may be the reasons that contributes to the relatively integrated failure pattern of coal specimens with anisotropy angle of 22.5\u0026ordm;and 45\u0026ordm;, since cracks easily developed along the bedding plane, specimen was destructed with less cracks generated, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. This is consistent with the lower AE activity parameter observed at these two anisotropy angles.\u003c/p\u003e\u003cp\u003eThe CDED has an overall reducing feature with the increasing loading-unloading rate, it respectively has the average value of 4.88\u0026times;10\u003csup\u003e4\u003c/sup\u003e J/m\u003csup\u003e3\u003c/sup\u003e, 5.50\u0026times;10\u003csup\u003e4\u003c/sup\u003e J/m\u003csup\u003e3\u003c/sup\u003e, and 4.70\u0026times;10\u003csup\u003e4\u003c/sup\u003e J/m\u003csup\u003e3\u003c/sup\u003e, at the loading-unloading rate of 0.025 MPa/s, 0.050 MPa/s, and 0.100 MPa/s. Greater value of CDED represents more deformation, greater stress increments, and more loading-unloading cycles exists in these specimens. Meanwhile, greater value of the UCS observed in specimens with the greater CDED energy density, namely, the UCS and the CDED are positively correlated, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e. Thus, a power function correlated relationship was proposed after multiple attempts attempts, this correlation can be described by Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e)\u003c/p\u003e\u003cp\u003e\u003cimg 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c+6NWUXfNjoqFggEAhOKgHGATbtxkmav0c2MFwQ6NI+kiI3y1B9jHsVkrtV43zUhVBFiSmSP2q3+pvZ9KJdccsmEENnvh4TQUJka/LWBCzfV9ljqxkaQizc7QYNAozJIVCxBRkrY6PxUHVOfHXfcMbEnIAGl0mcGIATMZNaJlLlTlTEJ1XnnnZde+cpXFmr3nPOjtkj/jTfe2LIJl112WWELp92f+cxnElMHz48tYc551LXUydtss82C+6y22mpF8OxRmXq8o52dYsIhRiDrddZZZ0Edc86jfuvzPgDdVlP/FiAbTuxPLrnkkmTyQMJMWlxbnneJjSEziZxzMlHkhDSVxFadmEMwD1F3Iah4yi+33HLJrBrOzD58n2gOYFm2iQRbP3Jc+3MejWnOOSGBviXsBTlrkZwjhLCu1yaU5cZ2uBGI1gcCnSIwZ86cwtSO8IQ5U6PrTjzxxLTWWmsVJnH13+RG+R0jRUQycRf7jVLXhNDAwAYPsWJDV1+ogR4hpEb1Qa0/3+m+AYV9jkG8VZo7d26nRSZS88MfgwAAEABJREFUIECOjIwkIH7qU59KH/vYxxJpVerwn/Yhe65BCBtdZoCBExLR6Hy3x0hcqTZb4eAcW8ZOyuaFTd1fksLrr78+7bbbbqk2hlEn5Ywlj06O9Bh4DdztyjCAMz3Yddddi+dkloNoIzsGY/sSsTmxeKPyeDSTCCOBJ510UuEABQOONfqCF6W8Tt2o1XfeeeeEEKqnCVDOubAb9WzLvL3a6lNIivLala8+QiqR9LLT9Y5pP0m1dgixZF+aMWNGV2GB1MMKMuxefWw4/fBO4+nGOQw5VMcykbCynfOMxLr0PLfffvvCYemmm25qa5JRllO7JS01OdGfWyV55K291m/vCm9ozm8Cn5OEk0Qz3dAe7fNuUu2qK/te/cO1TBh8DxBfkmP9C55ULUwmRv7z3YDr5ptvnkwiOK29853vdGmypb4xMSkOxJ9AIBAIBMaAACc136xG2kXjp/jKOIjvTzfF+6bLz6FT8rs+dU0IDY4qRZTZaDbMts4Hl0freLw2fZw1XHydVqlZw+obWu6zgTrooIOS+uec05FHHpmQRINZmafVVvuuueaaxA6v0QNzrQFGeaRP9sebsHoDbCscnDOz6PReBvgDDjggGShJDQ2+JDukHJ2WMZZ8SAeyjwC1I/PqQtXP5sH6vuIpkcqQFs6YMaOou32JFzWJT32d3Ev4HAM/osDeixSLREs/Nrhrf3mdl/G0005L4jUiBjnn9PznP7+YOCALCFiZ93/b8f1CAvV3ZK8dJogKG1jvFwLCwUv7xc7ceOON0x577FFIMh3zfDutGXLFW61UQyDhAo/Dadq0aYWzRG1/lh/m+qZ7IqOwQdyR77XXXruQVnZ6/zKf/qGN+nOrJI+85XXl1qQPmX/FK16RTMjYZJplI4O+V569563/I4xU4H7Lp59wnkEmv/3tbxc4XnzxxUUM0ze96U2JqQlcSZaZkpT3jG0gEAgEAr1CwLdVIlSrL9N3zLeJ9mOsvglU0gRa9WXb74oQGrh8FElifGRzzsoYlQxsBnIf2lEnutxxjz333LOwdxNHr1kqWW+nxSOpZvcIxvTp04uYagiGendSBnsq0hB2QwbK+muQDCoqg4wBsv78WPap39/xjne0xYL0opvyDZ5wVTaJ2dlnn50MtJ2UoS9wTEGgOsk/ljykeQZgdfQCiJ+oHMQPSSPJI51yrFliGkAqRE3uecuHSCDP+hjJmmNl8syQIKQh5/n9m4qQtJB6tsxXbqltN9xww9QqISj6RHnNeLZf+tKXij4LE88bwVEeQoYAMYMwIXGsm0RKjAh5n7QVGXQ9j3SkT38vjznuPeL9pt8gWo5JJGkMoRu9G85LJkuIr4+b/drkHp619rVK8shbe235W7+kxRCDU33UlVSV9A5OkvPSa1/72qRfIX76G7JtkqQP5JyT9q266qpp5syZRcT/8h6xDQQCgSFFYAqbzZabAIvwxve/HHeEv0L0jHWOERbQdjWqqrFbanSuK0JIUkN1aRAloWhUoDA0yFCz842umexjBjCgWSUDy/7ABz6QqJY6qQdVFRIEg0YDEskXsmFAaXS+k3tMZh6D5C677JJIzuBBBdjJ/UmzDOwkpp3k7zYPiQ07MJIeoX2o+Msycs4JgafibqUmNzERsNOzovpDDJSBjHhxvFCev2NlmvYfaRiVqZeOSQQyLm95vn6LTF9++eWpVaJyZb9Wf223+9rDq5Xkkvo25/mEVTnahgixCe1Wao7wkXr5oJDIen+VKbkfUkgiVv8MEF2TK+p77xRC6Zp2CSH3QfKutMvb7Xn9EtFDwKnVEWY2kexmqICZG5i0MUfJOadNNtmkCCuF8JlkMD0wGai9r36un/m21R6P34FAIBAITCYCvtHUyXgYbW2ZaDtIFY0RjuEgvnON6mYCbJxrdK4rQqgAg4JB0gBgvzax3/nqV79aqJcana/N2+43SZxB1sy9VWKv2K6sRud93BmGkwgYOBrlaXbMIINI5Py/AbnMqz7Uk+yOcn70+TJfN1u4mhm0wsE5hL2bcuU1MFvSj5OQ8DyO9UMi+UP4SHPqiTU8PD+km5SvWX1hph+95jWvWRD6B4GlGjXA19uAssvYcsst0yGHHJLkQViYP3jWSGSzF6zZ/Xt9XP3Uo9H7RzVuskJqB7Nu7u0jwh7Qe0AaVl7LscbKJCYLsC6Pw9QSSSSSsEUozUZJFkkafZjKvN1uXasu+nOrJI+89eWrh+euP5NqemYIIRUJ8ufdRfD0LWSWCYn2cAqhEl9kkUVGFeke+grJ8corrzzqXOwEAoFAINBrBEzIJaSvvmwrsPkm1SdjOKLHLto55i/146bvnvIIOnwH/a5PXRFCNzQ4kkAYLGsLUwlSFXpv9nm15+p/G0AMuNS2Bvf68/ZJiAAibmCrRFonfzfJAMh2kDTs7W9/ezeXFqt9ILtYOmlE7cUw4b3ItpCNYe252t+dtL8+v8G+FQ7OCVBZe10nv0mAqMAZqFKNdnLNePKQZOnsMGxVjr5mgDYj0rfKvDCn/qNKZq9GOlWes2UDpm/BmMTMfRAo5ySkChkgYaNSdExCjJEcsyvlGvxzzoXdmJdMGADkQt5eJxIpmOTcegLBDINHq3cGDmU9kFwOMvoIUk/qW55rtkXcqJe9C8qTavssEiWPCSAJK0KkLPdl23f00UcXHm4+UOrP1IDdoQmW+sg7lkR66Pnoz62SPPLW34PkWH8mDWQS4Z30HWEu4Jj8Zs8IIM9jz93HUR/RZ+SXp0wmJvoUSTX1c3k8toFAIBAITAQCvsOSb3Ijs5qx3pPAyPfct5DZVaNyuiKEBqQDDjggsbmjoy4//EgZqQqJAgPzcvBodEPHDCAGQB9qvx2rTyQ/DNzpylulNdZYo/7SlvsPPfRQsVSZuqurQaPlBXUnSVColYTaENS5PG2AMhgbVEhK2B6V5+q32ly2H8lg50aF5Xd9XvsGK4NtKxycGxkZkb3jBH8rllB7GvSRtY4vHmNG99B2HbNVEcgaT2iOJCS5Xg6DN+cJsx82gTCpLwOJJNVzH2pOzwFBQBTOOOOMIgi3spg0UC2W18MewZBIjMym5GebIc4Tr1Rllvl7uVVHpCTn1oSQ9E+bTTqosRFl7WJXSOWLpJGCdVI3hBspQphh5gPEiYsEErFE8GDhg2RGaQJUlus4YohMwkl+qmZSOKuayF/m7XZrVktKqz+3SvLIW1++bxEVN6cWuKqTdunf1CTqbVIAO98pk1tYvPWtb03ULvvvv3/hhU7SiPjyHjY50A88o/r7xX4gEAgEAr1EAM+i4TBG+ib1qmzjPYGCya2yG5XbFSE0IPK+NPBQ5xhIfPwFR0SUGPmTEDa6kWMGXR9iWxIIgaJ9tJ2bjOS+JGISu0HAd3tfg4JreZySKBmUSNYcmzFjRqJiM/A0Ktf969uvPB6Mwvjk3JoQNCpzrMfYWCFVlm5DIhCDsZY11uuQ/mbXqg+pJSkyO0CSadJAHlYIEbKIWNZfjwAgggZ7RM5Abk3qHXbYISF1pDwkaCRB7ArL6/VjJJ9dIacCz9B11n1mA1irMi2vmYgtFWazcr0rCLz+oo4mM6TxpOnsLdkWylN7PfImOYYMSX6TvLoWrt4DAcqRI/gweWBjy3FMXngh6H77BogHaTJ11llnJThRNXNGIUV1nTzyTkUSQ1CdfFBzzgmh9ayph72r3kFkDw7shpE99YWdKP6INpW7ZOKBbOsH8uY8ee/nVGBXxXtGmwKBQUPA2EfzYqJqUtpJ/X3DCJpc2yi/756yfBsRwkZ5HOuKELog51yEbOGRavAlIRCGBVGsH4zkLxPpDj03SQKJFDufbqV7ZVlj3bonqQPyhsCOtRyg804keSBpJJHgfW1QbFZms/aTtnKawN6bXdvr4wZ+qj1EvluVea/r0q480ljSKjjznjVoNwuIbqCnTkYIy3JJmUn89D2kBvFDMknUEPkyn+306dMTYuVekucLI0TC+X5I6o/kkuSpI5WmwOKIXX392BWKtam/e1e/+c1vJupPBFF/IzUrr2E+YTZKwiYosz6OHOsr9baWcBMBgHRSHUzueASTZJflTdXWpEwk/pLAc+YhyUf4cs5F/FF5qMPrP4zIrOPapM8gh+P5TqT4FwgEAoHAGBAwgfX99c2mdWxXBFtu32ratEZ5aW9900xuGwlSymu6JoTlhd1szcZ9XEkQeHBSe5GMTeYAwgmBOoikqH6Aa9UWdTeYtsrT7pwymrWfZ6OBqZVkqF353ZxHTMXZM5sQjLqbaxGAbvI3yptzLgKENxNZN7qm+bHRZ6hASb5Irkef6e895Mv7kHNvJVD6LSksAleSQJMwz5G9KclgfyMTtQsEAoFAYPgQMPEnuEDeCI3Gg4AJrgUGCDdoc1qVNSmEkNRBYGXhTdgq2UeANLpV5Xp1jq0T9a6QExwGupH4MEAnYaDqHWt9tLdZ+9kzUckR5Y61/G6u0xbqfsScWqzTa5GLE044oQjR4RoqWRI3dbffaSLa9twnghBSJ+vw3TzfTus9kflI1uGZc28JIUkqSSDJNQcbkjzHeM3qb+woJ7Jdzcr2/PUddWiWJ44HAoFAIDAKgSHb8a22uhbtFoeQsTSfMMqiE8xmmBsZZ1qVMymEUGw0gw8CQo1FFcfGh5SqVeV6cQ47FjzYvdjLGYw6LZfenVRT/Tu9plE+1zdrP/UW+0FEqdG1vTwmFhtVH3sxkqKcOycg1LY8cHUwdVJfxAuu9jtNOedEMkw6xS6r0+va5WNHx0lEuB9S0Hb5++k8CSEsSlx6VTcqdph41swl2Azq/9TM7A99JHp1r27KMRnQd7S7m+sibyAQCAQCw4QA1THhDXttY1w3bcdfcA9CAWWYhLe7flIIIbGn+HyXXHJJEd9NpUhFVNjviUzCkxgMGeHzsOnkXtRrBlMSJ/ZZpJrjGbyatZ/aDi4GaffspG5jzWOGYYbAkWRkZKTjYtgv8NKFA4kO1WbHFzfImPP81R+Qgganx3wIjjnnYr3jicZyzJVsciFyjVjn3DlBb1LUqMMw0ecRZFJB9+GBzdYEGWRzOeqCqd2JuwcCgUAgEAjUIYAUbr311gmPqTvVcldkCMI3ZHD69Okt85YnJ4UQ8uQjBWO7ZMkpNnwqaIAqKzIRW3HMOBUYBBlnMsYXFqNd4kHJw5WtI4cRhunjqV+z9iNXQtTwJuo1QaqtL3J78MEHJ84/yADHmnYYlOdJVTmesGNg71hb7lh+55wTNbOEKI+ljEbXwHLzzTdPnABIvxrl6ddjnj0PauStl5iQSnvX2BDair0oCoAtJxISyX7FJOoVCAQCgUAgMB8BHMQ3fP5eZ3993znQNYs52KiUSSGE9NabbbZZ4tBBVcgjhg1hzr2ViNQ2kBMJm0WOBuz3eNeIldhJkvecc85JRLS8N6m6a8vu9nez9ntg4p/Zdltmp/lJh6jMGZXyMhJGoxMMyjyutSoECVYZhsS9leRl6+sAAAeoSURBVEsCxT7TfjcJHrxAkZNurmuV1wuDXHfT+VuVN9nnkEGkUH/r1b3ZoJCMk3Czn/XeIcucmHhiT/SErFk7SJ31He9XszxxPBAIBAKBQGByEZgUQji5TUrFOreMManJDLTjSQgG9fZkt6FX9xN7SHxIg/94caDaLuvFlpB9ZqdqR2F5kB1OH2IgIsEko2V5w7ZlLnHUUUcltnRiKiLWSK1nVHUsyr4zHketqmM06O2L+gcCgcDgIVBJQohoiMdDAkHlO55Eb0/CMniPdn6NBRHmYToeDFyrDGXNL7W7v6SJM2fOTFYIufDCCxN7CIRwGMhPM6R4bVt1BaG2jCI7D7Etm+WP44FAIBAIBAKBwEQiUElCOJGARdkQ6C5RN1slRHxAErFtt902WW3D8e5Kqk5uNo/iQpG6IsdsNQVGrk4LoyWBQCAQCAQCg4RAEMKap8UTlwMFaVjN4aH8CQNYwGS8AFBXUxXzMidxZZ/IHjHnibMhHW+dJ/p6jiScljj6kJ5yeOLFPdH3jfIDgUAgEOgKgcg8NAgMBSFkwG7AnT17dtMHK0A0o3shVqjxmmYc8BOWGjz88MOT+Ifs2Bo1B168rAXEpO5tlKfbYyRhYk+uttpqiaQw5+ElgyV2VObw4BndS+/isvzYBgKBQCAQCAQCnSJQeUIoJp1g2JtuumkS/LcZMLwuBV7m/dosTxWOc15AzMQ2yrkxKRPA8qSTTkrrrrtuFZocbWiNwJSczTknUtIU/wKBQCAQCAT6AoHKE0JSMJG6zzzzzAXLrvUF8lNUCTEJLUFnO54qsIFDnmNQHw+Kw3ltzrmQEouTOJwIRKsDgUAgEJgKBFrfs/KEMOechI5Zb731EhIjUDU1XW0iPbzxxhtbI1WRs9SUJIQ8pw899NBUi4PfcLJMTrvmwlQ5OTeWMra7Ps4PLwI8rPUfzjTDi0K0PBAIBAKB/kKg8oRQrLx77703WRnF8nMHHHBAsthzbTr11FMLYtRfj2ZiaoP4CliMGO66666PwuL8889Pm222Wdub55zT6quvngQAJ4Vte8F/MngW4kO6P+mQ1WP+c3ho/w8rHvfff3/S/9iVDu3Dn6CGR7GBQCAQCIwVgcoTQvaD7OaQECAdc8wxicNEbdpnn33SrFmznK50QkAuvfTSxH4QiUPIanHwW/gTwaw7AWKllVZKyuOo0kl+q6TwOL799tsTYmj5uk6uq2qeYcRDUGor5lixSAiiqj7baFcgEAgEAoOGQOUJ4ezZsxOJRM45IUHWKUaEapOVPCyjxvv2tttuSySG1l3uv4c5vhrxHr777rtTzvOx2HHHHVMtDn6fcsopaf31109nnHFGgsURRxyRSFgb3Xn55ZdPDz/8cLrvvvsanX7UMQHDSSiFnRkZGUnDHndvGPEo+wsHr0FeAehRnTsOBAKBQCAw4AhUnhCuueaaad99902kUTk3t3ejwhJ3TzgW6wtXMQwI7+Fjjz02WUeapK5Z37XWMLXxeeedl3bfffdEvdsoL0ypja+++upGp0cdu+qqq9I999yThP/ZbrvtUrk+NOntRRddlIZtGbNGeJC0IukHHXRQZR2grFYjtiUTjlZ9cFTniZ1AYBgRiDYHApOMQOUJ4aKLLpoQoXbSCOdJvMSEW3bZZZP9SX4WE347KrrlllsuIXytbsZzGGacRlZcccWm+Q3opHxUzKSwzcpEdCzT5rzgy9T2wtpQYcPZKibsO50fhtQMD7hvvPHGabHFFkuwIdGuGh7XXntt0Z9WXnnlqjUt2hMIBAKBwEAjUHlCONBPZwAqv/baaxcSxJtvvjmxD2tUZc4DO+ywQ5ozZ07ae++9k3A1W221VZF1r732ShxZip0h+fNfPB6FB4LNJpONJdLcq6Dg/QLrvHnz0sUXX5xMAGDQL/WKegQCgUAgEAikFIQwesG4EKBq32CDDQpS10pKSLV8/PHHF/aZHFeom3POhfqak8u4KjGAFzfCY+7cuYntqjBIu+22W6oSaWIScNxxxxWTgY022mgAn1hUORAIBAKBsSIwGNcFIRyM59S3tSTV4iBC1X722Wd3VU8OP5wMqKe7urCima+44opElXrHHXeku+66q3CCqkpT2ZkivDvvvHNaeOGFq9KsaEcgEAgEApVBIAhhZR7l1DWEbSJHER7MX/7yl1Ona0FzKMk5J2FIpq72/XNnzhalOpWtZc65fyo3xpqwg7RSELK75557FsHhx1hUX18WlQsEAoFAYNARCEI46E+wT+qPFO6///5FwGF2cOI/IgOtqof88ACPFSvmo7TffvsVQcF32WWXJCzL/KOD+5eaWOgi9qVbb711WmqppQa3MVHzQCAQCAQqjkAQwo4ecGTqBAGkcJtttkkrrLBCakcGOykv8gw+AtTDW2yxRRLEPOfBl3gO/hOJFgQCgUAg0BiBIISNcYmjY0RA+Bjhe5ZYYokiAPYYi4nLKoCAvmBysPjii1egNdGEoUEgGhoIDCkCQQiH9MFHswOBQCAQCAQCgUAgECgRCEJYIhHbYUEg2hkIBAKBQCAQCAQCdQgEIawDJHYDgUAgEAgEAoFAoAoIRBu6QSAIYTdoRd5AIBAIBAKBQCAQCAQqiMD/AwAA//+nRm/SAAAABklEQVQDANS/+kKn19UGAAAAAElFTkSuQmCC\" style=\"width: 488px; height: 59.9565px;\" width=\"488\" height=\"59.9565\"\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e represents the cumulative dissipated energy density, J/m\u003csup\u003e3\u003c/sup\u003e, \u003cem\u003em\u003c/em\u003e is the material related parameter, J/(m\u003csup\u003e3\u003c/sup\u003e\u0026bull;MPa), \u003cem\u003en\u003c/em\u003e is the loading rate correlated parameter, \u003cem\u003eσ\u003c/em\u003e is the UCS of specimens with different anisotropy angles, MPa. The regressive analysis result was summarized in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eObviously, the experimental data has a good correlation with the Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, and respectively with correlation coefficient of 0.85, 0.97, and 0.79 at the loading-unloading rate of 0.025 MPa/s, 0.050 MPa/s and 0.100 MPa/s. Parameters of Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) are exhibited in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Based on Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) and Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e, this verifies the CDED positively correlated with the UCS in per loading-unloading rates.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eParameters of Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) obtained by regression analysis\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLoading rate (MPa/s)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003em\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eCorrelation coefficient\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.025\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e285.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.85\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.050\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e285.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.100\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e285.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.79\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eIn this study, the impact of the cyclic loading-unloading rate on the anisotropic mechanical response of coal were experimentally investigated. Research findings and conclusions were summarized as below.\u003c/p\u003e\u003cp\u003ea. The UCS and elastic modulus maintain a U-shaped anisotropic characteristics under different cyclic loading-unloading rates. The anisotropy of UCS and axial strain decreases, while the elastic modulus ascends with the increasing loading-unloading rate. The correlation of the UCS, the loading-unloading rate, and the anisotropic angle of coal specimens can be described by a cosine function.\u003c/p\u003e\u003cp\u003eb. The failure characteristics of coal are bedding plane related at anisotropy angles of 0\u0026deg;, 22.5\u0026deg;, and 45\u0026deg;, where the penetrating crack mainly propagate along the bedding plane. The after-failure coal specimen is more intact and the anisotropic failure feature of the coal specimen becomes more notable, as the loading-unloading rates increases.\u003c/p\u003e\u003cp\u003ec. The anisotropy of micro-failure characteristics revealed by the AE activity rises with the cyclic loading-unloading rate. The cyclic loading-unloading generates more damage as specimens with lower UCS, the damage variable caused by it exhibits a parabolic anisotropy feature at 0\u0026ordm;~90\u0026ordm;, and the greater value were generally observed at 22.5\u0026ordm; or 45\u0026ordm;, though this anisotropy decreases as the loading-unloading rate gain.\u003c/p\u003e\u003cp\u003ed. The dissipated energy density generated during cyclic loading-unloading process exhibits a U-shaped variation feature at anisotropy angle 0\u0026ordm;~90\u0026ordm;, with relatively lower value at 22.5\u0026ordm; and 45\u0026ordm;. Which shows a positively exponential correlation with UCS, namely specimens with greater uniaxial compressive strength has more energy dissipated during the cyclic loading-unloading process.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgments\u003c/h2\u003e\n\u003cp\u003eThe authors acknowledge the State Key Laboratory for Protection and Utilization of Water Resources in Coal Mining, the National Natural Science Foundation of China, the Key Laboratory of Deep Earth Science and Engineering and the China University of Mining and Technology, Beijing\u0026nbsp;for their financial support in completing this paper.\u003c/p\u003e\n\u003ch2\u003eFunding Declaration\u003c/h2\u003e\n\u003cp\u003eThis research is supported by the Open Fund of the State Key Laboratory for Protection and Utilization of Water Resources in Coal Mining (GJNY-21-41-03), the National Natural Science Foundation of China (52004288), the Major Program of the National Natural Science Foundation of China (52394191), Open Fund of the Key Laboratory of Deep Earth Science and Engineering (DUSEYU202302), China University of Mining and Technology (Beijing) Student Innovation Training Program Funding (NICE_RD_2022_135) and Fundamental Research Funds for Central Universities.\u003c/p\u003e\n\u003ch2\u003eData Availability Statements\u003c/h2\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eDuo Xu and Honghua Song wrote the main manuscript text ;Like Zhao and Guoqing Tang prepared all the figures;Shide Hu, Chenxi Duan, and Yunting Song analyzed the experimental data.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eWang, G., Qin, X., Han, D. \u0026amp; Liu, Z. 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Deformation Failure Characteristics and Loading Rate Effect of Sandstone Under Uniaxial Cyclic Loading and Unloading. \u003cem\u003eGeotechnical and Geological Engineering\u003c/em\u003e \u003cstrong\u003e37\u003c/strong\u003e, 1147-1154 (2019).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"coal, mechanical anisotropy, cyclic loading-unloading rate, failure characteristics, energy dissipation","lastPublishedDoi":"10.21203/rs.3.rs-7522397/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7522397/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, the influence of the loading-unloading rate on the uniaxial mechanical anisotropy of coal was investigated via uniaxial compress testaments, acoustic emission (AE) monitor and digital image correlation (DIC), and a series of coal specimens with five anisotropy angles. The results illustrate that the uniaxial compressive stress (UCS) and elastic modulus maintain a U-shaped anisotropic feature under different loading-unloading rates. The anisotropic feature of UCS and axial strain decreases, while the elastic modulus ascends with the increasing loading-unloading rate. The UCS, loading-unloading rate, and anisotropic angle of coal specimens are proved can be described by a cosine function. The impact of bedding plane on the failure characteristics of coal is more significant at anisotropic angles of 0\u0026deg;, 22.5\u0026deg;, and 45\u0026deg;, the penetrating crack mainly propagates along the bedding plane. The increasing loading-unloading rates contribute to a more intact after-failure coal specimen, which makes the anisotropic failure feature of the coal specimen more notable. Meanwhile, the anisotropy of micro-failure characteristics revealed by the AE activity also rises with the loading-unloading rate, which accords with the macro-failure characteristics. The cyclic loading-unloading process generates more damage as specimens with lower UCS, the damage variable caused by it exhibits a parabolic anisotropy feature at anisotropic angle 0\u0026ordm;~90\u0026ordm;, and the value at 22.5\u0026ordm; and 45\u0026ordm; is greater than other anisotropy angles, though this anisotropy feature of damage variable decreases as the loading-unloading rate gain. In addition, the dissipated energy density generated during cyclic loading-unloading process also shows a U-shaped variation feature at anisotropy angle 0\u0026ordm;~90\u0026ordm;, with relatively lower value at 22.5\u0026ordm; and 45\u0026ordm;, and positively exponential correlation with the UCS.\u003c/p\u003e","manuscriptTitle":"The Influence of Cyclic Loading-unloading Rates on the Uniaxial Mechanical Anisotropy of Coal","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-23 12:09:15","doi":"10.21203/rs.3.rs-7522397/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-29T11:27:33+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-22T08:38:02+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-22T08:30:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"20712086647408152199011002537322397589","date":"2025-09-16T01:52:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"30297583763220833370899353277011461597","date":"2025-09-15T11:13:17+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-15T10:15:50+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-15T10:02:14+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-09-15T09:30:47+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-10T06:54:36+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-09-10T06:51:17+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0dd7c0ae-cc61-4b55-9197-98b4a52f208a","owner":[],"postedDate":"September 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":55121558,"name":"Physical sciences/Energy science and technology"},{"id":55121560,"name":"Physical sciences/Engineering"},{"id":55121561,"name":"Earth and environmental sciences/Solid earth sciences"}],"tags":[],"updatedAt":"2025-12-01T16:07:05+00:00","versionOfRecord":{"articleIdentity":"rs-7522397","link":"https://doi.org/10.1038/s41598-025-26236-1","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-11-26 15:58:06","publishedOnDateReadable":"November 26th, 2025"},"versionCreatedAt":"2025-09-23 12:09:15","video":"","vorDoi":"10.1038/s41598-025-26236-1","vorDoiUrl":"https://doi.org/10.1038/s41598-025-26236-1","workflowStages":[]},"version":"v1","identity":"rs-7522397","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7522397","identity":"rs-7522397","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}