Microcrack fracturing of coal specimens under quasi-static combined compression-shear loading

Qingyuan He, Yingchun Li, Danqi Li, Chengguo Zhang

a State Key Laboratory of Coal Resources and Safe Mining, School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

b School of Minerals and Energy Resources Engineering, University of New South Wales, Sydney, 2052, Australia

c State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian,116024, China

d Department of Civil Engineering, Monash University, Clayton, Melbourne, VIC, 3800, Australia

Keywords:Microcrack initiation (CI)Microcrack damage (CD)Microcrack fracturing Acoustic emission Coal properties

ABSTRACT Coal pillars are usually loaded under combined compression-shear stresses at underground coal mines.Their long-term stability is critical to the utilization of underground structures, such as underground reservoirs at coal mines. In this study, a modified rock property testing system was used to explore the mechanical properties of coal specimens under quasi-static combined compression-shear loading conditions. The acoustic emission technique was applied to investigating the microcrack fracturing of coal specimens at various inclination angles. The experimental results show that specimen inclination has remarkable effects on the microcrack initiation, microcrack damage and ultimate failure of the coal specimen.The failure mode of the coal specimen tends to transit from axial splitting to shear failure with increasing specimen inclination, and its peak strength is closely associated with the microcrack damage threshold. In practice, it is recommended to consider coal strength under combined compression-shear loading when using empirical pillar strength formulae so that the effect of pillar inclination can be included.

1. Introduction

Pillars are commonly employed in underground coal mining,such as rib pillars between panels and load-bearing pillars in the room-and-pillar method. Recently, construction of underground reservoirs has become increasingly popular at coal mines in the west of China,where coal pillars serve as barriers to preserve water in the goaf.In this case,it is critical to ensure the long-term stability of coal pillars for the regular operation of underground reservoirs.Understanding the fracture process of coal is prerequisite for disclosing the failure mechanism of coal pillars(Bieniawski,1967a).The pre-failure behavior of coal (i.e. microcrack initiation and propagation before strength failure) affects both the stability and the permeability of coal structures as evidenced by previous studies on radioactive waste management(e.g.Su et al.,2000;Souley et al.,2001).Expanding knowledge on the mechanical properties of coal under various conditions is essential for design of coal pillars(Jaeger,1966; Liu et al., 2018).

Previous laboratory experiments on coal emphasized its behavior under the effects of CO2saturation (Ranjith et al., 2010;Vishal et al., 2015), water saturation (Yao et al., 2015, 2016), brine saturation (Zhang et al., 2018), and bedding planes (Zhang et al.,2014), etc. The external loading condition in these studies is either uniaxial compression or confined compression. The properties of coal specimens under combined compression-shear loading have been rarely reported. Pariseau (1982) and Foroughi and Vutukuri (1997) noted that the estimation of coal pillar stability in an inclined coal seam becomes complicated due to the presence of the shear loading component. Suorineni et al. (2011) described orebodies with axes oblique to the maximum in situ principal stress direction as ‘orebodies in shear’ and found that pillars under this combined compression-shear loading condition could fail if pure compression is assumed in the pillar design process. Moreover,Suorineni et al. (2014) argued that incorporation of the conventional uniaxial compressive strength (UCS) into the existing empirical pillar strength formulae could overestimate pillar strength,since this parameter only represents rock strength under pure compression. Also, numerical results suggested that pillar strength drops as its inclination increases (Ma et al., 2016a).Recently, Xu and Dai (2018) pointed out that explosion-induced stress waves could impose dynamic combined compression-shear loading on pillars in underground mining.

The above findings demonstrate the importance of pillar inclination on pillar stability and evoke laboratory tests under combined compression-shear loading conditions on different rock types, such as granite(Xu et al.,2015;Zhou et al.,2018)and sandstone(Xu and Dai, 2018; Du et al., 2020). Besides, combined compression-shear loading tests have been widely performed on various materials that are normally subjected to combined compression-shear loading in their actual working conditions,including the honeycomb(Ashab et al.,2016),the polymer bonded explosive(PBX)(Zhao et al.,2011)and the polymethyl methacrylate (PMMA) (Tao et al., 2015). The previous combined compression-shear loading test was either dynamic or quasi-static. The split Hopkinson pressure bar (SHPB)system was modified to unravel the dynamic failure of the specimen under combined compression-shear loading by clamping two specimens between a beveled incident bar(with two symmetric beveled edges)and two symmetrically placed standard transmission bars(i.e.without beveled edges)(Zhao et al.,2012),using a beveled incident bar and a beveled transmission bar that have beveled edges parallel to each other (Tounsi et al., 2016) or adding two oblique cushions between the standard incident bar and transmission bar (Tan et al.,2019). For quasi-static experiments, the universal material testing system(MTS)was mostly used,combined with the Arcan rig(Zhou et al., 2012), an experimental device with double beveled edges(Zhang et al.,2016)or other self-developed test rigs(Ling et al.,2018;Zhang et al., 2019), to simulate the combined compression-shear loading.

Previous studies on material properties under combined compression-shear loading revealed that both the elastic modulus(Zhou et al., 2013) and the peak strength (Zhou et al., 2018) of the material decrease as the specimen inclination increases,and these two properties are sensitive to the loading rate(Hou et al.,2011a).Others focused on understanding the effects of specimen inclination on its failure type(Nie et al.,2007)and plateau strength(Ashab et al., 2016) or developing the failure loci of the material in the shear-normal stress space (Hou et al., 2011b). Nevertheless,consideration is seldom given to the microcrack fracturing of materials under combined compression-shear loading.The microcrack initiation (CI) threshold indicates the onset of microcrack fracturing, while the microcrack damage (CD) threshold determines the long-term stability of a rock structure.

Nie et al.(2007)and Xin et al.(2009)numerically simulated the fracture process of borosilicate glass.They validated their numerical models by comparing the two-dimensional (2D) simulation results with the photographically recorded specimen failure patterns.However,the calibration is doubtful since a 2D numerical simulation only shows the microcrack fracturing inside of a specimen that could be inconsistent with what was observed from the surface of the specimen by high-speed camera imaging. Therefore, other quantitative data (e.g. the CI and CD thresholds) are required as the benchmark for more reasonable numerical model calibration.

In this paper,a modified rock property testing system is adopted to study the quasi-static failure of standard coal specimens under combined compression-shear loading. The acoustic emission (AE)technique is employed to observe the pre-failure microcrack fracturing of coal specimens at various inclination angles.The effects of specimen inclination on both the pre-failure process and the ultimate failure of coal specimens are studied to reveal the coal properties under quasi-static compression and shear loading conditions.

2. Modified combined compression-shear test system

Two main methods have been commonly used to simulate combined compression-shear loading in previous laboratory experiments (Tan et al., 2019), including using an irregular-shaped specimen (or called shear-compression specimen (SCS) in some literature (e.g. Rittel et al., 2002)) and changing the loading direction with respect to the axis of an standard specimen. Stress concentration is more likely to occur if an SCS is used,which results in premature failure of the specimen (Nie et al., 2007). Hence changing the loading direction is more suitable for brittle materials(e.g. rocks) (Tan et al., 2019).

The self-developed combined compression-shear test (CCAST)system was used in two previous studies to investigate the quasi-static failure of igneous rocks under combined and shear loading (He et al., 2019, 2020). The original C-CAST system was designed by Professor Fidelis T. Suorineni and developed in cooperation with the University of New South Wales, Australia(She, 2017). It aims to test the mechanical properties of standard rock specimens under quasi-static combined compression-shear loading. Further details of the original C-CAST system can be found in He et al.(2019).If the changing loading direction method is used to apply the combined compression-shear loading, the friction between the standard specimen surfaces and the loading device (e.g. the beveled bars in the dynamic test (Tounsi et al.,2016) and the Arcan rig in the quasi-static test (Zhou et al.,2012)) must be large enough (Hou et al., 2011a; Zhou et al.,2013). Otherwise, a slight slippage at the interface could lead to errors in predicting the mechanical behavior of the material in the elastic stage in a quasi-static experiment (Hou et al., 2011a). The double sided adhesive tape was used by some authors to fix the specimen(Ashab et al.,2015;Ling et al.,2018),which may provide insufficient friction. The C-CAST system utilizes a set of steel pieces to clamp the specimen ends to the adaptors, which eliminates the slippage at the interface of the specimen and the loading device.This approach is recognized in He et al.(2019)and He et al.(2020) and can provide reproducible test results.

In this study, two modifications are made to upgrade the original C-CAST system. Fig.1 gives a section view of the modified CCAST system installed in a servo-controlled MTS. The modified CCAST system has two identical adaptors, which is similar to the original one.Each adaptor is made up of a movable inner part and a fixed outer part (Fig. 2). In the combined compression-shear loading test, the inner part is rotated (relative to the outer part)to a specific inclination angle (e.g. 5°or 10°) based on the scales(the first modification).The scales replace the digital tiltmeter used to measure the inclination change of the inner part of each adaptor in the original C-CAST system.The top adaptor is connected to the upper loading platen by a self-developed detachable clamp, consisting of steel plates, bolts and nuts (the second modification)(Fig. 3). This totally eliminates the influence of the self-weight of the top adaptor on the coal specimen and also prevents the sudden fall of the adaptor when the coal specimen ruptures.It is different from the original C-CAST system that simply uses ropes to fasten the adaptor to the loading platen (through the steel rings at the sides of platen).

The external loading force is applied by a servo-controlled MTS to the modified C-CAST system through the lower loading platen.The axial stress and strain of the specimen in the combined compression-shear loading test are calculated by Eqs. (1) and (2),respectively, following the methods described by He et al. (2019).This is also consistent with the works of Mohr and Doyoyo(2002),Zhou et al. (2012), Tao et al. (2015) and Zhang et al. (2016).

Fig. 2. Adaptor of the modified C-CAST system.

Fig. 3. A self-developed detachable clamp system used to connect the top adaptor of the C-CAST system and the upper loading platen of the MTS.

where σθis the normal stress applied perpendicularly to the specimen surface at a given loading time, F is the loading force of the MTS at a given loading time,θ is the specimen inclination angle,A is the initial specimen cross-sectional area,εθ is the axial strain of the specimen at a given loading time,d is the platen displacement of the MTS,and l is the initial specimen length.The subscript θ in σθand εθdenotes the magnitude of the specimen inclination angle.

3. Combined compression-shear loading tests on coal specimens

A total of 20 laboratory experiments are performed in the State Key Laboratory of Coal Resources and Safe Mining at China University of Mining and Technology, Xuzhou, China. The coal specimens are sampled from the coal blocks collected at Zhangminggou Coal Mine in Shaanxi Province, China. Cylindrical specimens with dimensions of 50 mm(in diameter)×100 mm(in length)are used.A grinder is used to carefully flatten the ends of each specimen.

Four AE sensors are glued to the middle of the coal specimen in each test (Eberhardt et al.,1998). The operating frequency band of each AE sensor is from 100 kHz to 900 kHz.The AE signals are preamplified by 40 dB(Eberhardt et al.,1999a,1999b)and recorded by a DS5 AE monitoring system(Softland Times company,China)with a threshold value of 0.1 V (Eberhardt et al.,1998). The peak definition time(PDT),the hit definition time(HDT)and the hit locking time(HLT)are set to be 50 μs,100 μs and 500 μs,respectively(Kim et al., 2015).

3.1. Experimental procedures

The laboratory tests were divided into four different test scenarios,with the specimen inclination angles of 0°,5°,10°and 15°,respectively.Each test scenario was repeated five times under thesame testing condition (Zhou et al., 2012). First, the coal specimens were compressed at an inclination angle of 0°to determine their properties under the uniaxial compression condition. Then the coal properties at various specimen inclination angles (i.e.θ=5°,10°and 15°)were tested.The modified C-CAST system was loaded in pure compression at a velocity of 0.2 mm/min(Yao et al.,2016). The peak strength of the coal specimen under uniaxial compression(θ=0°)was specified as its UCS in the following text.The CI and CD thresholds of each coal specimen were determined by the AE data.

Table 1Peak strength of coal specimens at various inclination angles.

3.2. Reproducibility of test results

Fig. 4. Stress-strain curves of coal specimens at various inclination angles: (a) θ = 0°; (b) θ = 5°; (c) θ = 10°; and (d) θ = 15°.

Table 2CI and CD thresholds of coal specimens at various inclination angles.

First, the reproducibility of the test results was examined. The specimen peak strength in each test is listed in Table 1.The stressstrain curves of the coal specimens in different test scenarios are plotted in Fig.4.The highest and lowest strength values in each test scenario were excluded and then the mean strength value of the remaining three tests was used as the specimen strength at a given inclination angle,as suggested by the International Society for Rock Mechanics(ISRM) (Ulusay, 2014).

The absolute deviation, relative deviation, standard deviation and relative standard deviation of the test results in each test scenario are also provided in Table 1.Most of the relative deviation values in Table 1 are lower than 10%, with the exceptions in Test Cases 3-1(12.3%)and 4-2(16%).The standard deviation and relative standard deviation values are also within acceptable limits with the maxima being 1.36 MPa (θ = 0°) and 11.4% (θ = 15°), respectively.The above results suggest that the experimental procedure can provide reproducible results (Kahraman, 2001). In the following sections,the test results of Test Cases 1-2,1-3,1-5,2-1,2-4,2-5,3-1,3-4,3-5, 4-1, 4-2 and 4-3 are analyzed.

3.3. Determination of CI and CD thresholds

Scholz(1986)found that thousands of microcracks form before the rock fails and microfracturing events can be studied statistically through AE monitoring. Eberhardt et al. (1997) demonstrated that CI and CD thresholds can be determined by identifying the ‘sharp points’in the‘AE property rate vs.axial stress’curve.The applicable AE properties include ringdown counts, event duration, peak amplitudes,and rise times,etc.The definition of each AE property and further details of the ‘sharp points’ method can be found in Eberhardt et al. (1997).

Another method is to examine the slope change of the ‘cumulative AE property vs.axial stress’curve.Cumulative AE energy(Chang and Lee,2004;Ganne et al.,2007)and cumulative AE hits(Feng et al., 2015; Zhao et al., 2015) are commonly used in previous studies.AE energy derived from the AE event amplitude and event duration is not true energy (Eberhardt et al., 1999c). Its value is directly proportional to that of the true energy(Kim et al.,2015).

Fig. 5. CI and CD thresholds of the coal specimen in Test Case 1-3 (θ = 0°) determined by AE energy (a) and AE hits (b).

Fig. 6. CI and CD thresholds of the coal specimen in Test Case 2-5 (θ = 5°) determined by AE energy (a) and AE hits (b).

Some authors considered the axial stress at which the AE hit curve begins to increase linearly as the CI threshold and the axial stress at which the AE hit curve begins to increase nonlinearly or exponentially as the CD threshold (Ranjith et al.,2004; Feng et al.,2015;Yao et al.,2016).This is debatable.Eberhardt et al.(1997)and Moradian et al. (2006) clearly stated that the CI threshold is the axial stress at which the AE property rate begins to significantly increase and the AE property rates before and after CI are markedly different throughout loading.Eberhardt et al.(1998)also noted that AE energy increases dramatically shortly after CI. CD is the sign of unstable microcrack propagation and coincides with the further drastic increase of the AE rate.

Many others accept Eberhardt et al.(1997)and Moradian et al.(2006)’s opinion that defines the axial stress where the ‘cumulative AE property vs. axial stress’ curve starts to depart from linearity as the CI threshold and the axial stress where the slope of the curve further increases as the CD threshold(Ganne et al.,2007;Lu et al., 2013, 2015). Besides, the AE hit line method (Zhao et al.,2013) can also be used to obtain CI and CD thresholds. The drawback of this method is that it is only applicable to an S-shaped AE curve. However, most AE curves are actually J-shaped(Wen et al., 2018).

In this section,the CI and CD thresholds of the coal specimens at various inclination angles (i.e. θ = 0°, 5°, 10°and 15°) are determined by combining the above methods, including: (1)identifying the‘sharp points’in the‘AE energy rate vs.axial stress’curve and the ‘AE hit rate vs. axial stress’ curve (Eberhardt et al.,1997); (2) examining the slope change of the ‘cumulative AE energy vs. axial stress’ curve and the ‘cumulative AE hits vs. axial stress’ curve (Chang and Lee, 2004; Ganne et al., 2007); and (3)using the AE hit line method if the ‘cumulative AE hits vs. axial stress’ curve is S-shaped (Zhao et al., 2013).

The average AE properties from the four AE sensors were analyzed(Eberhardt et al.,1998).If the AE sensor detaches from the coal specimen before rock failure(i.e.before the axial stress reaches its maximum value),the average responses from the remaining AE sensors are used. Table 2 provides the CI (σci) and CD (σcd)thresholds of the coal specimens. Due to space limitation, the AE data of a part of the laboratory tests are presented in Figs. 5-8,including Test Cases 1-3(θ=0°),2-5(θ=5°),3-5(θ=10°)and 4-1(θ = 15°). The reason for this decision is that the strength value of each selected test is closest to the mean strength value of the corresponding test scenario and hence is more representative of the test results(Table 1).The axial stress,the cumulative AE energy and the cumulative AE hits in each sub-figure in Figs. 5-8 are normalized to the peak stress,the maximum cumulative AE energy,and the maximum cumulative AE hits in the corresponding test case, respectively.

Fig. 7. CI and CD thresholds of the coal specimen in Test Case 3-5 (θ = 10°) determined by AE energy (a) and AE hits (b).

3.4. Effect of specimen inclination on microcrack initiation

Tables 2 and 3 provide the CI threshold (σci)and its ratio to the specimen peak strength(σci/σc)of each test,respectively.The mean σciand σci/σcvalues of each test scenario are compared in Fig. 9a and b,respectively.The CI thresholds of the coal specimens decline almost linearly against the specimen inclination (see Fig. 9a). The σcivalues at 5°,10°and 15°inclination angles decrease by 26.3%,41.4% and 60.1%, respectively, compared with that under uniaxial compression.

Schmidtke and Lajtai (1985) found that σciis an inherent material property, independent of the specimen size. Others concluded that σcivalue of a specimen is unaffected by its shape(Bieniawski, 1967a), damage accumulation (Martin and Chandler,1994), sampling disturbance (Eberhardt et al., 1999c), and the grain size(Eberhardt et al.,1999b).However,this is not always the case since σciincreases with either a higher loading rate or larger confining pressure (Brace et al., 1966). The laboratory results in Chang and Lee (2004) indicated that the CI of the specimen is governed by the formation of shear cracks(although these authors stated that CI is dictated by tensile cracks,this statement is not true based on their results presented in Fig.20 in Chang and Lee(2004)).Alkan et al.(2007)also observed that cracks commence to re-open and new cracks form after the elastic deformation stage due to an increase in shear stresses.These findings confirmed the importance of shear stresses on CI. The C-CAST system in the combined compression-shear loading test applies an external shear loading component to the coal specimen and offers additional shear stresses that facilitate the initiation of microcracks at a low axial stress magnitude.This is evidenced by the decreasing CI thresholds at larger specimen inclination angles in Table 2 and Fig. 9a.

Hoek and Bieniawski(1965)pointed out that the CI of rocks can be predicted by the Griffith theory in which the friction coefficient between microcrack surfaces is an independent factor. Brace and Byerlee (1966) found that wear damage due to sliding at microcrack surfaces affects the friction coefficient in the modified Griffith criterion (McClintock and Walsh, 1963) which is therefore inconstant along microcrack surfaces. From this aspect, the combined compression-shear loading induces additional shear stresses within the coal specimen, which intensifies the sliding between microcrack surfaces at the elastic deformation stage.Hence,a lower axial stress level is needed to initiate the microcracks compared with that under the uniaxial compression condition.

Fig. 8. CI and CD thresholds of the coal specimen in Test Case 4-1 (θ = 15°) determined by AE energy (a) and AE hits (b).

Another important mechanical property of the coal specimen is the σci/σcratio, and two possible applications are to estimate the tensile strength of coal and to determine the mivalue (a material constant) in the Hoek-Brown failure criterion (Hoek and Brown,1980) based on Cai (2010)’s method. The σci/σcratios of the coal specimens at different inclination angles exhibit a descending tendency with the exception of 10°inclination angle (Table 3 and Fig. 9b). The non-monotonous tendency of σci/σcratios has also been found in previous studies.For example,Alkan et al.(2007)and Zhao et al. (2013) stated that the σci/σcratio decreases with larger confining pressure.Yao et al.(2016)concluded that the σci/σcratio of a coal specimen is independent of water contents.However,the actual experimental results in these studies are not so monotonous if a detailed re-examination is made (see Fig. 6 in Alkan et al.(2007), Fig. 11 in Zhao et al. (2013) and Fig. 11 in Yao et al.(2016)). Therefore, σci/σcratios may not change exactly monotonously with variation of the influencing factors. Specimen inclination has a certain effect on the σci/σcratio of coal. It generally decreases with increasing specimen inclination.

Rocks(e.g.coal)after CI still possess an increasing load-bearing capacity (Bieniawski, 1968), and the newly formed stable microcracks are not considered as damage to the peak strength (Hoek and Bieniawski,1965; Bieniawski,1967b). Nevertheless, a permanent volume increase occurs once the CI threshold is exceeded(Brace et al.,1966). This may increase the water absorption of coal and should be considered in waterproof pillar design in underground reservoir construction.

3.5. Effect of specimen inclination on microcrack damage

Tables 2 and 3 provide the CD threshold(σcd)and its ratio to the specimen peak strength(σcd/σc)of each test,respectively.The meanvalues of σcdand σcd/σcof each test scenario are compared in Fig.9a and b,respectively.The CD thresholds of the coal specimens exhibit an interesting tendency in which the σcdvalue at 5°inclination angle increases slightly compared with that under uniaxial compression. Then the σcdvalues decrease almost linearly with increasing specimen inclination(Fig.9a).The σcdvalues at 10°and 15°inclination angles decrease by 29.2% and 59.9%, respectively,compared with that under uniaxial compression. The reasons for this phenomenon are discussed below.

Table 3CI to peak strength ratios and CD to peak strength ratios of coal specimens at various inclination angles.

Fig.9. Effect of the specimen inclination angle on microcrack fracturing thresholds(a)and peak strength of coal specimens (b).

CD is associated with unstable microcrack propagation and the formation of macroscopic failure planes in the specimen.Figs.10-13 illustrate the failure patterns of the coal specimens in different test scenarios. The failure mechanism of the coal specimens under uniaxial compression(θ=0°)is of obvious axial splitting (Fig. 10). The combination of axial splitting and shear failure occurs in the coal specimens at 5°inclination angle as evidenced by the visible fractures in Fig.11a and b that consist of both a straight part and a curved part. Note that the axial splitting planes in Fig. 11a and b are not exactly aligned with the specimen axes as that under the uniaxial compression condition and are unparallel to the external loading direction either. The coal specimens at 10°and 15°inclination angles tend to fail along shear failure planes, as shown in Figs. 12a, b and 13a, b. This proves the reliability of the C-CAST system to simulate a combined compression-shear loading condition. The existence of the shear component changes the failure mode of the coal specimen,and shear failure tends to become dominant with an increasing specimen inclination angle.

Cai et al. (2004) found that the formation of tensile spalls and associated microcrack dilation could prevent the mobilization of friction and cohesion that only occurs when the rock is sufficiently damaged and fails in a shear-failure mode. Based on the failure patterns in Figs. 10 and 11, the coal specimens tend to fail along curved shear failure planes(combined with axial splitting)once the inclination angle increases to 5°. This could mobilize the friction and cohesion of the coal specimen and hence leads to a slight increase in σcdof the coal specimens at 5°inclination angle compared with that under uniaxial compression. Another effect of the induced external shear loading, besides the influence on the specimen failure pattern shown in Figs. 10-13, is to accelerate unstable propagation of microcracks.The CD thresholds of the coal specimens decrease gradually once the inclination angle increases to 10°and 15°. This indicates that the mobilized friction and cohesion are unable to compensate for the additional external shear loading applied to the coal specimen if the inclination angle reaches a certain value and the microcracks tend to propagate unstably at a lower axial stress magnitude.

The non-monotonous change of σcdassociated with various influencing factors was also found in previous studies, such as the influence of specimen damage accumulation(Martin and Chandler,1994) and confining pressure (Zhao et al., 2013). From the test results in Table 2, specimen inclination mobilizes the frictional strength components of the coal specimen at a small inclination angle. It accelerates unstable microcrack propagation once specimen inclination increases to a certain degree and further lowers the CD threshold as the specimen inclination angle increases.

The σcd/σcratios of the coal specimens and their variations at different inclination angles are provided in Table 3 and Fig. 9b,respectively. Some authors assumed the σcd/σcratio as an intrinsic property of the rock since this parameter is found to be unaffected by factors,such as confining pressure(Zhao et al.,2013),rock origin(Xue et al., 2014), grain size (Xue et al., 2014), and water content(Yao et al., 2016). The σcd/σcratios of the coal specimens at inclination angles of 0°,5°and 10°are very close to each other,whereas these ratios decrease to a mean value of 0.63 if the specimen inclination angle is 15°(Table 3).The σcd/σcratio of Test Case 4-3 is 0.81 that approximates the mean σcd/σcratios of the coal specimens at inclination angles of 0°,5°and 10°;while the σcd/σcratios of Test Cases 4-1 and 4-2 fall to 0.55 and 0.54,respectively.This difference could be explained by the different failure types of the coal specimens.The coal specimens in Test Cases 4-1 and 4-2 fail along clear shear failure planes and few spalls are observed before strength failure of these specimens (Fig. 13a and b). On the contrary,noticeable spalling occurs during the fracture process of the coal specimens in Test Cases 3-1 to 3-3 (θ = 10°) (Fig.12a-c) and Test Case 4-3(θ=15°)(Fig.13c).The coal specimens in these tests lose their integrity before strength failure due to spalling and tend to fail soon after unstable propagation of microcracks (i.e. higher σcd/σcratios).Coal is a heterogeneous material,and both its heterogeneity and the external loading condition could influence the fracture process of the coal specimen.The test results in Fig.13a and b show that the increasing external shear loading component at a larger specimen inclination angle dominates the microcrack fracturing process of the coal specimen and leads to a more regular shear failure plane with few spalls.

Previous studies on other types of rocks,different from the coal which is a type of soft rocks, suggest that the CD threshold corresponds to the long-term strength of the rock (e.g. Bieniawski,1967c) and represents the onset of its permanent damage (e.g.Lajtai et al., 1991). The start of unstable propagation of microcracks influences both the stability and the permeability of the rock. Souley et al. (2001) found that rock permeability increases significantly once the axial stress exceeds σcddue to macroscopic failure and the coalescence of microcracks. Also, the existence of pore pressure affects the mechanical properties of an intact rock as the effective stress leads to a reduction of its CD threshold(Alkan et al.,2007).The test results in Table 3 manifest the effects of specimen inclination on the unstable propagation of microcracks in coal and also suggest that a wider damage zone could form in a coal structure if the external loading includes both compression and shear.

Fig.10. Failure patterns of coal specimens in Test Scenario 1 (θ = 0°): (a) Test Case 1-2; (b) Test Case 1-3; and (c) Test Case 1-5.

Fig.11. Failure patterns of coal specimens in Test Scenario 2 (θ = 5°): (a) Test Case 2-1; (b) Test Case 2-4; and (c) Test Case 2-5.

Fig.12. Failure patterns of coal specimens in Test Scenario 3 (θ = 10°): (a) Test Case 3-1; (b) Test Case 3-4; and (c) Test Case 3-5.

Fig.13. Failure patterns of coal specimens in Test Scenario 4 (θ = 15°): (a) Test Case 4-1; (b) Test Case 4-2; and (c) Test Case 4-3.

3.6. Effect of specimen inclination on failure patterns and peak strength

Many factors influence the fracture process and the failure pattern of the rock,such as the stress direction and the distribution of external loading (Bieniawski, 1968). The photographically recorded coal specimen failure patterns in Figs.10-13 indicate that the specimen inclination affects appreciably the failure patterns.Coal specimens split axially (Fig.10) under uniaxial compression,while the specimens tend to fail along shear planes and fewer spalls are observed with increasing inclination angles (Figs. 11-13).Rupture or axial splitting is not a characteristic property of the specimen (Bieniawski, 1968). On the other hand, the ‘specimenloading machine’structure also affects the specimen failure pattern(Bieniawski, 1968) and the formation of macroscopic cracks(Scholz, 1986). The results in Figs. 10-13 are consistent with the above statements.The variation of external loading conditions(i.e.from uniaxial compression to combined compression-shear) has notable influence on coal specimen failure patterns.

The coal specimen peak strength at different inclination angles is provided in Table 1 and the mean values are listed in Fig. 9a. It illustrates that the peak strength increases slightly when the specimen inclination angle increases from 0°to 5°and then decreases gradually with further increase of the inclination angle.Hudson et al.(1972)considered that rock strength depends on the boundary conditions of the test rather than on an inherent material property.The only difference between the test scenarios in Table 1 is the specimen inclination angle that determines the amount of the external shear loading component.The additional shear loading lowers the CI thresholds of the coal specimens, and this effect becomes more noticeable with increasing specimen inclination(Table 2 and Fig. 9a). Nevertheless, the external shear loading also mobilizes the friction and cohesion of the coal specimen and leads to a slight increase in the CD threshold at a small inclination angle(θ = 5°). Then the CD threshold begins to decrease as specimen inclination angle increases. The test results presented in Fig. 9a suggest that a lower CI threshold does not necessarily result in lower peak strength of the coal specimen.The peak strength of the coal specimen under combined compression-shear loading is more related to its σcdmagnitude at which unstable microcrack propagation occurs. The changing loading direction method has been utilized in previous studies (which is also used by the modified CCAST system in this study)to simulate the combined compressionshear loading on standard specimens(Zhou et al.,2013;Ashab et al.,2015; Ling et al., 2018). The additional shear loading component was monitored by accompanied installations, such as quartz transducers in the dynamic tests(Zhao et al.,2012)and the optical strain field measuring system in the quasi-static tests (Ling et al.,2018), and is considered as a cause for the lower strength of the specimen under combined compression-shear loading (Nie et al.,2007; Hou et al., 2011a; Zhou et al., 2018). Besides, the failure loci developed by some other authors also suggested that the required compressive stress for the failure of the specimen (i.e. specimen peak strength) decreases as a larger shear loading component is applied (Zhou et al., 2013; Zhang et al., 2019).

Empirical pillar strength formulae have been developed for both coal pillars (Hustrulid, 1976) and hard rock pillars (Martin and Maybee, 2000) through back analysis of pillar case studies(Salamon, 1999;Esterhuizen et al.,2011).Rock UCS is accepted as a dominant factor for all the empirical relations whereas pillar inclination is rarely included. It is crucial to consider the peak strength tested in the combined compression-shear loading test as a new indicator reflecting the effect of the combined loading condition on coal and rock strength and to incorporate it into pillar strength formulae.This viewpoint is supported by Suorineni et al. (2014) and the numerical simulation in Ma et al. (2016a,2016b).

4. Conclusions

Underground coal pillars are generally subjected to combined compression-shear loading. In this study, a modified rock testing system is used to reveal the mechanical properties and the microcrack fracturing processes of coal specimens under quasistatic combined compression-shear loading. The following conclusions are made:

(1) Both the CI threshold and its ratio to the peak strength of the coal specimen decrease with increasing inclination angles.The CI threshold declines almost linearly.The CI threshold to peak strength ratio changes non-monotonously in a decline tendency.

(2) The CD threshold of the coal specimen increases slightly as the inclination angle changes from 0°to 5°and then decreases almost linearly with increasing specimen inclination.The external shear loading component induced by the combined compression-shear loading condition mobilizes the friction and cohesion of the coal specimen and leads to a slight increase in the CD threshold at small inclination angles. The main effect of the additional shear loading component is to accelerate unstable propagation of microcracks when the inclination angle increases to a certain value, resulting in gradual reduction of the CD threshold.

(3) The CD threshold to the peak strength ratio should be an intrinsic property of the coal specimen if the inclination angle is within 10°. This ratio tends to decrease once the inclination angle reaches 15°. The external shear loading component dominates the failure mode of the coal specimen in that case.The coal specimen at this inclination angle fails along a visible shear failure plane with few spalls.

(4) The coal specimen tends to fail along a macroscopic shear failure plane rather than splits axially with increasing inclination. Its peak strength at different inclination angles is closely related to its CD threshold. Specimen peak strength obtained from the combined compression-shear loading test is recommended to be incorporated in empirical pillar strength formulae to account for the effect of pillar inclination.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The work of this paper is supported by the Fundamental Research Funds for the Central Universities(Grant No.2018QNA31).The authors would like to thank Professor Fidelis T Suorineni for his contribution to developing the original C-CAST system and the postgraduate students at China University of Mining and Technology for their involvements in the laboratory experiments.