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Mechanical behavior and failure mechanism of pre-cracked specimen under uniaxial compression
Tectonophysics 712–713 (2017) 330–343
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Mechanical behavior and failure mechanism of pre-cracked specimen under uniaxial compression Ting Liu a,b, Baiquan Lin a,b, Wei Yang a,b,⁎ a b
Key Laboratory of Coal Methane and Fire Control (China University of Mining and Technology), Ministry of Education, 221116, PR China School of Safety Engineering, China University of Mining & Technology, Xuzhou 221116, PR China
a r t i c l e
i n f o
Article history: Received 15 November 2016 Received in revised form 11 May 2017 Accepted 2 June 2017 Available online xxxx Keywords: Pre-cracked specimen Failure mechanism Acoustic emission Stress field Particle Flow Code
a b s t r a c t As a desirable permeability enhancement method, hydraulic slotting has been widely used for enhanced coal bed methane (ECBM) recovery in China. Aiming at the problem that the action mechanism of the slot on the mechanical properties of the slotted coal is still unclear, this paper investigates the effects of flaw inclination on the strength, deformation and cracking process of the pre-cracked specimens. The result shows that the stress-strain curves can be divided into three categories based on the stress behaviors, dropping step by step or dropping sharply, after the peak. With an increase of the flaw inclination, the strength and elastic modulus of the precracked specimen increases gradually, which is verified by the numerical simulation and theoretical results. Analysis of the cracking processes indicates that the initiation position of the first crack in specimens with various flaw inclinations is different, which is caused by the various distributions of tensile and compressive stress concentration zones. The distribution of the stress field controls the cracking process which will in turn affect the stress field distribution. With the propagation of the cracks, the tensile stress concentration zones expand and the concentration degree lowers gradually, while the compressive stress concentration zones show the opposite variation trend. Based on the above results, an optimized slot arrangement method has been proposed for the field application of hydraulic slotting. © 2017 Published by Elsevier B.V.
1. Introduction Gas drainage, a basic method for gas disaster control, contains ground well gas drainage and underground borehole gas drainage (Xue et al., 2017). In 2014, the total coal bed methane (CBM) extracted in China is 17,000 Mm3, and that extracted from the underground is 13,300 Mm3, accounting for 78.2% of the total, implying that underground gas drainage is still the main method for gas control in China. Besides, the utilization amount of CBM extracted from the underground is 4500 Mm3, the utilization rate is only 34%. The reason is that the permeability of most coal seams in China is in the range of 10−19–10−18 m2, which is three orders lower than that in Austria and four orders lower than that in America (Zhou et al., 2016; Meng et al., 2015). Such a low permeability of the coal seam prevents the gas from flowing to the borehole, lowering the concentration of the CBM extracted. Generally, gas with the concentration b 20% cannot be used directly and will be discharged into the atmosphere, leading to the greenhouse effect (Li et al., 2015; Warmuzinsli, 2008; Bibler et al., 1998). Therefore, to improve the gas utilization rate, CBM with a higher concentration should
⁎ Corresponding author. E-mail address: [email protected] (W. Yang).
http://dx.doi.org/10.1016/j.tecto.2017.06.004 0040-1951/© 2017 Published by Elsevier B.V.
be extracted, which requires larger coal seam permeability (Zhang and Li, 2017). Exploitation of the protective coal seam has proven to be the most effective method for stress relief and permeability enhancement in coal seam group (Liu et al., 2016b; Kong et al., 2014). However, more commonly, the coal seam exists in the form of single coal seam, a protective coal seam cannot be found. In addition, with an increase of the mining depth, the initial coal seam gradually turns into coal and gas outburst seam. To solve the problem, that is the outburst elimination of the single and the initial coal seams, hydraulic slotting has been developed and applied (Liu et al., 2016a, 2016b; Lin et al., 2012). In the past decades, much research on the hydraulic slotting technique has been conducted and some meaningful results have been achieved. Lin et al. (2015) investigated the cracking modes and the corresponding energy evolution rules in slotting disturbed zones under different stress conditions. The research result contributed to the borehole arrangement in the field. Lin and Shen (2015) studied the coal-permeability enhancement mechanism of multilevel slotting by high-pressure waterjet. The result indicated that with slot number increases from 0 to 3, the coal strength decreases about 40%; and the porosity near the flaw increases about 30%, which was indirectly verified by the field application. Aiming at the problem of hole collapse in the soft coal seam, Lu et al. (2010) proposed a technique of drilling holes by waterjet in the
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roof/floor until the soft coal seam was reached. This technique was reported to be able to improve the drilling length and gas flow significantly. Lu et al. (2009, 2011) used the hydraulic slotting to release the energy stored in the soft and high gassy coal seam so as to improve the gas drainage efficiency and eliminate the outburst risk, which in turn increased the roadway driving speed. Liu et al. (2016b) investigated the pore structure and the resulting adsorption and seepage capacities variations of coal in the slotting disturbed zone. Based on the results, a microscopic model on permeability enhancement and outburst elimination was developed. Based on the framework of coal-methane co-exploitation, Zou et al. (2015) proposed an integrated technique, a combination of drilling-slotting-separation- sealing, to enhance coal permeability and CBM recovery. The field test result indicated that the gas concentration in the slotted borehole was 1.05–1.91 times higher than that in the traditional borehole, implying the effectiveness of the technique. The review about the hydraulic slotting indicates that the research to date has tended to focus on the adsorption and seepage characterizations, cracking modes of the slotting disturbed zone and the application effect in the field. Research about the effects of the spatial arrangement of the slot, especially the flaw inclination, on the mechanical properties and its guiding significance to the field application of hydraulic slotting is rarely reported. In this work, we investigated the effect of flaw inclination on the mechanical properties, especially the strength, deformation and cracking processes of the pre-cracked coal specimens by laboratory test and numerical simulation. In addition, the stress filed around the flaw was also studied to explore the action mechanism of the flaw on the mechanical characteristics of the coal. At last, based on the research result, an optimized slot arrangement was proposed for the field application of hydraulic slotting. 2. Research methods In order to investigate the mechanical properties and cracking process of specimens containing combined flaws with various inclinations, the uniaxial compression tests were conducted in the laboratory combining with the acoustic emission detection. In addition, the numerical simulation was also adopted to further explore the corresponding mechanical mechanism and verify the rationality of the experimental results. 2.1. Laboratory test 2.1.1. Test material The specimens used in the laboratory tests are artificial coal samples with the size of 120 mm × 60 mm × 30 mm (Fig. 1) and an average porosity of 4.3%. The mix proportion of the synthetic coal sample is coal: cement: binder: water = 108:27:9:20. The samples were pressed under a constant pressure of 40 MPa for 30 min and then transferred
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to the thermostat with a constant temperature of 25 °C for 30 days. After consolidation, a combined flaw was drilled at the center of the specimen. The circular hole is 6 mm in diameter, and the rectangular flaw is 20 mm long and 2 mm wide. Notice that the surfaces of the specimens were painted white to get a better observation of the crack initiation, propagation and coalescence processes. 2.1.2. Test methods and apparatus Uniaxial compression tests were conducted on the pre-cracked specimens to obtain the mechanical properties. In the tests, the loading rate was set as 0.1 mm/min, the stress-strain curve, UCS (Uniaxial Compressive Strength) and E (Elastic modulus) of each specimen were monitored. The loading processes were recorded by a digital camera to observe the crack initiation, propagation and coalescence in the specimens. In addition, the intensity characteristics of AE (acoustic emission) during the cracking process of each specimen were also monitored using an AE detector. Notice that each test was conducted for three times to reduce the experimental error caused by sample variability. 2.2. Numerical simulation 2.2.1. Fundamentals of PFC2D In PFC2D (Particle Flow Code in two dimensions), two kinds of particle bond models (PBM) are embedded, namely contact bond model (CBM) and parallel bond model (PBM) (Cho et al., 2007; Yoon, 2007). The PBM can transmit both force and moment between particles, while the CBM can only transmit the force acting at the contact point (Itasca, 2002; Lisjak and Grasselli, 2014). For the CBM, a marked reduction of the macro-stiffness will not be observed after the breakage of the bond as long as the particles still remain in contact. While for the PBM, the breakage of the bond will result in an immediate decrease of the macro-stiffness because the stiffness consists of both contact and bond stiffness (Liu et al., 2016a; Lee and Jeon, 2011). This property implies that the PBM is more realistic for rock-like material modeling. Therefore, the PBM is adopted in the current work to model the coal specimens. 2.2.2. Calibration of mesoscopic parameters To generate a parallel-bond model, a set of mesoscopic parameters should be determined. The model generated with the specified parameter set should reproduce the macro mechanical properties of the coal samples obtained in the laboratory (Wang et al., 2014). Here the stress-strain curve, UCS, E and the failure mode (macroscopic rupture plane) obtained from our laboratory tests were selected as the target variables and the ultimate goal of calibration is to minimize the gap between the variables. In the current work, a series of calibration schemes were conducted and the comparation between the final calibration results and laboratory test results has been depicted in Fig. 2. It can be seen that the shapes of the stress-strain curves are similar, even though a notable difference was observed in peak strains (with an error of −
Fig. 1. Coal samples used in the laboratory test. (a) physical map of coal samples with different flaw inclinations; (b) physical map of coal sample with a flaw inclination of 30°; (c) sketch map of coal sample.
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Fig. 2. Comparation between the numerical results of calibration and experimental results.
22.6%). The discrepancy can be attributed to the existence of a compacting section on the stress-strain curve (see Fig. 2) obtained in the laboratory test. For the UCS and E, the relative errors between the numerical and experimental results are − 0.91% and 6.4% (b10%), respectively. In addition, both the macroscopic rupture planes in the numerical and experimental results initiated from the top boundary and finally coalesced with the right boundary, implying that the failure modes are also analogous. Since the target variables are all acceptable, we can identify the ultimate mesoscopic parameter set, which is shown in Table 1. After generating the numerical model, the combined flaw was created by deleting particles in the designed area. The models produced here are 120 mm high and 60 mm wide and contain about 33,000 particles.
Table 1 Mesoscopic parameters used in the PFC2D model for the synthetic coal sample tested in laboratory. Objects
Micro parameters
Values Remarks
Particle
Particle minimum radius, Rmin (mm)
0.18
Particle radius ratio, Rmax/Rmin Particle density, ρ (kg/m3) Particle contact modulus, EC (GPa) Particle stiffness ratio, kn/ks Particle friction coefficient, μ Parallel-bond radius multiplier, γ Parallel-bond modulus, EP (GPa) Parallel-bond stiffness ratio, pb_kn/pb_ks Parallel-bond normal strength, mean (MPa) Parallel-bond normal strength, std.dev. (MPa) Parallel-bond shear strength, mean (MPa) Parallel-bond shear strength, std.dev. (MPa)
1.66 1000 0.4 1 0.5 1.06 1.6 3.44
Parallel bond
9.99 1.1
Uniform distribution
3. Experimental results 3.1. Stress-strain characteristics Fig. 3 depicts the stress-strain curves of specimens with different flaw inclinations. It is very obvious that for specimens with various flaw inclinations, the stress-strain curves present significantly different behaviors. Based on the characterization, the curves can be divided into three categories, namely type I, type II and type III. Type I (0° ≤ θ ≤ 30°): For specimens with flaw inclination of 0, 15 and 30°, the stress after the peak drops step by step, indicating that these specimens fail in a progressive mode. With an increase of the flaw inclination, the significance degree of this phenomenon decreases. Type II (45° ≤ θ ≤ 60°): When 45° ≤ θ ≤ 60°, the progressive failure is insignificant (specimen with θ = 45°), or for specimens with the same flaw inclination, both the progressive failure and transient failure may occur (specimen with θ = 60°). We call this range of flaw inclination as the transition stage. In the transition stage, the way of stress reduction after the peak is uncertain. Type III (75° ≤ θ ≤ 90°): For specimens with flaw inclinations of 75 and 90°, the stress after the peak drops sharply, implying that transient failure occurs in the specimens after the peak. 3.2. Strength and deformation Fig. 4 shows the strength and deformation characterizations of specimens with different flaw inclinations. To reduce the errors induced by experiment operation and heterogeneity of the samples, each test was conducted three times. The results show that although there exist some fluctuations, both the UCS and elastic modulus rise on the whole with an increase of the flaw inclination. It implies that the increase of the flaw inclination improves the mechanical strength and enhances the ability of resisting axial deformation. A further theoretical analysis was conducted in Section 5 to explore the mechanical mechanism of this phenomenon from the perspective of damage.
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3.3. Cracking process and AE characteristics
1.1
Analyses in Sections 3.1 and 3.2 show that specimens with different flaw inclinations have various mechanical properties, such as stress-
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Fig. 3. Stress-strain curves of precracked specimens with different inclination angles.
strain characterization, mechanical strength and elastic modulus. The mechanical properties of coal-rock mass are closely related to the corresponding cracking processes, namely crack initiation, propagation and
coalescence (Yang et al., 2014; Lee and Jeon, 2011; Du et al., 2016; Ren et al., 2016). Therefore, it is necessary to further investigate the cracking processes of the pre-cracked specimens so as to get a better
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Fig. 4. Strength and deformation of specimens with various flaw inclinations.
understanding of the variations of mechanical properties. In this section, the crack initiation, propagation and coalescence processes of specimens with flaw inclinations of 0, 30, 45, 60 and 90° were analyzed combining with the AE characteristics (Fig. 5).
3.3.1. θ = 0° [Fig. 5(a)] Fig. 5(a) depicts the cracking process of specimen with flaw inclination of 0°. When the axial stress increased to 7.6 MPa (point a), several AE signals were monitored and at the same time, cracks 1 and 2 initiated
Fig. 5. Cracking processes and AE characteristics of specimens with different flaw inclinations.
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from the surface of the circular hole were observed. As the loading continuous, cracks 1 and 2 propagated but no new crack formed before the peak. At the peak point a stress drop occurred and a strong AE signal was monitored (point b), meanwhile, crack 3 initiated from the left tip of the flaw and propagated toward the top boundary of the specimen. With an increase of the axial strain, crack 4 initiated from the right tip of the flaw and propagated to the top boundary which resulted in a dramatic drop of the axial stress (point c). After that a stress increase was observed due to the closure of the flaw which increased the axial supporting capacity. At point d, a sharp decrease of the stress and an intense AE signal were monitored and surface spalling was observed. Thereafter, no obvious stress change was monitored and the AE signal was relatively uniform. At point e, cracks 6 and 7 initiated from the left and right tips of the flaw and gradually coalesced with the bottom boundary, leading to the ultimate failure of the specimen. 3.3.2. θ = 30° [Fig. 5(b)] Fig. 5(b) shows the cracking process of specimen with flaw inclination of 30°. When the axial stress increased to 2.8 MPa (point a), several AE signals were monitored but no crack was observed on the surface of the specimen. The sporadic signals maybe resulted from the closure of the primary pores. At point b (9.14 MPa), cracks 1 and 2 initiated from the right and left tips of the flaw, respectively, accompanied by strong AE signals. At the peak point, crack 3 initiated from the right tip of the flaw and propagated toward the top boundary of the specimen, at the same time, a sharp stress drop and a strong AE signal were observed (point c). At about 250 s (point d), a stress drop and a strong AE signal were observed which were caused by the coalescence of crack 3 with top boundary. At point e, crack 4 initiated from the left tip of the flaw and propagated toward the bottom of the specimen on the whole. Hereafter, no observable crack and AE signal were monitored and the stress drop observed was mainly caused by the opening of the cracks which led to the ultimate failure of the specimen. 3.3.3. θ = 45° [Fig. 5(c)] Fig. 5(c) displays the cracking process of specimen with flaw inclination of 45°. When the axial stress reached 7.5 MPa, cracks 1 and 2 initiated from the right and left tips of the flaw and propagated toward the top and bottom of the specimen, respectively. Meanwhile, AE signals and a weak stress reduction were observed. From 200 s (point a) to 325 s (point d), no new cracks formed and the AE signals and the stress drops observed during this period of time were mainly caused by the propagation and opening of cracks 1 and 2. Besides, it may also be due to the initiation and propagation of microcracks inside the specimen. When the axial stress decreased to 2.4 MPa (point e), crack 3 and crack 4 initiated from the left and right tips of the flaw and propagated toward and finally coalesced with the bottom and top boundaries of the specimen, respectively. During the period before and after 350 s, the AE activity was relatively frequent, which was mainly resulted from the initiation and propagation of cracks 3 and4. 3.3.4. θ = 60° [Fig. 5(d)] Fig. 5(d) depicts the cracking process of specimen with flaw inclination of 60°. When the axial stress increased to 8.2 MPa (point a), some low-level AE activities were monitored but no obvious surface crack was observed, implying that microcracks formed inside the specimen. After the peak (point b), crack 1 initiated from the right tip of the flaw and then crack 2 initiated from the left tip of the flaw and propagated toward the bottom boundary of the specimen. With an increase of the axial strain, crack 2 propagated gradually and finally coalesced with the bottom boundary, while no obvious propagation of crack 1 was observed which was believed to be suppressed by the propagation of crack 2 (point c). At point d, crack 3 initiated from the right tip of the flaw and propagated toward the upper right of the specimen combining with a stress drop and several high-level AE activities. With the continuous rise of the axial strain, the existing cracks opened gradually and crack
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3 finally coalesced with the top boundary of the specimen, leading to the ultimate failure of the specimen (point e). 3.3.5. θ = 90° [Fig. 5(e)] Fig. 5(e) shows the cracking process of specimen with flaw inclination of 90°. It can be seen that between 50 and 100 s, there were some AE activities which were thought to be due to the closure of the primary pores or the sliding friction between the coal particles. While the axial stress reached 10.8 MPa (point a), some low-level AE activities were monitored but no obvious cracks were found, indicating the microcracks formed inside the specimen. After the peak, a sharp axial stress drop and high-level AE activities were monitored, which were accompanied by the initiations of crack 1 and crack 2 from the upper tip of the flaw and surface of the circular hole, respectively (point b). At point c, two far-filed cracks, crack 3 and crack 4, formed in the upper-left corner of the specimen. Hereafter, no obvious changes of the axial stress were found but the AE activities, caused by the opening of the existing cracks, had always been in a high level. 4. Numerical results Analyses in Section 3.3 show that specimens with different flaw inclinations have various cracking processes. According to Wong et al. (2002) and Zhang and Wong (2012), the cracking modes of rock-like materials are intimately connected with the distribution of stress filed inside the specimens. Therefore, exploration of the stress filed will greatly contribute to the further understanding of the failure processes of pre-cracked specimens with different inclinations. Stress is a continuum quantity which does not exist at each point in a particle assembly for the discreteness. In the PFC2D model, the local stress is measured by an averaging method which can make the step from the micro-scale to a continuum. The computation procedure relates the two in-plane force components of all contact and parallelbond forces acting on each particle for which the centroid lies within the measurement circle to a force per-unit-length of particle boundary, which must then be divided by a thickness value to obtain a stress quantity (Itasca, 2002). The expression used in PFC2D to compute the average stress tensor within a measurement circle can be given by Eq. (1) (Potyondy and Cundall, 2004): 0
1 ðC Þ B 1−n C ðP Þ ðC;P Þ ðC Þ σ ij ¼ @ Fj A ∑ ∑ xi −xi ni ðP Þ N P NC ∑V
ð1Þ
NP
where the summations are taken over the NP balls with centroids contained within the measurement circle and the NC contacts of these balls; n is the porosity within the measurement circle; V(P) is the volume and x(C) are the locations of a particle centroid and its of particle; x(P) i i P) is the unit normal vector directed from a contact, respectively; n(C, i is the force acting at particle centroid to its contact location; and F(C) j contact. In the current work, 400 measurement circles are arranged in an area of 60 mm × 60 mm around the combined flaw (see Fig. 6). The measurement circles set are 3 mm in diameter, and each contains 29– 37 particles with the average value of 34.425, which can generally reflect the local stress distribution inside the specimens. The basic principle of conversion from the parallel bond force to local stress has been depicted on the right half of Fig. 6. The upper-right portion shows the parallel-bond force chains inside the measurement circles at points ①, ②, ③ and ④. The red indicates the tensile force while the green represents the compressive force. The lower-right portion of Fig. 6 shows the stress distribution on lines AB and CD, which was calculated from the parallel-bond force according to Eq. (1).
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Fig. 6. Arrangement scheme of measurement circles and measuring principle of local stress.
4.1. Spatial distribution of stress field Fig. 7 shows the distribution of stress field inside the specimens with various flaw inclinations. The figures were drawn based on the local stress values recorded by the measurement circles combined with cubic spline interpolation method. Notice that the figures in the legend indicate the magnitude of the stress, and the positive value means the compressive stress while the negative value represents the tensile stress. The contours show the stress distribution around the combined flaws just before the initiation of the first crack. It can be seen from Fig. 7 that for specimens with flaw inclination of 0, 15, 30, 45 and 60°, there exist two obvious compressive stress concentration zones near the flaw tips and tensile stress concentration zones on the flaw surfaces. For specimen with flaw inclination of 90°, the compressive stress concentration zones locate on the flaw surfaces while the tensile stress concentration zones are negligible. With an increase of the flaw inclination, the tensile stress concentration zones gradually shift to the flaw tips while the compressive stress concentration zones transfer to the surfaces of the flaw. For example, the tensile stress concentration zones inside the specimen with flaw inclination of 0° locate in the middle of the flaw surface and the compressive stress concentration zones are located at the tips of the flaw; while for specimen with flaw inclination of 90°, the tensile stress concentration zones appear at the flaw tips and the compressive stress concentration zones lie on the surface of the circular hole. The stress distribution patterns can be utilized to explain the changes of crack initiation positions of specimens with different flaw inclinations. In Fig. 5(a), the first cracks initiated from the middle portion of the circular hole, which was caused by the concentration of the tensile stress at the points (Fig. 7(a)). For specimen with flaw inclination of 45°, the first cracks initiated from the tips of flaw and propagated toward the top and bottom of the specimen (Fig. 5(c)). This is also caused by the concentration of tensile stress at the flaw tips (Fig. 7(c)). For specimen with flaw inclination of 90°, the first cracks initiated from the circular hole surfaces (Fig. 5(e)), which is caused by the concentration of compressive stress at the positions. With the increase of the flaw inclination, the ranges of the tensile stress concentration zones gradually reduce while the ranges of the compressive stress concentration zones expand gradually. In addition, the increase of the flaw inclination leads to a decrease of the maximum value of the tensile stress, which increases the difficulty of crack initiation.
From the left part of Fig. 7, it can be seen that there are some fluctuations in the stress distributions. And with an increase of the flaw inclination, the fluctuation becomes larger, indicating that the stress distribution inside specimen with larger flaw inclination is more complicated, which results in a more complex cracking process and an increase of the uncertainty of rupture positions. One reason for this phenomenon is that the numerical model is an assembly of discrete particles, which leads to the discontinuity of the stress distribution. The other one is that the increase of the flaw inclination reduces the effect of flaw on stress distributions, leaving the stress inside the specimens with larger flaw inclinations in a state of random distribution. 4.2. Cracking processes and stress field evolution In this section, specimens with flaw inclinations of 0, 45 and 90° are taken as the typical examples to investigate the evolution of stress field combining with the stress-strain curves, crack initiation, propagation and coalescence processes and its related acoustic emission. Four timing nodes, namely the point just before the crack initiation, the point with stress level of 80% UCS before the peak, the peak point and the point with stress level of 80% UCS after the peak, are selected to analyze the evolution of stress field with the loading process. Fig. 8 shows the stress-strain curve, cracking process and stress field evolution of specimen with flaw inclination of 0°. At the point just before crack initiation (point (a), about 4 MPa), the tensile stress concentration zones mainly locate near the flaw surfaces while the compressive stress concentration zones mostly concentrate at the flaw tips. When the axial stress reached 6.4 MPa before the peak (point (b)), the first crack initiated from the middle portions of the circular hole and propagated toward the top and bottom boundaries, which led to the transfer of tensile stress concentration zones to the crack tips. Besides, the crack initiation and propagation also lowered the tensile stress concentration degree and increased the compressive stress concentration degree. At the peak point (point (c), 7.8 MPa), the initiation and propagation of cracks at the flaw tips further reduced the tensile stress concentration degree and increased the compressive stress concentration degree. When the axial stress lowered to 6.4 MPa after peak (point (d)), the range of tensile stress concentration zones are significantly larger than that of point (a), but the concentration degree reduces markedly. While for the compressive stress, compared with that of point (a), the range of concentration zones narrow remarkably, but
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(a) MPa Compressive stress concentration zone
Tensile stress concentration zone
Combined flaw
(b)
MPa Compressive stress concentration zone
Tensile stress concentration zone
Combined flaw
(c)
MPa Compressive stress concentration zone
Tensile stress concentration zone
(d)
Combined flaw
MPa Compressive stress concentration zone
Combined flaw
Tensile stress concentration zone
Fig. 7. Distribution of stress field around the combined flaws with different inclinations.
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Fig. 7 (continued).
the concentration degree improves notably. In addition, it is found that the compressive stress concentration degree on the left is greatly higher than that on the right, which is because that the cracked degree on the right is significantly higher than that on the left, leading to an obvious reduction of the supporting capacity of this part. Fig. 9 depicts the stress-strain curve, cracking process and stress field evolution of specimen with flaw inclination of 45°. Overall, the range of tensile stress concentration zone expands gradually but the concentration degree lowers with the loading process; while the range of compressive stress concentration zone narrows and the concentration degree increases gradually. At point (a), where the axial stress is 4.3 MPa, the tensile stress mainly concentrates at a small area around the flaw surface, while the compressive stress dominantly locates at the flaw tips. At point (b), two cracks initiated from the flaw tips, leading to an expansion of the tensile stress concentration zone and a sharp
increase of the concentration degree of the compressive stress. At the peak point, the propagation of the cracks results in a transfer of the compressive stress concentration zone to the point away from the flaw tips, which is due to the fact that the crack propagation leads to the loss of supporting capacity of the area around the flaw tips. When the axial stress lowers to 7.4 MPa after the peak, the entire target area is under compression and the stress concentration zone further transfers away from the flaw tips. Fig. 10 displays the stress-strain curve, cracking process and stress field evolution of specimen with flaw inclination of 90°. Compared with the other two specimens, the same phenomenon that the tensile stress concentration degree decreases and the compressive stress concentration degree increases with the loading process was also observed in this specimen. When the axial stress reached 7.2 MPa (point (a)), the compressive stress mainly concentrates on the circular hole surface and
Fig. 8. Stress-strain characteristic, cracking process and the corresponding stress field of specimen with flaw inclination of 0°.
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Fig. 9. Stress-strain characteristic, cracking process and the corresponding stress field of specimen with flaw inclination of 45°.
the tensile stress is dominantly located at the flaw tips, which is different from that in specimens with flaw inclinations of 0 and 45°. At point (b), some discrete micro-cracks occur inside the specimen, but no obvious changes on stress field are observed except the variation of the stress concentration degree. At the peak point (point (c)), two macro-
cracks initiated from the circular hole surface and propagated upward, leading to a transfer of the compressive stress concentration zone away from the circular hole surface. When the axial stress lowers to 9.1 MPa after the peak, the macro-cracks coalesced with the right and left boundaries and the entire area is under compression.
Fig. 10. Stress-strain characteristic, cracking process and the corresponding stress field of specimen with flaw inclination of 90°.
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5. Discussions 5.1. Crack initiation patterns for pre-cracked specimens In Section 3.3, the crack initiation, propagation, and coalescence processes for pre-cracked specimens with different flaw angles have been investigated, and it is found that various flaw inclinations lead to different crack initiation points and crack types. Based on the cracking processes observed in both the numerical simulations and laboratory tests, three types of crack initiation modes can be identified (Fig. 11). Type A: For specimens with small flaw inclinations, the first crack initiates from the middle of the hole and propagates along the loading direction. The mechanics foundation for the formation of this type of crack initiation pattern is that in these specimens, the maximum tensile stress is located directly above the circular hole and leads to the initiation of tensile crack from the hole surface. This type of crack initiation mode can be observed in specimens with flaw inclination angle θ = 0° and 15°. Type B: For specimens with moderate flaw inclinations, the first crack initiates from the flaw tips or points close to the flaw tips and propagates toward the upper and lower boundaries of the specimens. This type of crack is similar with that observed in rocks (Ashby and Hallam, 1986; Baud et al., 1996), meaning that our research results obtained from coal can also be extended to the rock engineering. The mechanics mechanism for the formation of this type of crack is that with
the increase of the flaw inclination, the tensile stress concentration zone shifts to the flaw tips along the flaw surface, and this moves the crack initiation position to the flaw tips. This type of crack can be found in specimens with flaw inclination angles of θ = 30°, 45° and 60°. Type C: The main difference between this type of crack initiation mode and the other two types is that it is more reasonable to call this type of crack as “cracking zone” rather than “crack”. Formation of this type of crack will lead to the spalling of the circular hole or hole collapse. In these specimens, the tensile stress concentration zone is negligible, while the crack initiation points (middle portion of the circular hole) are in the compressive stress concentration zones, which indicate that the type III crack initiation mode is caused mainly by a compressive stress field. This type of crack initiation mode can be observed in specimens with flaw inclination angles of θ = 75° and 90°.
5.2. Mechanical behavior and its application From the above investigations, we can see that UCS and E of the specimens increase with the inclination angle of the flaw with a length of 20 mm. However, as we know that the flaw size may has an effect on the evolution of the mechanical behavior. Therefore, in this section, we will further study the size effect of the flaw on the strength of the specimens. Fig. 12 shows the UCS and E variations of the specimens with inclination angle of the flaws with different sizes. It can be seen that for
Fig. 11. Crack initiation modes for specimens containing combined flaws with different inclinations. T represents the tensile crack, HSS stands for hole surface spalling.
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Fig. 12. Variation of mechanical strength of pre-cracked specimens with flaw inclination angle.
specimens with flaw length of 10 mm and 15 mm, the UCS fluctuates with an increase of the flaw inclination angle, and the elastic modulus show little changes. This indicates that for specimen with a flaw length b15 mm, its mechanical behaviors show little dependence on the flaw inclination angle. While for specimens with flaw lengths N20 mm, both the UCS and E rise with an increase of the flaw inclination angle. The results show that it is not always the case that the strength and modulus increase with the flaw inclination angle. It only occurs when the relative dimension of the pre-existing crack to the specimen greater than a certain value (for example, in this work, it is 1/3). Taking specimen with flaw length of 20 mm as an example, here we intend to explore the reasons for the variation trend from the perspective of cracking processes. For specimen with flaw inclination of 0°, the crack driven by the tensile stress initiated from the middle of the hole; with an increase of the flaw inclination, the crack initiation position gradually shifted to the flaw tips, and the driven force changed from tensile stress to compression-shear stress. As we know that the tensile strength of the coal-rock mass is generally lower than the compressive strength. Besides, it can be seen from Figs. 8–10 that for specimens with small flaw inclinations, the micro-cracks relatively concentrated, while for specimens with large flaw inclination, the micro-cracks are discrete, which do less damage to the strength of the specimens. In this section, we intend to analyze the general variation rule of the compression strength with flaw inclination from the perspective of damage. Notice that the following analyses are reasonable only when the flaw length is large enough.
Fig. 13. Strength weakening mechanism of pre-cracked specimen from the damage perspective.
Assuming that the damage of the rock is proportional to the work applied, Qin (2001) established a damage evolution model under uniaxial compression. 8 E0 2 > > ε < D ¼ 1− exp − 2Y E > > : σ ¼ exp − 0 ε2 E0 ε 2Y
ð2Þ
where D is the damage variable (0 b D b 1), E0 is the elastic modulus of the complete sample, Y is the constant for a specific material, it is the ratio of the external work to the damage, σ is the stress, and ε is the strain. By derivation, the strain corresponding to the peak point can be deqffiffiffiffi termined, which is εc ¼ EY0 . According to Eq. (2), the damage coefficient at the peak, which is a constant Dc ¼ 1− p1ffiffie, can be acquired. It can be seen from Fig. 13 that the effective bearing area (Se) of the specimen increases with the flaw inclination, leading to a decrease of the damage area (Sd). It is universally known that the damage coefficient is directly proportional to the damage area. Therefore, we can conclude that the damage caused by the combined flaw (D1) also decreases with the flaw inclination (the green curve in Fig. 12). The damage coefficient D2 shown in Fig. 12 is the difference between DC and D1, which is caused by the axial load. It shows that with an increase of the flaw inclination, D2 increases gradually, implying that more work should be done before reaching the peak. According to Eq. (2), for a specific material, the axial strain at the peak (εc) is a constant. Therefore, with an increase of the flaw inclination, the stress related to the peak increases. In other words, the UCS of the specimen increases with the inclination angle of flaw. The research result shows that slot with a smaller inclination has a greater weakening effect on coal strength, while that with a bigger inclination has less effect on coal strength. Based on the result, an optimized slot arrangement method is put forward, which is depicted in Fig. 14.
Fig. 14. Slot arrangement in coal seams with different hardness.
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gradually. The distributions and evolutions of the stress field lead to various crack initiation modes. (4) Based on the research result, an optimized slot arrangement method is proposed. In the hard coal seam, slots with smaller inclination should be created, while in the soft coal seam, slots with smaller inclination should be created to improve gas drainage efficiency. Acknowledgments
Fig. 15. Cracking state of specimen with multi-flaws.
For the hard coal seam, slots with smaller inclinations should be created to significantly weaken the strength of the coal mass, so as to promote the initiation and propagation of cracks around the slotted borehole. For the soft coal seam, slots with bigger inclinations should be cut to prevent the collapse of coal around the borehole while increasing the exposure area of the coal mass. Because the increase of the exposure area is thought to be conducive to the release of the gas stored in coal mass, while the collapse of the coal will block the passage, impeding gas migration. Fig. 15 shows the cracking state of specimen with multi-flaws. It can be seen that interactions exist among the flaws, and it has great influence on the final cracking state. Therefore, during the field application, both the measurement of single flaw and the interactions among the flaws should be considered to optimize the effect of permeability enhancement. 6. Conclusions In the current work, the mechanical characterizations of pre-cracked specimens with various flaw inclinations are investigated by laboratory test and numerical simulation. Some conclusions have been drawn as follows: (1) According to the variation behaviors of the stress after the peak, the stress-strain curves can be divided into three categories. For specimens with small flaw inclination, the stress after the peak drops step by step. When the flaw inclinations is in the range of 45°–60°, the specimens are in a transitional stage, which means that the stress after the peak may drop step by step or drop sharply. For specimens with flaw inclinations of 75 and 90°, the stress after the peak drops sharply. The UCS and elastic modulus increase with the flaw inclination on the whole, which is verified by the numerical simulation. (2) The cracking processes of specimens with various flaw inclinations are analyzed combining with the AE signals. It is found that the initiation positions of the first cracks in specimens with various inclinations are different. For specimens with 0° flaw, the first crack initiated from the middle portion of the circular hole. For specimens with flaw inclination of 30, 45 and 60°, the first cracks initiated from the tips of the flaw. While for specimen with 90°, the first crack (hole surface spalling) appeared on the hole surface. (3) For specimen with flaw inclination of 0°, the tensile stress concentration zone mainly locates at the middle portion of the circular hole, while the compressive stress concentrates at the tips of the flaw. With an increase of the flaw inclination, the tensile stress concentration zone gradually transfers to the flaw tips, while the compressive stress tends to concentrate on the surface of the flaw. The range of tensile stress concentration zone expands gradually but the concentration degree lowers with the loading process; while the range of compressive stress concentration zone narrows and the concentration degree increases
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Contents lists available at ScienceDirect
Tectonophysics journal homepage: www.elsevier.com/locate/tecto
Mechanical behavior and failure mechanism of pre-cracked specimen under uniaxial compression Ting Liu a,b, Baiquan Lin a,b, Wei Yang a,b,⁎ a b
Key Laboratory of Coal Methane and Fire Control (China University of Mining and Technology), Ministry of Education, 221116, PR China School of Safety Engineering, China University of Mining & Technology, Xuzhou 221116, PR China
a r t i c l e
i n f o
Article history: Received 15 November 2016 Received in revised form 11 May 2017 Accepted 2 June 2017 Available online xxxx Keywords: Pre-cracked specimen Failure mechanism Acoustic emission Stress field Particle Flow Code
a b s t r a c t As a desirable permeability enhancement method, hydraulic slotting has been widely used for enhanced coal bed methane (ECBM) recovery in China. Aiming at the problem that the action mechanism of the slot on the mechanical properties of the slotted coal is still unclear, this paper investigates the effects of flaw inclination on the strength, deformation and cracking process of the pre-cracked specimens. The result shows that the stress-strain curves can be divided into three categories based on the stress behaviors, dropping step by step or dropping sharply, after the peak. With an increase of the flaw inclination, the strength and elastic modulus of the precracked specimen increases gradually, which is verified by the numerical simulation and theoretical results. Analysis of the cracking processes indicates that the initiation position of the first crack in specimens with various flaw inclinations is different, which is caused by the various distributions of tensile and compressive stress concentration zones. The distribution of the stress field controls the cracking process which will in turn affect the stress field distribution. With the propagation of the cracks, the tensile stress concentration zones expand and the concentration degree lowers gradually, while the compressive stress concentration zones show the opposite variation trend. Based on the above results, an optimized slot arrangement method has been proposed for the field application of hydraulic slotting. © 2017 Published by Elsevier B.V.
1. Introduction Gas drainage, a basic method for gas disaster control, contains ground well gas drainage and underground borehole gas drainage (Xue et al., 2017). In 2014, the total coal bed methane (CBM) extracted in China is 17,000 Mm3, and that extracted from the underground is 13,300 Mm3, accounting for 78.2% of the total, implying that underground gas drainage is still the main method for gas control in China. Besides, the utilization amount of CBM extracted from the underground is 4500 Mm3, the utilization rate is only 34%. The reason is that the permeability of most coal seams in China is in the range of 10−19–10−18 m2, which is three orders lower than that in Austria and four orders lower than that in America (Zhou et al., 2016; Meng et al., 2015). Such a low permeability of the coal seam prevents the gas from flowing to the borehole, lowering the concentration of the CBM extracted. Generally, gas with the concentration b 20% cannot be used directly and will be discharged into the atmosphere, leading to the greenhouse effect (Li et al., 2015; Warmuzinsli, 2008; Bibler et al., 1998). Therefore, to improve the gas utilization rate, CBM with a higher concentration should
⁎ Corresponding author. E-mail address: [email protected] (W. Yang).
http://dx.doi.org/10.1016/j.tecto.2017.06.004 0040-1951/© 2017 Published by Elsevier B.V.
be extracted, which requires larger coal seam permeability (Zhang and Li, 2017). Exploitation of the protective coal seam has proven to be the most effective method for stress relief and permeability enhancement in coal seam group (Liu et al., 2016b; Kong et al., 2014). However, more commonly, the coal seam exists in the form of single coal seam, a protective coal seam cannot be found. In addition, with an increase of the mining depth, the initial coal seam gradually turns into coal and gas outburst seam. To solve the problem, that is the outburst elimination of the single and the initial coal seams, hydraulic slotting has been developed and applied (Liu et al., 2016a, 2016b; Lin et al., 2012). In the past decades, much research on the hydraulic slotting technique has been conducted and some meaningful results have been achieved. Lin et al. (2015) investigated the cracking modes and the corresponding energy evolution rules in slotting disturbed zones under different stress conditions. The research result contributed to the borehole arrangement in the field. Lin and Shen (2015) studied the coal-permeability enhancement mechanism of multilevel slotting by high-pressure waterjet. The result indicated that with slot number increases from 0 to 3, the coal strength decreases about 40%; and the porosity near the flaw increases about 30%, which was indirectly verified by the field application. Aiming at the problem of hole collapse in the soft coal seam, Lu et al. (2010) proposed a technique of drilling holes by waterjet in the
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roof/floor until the soft coal seam was reached. This technique was reported to be able to improve the drilling length and gas flow significantly. Lu et al. (2009, 2011) used the hydraulic slotting to release the energy stored in the soft and high gassy coal seam so as to improve the gas drainage efficiency and eliminate the outburst risk, which in turn increased the roadway driving speed. Liu et al. (2016b) investigated the pore structure and the resulting adsorption and seepage capacities variations of coal in the slotting disturbed zone. Based on the results, a microscopic model on permeability enhancement and outburst elimination was developed. Based on the framework of coal-methane co-exploitation, Zou et al. (2015) proposed an integrated technique, a combination of drilling-slotting-separation- sealing, to enhance coal permeability and CBM recovery. The field test result indicated that the gas concentration in the slotted borehole was 1.05–1.91 times higher than that in the traditional borehole, implying the effectiveness of the technique. The review about the hydraulic slotting indicates that the research to date has tended to focus on the adsorption and seepage characterizations, cracking modes of the slotting disturbed zone and the application effect in the field. Research about the effects of the spatial arrangement of the slot, especially the flaw inclination, on the mechanical properties and its guiding significance to the field application of hydraulic slotting is rarely reported. In this work, we investigated the effect of flaw inclination on the mechanical properties, especially the strength, deformation and cracking processes of the pre-cracked coal specimens by laboratory test and numerical simulation. In addition, the stress filed around the flaw was also studied to explore the action mechanism of the flaw on the mechanical characteristics of the coal. At last, based on the research result, an optimized slot arrangement was proposed for the field application of hydraulic slotting. 2. Research methods In order to investigate the mechanical properties and cracking process of specimens containing combined flaws with various inclinations, the uniaxial compression tests were conducted in the laboratory combining with the acoustic emission detection. In addition, the numerical simulation was also adopted to further explore the corresponding mechanical mechanism and verify the rationality of the experimental results. 2.1. Laboratory test 2.1.1. Test material The specimens used in the laboratory tests are artificial coal samples with the size of 120 mm × 60 mm × 30 mm (Fig. 1) and an average porosity of 4.3%. The mix proportion of the synthetic coal sample is coal: cement: binder: water = 108:27:9:20. The samples were pressed under a constant pressure of 40 MPa for 30 min and then transferred
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to the thermostat with a constant temperature of 25 °C for 30 days. After consolidation, a combined flaw was drilled at the center of the specimen. The circular hole is 6 mm in diameter, and the rectangular flaw is 20 mm long and 2 mm wide. Notice that the surfaces of the specimens were painted white to get a better observation of the crack initiation, propagation and coalescence processes. 2.1.2. Test methods and apparatus Uniaxial compression tests were conducted on the pre-cracked specimens to obtain the mechanical properties. In the tests, the loading rate was set as 0.1 mm/min, the stress-strain curve, UCS (Uniaxial Compressive Strength) and E (Elastic modulus) of each specimen were monitored. The loading processes were recorded by a digital camera to observe the crack initiation, propagation and coalescence in the specimens. In addition, the intensity characteristics of AE (acoustic emission) during the cracking process of each specimen were also monitored using an AE detector. Notice that each test was conducted for three times to reduce the experimental error caused by sample variability. 2.2. Numerical simulation 2.2.1. Fundamentals of PFC2D In PFC2D (Particle Flow Code in two dimensions), two kinds of particle bond models (PBM) are embedded, namely contact bond model (CBM) and parallel bond model (PBM) (Cho et al., 2007; Yoon, 2007). The PBM can transmit both force and moment between particles, while the CBM can only transmit the force acting at the contact point (Itasca, 2002; Lisjak and Grasselli, 2014). For the CBM, a marked reduction of the macro-stiffness will not be observed after the breakage of the bond as long as the particles still remain in contact. While for the PBM, the breakage of the bond will result in an immediate decrease of the macro-stiffness because the stiffness consists of both contact and bond stiffness (Liu et al., 2016a; Lee and Jeon, 2011). This property implies that the PBM is more realistic for rock-like material modeling. Therefore, the PBM is adopted in the current work to model the coal specimens. 2.2.2. Calibration of mesoscopic parameters To generate a parallel-bond model, a set of mesoscopic parameters should be determined. The model generated with the specified parameter set should reproduce the macro mechanical properties of the coal samples obtained in the laboratory (Wang et al., 2014). Here the stress-strain curve, UCS, E and the failure mode (macroscopic rupture plane) obtained from our laboratory tests were selected as the target variables and the ultimate goal of calibration is to minimize the gap between the variables. In the current work, a series of calibration schemes were conducted and the comparation between the final calibration results and laboratory test results has been depicted in Fig. 2. It can be seen that the shapes of the stress-strain curves are similar, even though a notable difference was observed in peak strains (with an error of −
Fig. 1. Coal samples used in the laboratory test. (a) physical map of coal samples with different flaw inclinations; (b) physical map of coal sample with a flaw inclination of 30°; (c) sketch map of coal sample.
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Fig. 2. Comparation between the numerical results of calibration and experimental results.
22.6%). The discrepancy can be attributed to the existence of a compacting section on the stress-strain curve (see Fig. 2) obtained in the laboratory test. For the UCS and E, the relative errors between the numerical and experimental results are − 0.91% and 6.4% (b10%), respectively. In addition, both the macroscopic rupture planes in the numerical and experimental results initiated from the top boundary and finally coalesced with the right boundary, implying that the failure modes are also analogous. Since the target variables are all acceptable, we can identify the ultimate mesoscopic parameter set, which is shown in Table 1. After generating the numerical model, the combined flaw was created by deleting particles in the designed area. The models produced here are 120 mm high and 60 mm wide and contain about 33,000 particles.
Table 1 Mesoscopic parameters used in the PFC2D model for the synthetic coal sample tested in laboratory. Objects
Micro parameters
Values Remarks
Particle
Particle minimum radius, Rmin (mm)
0.18
Particle radius ratio, Rmax/Rmin Particle density, ρ (kg/m3) Particle contact modulus, EC (GPa) Particle stiffness ratio, kn/ks Particle friction coefficient, μ Parallel-bond radius multiplier, γ Parallel-bond modulus, EP (GPa) Parallel-bond stiffness ratio, pb_kn/pb_ks Parallel-bond normal strength, mean (MPa) Parallel-bond normal strength, std.dev. (MPa) Parallel-bond shear strength, mean (MPa) Parallel-bond shear strength, std.dev. (MPa)
1.66 1000 0.4 1 0.5 1.06 1.6 3.44
Parallel bond
9.99 1.1
Uniform distribution
3. Experimental results 3.1. Stress-strain characteristics Fig. 3 depicts the stress-strain curves of specimens with different flaw inclinations. It is very obvious that for specimens with various flaw inclinations, the stress-strain curves present significantly different behaviors. Based on the characterization, the curves can be divided into three categories, namely type I, type II and type III. Type I (0° ≤ θ ≤ 30°): For specimens with flaw inclination of 0, 15 and 30°, the stress after the peak drops step by step, indicating that these specimens fail in a progressive mode. With an increase of the flaw inclination, the significance degree of this phenomenon decreases. Type II (45° ≤ θ ≤ 60°): When 45° ≤ θ ≤ 60°, the progressive failure is insignificant (specimen with θ = 45°), or for specimens with the same flaw inclination, both the progressive failure and transient failure may occur (specimen with θ = 60°). We call this range of flaw inclination as the transition stage. In the transition stage, the way of stress reduction after the peak is uncertain. Type III (75° ≤ θ ≤ 90°): For specimens with flaw inclinations of 75 and 90°, the stress after the peak drops sharply, implying that transient failure occurs in the specimens after the peak. 3.2. Strength and deformation Fig. 4 shows the strength and deformation characterizations of specimens with different flaw inclinations. To reduce the errors induced by experiment operation and heterogeneity of the samples, each test was conducted three times. The results show that although there exist some fluctuations, both the UCS and elastic modulus rise on the whole with an increase of the flaw inclination. It implies that the increase of the flaw inclination improves the mechanical strength and enhances the ability of resisting axial deformation. A further theoretical analysis was conducted in Section 5 to explore the mechanical mechanism of this phenomenon from the perspective of damage.
13.53
3.3. Cracking process and AE characteristics
1.1
Analyses in Sections 3.1 and 3.2 show that specimens with different flaw inclinations have various mechanical properties, such as stress-
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Fig. 3. Stress-strain curves of precracked specimens with different inclination angles.
strain characterization, mechanical strength and elastic modulus. The mechanical properties of coal-rock mass are closely related to the corresponding cracking processes, namely crack initiation, propagation and
coalescence (Yang et al., 2014; Lee and Jeon, 2011; Du et al., 2016; Ren et al., 2016). Therefore, it is necessary to further investigate the cracking processes of the pre-cracked specimens so as to get a better
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Fig. 4. Strength and deformation of specimens with various flaw inclinations.
understanding of the variations of mechanical properties. In this section, the crack initiation, propagation and coalescence processes of specimens with flaw inclinations of 0, 30, 45, 60 and 90° were analyzed combining with the AE characteristics (Fig. 5).
3.3.1. θ = 0° [Fig. 5(a)] Fig. 5(a) depicts the cracking process of specimen with flaw inclination of 0°. When the axial stress increased to 7.6 MPa (point a), several AE signals were monitored and at the same time, cracks 1 and 2 initiated
Fig. 5. Cracking processes and AE characteristics of specimens with different flaw inclinations.
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from the surface of the circular hole were observed. As the loading continuous, cracks 1 and 2 propagated but no new crack formed before the peak. At the peak point a stress drop occurred and a strong AE signal was monitored (point b), meanwhile, crack 3 initiated from the left tip of the flaw and propagated toward the top boundary of the specimen. With an increase of the axial strain, crack 4 initiated from the right tip of the flaw and propagated to the top boundary which resulted in a dramatic drop of the axial stress (point c). After that a stress increase was observed due to the closure of the flaw which increased the axial supporting capacity. At point d, a sharp decrease of the stress and an intense AE signal were monitored and surface spalling was observed. Thereafter, no obvious stress change was monitored and the AE signal was relatively uniform. At point e, cracks 6 and 7 initiated from the left and right tips of the flaw and gradually coalesced with the bottom boundary, leading to the ultimate failure of the specimen. 3.3.2. θ = 30° [Fig. 5(b)] Fig. 5(b) shows the cracking process of specimen with flaw inclination of 30°. When the axial stress increased to 2.8 MPa (point a), several AE signals were monitored but no crack was observed on the surface of the specimen. The sporadic signals maybe resulted from the closure of the primary pores. At point b (9.14 MPa), cracks 1 and 2 initiated from the right and left tips of the flaw, respectively, accompanied by strong AE signals. At the peak point, crack 3 initiated from the right tip of the flaw and propagated toward the top boundary of the specimen, at the same time, a sharp stress drop and a strong AE signal were observed (point c). At about 250 s (point d), a stress drop and a strong AE signal were observed which were caused by the coalescence of crack 3 with top boundary. At point e, crack 4 initiated from the left tip of the flaw and propagated toward the bottom of the specimen on the whole. Hereafter, no observable crack and AE signal were monitored and the stress drop observed was mainly caused by the opening of the cracks which led to the ultimate failure of the specimen. 3.3.3. θ = 45° [Fig. 5(c)] Fig. 5(c) displays the cracking process of specimen with flaw inclination of 45°. When the axial stress reached 7.5 MPa, cracks 1 and 2 initiated from the right and left tips of the flaw and propagated toward the top and bottom of the specimen, respectively. Meanwhile, AE signals and a weak stress reduction were observed. From 200 s (point a) to 325 s (point d), no new cracks formed and the AE signals and the stress drops observed during this period of time were mainly caused by the propagation and opening of cracks 1 and 2. Besides, it may also be due to the initiation and propagation of microcracks inside the specimen. When the axial stress decreased to 2.4 MPa (point e), crack 3 and crack 4 initiated from the left and right tips of the flaw and propagated toward and finally coalesced with the bottom and top boundaries of the specimen, respectively. During the period before and after 350 s, the AE activity was relatively frequent, which was mainly resulted from the initiation and propagation of cracks 3 and4. 3.3.4. θ = 60° [Fig. 5(d)] Fig. 5(d) depicts the cracking process of specimen with flaw inclination of 60°. When the axial stress increased to 8.2 MPa (point a), some low-level AE activities were monitored but no obvious surface crack was observed, implying that microcracks formed inside the specimen. After the peak (point b), crack 1 initiated from the right tip of the flaw and then crack 2 initiated from the left tip of the flaw and propagated toward the bottom boundary of the specimen. With an increase of the axial strain, crack 2 propagated gradually and finally coalesced with the bottom boundary, while no obvious propagation of crack 1 was observed which was believed to be suppressed by the propagation of crack 2 (point c). At point d, crack 3 initiated from the right tip of the flaw and propagated toward the upper right of the specimen combining with a stress drop and several high-level AE activities. With the continuous rise of the axial strain, the existing cracks opened gradually and crack
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3 finally coalesced with the top boundary of the specimen, leading to the ultimate failure of the specimen (point e). 3.3.5. θ = 90° [Fig. 5(e)] Fig. 5(e) shows the cracking process of specimen with flaw inclination of 90°. It can be seen that between 50 and 100 s, there were some AE activities which were thought to be due to the closure of the primary pores or the sliding friction between the coal particles. While the axial stress reached 10.8 MPa (point a), some low-level AE activities were monitored but no obvious cracks were found, indicating the microcracks formed inside the specimen. After the peak, a sharp axial stress drop and high-level AE activities were monitored, which were accompanied by the initiations of crack 1 and crack 2 from the upper tip of the flaw and surface of the circular hole, respectively (point b). At point c, two far-filed cracks, crack 3 and crack 4, formed in the upper-left corner of the specimen. Hereafter, no obvious changes of the axial stress were found but the AE activities, caused by the opening of the existing cracks, had always been in a high level. 4. Numerical results Analyses in Section 3.3 show that specimens with different flaw inclinations have various cracking processes. According to Wong et al. (2002) and Zhang and Wong (2012), the cracking modes of rock-like materials are intimately connected with the distribution of stress filed inside the specimens. Therefore, exploration of the stress filed will greatly contribute to the further understanding of the failure processes of pre-cracked specimens with different inclinations. Stress is a continuum quantity which does not exist at each point in a particle assembly for the discreteness. In the PFC2D model, the local stress is measured by an averaging method which can make the step from the micro-scale to a continuum. The computation procedure relates the two in-plane force components of all contact and parallelbond forces acting on each particle for which the centroid lies within the measurement circle to a force per-unit-length of particle boundary, which must then be divided by a thickness value to obtain a stress quantity (Itasca, 2002). The expression used in PFC2D to compute the average stress tensor within a measurement circle can be given by Eq. (1) (Potyondy and Cundall, 2004): 0
1 ðC Þ B 1−n C ðP Þ ðC;P Þ ðC Þ σ ij ¼ @ Fj A ∑ ∑ xi −xi ni ðP Þ N P NC ∑V
ð1Þ
NP
where the summations are taken over the NP balls with centroids contained within the measurement circle and the NC contacts of these balls; n is the porosity within the measurement circle; V(P) is the volume and x(C) are the locations of a particle centroid and its of particle; x(P) i i P) is the unit normal vector directed from a contact, respectively; n(C, i is the force acting at particle centroid to its contact location; and F(C) j contact. In the current work, 400 measurement circles are arranged in an area of 60 mm × 60 mm around the combined flaw (see Fig. 6). The measurement circles set are 3 mm in diameter, and each contains 29– 37 particles with the average value of 34.425, which can generally reflect the local stress distribution inside the specimens. The basic principle of conversion from the parallel bond force to local stress has been depicted on the right half of Fig. 6. The upper-right portion shows the parallel-bond force chains inside the measurement circles at points ①, ②, ③ and ④. The red indicates the tensile force while the green represents the compressive force. The lower-right portion of Fig. 6 shows the stress distribution on lines AB and CD, which was calculated from the parallel-bond force according to Eq. (1).
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Fig. 6. Arrangement scheme of measurement circles and measuring principle of local stress.
4.1. Spatial distribution of stress field Fig. 7 shows the distribution of stress field inside the specimens with various flaw inclinations. The figures were drawn based on the local stress values recorded by the measurement circles combined with cubic spline interpolation method. Notice that the figures in the legend indicate the magnitude of the stress, and the positive value means the compressive stress while the negative value represents the tensile stress. The contours show the stress distribution around the combined flaws just before the initiation of the first crack. It can be seen from Fig. 7 that for specimens with flaw inclination of 0, 15, 30, 45 and 60°, there exist two obvious compressive stress concentration zones near the flaw tips and tensile stress concentration zones on the flaw surfaces. For specimen with flaw inclination of 90°, the compressive stress concentration zones locate on the flaw surfaces while the tensile stress concentration zones are negligible. With an increase of the flaw inclination, the tensile stress concentration zones gradually shift to the flaw tips while the compressive stress concentration zones transfer to the surfaces of the flaw. For example, the tensile stress concentration zones inside the specimen with flaw inclination of 0° locate in the middle of the flaw surface and the compressive stress concentration zones are located at the tips of the flaw; while for specimen with flaw inclination of 90°, the tensile stress concentration zones appear at the flaw tips and the compressive stress concentration zones lie on the surface of the circular hole. The stress distribution patterns can be utilized to explain the changes of crack initiation positions of specimens with different flaw inclinations. In Fig. 5(a), the first cracks initiated from the middle portion of the circular hole, which was caused by the concentration of the tensile stress at the points (Fig. 7(a)). For specimen with flaw inclination of 45°, the first cracks initiated from the tips of flaw and propagated toward the top and bottom of the specimen (Fig. 5(c)). This is also caused by the concentration of tensile stress at the flaw tips (Fig. 7(c)). For specimen with flaw inclination of 90°, the first cracks initiated from the circular hole surfaces (Fig. 5(e)), which is caused by the concentration of compressive stress at the positions. With the increase of the flaw inclination, the ranges of the tensile stress concentration zones gradually reduce while the ranges of the compressive stress concentration zones expand gradually. In addition, the increase of the flaw inclination leads to a decrease of the maximum value of the tensile stress, which increases the difficulty of crack initiation.
From the left part of Fig. 7, it can be seen that there are some fluctuations in the stress distributions. And with an increase of the flaw inclination, the fluctuation becomes larger, indicating that the stress distribution inside specimen with larger flaw inclination is more complicated, which results in a more complex cracking process and an increase of the uncertainty of rupture positions. One reason for this phenomenon is that the numerical model is an assembly of discrete particles, which leads to the discontinuity of the stress distribution. The other one is that the increase of the flaw inclination reduces the effect of flaw on stress distributions, leaving the stress inside the specimens with larger flaw inclinations in a state of random distribution. 4.2. Cracking processes and stress field evolution In this section, specimens with flaw inclinations of 0, 45 and 90° are taken as the typical examples to investigate the evolution of stress field combining with the stress-strain curves, crack initiation, propagation and coalescence processes and its related acoustic emission. Four timing nodes, namely the point just before the crack initiation, the point with stress level of 80% UCS before the peak, the peak point and the point with stress level of 80% UCS after the peak, are selected to analyze the evolution of stress field with the loading process. Fig. 8 shows the stress-strain curve, cracking process and stress field evolution of specimen with flaw inclination of 0°. At the point just before crack initiation (point (a), about 4 MPa), the tensile stress concentration zones mainly locate near the flaw surfaces while the compressive stress concentration zones mostly concentrate at the flaw tips. When the axial stress reached 6.4 MPa before the peak (point (b)), the first crack initiated from the middle portions of the circular hole and propagated toward the top and bottom boundaries, which led to the transfer of tensile stress concentration zones to the crack tips. Besides, the crack initiation and propagation also lowered the tensile stress concentration degree and increased the compressive stress concentration degree. At the peak point (point (c), 7.8 MPa), the initiation and propagation of cracks at the flaw tips further reduced the tensile stress concentration degree and increased the compressive stress concentration degree. When the axial stress lowered to 6.4 MPa after peak (point (d)), the range of tensile stress concentration zones are significantly larger than that of point (a), but the concentration degree reduces markedly. While for the compressive stress, compared with that of point (a), the range of concentration zones narrow remarkably, but
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(a) MPa Compressive stress concentration zone
Tensile stress concentration zone
Combined flaw
(b)
MPa Compressive stress concentration zone
Tensile stress concentration zone
Combined flaw
(c)
MPa Compressive stress concentration zone
Tensile stress concentration zone
(d)
Combined flaw
MPa Compressive stress concentration zone
Combined flaw
Tensile stress concentration zone
Fig. 7. Distribution of stress field around the combined flaws with different inclinations.
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Fig. 7 (continued).
the concentration degree improves notably. In addition, it is found that the compressive stress concentration degree on the left is greatly higher than that on the right, which is because that the cracked degree on the right is significantly higher than that on the left, leading to an obvious reduction of the supporting capacity of this part. Fig. 9 depicts the stress-strain curve, cracking process and stress field evolution of specimen with flaw inclination of 45°. Overall, the range of tensile stress concentration zone expands gradually but the concentration degree lowers with the loading process; while the range of compressive stress concentration zone narrows and the concentration degree increases gradually. At point (a), where the axial stress is 4.3 MPa, the tensile stress mainly concentrates at a small area around the flaw surface, while the compressive stress dominantly locates at the flaw tips. At point (b), two cracks initiated from the flaw tips, leading to an expansion of the tensile stress concentration zone and a sharp
increase of the concentration degree of the compressive stress. At the peak point, the propagation of the cracks results in a transfer of the compressive stress concentration zone to the point away from the flaw tips, which is due to the fact that the crack propagation leads to the loss of supporting capacity of the area around the flaw tips. When the axial stress lowers to 7.4 MPa after the peak, the entire target area is under compression and the stress concentration zone further transfers away from the flaw tips. Fig. 10 displays the stress-strain curve, cracking process and stress field evolution of specimen with flaw inclination of 90°. Compared with the other two specimens, the same phenomenon that the tensile stress concentration degree decreases and the compressive stress concentration degree increases with the loading process was also observed in this specimen. When the axial stress reached 7.2 MPa (point (a)), the compressive stress mainly concentrates on the circular hole surface and
Fig. 8. Stress-strain characteristic, cracking process and the corresponding stress field of specimen with flaw inclination of 0°.
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Fig. 9. Stress-strain characteristic, cracking process and the corresponding stress field of specimen with flaw inclination of 45°.
the tensile stress is dominantly located at the flaw tips, which is different from that in specimens with flaw inclinations of 0 and 45°. At point (b), some discrete micro-cracks occur inside the specimen, but no obvious changes on stress field are observed except the variation of the stress concentration degree. At the peak point (point (c)), two macro-
cracks initiated from the circular hole surface and propagated upward, leading to a transfer of the compressive stress concentration zone away from the circular hole surface. When the axial stress lowers to 9.1 MPa after the peak, the macro-cracks coalesced with the right and left boundaries and the entire area is under compression.
Fig. 10. Stress-strain characteristic, cracking process and the corresponding stress field of specimen with flaw inclination of 90°.
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5. Discussions 5.1. Crack initiation patterns for pre-cracked specimens In Section 3.3, the crack initiation, propagation, and coalescence processes for pre-cracked specimens with different flaw angles have been investigated, and it is found that various flaw inclinations lead to different crack initiation points and crack types. Based on the cracking processes observed in both the numerical simulations and laboratory tests, three types of crack initiation modes can be identified (Fig. 11). Type A: For specimens with small flaw inclinations, the first crack initiates from the middle of the hole and propagates along the loading direction. The mechanics foundation for the formation of this type of crack initiation pattern is that in these specimens, the maximum tensile stress is located directly above the circular hole and leads to the initiation of tensile crack from the hole surface. This type of crack initiation mode can be observed in specimens with flaw inclination angle θ = 0° and 15°. Type B: For specimens with moderate flaw inclinations, the first crack initiates from the flaw tips or points close to the flaw tips and propagates toward the upper and lower boundaries of the specimens. This type of crack is similar with that observed in rocks (Ashby and Hallam, 1986; Baud et al., 1996), meaning that our research results obtained from coal can also be extended to the rock engineering. The mechanics mechanism for the formation of this type of crack is that with
the increase of the flaw inclination, the tensile stress concentration zone shifts to the flaw tips along the flaw surface, and this moves the crack initiation position to the flaw tips. This type of crack can be found in specimens with flaw inclination angles of θ = 30°, 45° and 60°. Type C: The main difference between this type of crack initiation mode and the other two types is that it is more reasonable to call this type of crack as “cracking zone” rather than “crack”. Formation of this type of crack will lead to the spalling of the circular hole or hole collapse. In these specimens, the tensile stress concentration zone is negligible, while the crack initiation points (middle portion of the circular hole) are in the compressive stress concentration zones, which indicate that the type III crack initiation mode is caused mainly by a compressive stress field. This type of crack initiation mode can be observed in specimens with flaw inclination angles of θ = 75° and 90°.
5.2. Mechanical behavior and its application From the above investigations, we can see that UCS and E of the specimens increase with the inclination angle of the flaw with a length of 20 mm. However, as we know that the flaw size may has an effect on the evolution of the mechanical behavior. Therefore, in this section, we will further study the size effect of the flaw on the strength of the specimens. Fig. 12 shows the UCS and E variations of the specimens with inclination angle of the flaws with different sizes. It can be seen that for
Fig. 11. Crack initiation modes for specimens containing combined flaws with different inclinations. T represents the tensile crack, HSS stands for hole surface spalling.
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Fig. 12. Variation of mechanical strength of pre-cracked specimens with flaw inclination angle.
specimens with flaw length of 10 mm and 15 mm, the UCS fluctuates with an increase of the flaw inclination angle, and the elastic modulus show little changes. This indicates that for specimen with a flaw length b15 mm, its mechanical behaviors show little dependence on the flaw inclination angle. While for specimens with flaw lengths N20 mm, both the UCS and E rise with an increase of the flaw inclination angle. The results show that it is not always the case that the strength and modulus increase with the flaw inclination angle. It only occurs when the relative dimension of the pre-existing crack to the specimen greater than a certain value (for example, in this work, it is 1/3). Taking specimen with flaw length of 20 mm as an example, here we intend to explore the reasons for the variation trend from the perspective of cracking processes. For specimen with flaw inclination of 0°, the crack driven by the tensile stress initiated from the middle of the hole; with an increase of the flaw inclination, the crack initiation position gradually shifted to the flaw tips, and the driven force changed from tensile stress to compression-shear stress. As we know that the tensile strength of the coal-rock mass is generally lower than the compressive strength. Besides, it can be seen from Figs. 8–10 that for specimens with small flaw inclinations, the micro-cracks relatively concentrated, while for specimens with large flaw inclination, the micro-cracks are discrete, which do less damage to the strength of the specimens. In this section, we intend to analyze the general variation rule of the compression strength with flaw inclination from the perspective of damage. Notice that the following analyses are reasonable only when the flaw length is large enough.
Fig. 13. Strength weakening mechanism of pre-cracked specimen from the damage perspective.
Assuming that the damage of the rock is proportional to the work applied, Qin (2001) established a damage evolution model under uniaxial compression. 8 E0 2 > > ε < D ¼ 1− exp − 2Y E > > : σ ¼ exp − 0 ε2 E0 ε 2Y
ð2Þ
where D is the damage variable (0 b D b 1), E0 is the elastic modulus of the complete sample, Y is the constant for a specific material, it is the ratio of the external work to the damage, σ is the stress, and ε is the strain. By derivation, the strain corresponding to the peak point can be deqffiffiffiffi termined, which is εc ¼ EY0 . According to Eq. (2), the damage coefficient at the peak, which is a constant Dc ¼ 1− p1ffiffie, can be acquired. It can be seen from Fig. 13 that the effective bearing area (Se) of the specimen increases with the flaw inclination, leading to a decrease of the damage area (Sd). It is universally known that the damage coefficient is directly proportional to the damage area. Therefore, we can conclude that the damage caused by the combined flaw (D1) also decreases with the flaw inclination (the green curve in Fig. 12). The damage coefficient D2 shown in Fig. 12 is the difference between DC and D1, which is caused by the axial load. It shows that with an increase of the flaw inclination, D2 increases gradually, implying that more work should be done before reaching the peak. According to Eq. (2), for a specific material, the axial strain at the peak (εc) is a constant. Therefore, with an increase of the flaw inclination, the stress related to the peak increases. In other words, the UCS of the specimen increases with the inclination angle of flaw. The research result shows that slot with a smaller inclination has a greater weakening effect on coal strength, while that with a bigger inclination has less effect on coal strength. Based on the result, an optimized slot arrangement method is put forward, which is depicted in Fig. 14.
Fig. 14. Slot arrangement in coal seams with different hardness.
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gradually. The distributions and evolutions of the stress field lead to various crack initiation modes. (4) Based on the research result, an optimized slot arrangement method is proposed. In the hard coal seam, slots with smaller inclination should be created, while in the soft coal seam, slots with smaller inclination should be created to improve gas drainage efficiency. Acknowledgments
Fig. 15. Cracking state of specimen with multi-flaws.
For the hard coal seam, slots with smaller inclinations should be created to significantly weaken the strength of the coal mass, so as to promote the initiation and propagation of cracks around the slotted borehole. For the soft coal seam, slots with bigger inclinations should be cut to prevent the collapse of coal around the borehole while increasing the exposure area of the coal mass. Because the increase of the exposure area is thought to be conducive to the release of the gas stored in coal mass, while the collapse of the coal will block the passage, impeding gas migration. Fig. 15 shows the cracking state of specimen with multi-flaws. It can be seen that interactions exist among the flaws, and it has great influence on the final cracking state. Therefore, during the field application, both the measurement of single flaw and the interactions among the flaws should be considered to optimize the effect of permeability enhancement. 6. Conclusions In the current work, the mechanical characterizations of pre-cracked specimens with various flaw inclinations are investigated by laboratory test and numerical simulation. Some conclusions have been drawn as follows: (1) According to the variation behaviors of the stress after the peak, the stress-strain curves can be divided into three categories. For specimens with small flaw inclination, the stress after the peak drops step by step. When the flaw inclinations is in the range of 45°–60°, the specimens are in a transitional stage, which means that the stress after the peak may drop step by step or drop sharply. For specimens with flaw inclinations of 75 and 90°, the stress after the peak drops sharply. The UCS and elastic modulus increase with the flaw inclination on the whole, which is verified by the numerical simulation. (2) The cracking processes of specimens with various flaw inclinations are analyzed combining with the AE signals. It is found that the initiation positions of the first cracks in specimens with various inclinations are different. For specimens with 0° flaw, the first crack initiated from the middle portion of the circular hole. For specimens with flaw inclination of 30, 45 and 60°, the first cracks initiated from the tips of the flaw. While for specimen with 90°, the first crack (hole surface spalling) appeared on the hole surface. (3) For specimen with flaw inclination of 0°, the tensile stress concentration zone mainly locates at the middle portion of the circular hole, while the compressive stress concentrates at the tips of the flaw. With an increase of the flaw inclination, the tensile stress concentration zone gradually transfers to the flaw tips, while the compressive stress tends to concentrate on the surface of the flaw. The range of tensile stress concentration zone expands gradually but the concentration degree lowers with the loading process; while the range of compressive stress concentration zone narrows and the concentration degree increases
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