To investigate the mechanism of fault slips in coal mines, a biaxial shear experiment was carried out under unloading condition based on the fault F16 in Yima city, China. Two rock samples were used in the experiment and each sample was composed of two triangular sandstone blocks which were put together to simulate the fault. One rock sample was used to do fault slip tests and it was called slip-test sample. The other sample for comparison with the slip-test one was untested, and it was named non-slip-test sample. During the biaxial shear experiment of the slip-test sample, normal and shear strains near the fault, acoustic emission (AE) signals, and the sliding displacement were measured. After the experiment, microscopic profiles of fault surfaces of both rock samples were examined by scanning electron microscope (SEM). In addition, a numerical simulation was conducted to model the slip of the fault F16. The results indicate that: (1) three fault slips occurred during the biaxial shear experiment, and the shear stress, normal and shear strains in the first slip showed the maximum variation among three slips; (2) Shear strains near the two ends of the fault had a more significate variation than that in the middle part, and the typical trend of shear strains was first dropping, then increasing rapidly, and then falling slowly to a specific value during the first slip; (3) The first slip had the largest sliding displacement of 29.89 \(\mu m\), and in the first slip three phases including slow slip, main shock and aftershock occurred based on AE monitoring results. (4) On the fault surface of non-slip-test sample, microstructures such as bulges, voids and veins were ubiquitous and notable, making the fault surface much rough, while similar microstructures were few and the fault surface of the slip-test sample was flattened after fault slips; (5) The slipping direction in the shallow part and deep part of the fault F16 were opposite during mining.
Introduction
In mining engineering fault slips, usually referring to unstable fault slips, often induce rockbursts and other disasters (Petukhov 1995; Ortlepp 2000; Whyatt et al. 2002; Zhang et al. 2012; Zhou et al. 2015; Sainoki and Mitri 2018; Tajduś et al. 2018; Wang et al. 2020). For example, the slips of the fault F16 which is a thrust fault with a length of 45 km, a dip angle of 15°—75°, and a throw of 50 m—500 m, have caused hundreds of rockbursts in Yima coal field of China up to now (Cai et al. 2015; Lu et al. 2019). Unfortunately, the mechanism of fault slip is still under debate (Sainoki and Mitri 2014, 2015a; Meng et al. 2016a, b; Yu et al. 2016; Manouchehrian and Cai 2017; Sainoki et al. 2017; Wang et al. 2017; Duan et al. 2019; Ma et al. 2019; Hu et al. 2020; Jiang et al. 2020; Liu et al. 2020; Rinaldi and Urpi 2020; Li et al. 2021). Some researchers found that fault’s properties play an important role in the fault slip (Zhang et al. 2000; Lee et al. 2001; Karami and Stead 2008; Candela et al. 2011; Asadi et al. 2012; Zhang 2014; Li et al. 2015; Sainoki and Mitri 2015b; Wu 2015; Deng et al. 2018; Meng et al. 2018). The properties of a fault mainly consist of its type, asperity, length, filling, drop height, etc. Other researchers proposed that the stresses including static and dynamic ones may affect fault behavior and cause fault slips (Sainoki and Mitri 2014; Sainoki et al. 2017; Manouchehrian and Cai 2017, 2018; Jiang et al. 2020; Li et al. 2021; Gao et al. 2021). In coal mines, the mining operation can weaken the surrounding rock mass and unload the in-situ stresses surrounding a fault (He et al. 2016; Wu et al. 2017; Rinaldi and Urpi 2020), and then result in fault slips (Batugin et al. 2016; Kong et al. 2019). In the past, researchers mainly focus on the fault slip under loading condition (Brace and Byerlee 1966; Lu et al. 2018; Meng et al. 2018, 2019; Xu et al. 2018). However, such loading condition is not consistent with the unloading stress path during mining. Recently, a few researchers have paid attention to the fault slip induced by mining unloading (Wu et al. 2014, 2017), but the results can't explain the focal mechanism of a fault during mining clearly. Thus, it is necessary to do more investigations to study this topic.
In this study the laboratory experiment and numerical modeling of the fault F16 slip were conducted under unloading condition. Multiple physical parameters such as stresses, strains, sliding displacements, AE characteristics, and SEM images of fault surfaces were recorded or examined during tests. In addition, the pattern and process of the fault F16 slip were analyzed.
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Laboratory experiment
Sample preparation and experimental system settings
Both biaxial shear and SEM experiments were done in this study (Table 1). Two sandstone samples for simulating the fault were cut from one large block which was collected in Yuejin coal mine near the fault F16. One sample was used in the biaxial shear experiment (Fig. 1a). After the experiment, six specimens taken from the two fault surfaces of the two rock samples were used in the SEM experiment. Among them, three specimens were taken from the fault surface of slip-test sample and the others from that of non-slip-test sample (Table 1). We assumed that they have the same original surfaces because they came from the same rock block.
Table 1
Summary of experiments in this study
Experiments
Samples name
Tests category or specimens quantity
Note
Biaxial shear
Slip-test sample
Test 1, 0.03 \(\mathrm{mm}/\mathrm{min}\)
Because only stable slip occurred in unloading rates of 0.03 and 0.06 \(\mathrm{mm}/\mathrm{min}\), both of two tests results are not shown in this study.
Test 2, 0.06 \(\mathrm{mm}/\mathrm{min}\)
Test 3 (fault slip test), 0.3 \(\mathrm{mm}/\mathrm{min}\)
SEM
Slip-test sample
3 specimens
For fault surfaces comparison before and after fault slips.
Non-slip-test sample
3 specimens
Fig. 1
Experimental system setup. a Fault sample. The grey rectangular area denotes the observation scope by DIC (Digital Image Correlation). b Monitoring instrumentations. The rock sample was set horizontally on the table of the load cell. c Overall view. d Local view. The view is obtained from the top of the sample
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Both rock samples with an inside artificial fault were 300 mm long, 200 mm wide, and 50 mm thick. The faults had a length of 312 mm (O to P) and an angle of \({32}^{^\circ }\) (Fig. 1a). To avoid touching the loading board, four corners of the samples were cut. The density of the sandstone samples was \(2700\mathrm{ kg}/{\mathrm{m}}^{3}\), Young’s modulus \(48\mathrm{ GPa}\), Poisson’s ratio 0.20, and static uniaxial compressive strength 67 MPa. To simulate the prolonged slip history of the fault F16, fault surfaces of the rock samples were polished so that they tightly contact with each other before tests.
At the beginning, the slip-test sample for biaxial shear experiment was tested for three times under different unloading rates. After that, some parts on the fault surfaces of both slip-test and non-slip-test samples were cut off and examined in the SEM cell. The dimension of SEM specimens was 1–3 cm long and 1 cm wide.
Monitoring methods and exprimental process
The biaxial shear experiment was conducted in room temperature and dry conditions at the State Key Laboratory of Earthquake Dynamics, China. A biaxial loading table was used for loading or unloading the rock sample in X and Y directions (Fig. 1b, d). Two pairs of loading boards surrounding the slip-test sample were used to measure the compressive force and displacement (Table 2). A total of 10 sets of strain gauges named S1 to S10 were fixed along the fault with an equal space of 31.2 mm between two neighbouring ones (Fig. 1a). Each set of gauges included three strain gauges, with the middle one vertical to the fault, and two others on both sides of the middle gauge with an angle of \({45}^{^\circ }\) (Fig. 1a).
Table 2
Summary of instrumentations
Physical quantities
Instruments
Sampling rates
Resolution
Recording
X force & displacement
Loading boards (X direction)
1000 Hz
\(1 \;N, 1\times {10}^{-6} \mathrm{\mu m}\)
Continuous
Y force & displacement
Loading boards (Y direction)
1000 Hz
\(1 \;N, 1\times {10}^{-6} \mathrm{\mu m}\)
Continuous
Fault images & displacement
High-speed camera
1000 Hz
2048 \(\times\) 256 pixels
Triggered
Local shear & normal strain
Three-component strain gauges (configuration in Fig. 1a)
1000 Hz
\(1\times {10}^{-6}\) strain
Continuous
AE signal
AE transducers
500 kHz
16 bits, \(1.53 \times {10}^{-6} \mathrm{V}\)
Continuous
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A high-speed camera named FastcanSA2-C3 was installed above the rock sample to record images during the biaxial shear experiment. The dimension of images was 61.44 cm long and 7.68 cm wide which can be converted into pixel values of 2048 pixels long and 256 pixels wide (grey rectangle in Fig. 1a). One pixel represents 30 \(\mu m\) after calibration. The light-emitting diode (LED) called C-600 provided a light source for the camera. Before fault-slip tests, the top surface of the slip-test sample was spayed by white speckles, so that the shear displacement of the fault could be processed by the DIC software. The high-speed camera was triggered by the AE monitoring system named DS5-8B, which included two AE transducers glued on the hanging wall and footwall respectively to capture the signals of fault slips. Once the electric fault-slipping signal was captured, the images in a period of 873.4 ms were photographed by the high-speed camera.
At the beginning of each fault-slip test, the X-direction force was loaded to 139.65 \(\mathrm{kN}\) at a rate of 1.10 \(\mathrm{kN}/\mathrm{s}\), meanwhile the Y-direction force was applied to 62.06 \(\mathrm{kN}\) at a loading speed of 0.49 \(\mathrm{kN}/\mathrm{s}\). Based on the loading area calculation (Fig. 1a), the stresses in the X (9.31 MPa) and Y (6.21 MPa) directions were determined respectively. Thus, the ratio of X-direction to Y-direction stresses was 1.50 to analog the stress environment in the field. That stress ratio was obtained based on the result of in-situ stress measurement. During fault-slip tests, the X-direction force (parallel to mining direction) was unloaded at a specific speed to simulate the mining operation, while the Y-direction force kept a constant value. In the biaxial shear experiment, a total of three tests were conducted at different unloading rates: 0.03 \(\mathrm{mm}/\mathrm{min}\), 0.06 \(\mathrm{mm}/\mathrm{min},\) and 0.3 \(\mathrm{mm}/\mathrm{min}\)(Table 1). The dramatical fault rupture was observed only in the test with the unloading rate of 0.3 \(\mathrm{mm}/\mathrm{min}\). On the contrary, the fault just slipped slowly in two other tests. Accordingly, the test at the unloading rate of 0.3 \(\mathrm{mm}/\mathrm{min}\) was mainly investigated in this study, which is consistent with the fault slip topic.
After the biaxial shear experiment, the SEM experiment was carried out at the State Key Laboratory of Coal Mining and Clean Utilization, China. Six specimens for the SEM experiment were cut off from the slip-test and non-slip-test fault samples. After processed by the metallic coating method, these specimens were placed into an SEM apparatus named Vega 3 Tescan. The magnifications of images in the SEM experiment were from 200 to 800.
Experimental results
Stress and strain changes near the fault
Figure 2a shows the variation of shear stress along the fault during the biaxial shear experiment. Figure 2b is the mechanical analysis of a fault microcell. The shear stress τ can be calculated from Eq. (1):
where σX is the compressive stress in the X direction; σY is the compressive stress in the Y direction; θ is the inclination angle of the fault. Note that τ is positive when the shear stress couple is counterclockwise. From Fig. 2a, at about 85 s, the fault began to slip and soon afterwards three significant stress drops occurred successively (see phases A-B, C-D, and E–F in Fig. 2a). Among them, the phase A-B with a stress drop of 0.36 MPa was the largest one.
Fig. 2
Shear stress drops during the fault slip. a Shear stress vs. time. b Mechanical model of the fault. τ is the shear stress and σN is the normal stress on the fault
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Figure 3 shows the relation between normal strains and time. The positions of gauges S2 to S10 are shown in Fig. 1a. The normal strains were obtained from strain gauges No. 2 in each set of strain gauges along the fault (Fig. 1a). During the fault slip test, the strain gauge No. 2 of S1 was damaged unintentionally, resulting in that the normal strain of S1 is missing in Fig. 3. In Fig. 3a, three fluctuations of strain curves including phases A-B, C-D, and E–F occurred at around 85 s, 89.5 s, and 91.5 s respectively. This is consistent with three shear stress drops in Fig. 2a. During the first strain fluctuation (phase A-B), the normal strains changed dramatically in a short time. When the fault slipped, the normal strains of S2, S3, and S4 first slumped, then surged, and then decreased gradually. At gauges S5 to S9, the normal strains just dropped to a specific value and then increased slowly to the value before the fault slip (S7, S8 and S9 in Fig. 3a) or declined gradually (S5 and S6 in Fig. 3a) during the phase A-B. Compared with the phase A-B, the strain curves in phases C-D and E–F didn’t change remarkably.
Fig. 3
Normal strains vs. time. The normal strains are the differential strains based on the values at 82 s. The labels marked S1 – S10 mean the sets of strain gauges. a The time which has been synchronized with the one in Fig. 2a is from 82 to 93 s. A-B, C-D, and E–F represent three fault slips corresponding to the three stress drops in Fig. 2a. b The curves are derived based on the magnification of Fig. 3a, and the time is from 85.02 s to 85.05 s
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Figure 3b shows the variation of normal strains during the time of 85.02–85.05 s. In Fig. 3b, the normal strains of S2, S3, and S4 had more significant changes than others when the fault slipped. The normal strains near the point O including S2, S3, and S4 (Fig. 1a) began to increase while others (except S10) declined slowly at around 85.033 s. It can be inferred that the fault rupture might be initiated from the focus near point O.
The shear strains of S1-S10 are illustrated in Fig. 4, which are similar to the normal strains in Fig. 3. Three variations including phases A-B, C-D, and E–F are presented in Fig. 4a. During the phase A-B, shear strains near two ends of the fault had a more significate variation than that in the middle part of the fault. The shear strains of S1, S2, S3, and S10 first dropped, then increased rapidly, and finally fell slowly to a stable value when the fault was slipping. At the gauges S4-S8, the shear strains first increased, and then decreased gradually. Figure 4b shows the detailed variation of shear strains from 85.02 s to 85.05 s. Due to the limited constraint, the shear strains at two ends of the fault fluctuated more significantly than that in the middle. Compared with S10, the rising time of shear strain at S2 was earlier than others since the hypocenter was located near S2 and the stress waves propagated from point O to point P along the fault.
Fig. 4
Shear strains vs. time. The shear strains are the differential strains based on the values at 82 s. The labels like S1 etc. on curves denote the numbers of strain gauges, and the numbers are the same as in Figs. 1a and 3a. a The time has been synchronized with other instruments, and the time here is from 82 to 93 s. Labels A-B, C-D, and E–F have the same meaning as in Figs. 2a and 3a. b The curves are derived by the magnification of that in Fig. 4a, and the time in the figure is from 85.02 s to 85.05 s
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Figure 5 is the relation between shear stress and shear strain at strain gauges S1. As the shear strain of S1 increased, the shear stress increased linearly firstly and then the increasing rate of the stress became lower than before when the fault was going to slip. As the fault was slipping, the shear strain first plunged and meanwhile the stress did not change much (stage a in Fig. 5). Subsequently, the shear strain increased with the stress drop (stage b in Fig. 5). Following that, the shear strain and stress declined slowly (stage c in Fig. 5). These stages of a, b, and c are consistent with three shear strain variations of a, b, and c in phase A-B of Fig. 4a.
Fig. 5
Relation between shear stress and shear strain. The data was recorded by the gauge S1
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Sliding displacement variation
The sliding displacement of the fault is shown in Fig. 6, where three fault slips including A-B, C-D and E–F are presented. The first slip A-B is the largest one with a total sliding displacement of 29.89 \(\mu m\). The two other sliding displacements were 8.15 \(\mu m\), which was much smaller than that in the first slip A-B.
Fig. 6
Sliding displacement of fault vs. time. The vertical ticks are the relative sliding displacement to the original position. The labels marked with A-B, C-D, and E–F are the same as in other figures
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By DIC (digital image correlation), the measured sliding displacement contour is shown in Fig. 7. The times of Fig. 7a, b are at 84.957 s and 85.127 s respectively. In Fig. 7a, the x displacement was low before fault slip and the maximal displacement was 21.6 \(\mu m\). As the x-direction loading board was unloaded (Fig. 4a), the fault slipped in a clockwise direction, namely the footwall of the fault slid to the direction of negative x (Fig. 7b). The maximal displacement of x was 89.0 \(\mu m\) located near the strain gauges of S10. Note that the x displacement in Fig. 7 is the accumulated sliding displacement, which is different from the sliding displacement in Fig. 6.
Fig. 7
Sliding displacement contour measured by DIC. The scope of this local view is marked by the grey zone in Fig. 1a. The black line OP represents the artificial fault which has the same label as in Fig. 1a. a Before the fault slip. b After the fault slip
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AE characteristics
Unlike the loading condition, fewer AE events were recorded during the fault slips caused by the unloading in this experiment. During the fault slip test, only one AE event was recorded by the AE transducer CH01 at around 85 s and there was no signal monitored during the other two slips (C-D and E–F in Figs. 3, 4 and 6) due to their low-released energy. Figure 8 is the waveform of the AE events captured by CH01 when the first fault slip happened. In Fig. 8, three stages including slow slip, main shock and aftershock are presented within a period of 3 \(ms\). Additionally, the main shock consists of three sub-events named I, II and III. The times of these three sub-events correspond to stages a, b and c respectively in Fig. 4a and 5.
Fig. 8
AE signals in the first fault slip A–B at around 85 s. The signals were recorded by AE sensor CH01 and its location is marked in Fig. 1a
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Macro-microscopic features of fault surfaces
The macro images of fault surfaces taken by a camera are shown in Fig. 9. Specimens for SEM observation were cut off from the upper points A and B, middle points C and D, lower points E and F on two fault surfaces. For comparison, these SEM specimens from the slip-test and non-slip-test rock samples were prepared as similar as possible. SEM specimens from the non-slip-test sample represent the original state unaffected by the fault slips, while the ones from the slip-test sample refer to the state after the fault slips. Figure 9a presents that the macro fault surface in the footwall of the non-slip-test sample was dark red and clean. After the fault-slip test, the color of the fault surface (Fig. 9b) turned into grey and was brighter than the original one (Fig. 9a). Moreover, multiple longitudinal scratches can be observed in Fig. 9b and many small white particles were adhered to the fault surface. In addition, Fig. 9b indicates that the lower part of the fault surface near point O is brighter than the upper part near point P, suggesting that the friction damage in the lower part is more serious than that in the upper part. According to Figs. 3a and 4a, the variations of normal and shear strains in the lower part were larger than those in the upper part during the fault slips. It can be inferred that when the fault slipped the sliding displacement in the lower part was larger than that in the upper part. Larger sliding displacements may produce more macro damages. Thus, the damage distribution in Fig. 9b is consistent with the strain variation.
Fig. 9
Macro images of the fault surfaces. The images were photographed from the top view of the footwall of the rock samples. O-P denotes the artificial fault which is marked in Fig. 1a. a The image represents the fault surface which is not influenced by the fault slips and is photographed on the non-slip-test rock sample. b The image represents the surface of the rock sample after the fault slip test
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To compare the micro features of fault surfaces between non-slip-test and slip-test rock samples, six observation points A-F were chosen at the upper, middle and lower parts of fault surfaces (Fig. 9). The micro images obtained by SEM are shown in Fig. 10.
Fig. 10
Microscopic images on the fault surfaces of non-slip-test rock sample (a–f) and slip-test rock sample (g–l): a 200 \(\times\), at the upper point A. b 800 \(\times\), at the upper point A. c 200 \(\times\), at the middle point C. d 800 \(\times\), at the middle point C. e 200 \(\times\), at the lower point E. f 800 \(\times\), at the lower point E. g 200 \(\times\), at upper point B. h 800 \(\times\), at upper point B. i 200 \(\times\), at the middle point D. j 800 \(\times\), at the middle point D. k 200 \(\times\), at the lower point F. l 800 \(\times\), at the lower point F. Note that the scopes within white or black rectangles in the images of the left column are amplificated into the images in the right column
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From Fig. 10a–f, the fault surface of the non-slip-test sample was rather rough. The micro images were all dark, which means the surface was clean, undamaged, and no additional scattered particles lied on it. In addition, we can see that the micro fault surfaces were uneven although it was flat in the macro view. Lots of microstructures such as bulges, voids and veins were observed on the fault surface. The images of 200 times were like hilly topography with bumps and indentations intersected. This shape could make the two surfaces of a fault bite tightly with each other. From the images of 800 times, more details were given. Irregular bulges, jagged terrace and sheared fractures were found in some local zones. These structures may increase the complication of the surface profile and result in a higher friction strength.
Figure 10g–l show the feature of the fault surface after the fault-slip test. Compare with Fig. 10a–f, the fault surface after slipping became smoother. Furthermore, large amounts of fine sand were found on the fault surface and could be removed by hand. Due to the existence of sand, the color of images turned into white from the dark. From the amplified images in Fig. 10h, j, l, scratches with white borders occurred during slips were distributed in many areas. Notable bright and dark zones were intertwined with each other. The bright zones could be produced by the strong friction, while the dark ones were made due to the slight friction. It was inferred that bright zones corresponded to micro voids, while dark zones were bulges before fault slips.
Numerical simulation
Stress and displacement field
It is a common understanding that the stress field variation may induce fault slips (Pereira et al. 2014; Sainoki and Mitri 2014, 2015a; Feng et al. 2015; Ma et al. 2019; Li et al. 2021; Taghipour et al. 2021). However, to obtain the accurate distribution and evolution of a stress field is a challenge due to the heterogeneity of rock mass and the limitation of stress measurement methods (Hubbert and Willis 1957; Brown and Hoek 1978; Zoback et al. 2003). By numerical modelling, the features of stress field distribution can be acquired similarly to well understand the mechanism of fault slip (Wei et al. 2020; Gao et al. 2021).
A simple model with a dimension of x × y × z = 3030 m × 50 m × 1271 m (the value in the z direction is the maximum height) was created by FLAC3D software to study the fault F16 slip. In the simulation model, the rock strata with different properties were assigned to reflect the heterogeneity of rock materials. The properties of rock and the fault F16 were determined by referring to the parameters in Lu et al. (2019) and Wei et al. (2020). The bottom, front and back boundaries were fixed in normal directions. The top boundary was free. Left and right boundaries were applied with the normal stress to simulate the horizontal tectonic stress. A gravitational acceleration of 9.8 m/s2 was applied to the whole model. The ratio of horizontal stress to vertical stress was 1.50 which is consistent with the loading ratio in the biaxial shear experiment. The fault F16 was simulated by the interface command, which can make the fault slip. After the initial force balance was completed, a block of coalbed was removed by five steps according to the mining plan and then the model continued calculating to reach the final force balance.
Figure 11 shows the distribution of the horizontal stress (the compressive stress is negative, and the tensile stress is positive) before and after the coalbed No. 2–3 was mined out. In Fig. 11, due to the mining activities the stress field near the fault F16 had changed significantly. Along the fault F16, a low-stress zone was located in the middle part and a high stress zone in the deep part of the fault F16 after the coal was excavated. Around the mining gob, there was a large area of tensile or low compressive stresses in the roof. The path of the horizontal stress toward the fault F16 was cut off by that tensile stress zone (Fig. 11) and the footwall of the fault F16 was unloaded. Therefore, the shallow part of the fault F16 was affected strongly by the coal mining since it was above the coalbed No. 2–3. In the deep part of the fault F16, the stress field was relatively less influenced because it was far from the mining zone.
Fig. 11
Cross-section view of the horizontal stress distribution. The compressive stress is negative, and the tensile stress is positive in the legends. a Before the mining out of the coalbed No. 2–3. b After the mining out of the coalbed No. 2–3
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The stress distribution in the site is more complicated than that in Fig. 11 because of the involvement of cracks mainly induced by roof fracturing. Moreover, if one or two layers of roof were tough and thick, the roof would not be easy to fracture. That roof in the footwall will spike down against the fault F16 to the gob under the tectonic stress. In addition, the underground water may play an important role in the stress field of a fault. Due to coal mining, water will flow down via the roof cracks. Then, the water pressure in the fault gouge will decrease, and there will be more contact between the two fault walls to make a higher friction strength. Thus, water loss might block the fault slip (Kim and Jeon 2019).
Fault slip pattern under unloading condition
Figure 12 presents the vertical and horizontal displacements after the coal mining. Figure 13a shows the relative shear displacement of the fault F16. According to Figs. 12 and 13a, a simple mechanical model to interpret the slip pattern of fault F16 is illustrated in Fig. 13b. Before the coal mining, the stress ratio at points A and B was σx: σy = 1.5. After the coal was mined out, the roof strata must subside for a drastic displacement (Fig. 12a), which made the vertical stress σy decreased faster than σx and the stress ratio became σx: σy = 2.0 at the unit A in the shallow part of the fault F16, namely the stress in the y direction of the unit A was unloaded. Driven by the changed stress field, the shallow part of the fault F16 slipped in a counterclockwise direction (Fig. 13a, b). Because of the significant subsidence of the roof, the fault located at a specific zone in the shallow part of the fault F16 was separated, as shown in Fig. 13a.
Fig. 12
Cross-section view of displacement distribution after the coal mining. a Vertical displacement. b Horizontal displacement. Note that the rectangles represent the loading cells which are similar to the rock samples in the biaxial shear experiments, and the red arrows at points A and B mean the stresses in that directions are higher than another ones. The abnormally-high horizontal displacement in the bottom of the model occurred due to the buckling deformation after the coal mining
Fig. 13
Slip pattern of fault F16 due to the coal mining. a Shear displacement of the fault F16. Note that the shear displacement in the figure is an accumulated displacement during mining rather than the slip displacement when rockbursts happened, and the slipping directions in the figure is relative but absolute ones. b A simple mechanical analysis of the fault F16 slip
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After the coal mining, σx at the unit B near the deep part of the fault F16 decreased due to the mining out of the coal in the footwall while σy is constant or decrease to a value less than σx, resulting in σx: σy = 0.5. Accordingly, driven by the relatively larger stress σy the rock mass in the footwall of fault F16 was pushed toward the gob (Fig. 12b). That movement induced the displacement of footwall in the deep part was higher than that of hanging wall, which made the fault F16 in the deep part slip clockwisely (Fig. 13a).
Based on results of the physical experiment and numerical simulation, we can find that fault slips may indeed happen under unloading condition. Obviously, results of the numerical simulation described in this section are consistent with those in the physical experiment.
Discussion
Monitoring results of seismic events
To analyze the slip pattern of the fault F16, the results of seismic events monitored during coal mining are shown in Fig. 14, indicating that lots of seismic events were located near fault F16. This may be explained by the numerical simulation mentioned above. The numerical simulation results show that the fault F16 at the middle part may slip in a counterclockwise direction (Figs. 12a and 13a). If this fault slip is true, it would induce seismic events surrounding or close to the slip zone. Optimistically, the locations of seismic events in Fig. 14 have validated this hypothesis.
Fig. 14
Location of the monitored seismic events. The cross-section image is parallel to the dip of fault F16. The monitoring period is from July 2009 to October 2010 including the roadway driving and the early mining of panel No. 25110. (Modified based on Fig. 8 in Cai et al. (2015) and Fig. 2 in Lu et al. (2019))
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According to the monitored results of seismic events, a few events were situated around the deep part of fault F16, indicating that the deep part of fault F16 slipped as the coal mining approached the fault. Numerical simulation shows that the fault F16 in the deep part may slip in a clockwise direction (Figs. 12b and 13a). The fault slip pattern is consistent with the results in Donnelly et al. (2008). In the coal mines, the slip of fault F16 is difficult to be observed directly because no roadway has reached fault F16 until now. The analysis results in this study give us an understanding of the mechanism of the fault slip in Yima mining area. Besides, the slip of fault F16 may release a large amount of energy and could trigger a rockburst, which is another complicated topic and needs more investigations in the future.
Microscopic mechanism of fault slip
It is testified that normal stress and shear rates can affect the slip behavior of a fault (Xu et al. 2018; Meng et al. 2019). Based on the analysis of macro-microscopic features on fault surfaces, the microscopic model of the fault slip mechanism is presented in Fig. 15. As reported in Mehrishal et al. (2016), due to different boundary conditions three types including dilatant shear, dilatant-deformation shear and non-dilatant shear may occur on the fault surfaces during a fault slip. Under unloading condition in this study, the normal stress \({\sigma }_{N}^{^{\prime}}\) after mining was lower than that \({\sigma }_{\text{N}}\) before mining when the slip started. The shear rate is 0.3 mm/min in the physical experiment, and it is relatively low compared with the shear rates of 0.1–50 mm/min in Mehrishal et al. (2016). Therefore, the fault under unloading condition may make a dilatant-deformation slip as shown in Fig. 15. If the normal stress is low, the damage depth of micro bulges will be shallow, and the dilatant displacement will be low. In this case, interlaced bright and dark zones emerged on the fault surface after fault slips in the micro view due to the low normal stress. Meanwhile, if the shear rate is low, more time can be used for the shear stress to shear the bulges, thus the shear deformation will be larger. That is the reason why most of the micro bulges on the microscopic fault surface disappeared and lots of small particles were produced under unloading condition in this study.
Fig. 15
The fault slip model under unloading condition (Modified based on Fig. 19 in Mehrishal et al. (2016))
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Differences of fault slip between loading and unloading conditions
Fault slip mechanism under loading and unloading conditions are similar despite their different stress fields. However, the mechanical behavior of the fault slip is discrepant (Wu et al. 2014, 2017). As reported in Xu et al. (2018) and Meng et al. (2019), once the stick–slip started abundant slip events occurred while the shear stress was loading. In contrast, there had been only a few slip events until the stop of unloading (Fig. 2a). This phenomenon is related with the unloading and loading conditions. To compare the behaviors under two conditions, more direct shear experiments are necessary in the future.
Effect of unloading rates
In this study it was noticed that the emerging of unstable fault slips depended on unloading rates, and only as an unloading rate was increased up to a specific value the unstable fault slip could happen. Even though the topic is not the concern in this study, but it is an interesting phenomenon. Special experiments with different unloading rates should be conducted in the future to get the reliable conclusion. An unstable fault slip can release a large amount of energy, while stable fault slips usually occur with their low-energy release. Such unstable fault slips are more dangerous than stable fault slips. Thus, this study focused on the unstable fault slip test rather than the stable ones to explain the mechanism of fault slips. In mining engineering, unloading rates correspond to different mining speeds, which can strongly affect the roof movement, fault slip, etc. Thus, unloading rate is an important factor to be considered. Wu et al. (2017) argued that a larger normal unloading rate could cause higher strain energy and larger slip displacement. In addition, Xu et al. (2018) found that loading shear rates could influence the slip behavior significantly and the high loading rate could promote abrupt slips. Whether the unloading condition has the similar effect on the fault slip or not is still a question. To answer this question, more experiments are needed.
Other factors
For both earthquake stick-slips and mining-induced fault slips, the initial stress state (e.g., normal and shear stresses) dominates the slip behavior of faults to a large extent (Wu et al. 2017; Xu et al. 2018). In addition, rock types, stiffness of loading or unloading systems, gouges, and contacting time between fault surfaces may also affect fault slips strongly (Byerlee and Brace 1968; Johnson et al. 2016). As for deep-source earthquakes, temperature is an important factor because it may be over 100 Celsius degrees (Brace and Byerlee 1970). But such a temperature is not much important for mining-induced fault slips, because most of the mining depth is lower than 1 km and the low temperature does not markedly influence the mechanical properties of rock or coal. Fluid in the fault is a significant factor for coal mines due to the loss of water (Donnelly 2009), and for the oil and gas exploitation because of the fluid injection (Ellsworth 2013). In this study temperature and fluid are not considered, but more experiments can be tried in the future. In addition, the effect of stress waves on fault slips is suggested to be considered in either earthquake or mining engineering (Johnson et al. 2012; Sainoki 2016), especially the types of stress waves e.g., P-waves, S-waves, and Rayleigh waves (Ghosh et al. 2009; Gao et al. 2021).
Conclusions
Based on this study, the following conclusions can be drawn:
1.
Three fault slips along with three shear stress drops occurred during the test with an unloading rate of 0.3 mm/min. And the shear stress, normal and shear strains in the first slip showed the maximum variation among the three slips.
2.
During the first slip, shear strains near the fault may change more drastically than normal strains. In addition, shear strains near two ends of the fault had a more significate variation than that in the middle part. The typical trend of shear strains was first dropping, then increasing rapidly, and finally falling slowly to a stable value during the first fault slip.
3.
The first slip was the main fault slip with the largest sliding displacement of 29.89 \(\mu m\), and the two other slips slid for only 8.15 \(\mu m\). In a period of 3 \(ms\), the first fault slip consisted of three phases which were slow slip, main shock and aftershock based on the AE monitoring result.
4.
Many microstructures such as bulges, voids, veins, and fractures etc. were observed on the fault surface of the non-slip-test rock sample. After the biaxial shear experiment, the fault surface of the slip-test rock sample was flattened by the shear stress remaining fewer microstructures, more scratches, and dark zones. Additionally, a lot of fine sand stripped from the rock sample were found on the fault surface.
5.
Due to the coal mining, both the shallow and deep parts of the fault F16 may slip according to the numerical simulation and seismic monitoring results. Moreover, the shallow part of the fault F16 may slip counterclockwisely and the deep part clockwisely.
Acknowledgements
Authors acknowledge the financial support from National Natural Science Foundation of China (No. 51874176, 52034009) and China Coal Research Institute (No. 2019CX-II-12, 2020CX-I-08).
Declarations
Conflict of interest
The authors declare that they have no competing interests that could influence the work reported in this paper.
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