Rockburst in Sandstone Containing Elliptic Holes with Varying Axial Ratios

Rockburst disaster is one of the prominent problems faced by deep underground engineering. In this study, rockburst in four elliptical holes with different axial ratios in sandstone under biaxial loading is studied as an analogue for underground roadways. Video and acoustic emission (AE) equipment is used to monitor the biaxial loading tests. Experimental results indicate that each of the elliptical holes goes through four stages: quiet period, small particle ejection, spalling, and rockburst.+e duration of quiet and spalling periods increased with increasing axial ratio of ellipse. +e duration of the ejection and rockburst periods remains unchanged. All the four elliptical holes have V-shaped pits after rockburst occurs.+e fragments produced during rockburst are divided into coarse, medium, fine, and micro grains. +e quantity of coarse and medium grains increases with increasing axial ratio. +e mass ratio of coarse and medium grains increases and that of fine and micro grains decreases. +e depth, angle, and area of the V-shaped pits decrease with increasing axis ratio. Tensile cracks play an important role in rockburst failure. Tensile cracks are the dominant crack types formed during rockburst and account for over 70% of all cracks in the samples. +e number of tensile cracks increased and the number of shear cracks decreased. +is paper has some reference value for practical engineering design and prevention of rockburst.


Introduction
Rockburst is a strong destructive phenomenon in underground engineering [1,2].In the mining field, rockburst commonly occurs in the process of underground roadway excavation.During a rockburst, a large number of rock blocks of different sizes are thrown across the roadway, causing significant damage to machinery and personnel [3].With the further exploitation of shallow energy sources, more and more mines are increasing in depth in China.Compared with shallow roadways, deep roadways bear greater ground stress levels and thus experience more rockbursts [4].Rockburst is commonly abrupt and severe, and predicting the location of rockburst is quite difficult.ese characteristics are significant obstacles to installing support structures in deep roadways [5].At present, there is no unified conclusion about the mechanism of rockburst.Researching rockburst can provide reference for practical roadway engineering support, ensure the safe operation of deep roadways, and guarantee the safety of personnel and machinery.
e specimen used by Su et al. [16] was 100 × 100 × 200 mm and was also subjected to rockburst testing.
ese experiments have obtained similar in situ rockburst phenomena; however, the above experiments are based on block-shaped samples and represent the properties of an individual rock type instead of a complete rock mass.erefore, it is necessary to develop an indoor rockburst model experiment to analyze the complete roadway structure.
For experimental laboratory studies examining underground roadway structure, most scholars adopt the method of opening holes in rock blocks to simulate actual roadway excavation and failure (rockburst) [20][21][22][23][24][25][26][27][28][29][30][31][32].For example, Fakhimi et al. [22] simulated brittle failure of roadway surrounding rock caused by excavation of an underground roadway using biaxial loading of sandstone.He et al. [25] applied a true-triaxial load to the sandstone containing a hole to simulate the ground stress level and then applied a disturbance load to the sandstone to simulate the impact rockburst on the deep roadway.Gong et al. [30] applied triaxial loading to sandstone samples containing a hole and continuously increased the vertical load to simulate roadway spalling caused by stress concentration.Gong et al. [31] also discussed the different spalling phenomena of the hole under four different initial stress states.Hu et al. [32] applied biaxial loading to granite samples containing a hole, and the acoustic emission (AE) characteristics of circular hole in the process of rockburst were obtained.e shape of the cavity will have a certain impact on roadway failure [33][34][35][36][37].All the above studies are based on the study of circular holes.In the deep engineering, the shape of deep roadways is usually round, U-shaped, or elliptical.Particularly, when the deep roadway is surrounded by high tectonic stress, the shape of the roadway is easily deformed from a circle to an ellipse.However, there are few laboratory experiments on rockburst in elliptical roadways.
According to elastic theory, the optimal roadway cross section is an ellipse with the maximum principal stress parallel to the long axis [33].However, it is difficult to excavate the optimal elliptic section due to intense stress levels [38].Generally, the maximum principal stress will be at an angle to the long axis of the ellipse.In this study, the maximum principal stress parallel and short axis directions are selected such that the long axis is fixed, and the length of the short axis is varied to examine the rockburst phenomenon in an elliptical roadway with different axis ratios.
e rockburst phenomenon of four elliptical holes with different axial ratios by using self-developed experimental equipment under the biaxial loading was explored.Firstly, the experimental device, specimen, and loading path are described.e characteristics of each stage in the rockburst process are then introduced.Finally, the duration time at each stage, fragment characteristics, V-shaped pit characteristics, and AE characteristics for four different axial ratios are analyzed and discussed.

Materials and Methods
2.1.Rock Specimens.Specimens used in the experiment are red sandstone taken from North China.Homogeneous rock blocks are selected and processed into 110 mm × 110 mm × 50 mm rectangular blocks.Later, elliptical holes with different long to short axis ratios were drilled through the square face of the rectangular block.e length of the elliptical long axis a is 50 mm, the elliptical short axis b is 20 mm, 30 mm, 40 mm, and 50 mm, and the axial ratios of the ellipses (a : b) are 2.5, 1.67, 1.25, and 1, respectively.It is required that the diameter deviation of the aperture is within 0.5 mm, the flatness of each surface is within ±0.05 mm, and the vertical deviation of the adjacent two surfaces is within ±0.25 °. e prepared sandstone specimens are shown in Figure 1(a), and the specimen with a short axis b of 40 mm is taken as an example.e specific sample size is shown in Figure 1(b).e uniaxial compressive strength of the sandstone is 87.07 ± 1.5 Mpa, the density is 2550 ± 4 kg/m 3 , the velocity of P-wave is 3230 ± 27 m/s, the average elastic modulus is 17.32 GPa, and the average Poisson's ratio is 0.21.

Experimental Equipment.
In this experiment, the impact rockburst experimental device was used [26].e experimental system consists of five parts: the main stand, hydraulic power source, measuring and controlling device, image acquisition system, and AE system (Figure 2(a)).e maximum load capacity of the main engine is 500 kN, and the load accuracy is less than 0.5%.e maximum displacement is 150 mm, and the displacement accuracy is less than 0.4%.e loading system has three independent directions and can carry out uniaxial, biaxial, and triaxial experiments.In this experiment, two loading directions (vertical and horizontal) are adopted for the biaxial loading tests.Video equipment is placed directly in front of the specimen such that the shooting direction is perpendicular to the surface of the specimen to ensure that the entire hole is captured.e PCI-2 AE system was employed to monitor the experiment, which is developed by the PAC Company.
e system includes AE sensor, preamplifier, acquisition card, AE system software, and cable accessories.
e AE sensor is WD series broadband sensor, whose frequency response range is 0∼1 MHz.In this experiment, the sampling rate is set as 2 Msps, that is, 2 M data points are collected every second.e amplifier gain is 40 dB.In the process of the experiment, there will be interference from the electrical, instrumental, and environmental noises.erefore, the threshold value is set to 50 dB to filter out the signal whose magnitude is lower than 50 dB.e threshold value of 50 dB is suggested according to the laboratory testing conditions.e AE sensor is fixed behind the specimen (Figure 2(b)).

Experimental Methodology.
e sandstone blocks are placed in the specimen box, and the position of the specimens is adjusted.e long axis direction of the specimens is always in the horizontal direction, and the short axis is in the vertical direction.e specimen box is placed in the middle of the loading chamber.An initial stress is applied at a rate of 0.5 kN/s in the vertical and horizontal directions and is held for one minute.e vertical direction is switched to displacement control mode with a rate of 0.004 mm/s, and the specimen is loaded until a rockburst occurs in the hole, at which point, loading is immediately stopped to ensure that the whole specimen is not destroyed.e video recorder and AE device are activated when loading is initiated.
In this paper, a 500 m stress level is used as the initial stress.According to the statistical North China geostress formula [39], the horizontal stress is 10.2 MPa, and the 2 Advances in Materials Science and Engineering vertical stress is 13.6 MPa. e problem is simplified to a plane strain problem without considering the effect of the axial stress in the direction of the hole (Figure 3).By continuously increasing the vertical stress, rockburst of an elliptical roadway caused by tangential stress concentration in the roadway is simulated.e stress path is shown in Figure 4.In order to reduce random error, three experiments were performed for each elliptical ratio, and one representative specimen for each elliptical ratio is selected for analysis.e experimental loading plan is shown in Table 1.Specimens are named by the long to short axis ratio.For example, S-1.25-1 means that S represents sandstone specimens, 1.25 represents the ratio of long axis to short axis, and 1 represents the first specimen.Advances in Materials Science and Engineering

Experimental Results and Discussion
(1) When the rock specimen is installed, it is vertically and horizontally loaded to 10.2 MPa at a rate of 0.5 kN/s.en, the horizontal force is held constant, and the vertical force is increased to 13.6 MPa at a rate of 0.5 kN/s.At this time, the rock specimen has reached the initial stress level.In order to prevent local stress concentration caused by uneven stress on the surface of the specimen, after loading to the initial stress level, the load is maintained for 1 minute, and the fit of the loading plate to the sample is carefully checked.e sample is now considered to be in a stable initial stress state (σ v0 � 13.6 MPa and σ h � 10.2 MPa).At this time, the elliptical hole is stable and there is no damage to the sample (Figure 6(a)).( 2) After 1 minute the initial stress level, the vertical direction is changed to the displacement loading mode, and the loading rate is set to 0.004 mm/s.After loading for 437.12 s, small particles began to eject from the right side of the hole.e overall structure of the hole was relatively complete, and no major damage was observed (Figure 6 (3) When the vertical load is continuously applied, small particle ejection decreases.Instead, the right side of the elliptic hole in this sample shows the phenomenon of stripping from the parent body and shows upward warping or downward bending.When the vertical stress is 49.80 MPa (Figure 6(g)), obvious flake peeling can be seen.e angle of the flake structure leaving the matrix increases with loading (Figure 6(h)).When the vertical stress reaches 50.11MPa, the upward warping angle of the flake structure reaches its maximum (Figure 6(i)).When the vertical stress reached 50.38 MPa, the flaky sample suddenly undergoes spalling because of its own gravity and the influence of the surrounding stress.Due to the spalling of rock blocks, obvious rockburst pits are formed at the site of failure.Spalling continues to occur with further loading (Figure 6(k)-6(s)).With the continuous development of this process, the size and depth of the pits gradually increase, gradually forming a V-shaped pit.With the increase of vertical stress from 50.33 MPa to 53.07 MPa, large spalling occurred six times.In theory, the deformation produced on the left and right sides of the hole should be symmetrical.However, due to the influence of rock heterogeneity and machine loading, the deformation on the left and right sides of the hole is not the same.Deformation on the right side of the sample begins earlier than the left side; however, both sides went through the same process, including small particle ejection (Figure 6(l)) and spalling (Figures 6(o) and 6(q)-6(s)).After this process, the left and right sides of the sample formed a V-shaped pit.(4) When loaded for 495.80 s (σ v � 48.01 MPa), rock blocks of different sizes are ejected from the right hole wall, accompanied by a clear and loud sound, and rockburst occurs (Figure 6(t)).Loading is stopped immediately, and the sample is quickly unloaded.e final state of the sample is shown in Figure 6(u).
It should be pointed out that because of the slow loading rate, loading stopped immediately after the rockburst, so complete failure of the specimen did not occur, except for a small amount of fragment spalling from the surface of the specimen, other damage occurred in the hole.e overall shape of the specimen after experiment is shown in Figure 7(a).V-shaped pits are formed on both sides of the specimen (Figure 7(b)).

Rockburst Process.
e elliptical hole experienced four processes: a quiet period, small particle ejection, spalling, and rockburst (Figure 8).During the quiet period, the vertical stress gradually increases until σ v � 48.76 MPa (437.12 s), and the structure of the hole is basically intact without damage.Subsequently, small particles are ejected  Advances in Materials Science and Engineering from the right side of the hole, and the sample moved from quiet period to the small particle ejection period, which lasted for 8.48 seconds.When σ v � 50.38 MPa (449.72 s), spalling occurs and the specimen enters into the spalling period.e vertical force increases continuously, and spalling continues, which lasts for 49.84 seconds.Rockburst occurred suddenly in 495.70 seconds on the right wall of the hole and lasted for 0.1 seconds.
(1) Quiet period: from initial loading to small particle ejection, there is no obvious change around the hole, and the specimen is in a quiet state.With increasing vertical stress, in fact, the hole wall cracks slightly, but these cracks are not observable by the human eye.(2) Small particle ejection period: during this period, small particles are ejected from the hole wall.ere was no obvious damage around the hole wall, but some cracks had been formed around the hole.e strain energy accumulated by vertical loading caused small particles to eject from the sample.
(3) Spalling period: with increasing stress level, more fractures began to form and the sample began to fail.With continuous loading, the rock mass suddenly slides under the action of stress on the inner wall of the hole and gravity.As the loading proceeds, new blocks will slip, and damage to the hole continues to increase.
In the hole wall, there are obvious V-shaped pits.(4) Rockburst period: during this period, particle ejection suddenly occurs.A large number of blocks of different sizes are ejected from the inner wall of the hole, accompanied by a loud sound.A large amount of energy is released during this period, at which time V-shaped pit became deeper.
Elliptical roadways with different long-short axis ratios undergo the same experimental process.e experimental failure phenomena for the other three groups of typical specimens are shown in Figure 9.After the rockburst, the three groups of typical specimens also produced V-shaped pits.And Figure 10 shows the overall shape of the specimens   8 Advances in Materials Science and Engineering and the V-shaped pits with different axis ratios after rockburst.

Time Characteristics of Rockburst
Process. e duration time for each of the four stages in the overall rockburst process for each elliptical hole is measured (Table 2).e relationship between the duration of different stages and the axis ratio is plotted (Figure 11).For holes with increasing axis ratio, the duration of the quiet period and spalling period tends to increase.A larger axis ratio will increase the quiet period, which will help to increase roadway life.e spalling period for specimens with larger axis ratios is also longer.In the spalling stage, there are numerous visible signs of rock failure, and personnel and mechanical equipment can be evacuated.Roadways with larger long axis ratios will have more evacuation time before a severe rockburst occurs.
e duration of the small particle ejection and rockburst periods varies little with respect to the short axis (Figure 11

Fragment Characteristics of Rockburst.
After the experiment, the fragments in the hole are collected without considering the fragments falling outside of the hole.
Fragments were screened using a particle sieve.ere are seven sizes of particle sieve, which are 0.075 mm, 0.25 mm, 0.5 mm, 1 mm, 2 mm, 5 mm, and 10 mm.After screening, fragments were divided into four particle classes: coarse, medium, fine, and micro grains, which corresponded to  Figure 12 shows the fragments of specimens with different axis ratios.ere were no coarse grains with an axis ratio of 2.5.e number of coarse grain with an axis ratio of 1.67 and 1.25 was one, and the number of coarse grain with an axis ratio of 1 was three.For medium grains, the number of fragments with an axis ratio of 2.5 is one, the number of fragments with an axis ratio of 1.67 is five, the number of fragments with an axis ratio of 1.25 is twenty-one, and the number of fragments with an axis ratio of 1 is thirty-eight.With increasing axis ratio, the number of coarse grains and medium grains increases.Coarse grains and the medium grains have an irregular flake structure, the fine debris has a granular shape, and the finest debris is powder.
Table 3 shows particle size statistics and the mass of fragments with different axis ratios.e proportion of micro grains is the smallest, and the fragments mainly consist of coarse, medium, and fine grains.According to the statistical results of fragments, the mass percentage distribution is plotted, as shown in Figure 13.For coarse and medium grains, the proportion of fragment mass decreases with increasing axis ratio, and no coarse debris occurs when the axis ratio is 2.5.With increasing number of coarse and medium grains, the total mass of rockburst fragments tends to increase, which indicates that the volume of the generated fragments increases, indicating that the damage degree of the hole increases in the whole process.For micro and fine grains, the proportion of fragments decreases with increasing axis ratio.Micro and fine grains have a small size and large surface area.
is type of fragment requires more energy and has a higher degree of fragmentation, indicating that the larger the axis ratio is, the higher the degree of fragmentation is.

Pit Characteristics of Rockburst.
V-shaped pits are formed in the specimens with different axis ratios during the experiment.e rockburst pits are described by the area, depth, and V-shaped angle (Figure 14).After the experiment, photographs of the rock specimens were taken, and an outline of the whole rock specimens and the rockburst pits was drawn according to the photographs by the AUTOCAD software.
en, the outlines of the V-shaped pits were simplified to a straight line to make it easy to get the area, depth, and V-shaped angle.Figure 15 shows the progress to get the contour map of rockburst pit.It should be noted that the depth of the rockburst pit along the axial direction of the elliptical hole is not consistent due to the heterogeneity of the rock specimens and the loading mode of the testing machine.e pit with the maximum depth is selected for depth contouring.Pit depth contours of all specimens with different axis ratios are drawn (Figure 16).e relationship between the pit area, depth, and V-shaped angle are plotted against the axis ratio (Figure 17).
With increasing axis ratio, area, depth, and V-shaped angle all tend to decrease (Figure 17).When the axis ratio is small, the area of the hole is small, and the amount of fragments generated by the rockburst is less, which is consistent with Section 3.3.1.Elliptical holes with a small axis ratio will help to reduce damage to machine and personnel caused by rockburst fragments.
3.3.4.AE Characteristics of Rockburst.AE signal analysis mainly includes parameter analysis and waveform analysis.
e former involves statistical analysis of characteristics of AE signal parameters such as AE count, amplitude, duration, energy rate, and rising time.e latter uses some function transformation to obtain the AE waveform characteristics.For example, fast Fourier transform is used to obtain the main frequency of AE waveform.is paper focuses on the first case, that is, the study of AE parameters.In this paper, the first analysis method is used to analyze the types of AE cracks.AE characteristics are generally considered an effective way to reflect fracture failure mode.Studies have shown that RA value and average frequency AF in AE parameters can reflect crack type inside a material structure [32,40].RA value is the ratio of rise time to amplitude, while average frequency AF is obtained by the ratio of count to duration.Generally speaking, AE signals with low AF and high RA values commonly represent the generation or development of shear cracks; on the contrary, high AF and low RA values represent the generation or development of tensile cracks (Figure 18) [40].
In order to determine the proportion of shear and tensile cracks, a reasonable AF/RA value needs to be determined.erefore, a three-point bending experiment and straight shear experiment was carried out.It is generally believed that tensile cracks account for the main part in the three-point bending test, and shear cracks account for the main part in the shear test.An AF/RA of 1.2 was determined to distinguish between shear and tensile cracks (Figure 19).If the ratio is less than 1.2, the crack is considered to be a shear crack; if it is greater than 1.2, the crack is considered to be a tensile crack.
Figure 20 shows the scatter distribution of AF and RA for typical specimens with different axial ratios.e distribution of the four groups of experiments is roughly the same, and the total number of data points is similar.With increasing axis ratio, the number of points with a 200-500 kHz average frequency gradually increases, while the number of points with a 200-500 mv/s RA gradually decreased.
In order to understand the different characteristics of specimens with different axial ratios, the number of tensile and shear cracks was calculated.e relationship between crack type and the axial ratio was plotted (Figure 21).e percentage of tension cracks is over 70% for all samples, indicating that spalling and rockburst are largely tensional deformation.A linear fitting shows that the proportion of tension cracks increases while that of shear cracks decreases with increasing axis ratio.An elliptical hole with a large axis ratio has a smaller curvature which can provide strong support for the rock surrounding the hole.After loading, the accumulated strain energy in surrounding rock is larger, crack propagation is complete, and tensile failure is obvious.When the axis ratio is small, the accumulated strain energy of surrounding rock is less, and crack propagation is incomplete; hence, the tensile failure is weakened.

Conclusions
In this paper, the rockburst phenomena of elliptical holes with different axis ratios in cuboid specimens are obtained by biaxial loading.e rules and characteristics rockburst are recorded using a video recorder and AE equipment.e main conclusions are as follows: (1) e rockburst process of elliptical holes with different axis ratios is consistent and can be summarized as having a quiet period, small particle ejection period, spalling period, and rockburst stage.Statistical results show that with increasing axis ratio, the duration of quiet and spalling periods increases, and the duration of small particle ejection period and rockburst stage does not significantly change.
(2) Rockburst fragments can be divided into coarse, medium, fine, and micro grains.e number of coarse and medium grains decreases with increasing axis ratio.
e proportion of coarse and medium grains decreases, while the proportion of fine and micro grains increases with the increasing axis ratio.
e larger the axis ratio is, the lower the total amount of fragments is, but the higher the degree of fragmentation is.(3) V-shaped pits are produced in the process of rockburst for specimens with different axis ratios.e area, depth, and V-shaped angle of rockburst pits decrease with increasing axis ratio, indicating that the damage area caused by rockburst will decrease with increasing axis ratio.Advances in Materials Science and Engineering (4) e relationship between RA and AF in AE is used to discriminate between tension and shear cracks during rockburst.Tension cracks in rock specimens with different axis ratios play a major role in the rockburst process.Tensile cracks account for over 70% of all cracks in the specimens, indicating that tension failure is the main failure mode in the rockburst process.With increasing axis ratio, the number of tension cracks increases, and tensile failure becomes more obvious.

3. 1 .
Rockburst Phenomena.Figure5shows the typical measured stress paths of four specimens with different axial ratios.According to the test loading curve, the test process can be divided into two stages: initial stress stage and continuous loading stage.Here, S-1.25-1 is taken as an example to describe the typical experimental phenomena in the loading process.

Figure 1 :Figure 2 :
Figure 1: Photographs showing (a) the sandstone specimens and (b) the individual specimen size.

Figure 3 :
Figure 3: Schematic diagram of the experimental loading path.
(b)).At this time, the vertical stress state was σ v � 48.76 MPa.At a vertical stress of 49.25 MPa, the ejection of small particles occurs again in the same area on the right side of the sample (Figure 6(c)).At this time, obvious damage can be observed on the right side of this area.With increasing vertical stress, small particles are continuously ejected from the right side of the sample.e damage area continuously increases, and the surrounding rock mass is continuously damaged (Figures 6(d)-6(f )).

Figure 4 :
Figure 4: Schematic diagram of the stress path through time.

Figure 11 :
Figure 11:  Graphs showing the relationship between the duration of different stages and the axis ratio for the (a) quiet period, (b) small particle ejection period, (c) spalling period, and (d) rockburst period.

Figure 13 :
Figure 13: Distribution of fragment mass by grain size.

Figure 15 :
Figure 15: Processing of a rockburst pit into a contour map.

Figure 21 :
Figure 21: Graph showing the relationship between the number of different cracks and axis ratios.

Table 2 :
Duration of different periods for specimens with different axis ratios.≥ 10 mm, 5 mm ≤ d < 10 mm, 0.075 mm ≤ d < 5 mm, and d < 0.075 mm, respectively.e mass of the fragments in each stage of the sieve was weighed using a high sensitivity electronic balance.

Table 3 :
Mass and percentage of different grain groups.