Measurement and prediction of granite damage evolution in deep mine seams using acoustic emission

With unceasing increase of mining depth and development intensity, mining disasters such as rock burst have been increasing frequently, which often result in catastrophic accidents. Therefore, it is imperative to accurately forecast underground disasters. Previous research has suggested that the combination of drill-hole pressure relief and acoustic emission (AE) monitoring serves as an effective measure method towards the forecasting and prevention of disastrous accidents. However, the AE evolution mechanism of underground rock damages remains a challenge; more specifically, the relationships among the drilling hole positions, depths and diameters, and the stress–strain and AE characteristics of the rocks are discussed little in the literature. In order to bridge this research gap, the particle flow code (PFC2D) is employed to systemically investigate the hidden patterns among the mechanical properties, AE and damage evolution of the rock mass with different positions, depths and diameters of the drilling holes. Analysis results demonstrate that the drilling position influences the rock stress–strain and AE characteristics in the plastic deformation stage and the residual stage while the hole depth affects the drilling process. More specifically, the initial AE strength, AE impact at the peak moment, AE fluctuations and induction time are significantly influenced by the drilling position and depth. Furthermore, the drilling position and depth change the evolution law in the damage acceleration and stable development stages, while the hole diameter has little effect on the AE signal during the rock drilling process.


Introduction
On account of the intensity associated with the continuous development of the improvement of mineral resources, rock burst and other mining disasters and accidents have increased. Hence, there is a precipitous, urgent requirement for forecasting and identifying these incidents [1,2].
There is extensive research towards the urgent need for the prevention and control of mining disaster. Numerous publications have contributed to solve the problem of pressure impact. Several subject-matter areas are considered in the study of the mechanism of percussive ground pressure, which may include theories involving strength, stiffness, energy, bursting liability, instability, fractal, fracture, damage, mutation, bifurcation, dissipative structure, and chaos [3][4][5][6][7]. In the study of percussive ground pressure control, there are basically three methods [8][9][10]: (1) mining optimization (or change mining sequence), which mainly includes optimizing the shape of the roadway and stope, the setting up of permanent pillar, filling, and changing mining order; (2) artificial support, which mainly includes bolt, anchor rope sprayed concrete, steel arch and concrete lining, flexible material support, and small sections into the lane; (3) pretreatment of ground pressure, which includes water injection softening, blasting weakening, cutting and unloading pressure, drilling holes and so on.
Drilling-hole-based pressure relief is among the effective approaches to control the impact of ground pressure, and hence, it has gradually attracted much attention. Liu et al [11] investigated the mechanisms of preventing and controlling the impact pressure of large-diameter drilling holes using rock mechanics experiments. Wang et al [12] proposed a FLAC3D system to analyze the dynamic effects of the parameters (length, diameter and row spacing) on the stability of the surrounding rock in the deep roadway. Li et al [13] studied the effects of the drilling hole unloading pressure in the stress concentration area in a roadway based on ADINA finite element analysis. Wen et al [14] studied the influence of the drilling hole diameter and hole spacing on the effect of the drilling hole unloading pressure by using the FLAC3D system. Jia et al [15] studied the influence of the diameter, spacing and depth of the drilling hole on the strength of a rock sample and analyzed the sample failure mode using different parameters through laboratory tests. In addition, particle flow PFC software was employed to investigate the crack propagation morphology and crack number of rock samples using different drilling parameters. Furthermore, recent research results demonstrated that the AE signal can reflect the stressstrain characteristics of the rocks during the pressure relief process [16]. Because rocks will radiate acoustic waves in the process of damage, by analyzing the AE signal it is possible to accurately predict pressure relief performance and to effectively control the pressure impact. Without the use of a traditional strain gauge, the sensor installation problem can be solved by an AE data acquisition system. The stability of a rock mass can be monitored by AE evolution law for the purpose of preventing impact pressure [16,17]. As a result, the AE technique provides promising potential in the application of mining pressure prediction and control. However, very limited research in the literature has addressed the influence mechanisms of the drilling parameters on AE characteristics as well as the stress-strain characteristics of rocks. In a previous work Jia et al [15] found that the diameter, spacing and depth of the drilling hole may significantly change the rock stress-strain characteristics, but they did not use AE sensors in their investigation. It is therefore worth analyzing the effects of the drilling hole parameters on the AE signal and the rock mechanic characteristics.
In order to address the aforementioned challenge, PFC2D is employed to systemically investigate the hidden patterns among the mechanical properties, acoustic emission (AE) and damage evolution in the rock pressure relief process with different positions, depths and diameters of the drilling hole. The innovation of this work lies in understanding the effects of different drilling parameters on the rock pressure relief (such as mechanical and damage characteristics) based on AE analysis. The findings of this research add new insight to understanding the evolution law of rock damages using AE analysis. The research results can provide a theoretical basis for further investigation of rock instability mechanism and may have important practical significance for safe and green mining.
The contributions of this work are described as follows.
(1) A particle flow rock model, validated by laboratory experiment data, is established using PFC2D to perform AE monitoring on rock damages. (2) A hidden pattern among the mechanical properties, AE and damage evolution characteristics is discovered for the granite under different drilling hole positions, depths and diameters.

Introduction of particle flow
The particle flow theory was created on the basis of the discrete element method [18], which is suitable for analyzing the fracture mechanisms and large deformation processes of material damage. PFC is a kind of particle flow analysis software, which is able to model discrete particles and the connections among particles. So PFC can simulate the contact fracture mechanics of the particles such as particle bond failure. Compared with other software such as ANSYS (based on finite element method), the contact fracture mode established by PFC is more realistic and suitable to calculate the crack growth (damage evolution) of rock materials. Moreover, even subject to the limitations of particle volume and computation complexity, PFC is still competent for calculation of the contact fracture responses of very small models such as a rock model. Previous works [19][20][21] have proven the PFC calculation results can be used as a reference for field and indoor tests. As a result, it is reasonable to use PFC software to perform the present research.
In simulating particle bond failure, the particle flow program provides two kinds of bonding models: contact bonding and parallel bonding models, respectively [19]. The contact bonding model considers the bonding of points between particles, which cannot transfer torque but only force when the particles produce relative displacement. So this kind of bonding model is suitable for bulk materials such as soil. The parallel bonding model considers the bonding between particles, which can transfer torque. So it is suitable for solid materials such as rock. As shown in figure 1, the parallel key can be described as a set of elastic springs that are evenly distributed on the rectangular cross-section at the contact surface of two particles and centered on the contact point [20]. Once the bonding key between two particles breaks, a fracture crack will be generated. The energy change due to the fracture crack in these two particles is used to characterize the AE, that is, a fracture crack will generate an AE and the bonding breaking energy determines the acoustic intensity. In addition, if the distance of multiple fracture cracks is very close, only one AE is produced. In the process of micro-crack propagation inside the rock, the fracture energy will be released as sound waves, i.e. AE by PFC. In this work the parallel bond model in PFC2D was selected to build the rock model to analyze the AE response.
The maximum normal and shear stresses of the bonding key (σ and τ ), can be expressed as follows: where A and I are the area of the parallel key section and the rotational inertia; T is the tension; M is the bending moment; M t is the torque; V is the tangential force. The sectional area of the parallel bond model and rotational inertia can be expressed as follows: where t is the thickness of the parallel bond model.

Parameters validation of rock model
PFC uses micromechanical parameters to characterize the mechanical properties of particles and bonding keys. Before establishing the numerical model, the micromechanics parameters of the rock model must be assigned according to the experimental results in laboratory tests. By adjusting the microscopic mechanical parameters of the rock model, a suitable set of parameters can be applied to make the numerical calculation results basically consistent with the experimental measurements. By doing so, the numerical rock model can be regarded as reliable for simulating the fracture mechanics of a real rock. In order to obtain the desired set of parameters, the simulation conditions should be similar to laboratory test conditions. A trial and error method is usually adopted to adjust the parameters by repeating the simulations and comparing the experiment results. In this paper the parameters presented in [21] that discussed three axial compressive tests of underground water seal oil cave in Huangdao region were used to conduct the numerical simulations. After trial and error processing, a set of microscopic physical mechanics parameters were obtained, as shown in table 1. With these macroscopic mechanical parameters the stress characteristics of the numerical rock model at a confining stress of 6 MPa become consistent with these of the real yellow granite specimens in the same operation conditions. The elastic modulus, Poisson ratio and compressive strength values of the numerical model (granite specimen) are 28.7 GPa (28.4 GPa), 0.2300 (0.2285) and 130.5 MPa (132.8 MPa), respectively. A comparison of the stress-strain curve and failure mode between the numerical model and experimental granite specimen is shown in figures 2 and 3, where the simulation results are consistent with the experiment results.

Particle-flow-based rock model
When the bonding strength between particles is smaller than the intensity of transmission between the particles, the particle bond will break, i.e. micro-cracks corresponding to the inter ior of the rock form [22]. In the process of micro-crack propagation inside the rock, the damage energy will be released in AE. Therefore, in the process of rock compression using PFC one can monitor the number of parallel bonding breaks at each time and the bonding break energy to study the AE characteristics of rock damage evolution.
In order to analyze the influence of the drilling hole position, depth and diameter on rock mechanics and AE characteristics, three test groups were designed as illustrated in table 2. The simulation model in each group adopts the same parameters as the above intact rock. Figures 4-6 are models of the three groups, respectively. The effects of particle shape and particle distribution were not considered in this work. By means of the radius expansion method, enough particles were generated in the setting region to satisfy the porosity. After each complete model was generated, some particles were removed according to the test plan. The unbalanced force generated during the model generation was eliminated by circulation. The top wall of the mobile model was loaded and the same strain rate 0.008 mm s −1 was applied to the model. In order to prevent the particles from overflowing, the loading wall was properly extended.  Figure 7 shows the stress-strain characteristics of the numerical rock model using the parameters in table 1. One can observe that the stress-strain characteristic curve can be divided into three phases. The first stage is the elastic stage, which shows linear relationship between the stress and strain of the rock. The elastic modulus of the rock remains the same in this linear deformation stage. The second one is the plastic deformation stage, which appears at the peak of the rock deformation. In this stage, the stress-strain curve shows concave characteristics. The third one is the residual damage stage. In this stage, the stress-strain curves show wave form and the stress decreases rapidly as the strain increases. .64%, respectively. From these three-set simulation results one can note that when the drilling hole position is 10 mm, it is closer to the stress loading wall than the other two positions; so the hole is subject to larger stress disturbances, which may increase the deformation speed of the rock, resulting in a higher stress intensity and a large deformation at the peak. Figure 9 shows the failure mode of the numerical granite model with different drilling hole positions. It can be seen that the angle between the rock primary damage side and horizontal direction increases with the increase of the drilling hole position. When the hole position is 10 mm, the primary damage side is connected to the drilling hole and stretches downward. This explains why its stress-strain curve presents two peaks in figure 8. The first peak is generated when the main surface and the borehole connection are destroyed and the second peak is the destruction of the primary side. When the hole position is 0 and −10 mm, the primary damage side is only connected to the drilling hole but does not stretch downward. Moreover, when Y = −10 mm the rock fracture propagates along the primary side and a small crack trace. The small cracks increase the complexity of the stress-strain residual stage. Figure 10 shows the stress-strain characteristic curve of numerical granite in    Figure 11 shows the failure mode of the numerical granite in different drilling hole depth conditions. It can be seen that the angle between the primary damage side and horizontal direction increases with the increase of drilling depth. The effect of the drilling depth is that the primary damage side is longer with smaller depth while with the increase of the drilling hole depth the fracture width increases.      Figure 12 shows the stress-strain characteristic curve of the numerical granite in different drilling hole diameter conditions. It can be seen that the drilling hole diameter has limited influence on the fracture process of the numerical granite. With the same drilling hole position (Y = 0 mm) and depth (D1 = 10 mm), the peak strength and peak strain of the numerical granite slightly increase with increase of the drilling hole diameter and the elastic modulus is basically unchanged. Compared with the drilling hole position and drilling hole depth, the drilling hole diameter is insensitive to the influence of mechanical parameters such as hard rock strength and deformation. In practical engineering, the influence of drill diameter can be ignored. The expected pressure relief effect can be achieved by selecting the proper drilling hole position and depth.   Figure 13 shows the failure mode of the numerical granite with different drilling hole diameters. It can be noticed that the angle between the primary damage side and horizontal direction is almost unchanged.

Influence of the drilling hole depth.
As a result, the rock stress-strain characteristics of different drilling hole positions, depths and diameters are different. The drilling position has the largest influence, followed by the drilling depth, and diameter. Figure 14 shows the stress-strain-AE hits of the numerical granite, and figure 15 shows the AE hits step curve. In uniaxial compression conditions, the rock AE characteristics are presented as follows. (1) At the elastic stage, the frequency of AE is reduced. This is because as the established model is not fully embossed and closed, there is no AE impact at the initial stage. This is different from the actual rock mechanics AE test. Due to the internal porosity, crack closure and friction, the real rock is often accompanied by a certain AE. (2) At the plastic deformation stage, the rock produces more AE hits. The internal crack of the rock evolves and develops frequently, which is the key stage of rock stability. When the damage reaches a certain level, the rock will be fractured and strong AE signals will be generated. (3) At the residual stage, the internal crack further expands and the AE impact signal rapidly decreases. Figure 16 illustrates the stress-strain-AE hits curve of the numerical granite in different drilling hole position conditions. One can observe that drilling hole position has a great influence on the AE hits. Drilling hole position had an influence on the strain value of the initial AE. When Y = 10 mm, the strain value of the initial AE is 0.20%; when Y = 0 mm, the strain value is 0.20%; when Y = −10 mm, the strain value is 0.11%. Thus, the closer the drilling hole is to the loading wall the more vulnerable the rock is. At the peak time, the AE impact strength decreases with the drilling hole position from top to bottom. When Y = 10, 0 and −10 mm, the AE impact strength is 19, 17 and 15 times/step, respectively. At the residual stage the AE hits increases continuously with the drilling hole positions from top to bottom. When Y = 10, 0 and −10 mm, the AE impact is about 0.09%, 0.11% and 0.19%, respectively.

Influence of the drilling hole position.
Drilling hole position had an influence on the AE fluctuation rule. When Y = 10 mm, the rock changes smoothly at the elastic stage. The AE impact increases after entering the plastic deformation stage. Two peak values are observed in figure 16(a). This rule illustrates the rationality of AE monitoring for the rock damage. After entering the residual stage, the AE impact steadily declines until failure of the rock. When Y = −10 mm, the AE fluctuation is close to the real rock. When Y = 0 mm, the AE fluctuation is greater than that of Y = 10 and −10 mm. Figure 17 shows the AE hits step curve of the numerical granite in different drilling hole position conditions. It can be seen that the drilling hole position has limited influence on the AE hits but may influence the AE induction time. The induction time decreases with the drilling hole position from top to bottom. When Y = 10, 0 and −10 mm, the AE induction time is 59 260, 49 321 and 38 315 steps. Moreover, the drilling position influences the AE maximum impact point, respectively. The impact time has a tendency to increase first and then to decrease with the drilling hole position from top to bottom. When Y = 10, 0 and −10 mm, the AE maximum impact point is located at steps 109 992, 113 253 and 106 919, respectively. Figure 18 shows the stress-strain-AE hits curve of the numerical granite in different drilling hole depth conditions. It can be seen that the influence of the drilling hole depth on the AE hits is obvious.

Influence of the drilling hole depth.
The greater the drilling hole depth the greater the rock fracture. At the elastic stage, there is no internal crack generation. At the peak time, the AE intensity increases with the increase of the drilling hole depth. At the residual stage, the AE intensity decreases with the increase of the drilling hole depth. Figure 19 depicts the AE hits step curve of the numerical granite in different drilling hole depth conditions. One can observe that the influence of the drilling hole depth on the evolution rule of AE hits step curve is small, but there is a certain effect on the point of AE peak impact. The AE time period is also different with different depths. Figure 20 illustrates the stress-strain-AE hits curve of the numerical granite in different drilling hole diameter conditions. One can observe that drilling hole diameter has little effect on the stress-strain-AE hits curve. Figure 21 shows the AE hits step curve of the numerical granite with different drilling hole diameters. It can be seen that the evolution rule of AE hits step curve is almost the same with different drilling diameters.

Influence of the drilling hole diameter.
Based on these analysis results, the AE characteristics will be influenced by different drilling hole positions, depths and diameters. The influence importance order is drilling position, depth and diameter.

Failure model based on AE impact parameters
A large number of studies have shown that the AE impact parameter can reflect the change of material performance. It is proportional to the strain energy released by the dislocation motion, fracture and crack propagation in the material [23,24]. Therefore, this paper describes the evolution characteristics of rock damage using AE analysis.
Kachanov [25] defined the damage variable as where A d is the material damage section area at a given moment; A is the sectional area at the initially moment when the material is free of damage.
Assuming that the cumulative AE frequency is K 0 , when the carrying capacity is completely lost the AE accumulative count K w is When the rock fracture surface damage reached A d , the corresponding AE accumulative count K d is Hence, It is difficult to achieve absolute complete failure mode in the process of rock compression. Refer to [26,27], the damage variable is corrected as where D u is the critical damage value. The damage threshold is normalized by the linear function transformation method: where σ p is the peak intensity and σ c is the residual intensity. Based on AE impact characteristics and strain equivalence principle [28], the uniaxial compression damage constitutive model can be described as Figure 22 shows the stress-strain fitting curve based on equation (9), which shows good agreement with the numerical calcul ation results. Figure 23 shows the damage evolution curve of the numerical granite. It can be seen that the damage evolution process can be divided into three stages. The first one is the damage stable development stage. In this stage, the damage variable gradually increases, and the initial crack of the rock gradually expands, and new crack is growing. The second stage is the damage accelerate development stage. The damage variable increases rapidly to the critical value. The micro cracks in the rock rapidly develop into joint fissures, and macroscopic damage appears. The third stage is the damage peak stationary stage, where the damage variable reaches the maximum and the rock gradually loses its bearing capacity. Figure 24 shows the damage evolution curve of the numerical granite in different drilling hole position conditions. It can be seen that the influence of the drilling hole position on the damage evolution rule is mainly in the accelerated development and damage peak stationary stages. As the drilling hole position changes, the initial strain of the damage acceleration value is 0.28%. However, the slope of the initial acceleration damage increases gradually. As the drilling hole position changes from top to bottom, the strain of the damage acceleration decreases gradually and the value is not large. Figure 25 depicts the damage evolution curve of the numerical granite in different drilling hole depths conditions. The drilling depth influences the damage evolution mainly in the accelerated development and damage peak stationary stages. As the drilling depth increases, the initial strain of the damage acceleration phase is 0.26% and is maintained. However, the slope of the initial damage increases initially and decreases afterwards, while the slope of the acceleration damage decreases initially and increases afterwards. When the drilling hole depth is 15 mm, the continuous strain range of the initial damage slope is the biggest and the range values are 1.5 times the 10 and 20 mm depths. The strain values in the damage peak stationary stage increases initially and decreases afterwards with the increases of the drilling hole depth. Hence, the evolution path of rock damage evolution curve is different at different drilling hole depths. Figure 26 illustrates the damage evolution curve of the numerical granite in different drilling hole diameters conditions. It observes that the drilling hole diameter has little effect on the damage evolution law.

Influence of the drilling hole diameter.
Overall, the characteristics of rock damage evolution with different drilling hole positions, depths and diameters are different. The importance order is position, depth and diameter factors.

Conclusion
This paper takes granite geology as the engineering background. The influence of different drilling hole positions, depths and diameters on rock mechanics and AE characteristics is explored based on the PFC2D numerical model. Important parameters such as the drilling hole position, depth and diameter are systematically analyzed in the pressure relief process. The following conclusions can be drawn.
(1) The drilling hole position has little influence on the elastic stage of the numerical granite stress-strain curve but exhibits some influence on the plastic deformation and the damage residual stages. The peak strength and peak strain of the numerical granite were decreasing with the top and bottom of the drilling hole positions, but the elastic modulus was basically unchanged. The drilling hole depth has certain influence on the elastic stage, plastic deformation stage and damage residual stage of the numerical granite stress-strain curve. The peak strength and elastic modulus of the numerical granite decreased continuously. The peak strain shows a tendency to decrease first and then increase. Drilling hole diameter has less influence on the whole three stress-strain stages. and the maximum impact time were all affected by the drilling hole position and the drilling hole depth. As the drill position moved from top to bottom, the following phenomenon occurred: the strain value of the initial AE decreased continuously, the impact intensity of AE at peak time was decreasing, the strain range that produces stronger AE impact increased continuously, the time for initiating the initial AE was reduced and the time that produces the loudest launch had a tendency to increase first and then decrease. As the drilling hole depth increased, the following phenomenon occurred: the strain value induced by initial AE increased, the impact intensity of AE at peak time increased, fluctuation was complicated first and then became simple, the strain range that produces the stronger AE impact had the tendency to increase first and then decrease and there was a tendency for the duration of the intense AE to be shorter and shorter. The drilling hole diameter had less influence on AE characteristics.
(3) It may be observed that the influence of the drilling hole depth and the drilling hole position on the damage evo lution rule of numerical granite is mainly in the accelerated development and damage peak stable stages. As the drilling hole position changes from top to bottom, the initial strain of the damage acceleration value is 0.28% and it also remains basically unchanged. However, the slope of the initial acceleration damage increases gradually. Subsequently, the accelerated damage slope has the tendency of gradually decreasing with the drilling hole from top to bottom. There is an increasing trend of strain value at the moment of the peak of damage and the peak plateau duration gets shorter and shorter. As the drilling hole depth increases, the initial strain of the damage acceleration phase is 0.26% and it is also basically unchanged. The slope of the initial acceleration damage increases initially and decreases afterwards; the slope of the acceleration damage decreases initially and increases afterwards. The strain values of the damage peak stable stage increase initially and decrease afterwards when the drilling hole depth increases. The drilling hole diameter has little effect on damage evolution.