Theoretical analysis of drilling cuttings considering stress zoning of surrounding rock and its application in stress detection

Drilling cuttings method is a commonly used method to detect the risk of rockburst, which has been widely recognized and applied in coal mines. However, in the current theoretical research on the relationship between drilling cuttings method and coal stress, it is generally considered that the mechanical parameters of coal at different positions of roadway are unchanged, and the influence of surrounding rock plastic zone and elastic zone is not considered. Therefore, according to the secondary distribution characteristics of roadway side stress, the theoretical calculation formula of drilling cuttings in the plastic zone and elastic zone of the roadway side is established in this paper. The example shows that the distribution of cuttings on the roadway side is obviously consistent with the abutment pressure. The cuttings in the plastic zone and the elastic zone are in linear and power function with the coal stress, respectively, and the cuttings in the plastic zone are greater than those in the elastic zone. With the increase of the hole diameter, the slope of the relationship curve between the drill‐cutting weight and stress gradually increases, and the response of the drill‐cutting weight with a large hole diameter to the change of coal stress is more obvious. The numerical simulation results show that the error of the theoretical calculation formula of the drilling cuttings method is less than 9%, which can meet the engineering application needs of estimating the drill‐cutting weight in coal and the stress of coal. Using the theoretical formula, the stress field in the leading area of the working face is measured, and the leading influence range and the accurate position of the high stress concentration area are determined, which provides more comprehensive stress information for the early warning of impact danger and pressure relief.


| INTRODUCTION
As a typical mine dynamic disaster, the occurrence frequency and intensity of rockburst gradually increase with the increase of coal mining depth. [1][2][3][4] The research shows that the key factor of rock bursts is high stress concentration. [5][6][7][8] Therefore, determining the stress distribution and evolution law of the coal body in the process of coal seam mining has an important guiding role in revealing the mechanism of rock burst, early warning, and prevention.
To monitor and warn the rockburst, experts at home and abroad have put forward many methods, such as the microseismic method, 9,10 the geoacoustic method, 11,12 the coal stress method, and the drilling cuttings method. [13][14][15] The drilling cuttings method is to evaluate the stress distribution and concentration area of the coal body by using the amount of pulverized coal discharged from the borehole. The drill-cutting weight is the direct response to coal stress. Therefore, the drilling cuttings method is a common and highly recognized technical means in coal mine rockburst hazard monitoring. Qin et al. 16 improved the drill cuttings method to reflect the stress variation in the deeper part of the coal body. Wang et al. 17 deduced the theoretical formula of the drilling cutting weight in the plastic coal mass, and the results were consistent with the field measurement results. Tang et al. 18 derived one new formula for drilling cutting weight based on the effective stress, which is effective in the prediction of coal and gas outbursts.
As the drilling cuttings method is a practical engineering technology, the relevant theoretical analysis is relatively few, and it is generally assumed that the coal strength in different areas of roadway depth has no effect on the drillcutting weight. In practical engineering, affected by high stress and mining, the roadway side is divided into a plastic zone and an elastic zone. The mechanical parameters of coal in the two zones have changed. Therefore, under the same stress conditions, the drill-cutting weight will also change. However, there is no quantitative theory to study the drill-cutting weight in the elastic zone and plastic zone, respectively. Therefore, based on the stress zoning of roadway surrounding rock, this paper deduces and obtains the calculation formula of drilling cuttings in the plastic zone and elastic zone, verifies the accuracy of the formula by means of numerical simulation, and carries out field application.
2 | THEORETICAL ANALYSIS OF DRILLING CUTTINGS METHOD 2.1 | Relationship between drilling cuttings and coal stress After the excavation of the roadway, the stress of the coal body is rebalanced to form the abutment pressure. The roadway side coal body can be divided into a fracture zone, a plastic zone, and an elastic zone (including a stress concentration zone and an initial stress zone). For rockburst, the stress concentration zone is the key factor to induce rockburst. The range of the fracture zone is small with low stress, and the initial stress zone is located in the deeper position of the sideway. These two zones have little effect on rockburst. The purpose of the drilling cuttings method is to obtain the position of the stress concentration zone. Therefore, to facilitate analysis, the zones of roadway coal are divided into the plastic zone and the elastic zone, and the study area is mainly the stress concentration zone, as shown in Figure 1.
According to the elastoplastic distribution of the secondary stress state of the deep buried circular cavern, the vertical stresses in the plastic zone and the elastic zone are, respectively,  where σ v-p is the vertical stress in the plastic zone; σ v-e is the vertical stress in the elastic zone; p 0 is the initial stress before roadway excavation; R a is the roadway radius; R p is the radius of roadway plastic zone, which can be calculated according to formula (3); ζ is the slope of the coal strength curve; σ c is the uniaxial compressive strength of coal, which can be calculated according to formulas (4) and (5), respectively; R is the distance between stress calculation point and roadway center; σ R0 is the radial stress of coal at the boundary of the plastic zone, which can be calculated according to formula (6): where φ is the internal friction angle of coal, and c is the internal cohesion of coal. The drilling cuttings method is often used to detect the stress distribution of roadway side coal. In the process of drilling, the amount of pulverized coal discharged m includes two parts: one part is the amount of coal core m 1 produced by the bit-breaking coal, which is only related to the bit diameter. The other part is the amount of accessory pulverized coal m 2 generated by drill pipe cutting hole wall after drilling deformation under high stress, namely, where φ is the inter The amount of pulverized coal produced by the drill bit is where r d is the radius of drilling cuttings hole, ρ is the coal density, and L is the drilling length for calculating the amount of pulverized coal, generally 1 m. The additional pulverized coal amount of m 2 is mainly related to the radial deformation of the hole wall. It is assumed that the horizontal stress and vertical stress of the coal body are σ 0 before drilling. After drilling, the surrounding coal body is divided into the elastic zone and the plastic zone. The radial displacement u on the hole wall surface can be calculated by the following formula: where μ is Poisson's ratio of coal, E is the elastic modulus of coal, r p is the radius of plastic zone of borehole, which can be calculated according to formula (3).
According to the deformation of the hole wall, the amount of pulverized coal in the accessories can be obtained as follows: Substituting formulas (8)-(10) into formula (7), the total mass of pulverized coal by drilling cuttings method can be obtained as follows: It should be noted that, compared with the elastic zone of the roadway side, the coal in the plastic zone of the roadway side is in the postpeak stage, and its uniaxial compressive strength will be reduced, so the ratio between σ v-p and peak stress σ max can be used to modify the uniaxial compressive strength, that is, where σ cr is the uniaxial compressive strength of coal in the plastic zone. By using formulas (1), (2), and (11), the characteristic curves of drilling cuttings distribution at different depths of roadway can be obtained.

| Analysis of influencing factors of drilling cuttings
To compare and analyze the influence of coal stress, borehole diameter and other factors on the drill-cutting weight, it is assumed that in a certain engineering site, the initial in situ stress p 0 is 20 MPa, the roadway radius R a is 2 m, the coal density ρ is 1400 kg/m 3 , the slope of strength curve ζ is 2, uniaxial compressive strength σ c is 10 MPa, elastic modulus E is 1 GPa, Poisson's ratio μ is 0.25. The diameter of drilling cuttings D d is 40 mm, and the drilling depth is 15 m. Then, the stress distribution and drilling cuttings of the coal on the roadway side are shown in Figure 2. The curve shows that with the increase of stress, the drill-cutting weight also increases, and the distribution of drilling cuttings is obviously consistent with the stress distribution, that is, in the plastic zone, the drill-cutting weight and the stress of the coal body gradually increase; in the elastic region, both decrease gradually. As the strength of coal in the plastic zone is weaker than that in the elastic zone, the drillcutting weight in the plastic zone is greater than that in the elastic zone under the same stress, as shown in Figure 2B. Figure 3 shows the relationship between the amount of cuttings and the stress in the roadway side with different hole diameters. Under the same hole diameter, the drillcutting weight in plastic coal is significantly greater than that in elastic coal, and the difference in drilling cuttings first increases and then decreases with the stress of coal. When the stress is zero or at the peak point, the drill-cutting weight is the same. With the increase of the hole diameter, the slope of the relationship curve between the drill-cutting weight and stress increases gradually, indicating that the response of the drill-cutting weight with a large hole diameter to the change of coal stress is more obvious. At the same time, the difference in the drill-cutting weight between the plastic state and the elastic state also increases with the increase of the diameter of drilling cuttings.
The relationship between the drill-cutting weight and stress of coal bodies with different strengths is shown in Figure 4. With the increase in coal strength, the peak stress of roadway side coal increases, but the drill-cutting weight decreases. At the same time, the slope of the relation curve between the drill-cutting weight and stress, and the difference between the drill-cutting weight in the plastic zone and the elastic zone under the same stress also decrease with the increase of coal strength.

| Simulation scheme
The coal body drilling cuttings model is established by using PFC2D, and the size of the coal body model is 300 × 300 mm 2 . To reduce the size effect, 19 the radius of the particles was set to 0.15-0.3 mm, and the average ratio of specimen size to particle radius was 1333. With a particle diameter of 0.3-0.6 mm and a borehole diameter of 40 mm, as shown in Figure 5. The parallel bonding model is selected as the constitutive model, and the specific mechanical parameters are calibrated by the trial and error method. The specific parameters are listed in Table 1.
In this paper, the complete coal body is used to simulate the coal body in the elastic zone and the postpeak coal body is used to simulate the coal body in the plastic zone. For the coal in the elastic zone, the axial stress σ 1 and lateral stress σ 3 load to set stress σ 0 , and then directly drill the hole, as shown in Figure 5B. And the stress σ 0 is set to 10, 20, 30, and 40 MPa, respectively. For the coal body in the plastic zone, the coal body experienced the peak of uniaxial compression and is used as the drilling test object. The stress loading path is shown in Figure 5C. The design scheme of the postpeak stress and the set stress σ 0 is shown in Table 2.
The drilling process is simulated by deleting particles. To more accurately simulate the drilling cuttings method, the first drilling is carried out after the model is loaded to the set stress, which is that the particles within the 40 mm diameter in the middle of the model are deleted. Then, the stress is kept constant and the simulation calculation is continued. When the new balance is reached, the second drilling is carried out and the particles within the 40 mm diameter are deleted. The total mass of deleted particles is calculated by using particle density and diameter, which is the drilling-cutting weight.

| Result analysis
Taking the coal body in the elastic zone as an example, the displacement nephogram and fracture distribution after the drilling cuttings method are shown in Figure 6. When the coal stress is 10 MPa, the deformation of the borehole sidewall is very small, and only a few cracks are generated within 10 mm around the borehole wall. When the stress increases to 20 MPa, the crack range extends to 60 mm around the hole. With the increase of stress, the deformation and fracture range of the coal body around the borehole increase. When the stress reaches 30 MPa, the width of the drilling deformation zone reaches 90 mm, and the crack extends to the edge of the model. At this time, hole collapse is easy to occur, resulting in a sharp increase in the drill-cutting weight. Compared with the elastic zone, the cracks of the coal body in the plastic zone are obviously increased after drilling, and the range of the deformation zone around the drilling is expanded. The relation curves between the drill-cutting weight and the stress of the coal in the elastic zone and plastic zone are shown in Figure 7. Under the same stress, the drill-cutting weight in the plastic zone is greater than that in the elastic zone, which is consistent with the theoretical analysis. With the increase of coal stress, the drill-cutting weight in the elastic zone and plastic zone also increases. The relationship between them and coal stress is linear and power function, respectively.
To further verify the correctness of the theoretical calculation of the drilling cuttings method, the relative errors between the numerical simulation results and the theoretical calculation results under the same stress are analyzed, as shown in Table 3. In the plastic zone, the maximum error of the theoretical results is less than 9%, and the average error is 6.61%. In the elastic region, the maximum error of the theoretical results is less than 8%, and the average error is 3.75%. For coal, a heterogeneous material, its mechanical parameters are very discrete, for example, the confidence interval of uniaxial compressive strength is (1 ± 20%) or even higher. The error of the theoretical calculation method of the drilling cuttings method proposed in this paper is less than 9%, which can meet the engineering application needs of the estimation of the drill-cutting weight in the coal and the coal stress.

| ENGINEERING APPLICATION
In the above research work, the quantitative function relationship between coal stress and drill-cutting weight is obtained by theoretical analysis, and it is verified by numerical simulation. In the following energy practice, the coal stress distribution law is researched by using the theoretical formula.

| Project overview
To study the equivalent stress distribution characteristics of the working face by drilling cuttings method, the 10304 working face of the Xinglongzhuang coal mine was selected as the field test site. The working face has a buried depth of 470 m, strike length of 2370 m, and dip length of 211 m, and passes through a Liujialou No. 2 fault. The west side of the working face is the goaf of working face 10305, and the east side is the goaf of working face 10303, which is an island working face, as shown in Figure 8.
The average thickness of the coal seam is 8.8 m, and the uniaxial compressive strength of the coal σ c is 19.34 MPa, Young's modulus E is 1.38 GPa, and density is 1436 kg/m 3 . The immediate roof is siltstone, with a thickness of m 1 of 2.4 m. The main roof contains two layers of rock strata, and the lower #1 main roof is medium-grained sandstone with a thickness of 11.5 m. The upper #2 main roof is sandstone interbedding, with a thickness of 22.6 m.

| Drilling scheme
To monitor and analyze the stress distribution within a certain depth range of the lateral coal of the roadway and its change with mining, the drilling test is carried out at the track roadway side. The roadway is 4 m wide and 3 m high. Drilling is carried out along the center of the coal wall. The measuring points are arranged at 15, 45, 75, and 105 away from the working face, and holes with a depth of 14 m and a diameter of 42 mm are drilled, respectively, as shown in Figure 8. Drilling and powder extraction shall be carried out once a day, which shall move forward in turn with the advance of the working face. When the initial drilling was carried out, the roof was in a stable stage.

| Result analysis
The cloud chart of drilling cuttings within 105 m in front of the working face is shown in Figure 9A, and the cloud chart of coal body stress obtained by using the theoretical formula in this paper is shown in Figure 9B. The cloud chart analysis shows that the distribution of drilling cuttings is obviously consistent with the stress distribution of coal. The closer to the working face, the higher the drill-cutting weight and the coal stress. The coal stress at 15 m away from the working face and at the hole depth of 9-12 m reaches 50 MPa. (1) According to the secondary distribution characteristics of the roadway side stress, the theoretical calculation formulas of the drilling cuttings in the plastic zone and the elastic zone of the roadway side are established, respectively. The numerical simulation results show that the error of the theoretical calculation formula of the drilling cuttings method is less than 9%, which can meet the engineering application needs of the estimation of the drilling cuttings in the coal body and the coal body stress. (2) Under the same stress, the amount of pulverized coal in the plastic zone is greater than that in the elastic zone. When the stress is zero or at the peak point, the drill-cutting weight is the same. The relationship between the drill-cutting weight in the plastic zone and elastic zone and the coal stress is in linear and power function, respectively. (3) With the increase of the hole diameter, the slope of the relationship curve between the drill-cutting weight and stress increases gradually, and the response of the drill-cutting weight with a large hole diameter to the change of coal stress is more obvious.
With the increase in coal strength, the peak stress of roadway side coal increases, but the drill-cutting weight decreases. (4) Using the drilling cuttings method can effectively obtain the stress distribution information of the coal body in the working face, determine the advanced influence range and high stress concentration area, and provide more comprehensive stress information for the impact risk early warning and pressure relief.