Testing apparatus for whole process of coal borehole deformation and crack development, and evaluation method

By designing the full process test device for drilling deformation-crack evolution of coal body, using loading and monitoring mechanisms to monitor drilling deformation and coal body micro-cracking information in real time, the problem of lack of effective drilling deformation monitoring and quantitative evaluation methods at this stage is solved, and the full process testing and quantitative evaluation of the drilling deformation process are realized.

WO2025102542A1PCT designated stage expired Publication Date: 2025-05-22SHANDONG UNIV OF SCI & TECH +1
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Patent Information

Application Number
PCT/CN2024/075725
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2023-11-15
Filing Date
2024-02-04
Publication Date
2025-05-22

AI Technical Summary

Technical Problem

At this stage, effective drilling deformation monitoring and quantitative evaluation methods are lacking, which makes it difficult to fully understand the drilling deformation process in the study of pressure relief effects of large-diameter drilling.

Method used

Design a test device for the whole process of coal drilling deformation-crack evolution, including a loading mechanism and a monitoring mechanism. The loading mechanism realizes three-way stress loading through the outer frame, pressure-bearing plate, loading cylinder and gasket. The monitoring mechanism uses industrial cameras, acoustic emission detectors and information collection units (such as micro cameras or drilling deformation monitoring sensors) to monitor drilling deformation and coal body micro-rupture information in real time.

Benefits of technology

The entire process of drilling from deformation to closure is achieved. By quantitatively analyzing the overall fracture degree, crack expansion index and drilling closure degree, multi-angle quantitative evaluation of drilling deformation is provided.

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Abstract

A testing apparatus for the whole process of coal borehole deformation and crack development, and an evaluation method, relating to the field of coal borehole deformation testing. The testing apparatus mainly comprises a loading mechanism (1) and a monitoring mechanism (2). The loading mechanism (1) comprises an outer frame (11), a pressure-bearing plate (13), loading cylinders (12), cushion blocks (14), and a coal specimen (15). The monitoring mechanism (2) comprises an industrial camera (21), acoustic emission detectors (22), and an information acquisition unit. The information acquisition unit is used for monitoring and acquiring internal state information of a borehole (151), and can be implemented using a miniature camera (23) or a borehole deformation monitoring sensor (24). The testing apparatus employs the pressure-bearing plate (13) made of high-strength transparent material to implement visual observation of a pressure-bearing surface under three-way stress loading, so that deformation of the borehole (151) and micro-fracture information of nearby coal can be monitored intuitively or by using a monitoring apparatus. For monitoring the state of the borehole (151), either the borehole deformation monitoring sensor (24) or the miniature camera (23) can be selected for use, thereby providing diversified methods for whole-process monitoring, making monitoring information more comprehensive, and achieving whole-process testing of the borehole (151) from deformation to closure.
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Description

A testing device and evaluation method for the entire process of coal drilling deformation-crack evolution Technical Field

[0001] The present invention relates to the field of coal body borehole deformation testing, and in particular to a coal body borehole deformation-crack evolution whole process testing device and evaluation method. Background Art

[0002] Rock burst is a typical mining dynamic phenomenon that can rapidly and violently release the large amounts of elastic deformation energy accumulated in coal and rock masses, causing damage to the coal and rock masses and generating strong vibrations. The force then throws the broken coal and rock into the mining space, generating a strong noise that can damage equipment, damage to the mines and tunnels, and cause casualties. Large-diameter drilling is a key method for preventing and controlling rock burst. Due to its low construction difficulty and effective pressure relief, this technology is widely used.

[0003] Large-diameter borehole pressure relief involves constructing large-diameter boreholes to reduce stress concentration in the surrounding coal mass or alter the mechanical properties of the surrounding coal mass, thereby eliminating or minimizing the risk of deformation and failure of the surrounding rock mass. The effectiveness of borehole pressure relief is closely related to borehole deformation and the extent of coal fracture surrounding the borehole. As the borehole deforms, shrinks, and collapses, cracks in the surrounding coal mass continue to expand, gradually exerting the pressure relief effect. Therefore, monitoring borehole deformation and surrounding coal mass helps study the effectiveness of borehole pressure relief and effectively guides the design of pressure relief parameters. Technical issues

[0004] Currently, research on the pressure relief effects of drilled coal bodies primarily focuses on the overall mechanical properties and impact propensity of the coal body, with little attention paid to the deformation process of the borehole itself. Consequently, there is a lack of effective methods for monitoring and quantitatively evaluating borehole deformation. Therefore, this paper proposes a device and method for testing the entire process of coal borehole deformation and crack evolution. Technical Solutions

[0005] The purpose of the present invention is to provide a coal borehole deformation-crack evolution whole process testing device and evaluation method, which can monitor the deformation of the borehole and the micro-fracture information of the nearby coal body while loading the coal body specimen containing the borehole.

[0006] In order to achieve the above objectives, the technical solutions adopted by the present invention are as follows:

[0007] A device for testing the entire process of coal drilling deformation and crack evolution, comprising a loading mechanism and a monitoring mechanism; the loading mechanism comprises an outer frame, a pressure plate, a loading cylinder, a pad, and a coal specimen; the pressure plate is fixedly mounted at one end of the outer frame, a through hole being formed at the center of the pressure plate; the coal specimen is disposed between the outer frame and the pressure plate; a drill hole is formed in the coal specimen at a position corresponding to the through hole; the coal specimen, except for one side connected to the pressure plate and the opposite side, is in contact with the pad, the loading cylinder being disposed on the pad; and a hole is formed in the pad.

[0008] The monitoring mechanism includes an industrial camera, an acoustic emission detector and an information collection unit; the industrial camera is placed in front of the pressure plate and opposite to the through hole; the acoustic emission detector is placed in the hole opened in the pad and arranged on the surface of the coal specimen; the information collection unit is used to monitor and obtain drilling status information.

[0009] Preferably, the information collection unit is configured as a micro camera, and the micro camera is disposed in a through hole provided in the pressure plate.

[0010] Preferably, the information acquisition unit is configured as a borehole deformation monitoring sensor; the borehole deformation monitoring sensor comprises a water bag, a catheter and a flow monitor; the water bag is placed inside the borehole of the coal specimen, and the flow monitor is connected to the water bag via a catheter.

[0011] Preferably, the outer frame includes a first support plate, a second support plate and multiple groups of support rods; the first support plate and the second support plate are arranged in parallel, and the four corner positions of the first support plate are correspondingly connected to the four corner positions of the second support plate through support rods; the first support plate is arranged at one end of the support rod, and the second support plate is arranged at the middle position of the support rod; the pressure plate is fixedly set at the other end of the support rod, and the coal specimen is set between the pressure plate and the second support plate.

[0012] Preferably, the holes are arranged along the diagonal lines of the pad.

[0013] Preferably, the pressure plate is made of high-strength transparent material.

[0014] An evaluation method for a coal body borehole deformation-crack evolution whole process testing device, using the above-mentioned coal body borehole deformation-crack evolution whole process testing device, includes the following steps:

[0015] Step 1: Select coals of various strengths as test samples, make multiple cubic coal specimens, drill holes in the middle of the coal specimens in advance to obtain coal specimens with holes, and create artificial speckle fields on the surfaces of the coal specimens where the holes are located;

[0016] Step 2: Install the coal specimen, place a spacer between the coal specimen and the loading cylinder, place the acoustic emission detector in the hole opened in the spacer, and arrange the acoustic emission detector on the surface of the coal specimen;

[0017] Step 3: Arrange an industrial camera in front of the transparent pressure plate, facing the through hole of the pressure plate;

[0018] Step 4: For drilling status monitoring, use method 1 or method 2 for comprehensive analysis:

[0019] Method 1: Place a micro camera in the through hole opened in the front pressure plate of the drill hole to capture the shape of the inner hole wall of the drill hole;

[0020] Method 2: Place the water bag of the borehole deformation monitoring sensor in the borehole, connect the flow monitor to the water bag through a catheter, and monitor and obtain information on the entire deformation and closure process of the borehole;

[0021] Step 5: For the coal body loading scheme: the horizontal stress σ2=σ3 of the coal body specimen remains unchanged during the loading process. Multiple sets of stress values ​​are designed in sequence. The vertical stress σ1 of the specimen is loaded using a displacement control method. The loading speed is set. During the test, σ1, σ2, and σ3 are loaded synchronously to the horizontal stress design value. σ2 and σ3 remain unchanged, and σ1 is continued to be loaded.

[0022] Step 6: Start the micro camera or the drilling deformation monitoring sensor to collect data, and load the cylinder until the drilling hole is closed and continue to load 2mm, then stop the test;

[0023] Step 7: Based on the monitoring data, conduct a quantitative analysis of the cracking and deformation of the coal body around the borehole:

[0024] Overall fracture degree:

[0025] ,

[0026] in, is the cumulative number of ringings at a certain moment i, The cumulative number of ringings of acoustic emission after the test is completed;

[0027] Crack Extension Index:

[0028] ,

[0029] Among them, a, b, c, d are weight coefficients, , , , is the number of acoustic emission events within different radii from the center of the borehole;

[0030] Drilling closure:

[0031] ,

[0032] Among them, A i is the drilling area at a certain time i, A 初 is the drilling area at the initial moment;

[0033] or

[0034] ,

[0035] Among them, V i is the cumulative water discharge at a certain moment i, V 总 is the total water volume in the water bag. Beneficial effects

[0036] The beneficial technical effects of the present invention are:

[0037] The present invention relates to a testing device and evaluation method for the entire process of coal borehole deformation and crack evolution. By adopting a pressure plate made of high-strength transparent material, visual observation of the pressure surface containing the hole under triaxial stress loading is achieved, which is convenient for intuitively monitoring the deformation of the borehole and the micro-fracture information of the nearby coal body or using a monitoring device; by monitoring the borehole status, it is possible to choose to use a borehole deformation monitoring sensor or a micro camera, providing diversified methods for full-process monitoring, with more comprehensive monitoring information, and realizing the entire process testing of the borehole from deformation to closure; by quantitatively characterizing the borehole deformation, quantitative evaluation of the borehole deformation is achieved from multiple angles such as overall fracture, expansion of cracks around the hole, and shrinkage deformation of the borehole itself. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] FIG1 is a perspective schematic diagram of a testing device according to an embodiment of the present invention;

[0039] FIG2 is a perspective schematic diagram of an outer frame according to an embodiment of the present invention;

[0040] FIG3 is a schematic diagram of the assembly of a coal specimen, a spacer, an acoustic emission detector, and a loading cylinder according to an embodiment of the present invention;

[0041] FIG4 is a schematic structural diagram of a coal specimen and an acoustic emission detector according to an embodiment of the present invention;

[0042] FIG5 is a schematic structural diagram of a drilling deformation monitoring sensor according to an embodiment of the present invention;

[0043] FIG6 is a schematic diagram of the assembly of a coal specimen and a borehole deformation monitoring sensor according to an embodiment of the present invention;

[0044] FIG7 is a cross-sectional view of a coal specimen, a micro camera, and a pressure plate according to an embodiment of the present invention;

[0045] FIG8 is a stress loading path of a coal body containing a borehole according to an embodiment of the present invention;

[0046] Among them, 1-loading mechanism: 11-outer frame, 111-first support plate, 112-second support plate, 113-support rod;

[0047] 12-loading cylinder; 13-pressure plate, 131-through hole; 14-pad; 15-coal specimen, 151-drill hole;

[0048] 2-Monitoring mechanism: 21-Industrial camera, 22-Acoustic emission detector, 23-Micro camera;

[0049] 24-borehole deformation monitoring sensor, 241-water bag, 242-catheter, 243-flow monitor. Modes for Carrying Out the Invention

[0050] To make the objectives, technical solutions, and beneficial effects of the present invention more clearly understood, the present invention is further described below in conjunction with specific embodiments and with reference to the accompanying drawings. Certain embodiments of the present invention will be more fully described below with reference to the accompanying drawings, some, but not all, of which are illustrated. The various embodiments of the present invention may be implemented in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that the present invention satisfies applicable legal requirements.

[0051] In the description of the present invention, it should be noted that the terms "inner," "outer," "upper," "lower," "front," and "rear," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0052] The present invention relates to a device for testing the entire process of coal borehole deformation and crack evolution, comprising a loading mechanism 1 and a monitoring mechanism 2. As shown in Figures 1 to 4 , the loading mechanism 1 includes an outer frame 11, a loading cylinder 12, a pressure plate 13, a spacer 14, and a coal specimen 15, among other structural components.

[0053] As shown in FIG2 , the outer frame 11 includes a first support plate 111, a second support plate 112, and multiple groups of support rods 113. The first support plate 111 and the second support plate 112 are arranged in parallel, and the four corners of the first support plate 111 are connected to the four corners of the second support plate 112 via support rods 113. The first support plate 111 is arranged at one end of the support rod 113, and the second support plate 112 is arranged in the middle of the support rod 113. As shown in FIG1 , a pressure plate 13 is fixedly arranged at the other end of the support rod 113. A through hole 131 is provided at the center of the pressure plate 13. The pressure plate 13 is made of a high-strength transparent material. The pressure plate 13 is used to limit the displacement of the coal specimen 15 and facilitate the use of an industrial camera 21 to take speckle images. The coal specimen 15 is arranged between the pressure plate 13 and the second support plate 112. By adopting the pressure plate 13 made of high-strength transparent material, visual observation of the pressure surface containing holes under three-dimensional stress loading is achieved, which is convenient for visually monitoring the deformation of the borehole and the micro-fracture information of the nearby coal body or using a monitoring device.

[0054] As shown in Figure 3 , a drilled hole 151 is drilled into the coal specimen 15 at the location corresponding to the through hole 131. Except for the side connected to the pressure plate 13 and the opposite side, all other surfaces of the coal specimen 15 contact the connecting pad 14. A loading cylinder 12 is mounted on the pad 14. The position of the loading cylinder 12 is adjusted to accommodate loading tests on coal specimens 15 of varying sizes, and the loading of the coal specimen 15 is controlled by the loading cylinder 12. As shown in Figure 4 , holes are provided in the pad 14 for mounting an acoustic emission detector 22, arranged along the diagonal lines of the pad 14.

[0055] As shown in Figure 4, the monitoring mechanism 2 includes components such as an industrial camera 21, an acoustic emission detector 22, and an information collection unit. The industrial camera 21 is placed in front of the pressure plate 13, facing the through-hole 131 located in the center of the pressure plate 13. An artificial speckle field is generated on the surface of the coal specimen 15 connected to the pressure plate 13. The industrial camera 21 captures speckle images throughout the test. Digital speckle correlation (DIC) is used to obtain the surface deformation field of the coal specimen 15, and digital image processing (DIP) is used to obtain data such as the shape and surface area of ​​the borehole 151. The acoustic emission detector 22 is placed in a hole formed in the spacer 14 and positioned on the surface of the coal specimen 15. Microfracture information in the coal near the borehole 151 is monitored using the acoustic emission detector 22.

[0056] The information collection unit can be used to monitor and obtain status information of the borehole 151 .

[0057] As shown in FIG7 , the information collection unit is configured as a micro camera 23 . The micro camera 23 is disposed in a through hole 131 provided in the pressure plate 13 . The micro camera 23 can capture the shape of the inner wall of the drill hole 151 .

[0058] As shown in Figures 5 and 6, the information collection unit can also utilize a borehole deformation monitoring sensor 24. This sensor 24 includes a water bag 241, a conduit 242, and a flow rate monitor 243. The water bag 241 is placed inside the borehole 151 created in the coal specimen 15, and the flow rate monitor 243 is connected to the water bag 241 via the conduit 242. The sensor 24 monitors and obtains information about the entire deformation and closure process of the borehole 151.

[0059] By monitoring the status of the borehole 151, the device can choose to use the borehole deformation monitoring sensor 24 or the micro camera 23, providing a diversified method for full-process monitoring, more comprehensive monitoring information, and realizing the full-process testing of the borehole 151 from deformation to closure.

[0060] Referring to Figures 1 to 8 , an evaluation method for a device for testing the entire process of coal borehole deformation and crack evolution is provided. The method employs the device for testing the entire process of coal borehole deformation and crack evolution, and includes the following steps:

[0061] Step 1: Select 3 to 4 types of coal strength as test samples, and prepare multiple cubic coal specimens 15 with dimensions of 100 × 100 × 100 mm. Drill holes 151 with diameters of 8, 10, 12, 14, and 16 mm are pre-drilled in the middle of the coal specimens 15 to obtain the coal specimens 15 containing the drill holes 151. An artificial speckle field is then produced on the side of the coal specimens 15 connected to the pressure plate 13.

[0062] Step 2: Install the coal specimen 15, place a spacer 14 between the coal specimen 15 and the loading cylinder 12, place the acoustic emission detector 22 in the hole opened in the spacer 14, and arrange the acoustic emission detector 22 on the surface of the coal specimen 15;

[0063] Step 3: Arrange an industrial camera 21 in front of the transparent pressure plate 13 and facing the through hole 131 of the pressure plate 13;

[0064] Step 4: For drilling status monitoring, use method 1 or method 2 for comprehensive analysis:

[0065] Method 1: A micro camera 23 is arranged in the through hole 131 formed in the front end pressure plate 13 of the borehole 151 to photograph the shape of the inner wall of the borehole 151;

[0066] Method 2: The water bag 241 of the borehole deformation monitoring sensor 24 is placed in the borehole, and the flow monitor 243 is connected to the water bag 241 via a catheter 242 to monitor and obtain the entire deformation-closing process information of the borehole 151;

[0067] Step 5: For the coal body loading scheme: the horizontal stress of the specimen σ2=σ3 remains unchanged during the loading process, and the stress values ​​are designed to be 50%, 80%, 100%, 120% and 150%σ c , the vertical stress σ1 of the specimen was loaded in a displacement-controlled manner, and the loading speed was set to 0.01, 0.02, 0.04, 0.06, 0.08 and 0.1 mm / min. During the test, after σ1, σ2 and σ3 were loaded synchronously to the horizontal stress design value, σ2 and σ3 remained unchanged, and σ1 was continued to be loaded;

[0068] Step 6: Start the micro camera 23 or the drilling deformation monitoring sensor 24 to collect data, and load the cylinder 12 until the drilling hole 151 is closed and then continue to load for 2 mm, then stop the test;

[0069] Step 7: Based on the monitoring data, conduct a quantitative analysis of the coal fracture and deformation around borehole 151:

[0070] Overall fracture degree:

[0071] ,

[0072] in, is the cumulative number of ringings at a certain moment i, The cumulative number of ringings of acoustic emission after the test is completed;

[0073] Crack Extension Index:

[0074] ,

[0075] Among them, a, b, c, d are weight coefficients, , , , is the number of acoustic emission events within different radii from the center of the borehole 151;

[0076] Drilling closure:

[0077] ,

[0078] Among them, A i is the drilling area at a certain time i, A 初 is the drilling area at the initial moment;

[0079] or

[0080] ,

[0081] Among them, V i is the cumulative water discharge at a certain moment i, V 总 is the total amount of water in the water bag 241.

[0082] This embodiment has been described in detail with reference to the accompanying drawings. Based on this description, those skilled in the art should have a clear understanding of the present invention's device and method for testing and evaluating the entire process of coal borehole deformation and crack evolution. By quantitatively characterizing borehole deformation, quantitative evaluation of borehole deformation is achieved from multiple perspectives, including overall fracture, crack expansion around the borehole, and shrinkage deformation of the borehole itself.

[0083] Of course, the specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A coal body drilling deformation-crack evolution whole process testing device, characterized in that: It includes loading mechanism and monitoring mechanism; The loading mechanism comprises an outer frame, a pressure plate, a loading cylinder, a cushion block and a coal specimen; The pressure plate is fixedly arranged at one end of the outer frame, and a through hole is opened at the center of the pressure plate; the coal specimen is arranged between the outer frame and the pressure plate; a drill hole is opened at the position of the coal specimen corresponding to the through hole, and the coal specimen is in contact with the cushion block except for one side connected to the pressure plate and the opposite side, and the loading cylinder is arranged on the cushion block; a hole is opened on the cushion block; The monitoring mechanism includes an industrial camera, an acoustic emission detector and an information collection unit; The industrial camera is placed in front of the pressure plate and opposite to the through hole; the acoustic emission detector is placed in the hole opened in the cushion block and arranged on the surface of the coal specimen; the information acquisition unit is used to monitor and obtain drilling status information.

2. A coal body drilling deformation-crack evolution whole process testing device according to claim 1, characterized in that: The information acquisition unit is configured as a micro camera, and the micro camera is disposed in a through hole formed in the pressure plate.

3. A coal body drilling deformation-crack evolution whole process testing device according to claim 1, characterized in that: The information acquisition unit is configured as a drilling deformation monitoring sensor; The borehole deformation monitoring sensor comprises a water bag, a catheter and a flow monitor; the water bag is placed inside the borehole of the coal body specimen, and the flow monitor is connected to the water bag through the catheter.

4. A coal body drilling deformation-crack evolution whole process testing device according to claim 1, characterized in that: The outer frame includes a first support plate, a second support plate and a plurality of support rods; The first support plate and the second support plate are arranged in parallel, and the four corner positions of the first support plate are correspondingly connected to the four corner positions of the second support plate through support rods; the first support plate is arranged at one end of the support rod, and the second support plate is arranged at the middle position of the support rod; the pressure plate is fixedly arranged at the other end of the support rod, and the coal body specimen is arranged between the pressure plate and the second support plate.

5. The device for testing the whole process of coal drilling deformation and crack evolution according to claim 1, characterized in that: The holes are arranged along the diagonal lines of the pad.

6. The whole process testing device for coal drilling deformation and crack evolution according to claim 1, characterized in that: The pressure bearing plate is made of high-strength transparent material.

7. An evaluation method for a coal body drilling deformation-crack evolution whole process testing device, using the coal body drilling deformation-crack evolution whole process testing device as claimed in any one of claims 1 to 6, characterized in that: The steps include: Step 1: Select coals of various strengths as test samples, make a plurality of cubic coal specimens, drill holes in the middle of the coal specimens in advance to obtain coal specimens with holes, and make artificial speckle fields on the surfaces of the coal specimens where the holes are located; Step 2: Install the coal specimen, place a cushion block between the coal specimen and the loading cylinder, place the acoustic emission detector in the hole opened in the cushion block, and arrange the acoustic emission detector on the surface of the coal specimen; Step 3: Arrange an industrial camera in front of the transparent pressure plate and facing the through hole of the pressure plate; Step 4: For drilling status monitoring, use method 1 or method 2 for comprehensive analysis: Method 1: a micro camera is arranged in the through hole opened in the front end pressure plate of the drilling hole to photograph the shape of the inner hole wall of the drilling hole; Method 2: Place the water bag of the borehole deformation monitoring sensor in the borehole, connect the flow monitor to the water bag through a catheter, and monitor and obtain the overall deformation-closing process information of the borehole; Step 5, for the coal body loading scheme: the horizontal stress σ2=σ3 of the coal body specimen remains unchanged during the loading process, and multiple groups of stress values ​​are designed in sequence. The vertical stress σ1 of the specimen is loaded by displacement control, and the loading speed is set. During the test, σ1, σ2, and σ3 are loaded synchronously to the horizontal stress design value, σ2 and σ3 remain unchanged, and σ1 continues to be loaded; Step 6: Turn on the micro camera or the borehole deformation monitoring sensor to collect data, load through the loading cylinder, and continue to load 2mm after the borehole is closed, then stop the test; Step 7: Based on the monitoring data, conduct quantitative analysis on the cracking and deformation of the coal body around the borehole: Overall rupture degree: , in, is the cumulative number of ringings at a certain time i, It is the cumulative number of ringings of acoustic emission after the test; Crack Extension Index: , Among them, a, b, c, d are weight coefficients, , , , is the number of acoustic emission events within different radii from the center of the borehole; Drilling closure: , Among them, A i is the drilling area at a certain time i, A 初 is the drilling area at the initial moment; or , Among them, V i is the cumulative water discharge at a certain time i, V 总 is the total amount of water in the water bag.

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