A method combining DIC and strain gauge to test rock crack growth toughness under static load

Abstract

The present invention discloses a method for testing the propagation toughness of rock cracks under static loads by combining DIC and strain gauges. The method comprises applying a static load to a cracked rock specimen, then calculating the real-time crack tip opening displacement in the crack propagation path using a numerical image processing system (DIC), obtaining the crack propagation velocity based on the crack tip opening displacement, obtaining the propagation toughness value of the rock crack propagation process under static load, and evaluating the rock crack propagation process using the propagation toughness value. The present invention uses an industrial camera and a strain gauge to simultaneously measure the crack initiation time, accurately determining the initiation time of the rock crack, providing a better experimental data basis for the subsequent determination of the crack propagation velocity and calculation of the crack propagation toughness, and using the crack initiation toughness and crack propagation toughness to evaluate the strength of the cracked rock, thereby achieving further application of the crack propagation velocity data and enabling the evaluation of the entire crack propagation process of the rock specimen.

Description

Technical Field

[0001] The invention relates to a method for testing rock crack propagation toughness under static load by combining DIC with a strain gauge, and belongs to the technical field of rock mechanics. Background Art

[0002] As the most common load-bearing medium within tunnel surrounding rock in underground engineering, the study of its brittle mechanical fracture characteristics is crucial. Crack propagation rate and crack propagation toughness within rock are among the most important evaluation parameters. Accurately testing rock crack propagation toughness plays a crucial role in assessing the stability of crack propagation processes. Geological tectonic forces and human activities can cause cracks of varying shapes, orientations, and angles within rock. Tensile cracks—Type I cracks—are the most dangerous cracks within rock and are the most frequently analyzed by researchers. When rock is subjected to an external load, the combined effect of Type I cracks and the external load will cause rapid cracking and expansion of the rock at the stress concentration point at the crack tip, ultimately leading to damage to underground engineering and causing serious consequences. During the rapid crack expansion process, the crack expansion toughness value will change along the crack expansion path. If we can clearly understand the changing law of crack expansion toughness during the rapid expansion of Type I cracks, we need to accurately test the expansion toughness of cracked rock. In addition, we can also set corresponding crack arrest components on the rock crack expansion path according to the evolution law of crack expansion toughness, so as to enhance the stability of cracked rock.

[0003] On the other hand, the crack propagation toughness of cracked rock is closely related to the crack propagation rate. With the rapid development of non-contact imaging technology and crack propagation meter testing systems, the testing of rock crack propagation rate has become increasingly accurate, which has greatly promoted the calculation of the propagation toughness of cracked rock. However, both high-speed camera testing systems and crack propagation meter testing systems have some drawbacks. They are better for rock materials with high crack propagation rates, but the crack propagation rate test error is large for cracked rock materials with low crack propagation rates. Because the loading time of cracked rock specimens under static load is long, the range of crack propagation rate testing is also long. At this time, the general high-speed camera testing technology cannot meet the test time requirements. Summary of the Invention

[0004] In order to overcome the defects existing in the prior art, the present invention aims to provide a method for combining DIC and strain gauge testing of rock crack propagation toughness under static load. The present invention uses industrial cameras and strain gauge testing technology to simultaneously measure the crack initiation time, accurately determine the initiation time of rock cracks, and provide a better experimental data basis for the subsequent determination of crack propagation rate and calculation of crack propagation toughness. Subsequently, the crack propagation toughness is determined using theoretical analytical solution formulas or finite element numerical simulations, and the strength of cracked rock is evaluated using crack initiation toughness and crack propagation toughness, thereby achieving further application processing of crack propagation rate data and being able to evaluate the stability of rock samples.

[0005] The present invention provides a technical solution to solve the above technical problems: a method for testing the crack growth toughness of rock under static load by combining DIC and strain gauge, comprising the following steps:

[0006] A. Prepare a cracked rock specimen and attach a strain gauge to the crack tip of the cracked rock specimen.

[0007] B. Apply static load to the cracked rock specimen to obtain load-time curve, strain gauge fracture time curve and front image data information;

[0008] C. Perform simultaneous domain processing based on the load time history curve and the strain gauge fracture time curve. The characteristic of simultaneous domain processing is that the start acquisition time of the load time history curve and the start acquisition time of the strain gauge must be triggered simultaneously, and then the crack initiation time of the cracked rock can be determined;

[0009] D. Determine the cracking initiation time of the front side of the cracked rock based on the front side image data;

[0010] E. Determine the crack initiation time based on the crack initiation time of the cracked rock and the crack initiation time of the front of the cracked rock;

[0011] F. Based on the image data information captured by the industrial camera, the crack tip opening displacement and crack extension time t when the crack extension length S is obtained, and the crack extension speed is obtained based on the crack tip opening displacement time history curve and the image shooting time interval information;

[0012] G. Substitute the crack initiation time, crack propagation velocity, and load time history curve into the theoretical analytical solution formula or finite element numerical model for calculation to determine the crack propagation toughness, crack initiation toughness, and crack arrest toughness of the cracked rock;

[0013] H. Evaluate the fracture characteristics of rock cracks during their propagation based on the crack propagation toughness, crack initiation toughness, and crack arrest toughness, and determine the general law of crack propagation toughness during the crack propagation process;

[0014] When the crack propagation toughness is less than the initial toughness, the crack propagation at this moment is rapid and the crack rock stability is poor;

[0015] When the crack propagation toughness is greater than the initial toughness and less than the arrest toughness, the crack propagation at this moment is slowed down and the crack rock stability is good;

[0016] When the crack propagation toughness is greater than the crack arrest toughness, the crack propagation at that moment is stagnant.

[0017] A further technical solution is that in step A, the front and back surfaces of the cracked rock sample are polished and ground, and black and white speckles are sprayed on the front and back surfaces of the cracked rock sample.

[0018] The crack contained in the cracked rock sample in step A is a type I tensile crack, which can better monitor the crack propagation path. To this end, the cracked rock sample can be a straight crack grooved Brazilian disc sample or a side-cracked rock rectangular parallelepiped sample. As long as the prefabricated crack in the cracked rock is a type I crack, it can be used as a test sample, and the strain gauge at the crack tip should be close to the crack tip so that the crack initiation moment can be detected in time.

[0019] A further technical solution is that in step B, an electro-hydraulic servo press is used to statically load the cracked rock sample, and an oscilloscope and an industrial camera are used to collect experimental data on the front and back sides thereof.

[0020] A further technical solution is that, in step B, when static load is applied, butter is applied on the front and back surfaces of the cracked rock sample.

[0021] A further technical solution is that in step C, the load time history curve and the strain gauge fracture time curve are processed in the same domain to obtain the crack initiation time of the cracked rock.

[0022] A further technical solution is to process the front image data information in step D to obtain image information of each frame, and then import it into the DIC data processing system in the computer acquisition system; determine the initiation time when the crack tip is first formed as the initiation time of the front of the cracked rock.

[0023] A further technical solution is that the calculation formula in step E is:

[0024] t v =(t1+t2) / 2

[0025] Where: t v is the crack initiation time; t1 is the crack initiation time of the cracked rock; t2 is the crack initiation time of the front side of the cracked rock.

[0026] A further technical solution is that in step F, the MATALB program is used to intercept the frame number processing of the front image data information, the crack propagation path of each frame image is observed in real time, the crack propagation path is obtained within the same shooting time interval, and then monitoring points are set in the numerical image processing system according to the crack propagation path to obtain the crack tip opening displacement, the opening displacement of the crack tip is differentiated once to obtain the jumping point of the opening displacement, and then the extreme points of each monitoring point are extracted, and finally the crack propagation speed is calculated according to the crack propagation length.

[0027] A further technical solution is that the calculation formula in step G is:

[0028]

[0029]

[0030] f I (a / R,β=0)=56.762(a / R) 6 -140.28(a / R) 5 +138.8(a / R) 4 -68.414(a / R) 3 +18.92(a / R) 2 -2.132(a / R)+1.096,R 2 =1

[0031] Where: K I 0 is the static stress intensity factor under static load; P max (t) is the load time history curve inside the electro-hydraulic servo press; f I (a / R, β=0) is the shape factor of the cracked rock specimen; a is the half length of the crack notch; R is the radius of the Brazilian disk specimen; K I d (t) is the propagation toughness of the crack in the cracked rock specimen; v is the crack propagation velocity.

[0032] A further technical solution is that the specific process of calculating and determining the crack propagation toughness of the cracked rock using the finite element numerical model in step G is to obtain the load time history curve of the electro-hydraulic servo press and input it into the finite element model as a load condition, and then perform modeling numerical calculations in the finite element model according to the rock material parameters, and derive the crack tip stress intensity factor time history curve of real-time crack propagation, and then jointly determine the crack propagation toughness of the cracked rock using the crack initiation and propagation time and the crack propagation speed to determine the propagation toughness of the cracked rock.

[0033] The present invention has the following beneficial effects:

[0034] 1. High test accuracy;

[0035] The present invention can use an industrial camera and a strain gauge test system to conduct comparative analysis on the front and back of a cracked rock specimen, fully accounting for test errors caused by the initiation of microscopic cracks that are invisible to the naked eye. The measurement error range of the industrial camera and the strain gauge test system is within 10μs, overcoming the disadvantage of high-speed camera image information being observed with the naked eye. This can better determine the initiation time and load of cracked rock, and provide better basic experimental data for calculating the propagation toughness of cracked rock.

[0036] 2. Wider scope of application;

[0037] It can not only test the evolution state of the displacement field on the cracked rock surface during the entire static load loading process, but can also be well used to accurately test the initiation load at the moment of cracking. Similarly, it can also be used to test the crack propagation speed of cracked rocks under dynamic loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a flow chart of the present invention;

[0039] Figure 2 Schematic diagram of the implementation of straight-cut groove Brazilian disc crack rock specimen;

[0040] Figure 3 For attachment Figure 4 Schematic diagram of determining crack initiation moment using strain gauges for straight-cut groove Brazilian disc cracked rock specimens;

[0041] Figure 4 Schematic diagram of crack initiation moment determination using the DIC method for a straight-cut groove Brazilian disc cracked rock specimen;

[0042] Figure 5 Schematic diagram for determining crack growth rate of straight-cut groove Brazilian disc cracked rock specimen;

[0043] Figure 6 Schematic diagram of the calculation results of crack propagation toughness of straight-cut groove Brazilian disc cracked rock specimen;

[0044] Figure 7 Schematic diagram of a non-standard side-opened single crack triangle (SCT) rock specimen;

[0045] Figure 8 Schematic diagram of the finite element numerical model of a non-standard side-opened single crack triangular (SCT) rock specimen;

[0046] Figure 9 Schematic diagram for determining the crack initiation toughness and crack propagation toughness of a non-standard side-opening single crack triangle (SCT) rock specimen;

[0047] Figure 10 Schematic diagram of the calculation results of crack propagation toughness of non-standard side-opening single crack triangle (SCT) rock specimen. Implementation Method

[0048] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0049] Example 1

[0050] A method for combining DIC and strain gauge to test the rock crack growth toughness under static load, the specific implementation steps of the measurement method are as follows: Figure 1 As shown:

[0051] Step 1: Prepare a standard Brazilian disc specimen with cracks, such as Figure 2 As shown, a prefabricated crack groove is set, the groove crack length 2a = 50mm, the width 1mm, the Brazilian disk radius R = 50mm, the Brazilian disk thickness B = 30mm, the crack line is parallel to the loading direction of the voltage servo press, and then the front and back of the cracked rock sample are polished and ground so that the error of the front and back surfaces of the sample does not exceed ±0.01mm. Then, black and white speckles are sprayed on the front of the cracked rock sample, and two strain gauges are attached to the back of the cracked sample.

[0052] The second step: static load application was performed on the cracked rock specimen using an electro-hydraulic servo press. Before loading, the strain gauges on the cracked rock specimen were connected to the bridge box, followed by the ultra-dynamic strain gauge. The data was then processed by an oscilloscope and a computer processing system. Simultaneously, the front of the cracked rock was illuminated by a lighting system, and then photographed using an industrial camera. The camera was then connected to a computer system for DIC data processing. At the start of loading, the industrial camera, loading system, and strain gauge test system all began data acquisition at time zero, achieving simultaneous experimental data acquisition.

[0053] The third step is to further extract the load displacement curve in the hydraulic loading system, and then extract the strain gauge fracture time curve in the oscilloscope, and process the two curves in the same domain, such as Figure 3 As shown, the crack initiation time t1 of the cracked rock is obtained;

[0054] Step 4: The video and image information captured by the industrial camera are further processed using MATLAB to obtain the image information of each frame, which is then imported into the DIC data processing system in the computer acquisition system; the initiation time of the first formation of the crack tip is determined as the initiation time t2 of the crack rock front, as follows: Figure 4 As shown, it is then averaged with the crack initiation time determined by the strain gauge t v =(t1+t2) / 2, to get a more accurate crack initiation time t v ;

[0055] Step 5: Further process the image information of each frame of the video captured by the industrial camera to obtain the image information of the entire fracture process, and then set monitoring points on the crack propagation trajectory to observe the crack tip opening displacement, such as Figure 5 As shown in (b) and (c), the sudden starting point of the opening displacement of the crack tip No. 1 as the monitoring point is 0 μs, and the sudden starting point of the opening displacement of the crack tip No. 2 monitoring point at a distance of S = 5 mm from the crack tip is time t. The obtained crack growth velocity v = S / t, then the crack growth velocity at each stage in the crack growth path can be obtained based on a series of monitoring points No. 1 to No. 8 at the crack tip;

[0056] Step 6: Substituting the crack tip opening displacement and the loading value at the crack initiation time into the crack Brazilian disk theory formula can accurately determine the crack initiation toughness and crack propagation toughness, such as Figure 6 As shown;

[0057]

[0058]

[0059] f I (a / R,β=0)=56.762(a / R) 6 -140.28(a / R) 5 +138.8(a / R) 4 -68.414(a / R) 3 +18.92(a / R) 2 -2.132(a / R)+1.096,R 2 =1

[0060] Where: K I 0 is the static stress intensity factor under static load; P max (t) is the load time history curve inside the electro-hydraulic servo press; f I (a / R, β=0) is the shape factor of the cracked rock specimen; a is the half length of the crack notch; R is the radius of the Brazilian disk specimen; KI d (t) is the propagation toughness of the crack in the cracked rock specimen; v is the crack propagation velocity;

[0061] Step 7: Finally get the whole process of crack propagation (such as Figure 6 The crack growth toughness value is calculated and the stability of the crack growth process is evaluated based on the crack growth toughness.

[0062] When the crack extension distance is 0-4.4 mm, the crack extension toughness is greater than the initial toughness and less than the crack arrest toughness, that is, the crack extension in this range is slowed down and the crack rock has good stability;

[0063] When the crack extension distance is 4.4-17.6 mm, the crack extension toughness is less than the initial toughness, that is, the extension situation in this range is that the crack expands rapidly and the crack rock stability is poor;

[0064] When the crack extension distance is 17.6-22 mm, the crack extension toughness is greater than the initial toughness and less than the crack arrest toughness, that is, the crack extension in this range is slowed down and the crack rock stability is good;

[0065] According to the calculation results, we can know that the crack initiation toughness is small, which is caused by the sharpening of the crack tip, and there is crack arrest toughness during the crack propagation process, which means that the crack propagation is most likely to stagnate at this moment and it is also easy to form crack arrest components. This can provide experimental data for the setting of crack arrest components in underground engineering.

[0066] Example 2

[0067] The detailed description of the implementation case 2 is as follows:

[0068] Step 1: Prepare non-standard SCT specimens with cracks, such as Figure 7 As shown, the sample is 200 mm wide, 325 mm high, and 30 mm thick. The upper opening is an equilateral triangle with a side length of 75 mm, and the lengths of the left and right sides are 62.5 mm respectively. Then, a prefabricated crack groove 13 is cut at the opening of the triangle. The groove crack 13 is 30 mm long and 1 mm wide, and the corresponding crack tip is sharpened. The crack line is parallel to the loading direction of the voltage servo press. Then, the front and back of the SCT sample are polished and ground so that the error of the front and back surfaces of the sample does not exceed 0.01 mm. Black and white speckles are sprayed on the front of the cracked rock SCT sample 14, and two strain gauges are attached to the back of the cracked sample.

[0069] The second step: static load application was performed on the cracked rock specimen using an electro-hydraulic servo press. Before loading, the strain gauges on the cracked rock specimen were connected to the bridge box, followed by the ultra-dynamic strain gauge. The data was then processed by an oscilloscope and a computer processing system. Simultaneously, the front of the cracked rock was illuminated by a lighting system, and then photographed using an industrial camera. The camera was then connected to a computer system for DIC data processing. At the start of loading, the industrial camera, loading system, and strain gauge test system all began data acquisition at time zero, achieving simultaneous experimental data acquisition.

[0070] The third step is to further extract the load displacement curve in the hydraulic loading system, and then extract the strain gauge fracture time curve in the oscilloscope, and process the two curves in the same domain, such as Figure 3 As shown, the crack initiation time t1 of the cracked rock is obtained;

[0071] Step 4: The video and image information captured by the industrial camera 12 is further processed using MATLAB to obtain image information of each frame, which is then imported into the DIC data processing system in the computer acquisition system 10; the initiation time of the first formation of the crack tip is checked to determine the initiation time of the cracked rock front, and then the initiation time is averaged with the initiation time determined by the strain gauge 15 to obtain a more accurate crack initiation time, such as Figure 5 As shown;

[0072] The fifth step: further process the image information of each frame of the video captured by the industrial camera to obtain the image information of the entire fracture process, and then set monitoring points on the crack propagation trajectory to observe the crack tip opening displacement, and then use the sudden change point of the crack tip opening displacement as the crack propagation trajectory point, and then compare it with the image information interval sample to obtain the crack propagation speed, such as Figure 5 As shown in the figure, the crack tip No.1 as the monitoring point suddenly starts to open at 0μs (as shown in the figure). Figure 5 b), the crack tip No. 2 monitoring point at a distance of S = 5 mm from the crack tip suddenly starts opening at time t, and the crack growth rate v = S / t is obtained. Then, the crack growth rate at each stage of the crack growth path can be obtained based on a series of monitoring points No. 1 to No. 8 at the crack tip (e.g. Figure 5 c);

[0073] Step 6: Further numerical simulation methods are used to obtain the propagation toughness and crack arrest toughness of non-standard rock cracks. Since there is no theoretical solution for SCT non-standard rock samples, ABAQUS is used to establish a finite element numerical model, such as Figure 8 As shown,

[0074] Step 7: C3D15 grid units are further used to divide the crack tip area grid, and C3D20 grid units are used to divide the other crack area grids. Then numerical calculations are performed to establish a numerical model by corresponding the load time history curve and the crack propagation path. Then, the crack initiation toughness and crack propagation toughness are determined based on the crack initiation time, crack tip opening displacement and crack propagation speed. The calculation is performed using the following formula: Figure 9 As shown;

[0075]

[0076] Step 8: Further obtain the whole crack growth process (such as Figure 10 The crack propagation toughness value is shown in Figure 2, and the crack initiation toughness is 6.89 MPa·m 1 / 2 ; and evaluate the stability of the crack growth process based on the crack growth toughness;

[0077] When the crack extension distance is 30-75 mm, the crack extension toughness is always smaller than the initial toughness, that is, the crack extension in this range is rapid and the crack rock stability is poor;

[0078] According to the calculation results, we can know that the crack initiation toughness is small, which is caused by the sharpening of the crack tip. In addition, the crack propagation toughness gradually fluctuates during the crack propagation process, indicating that the crack propagation toughness value is constantly changing. This has great reference value for understanding the crack propagation process of rock materials.

[0079] The above description does not limit the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can use the technical content disclosed above to make some changes or modifications to equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for testing rock crack growth toughness under static load by combining DIC and strain gauge, characterized in that: The following steps are involved: A. Prepare a cracked rock specimen and attach a strain gauge to the crack tip of the cracked rock specimen. B. Apply static load to the cracked rock specimen to obtain load-time curve, strain gauge fracture time curve and front image data information; C. Perform simultaneous domain processing based on the load time history curve and the strain gauge fracture time curve. The characteristic of simultaneous domain processing is that the start acquisition time of the load time history curve and the start acquisition time of the strain gauge must be triggered simultaneously, and then the crack initiation time of the cracked rock can be determined; D. Determine the cracking initiation time of the front side of the cracked rock based on the front side image data; E. Determine the crack initiation time based on the crack initiation time of the cracked rock and the crack initiation time of the front of the cracked rock; t v =(t 1+ t2) / 2 Where: t v is the crack initiation time; t1 is the crack initiation time of the cracked rock; t2 is the crack initiation time of the front of the cracked rock; F. Based on the image data information captured by the industrial camera, the crack tip opening displacement and crack extension time t when the crack extension length S is obtained, and the crack extension speed is obtained based on the crack tip opening displacement time history curve and the image shooting time interval information; In step F, the front image data information is intercepted and processed by the MATLAB program, and the crack propagation path is observed in real time for each frame of the image. The crack propagation path is obtained within the same shooting time interval, and then monitoring points are set according to the crack propagation path in the numerical image processing system to obtain the crack tip opening displacement. The crack tip opening displacement is differentiated to obtain the jump point of the opening displacement, and then the extreme points of each monitoring point are extracted. Finally, the crack propagation speed is calculated according to the crack propagation length. G. Substitute the crack initiation time, crack propagation velocity, and load time history curve into the theoretical analytical solution formula or finite element numerical model for calculation to determine the crack propagation toughness, crack initiation toughness, and crack arrest toughness of the cracked rock; The calculation formula of the theoretical analytical solution formula is: Where: K I 0 is the static stress intensity factor under static load; P max ( t ) is the load-time curve inside the electro-hydraulic servo press; is the shape factor of the cracked rock specimen; a is the half length of the crack groove; R is the radius of the Brazilian disk specimen; K I d (t) is the propagation toughness of the crack in the cracked rock specimen during the crack propagation process; v is the crack growth rate; H. Evaluate the fracture characteristics of rock cracks during their propagation based on the crack propagation toughness, crack initiation toughness, and crack arrest toughness, and determine the general law of crack propagation toughness during the crack propagation process; When the crack propagation toughness is less than the crack initiation toughness, the crack propagation at this moment is rapid and the crack rock has poor stability; When the crack propagation toughness is greater than the crack initiation toughness and less than the crack arrest toughness, the crack propagation at this moment is slowed down and the crack rock stability is good; When the crack propagation toughness is greater than the crack arrest toughness, the crack propagation at that moment is stagnant.

2. The method of combining DIC and strain gauge to test rock crack growth toughness under static load according to claim 1, characterized in that: In the step A, the front and back surfaces of the cracked rock sample are polished and ground, and black and white speckles are sprayed on the front and back surfaces of the cracked rock sample.

3. The method of combining DIC and strain gauge to test rock crack growth toughness under static load according to claim 1, characterized in that: In the step B, an electro-hydraulic servo press is used to statically load the cracked rock sample, and an oscilloscope and an industrial camera are used to collect experimental data on the front and back sides of the cracked rock sample.

4. The method of combining DIC and strain gauge to test rock crack growth toughness under static load according to claim 1, characterized in that: In step B, when static load is applied, butter is applied to the front and back surfaces of the cracked rock specimen.

5. The method of combining DIC and strain gauge to test rock crack growth toughness under static load according to claim 1, characterized in that: In step C, the load time history curve and the strain gauge fracture time curve are processed in the same domain to obtain the crack initiation time of the cracked rock.

6. The method of combining DIC and strain gauge to test rock crack growth toughness under static load according to claim 1, characterized in that: In step D, the front image data information is processed to obtain image information of each frame, which is then imported into the DIC data processing system in the computer acquisition system; the initiation time when the crack tip is first formed is determined as the initiation time of the front side of the cracked rock.

7. The method of combining DIC and strain gauge to test rock crack growth toughness under static load according to claim 1, characterized in that: The specific process of calculating and determining the crack propagation toughness of the cracked rock using the finite element numerical model in step G is to obtain the load time history curve of the electro-hydraulic servo press and input it into the finite element model as the load condition, then perform modeling numerical calculations in the finite element model based on the rock material parameters, derive the crack tip stress intensity factor time history curve of real-time crack propagation, and then jointly determine the crack propagation toughness of the cracked rock using the crack initiation and propagation time and the crack propagation speed to determine the propagation toughness of the cracked rock.

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