Method for determining rock cracking strength threshold based on localized displacement difference wave fluctuation

Abstract

A method for determining rock cracking strength threshold based on localized displacement difference wave fluctuation belongs to the technical field of rock mechanics and underground geotechnical engineering, and can solve the problems of slight local deformation influence, strong randomness and subjectivity and the like existing in the existing rock cracking stress strength threshold determination method, carries out rock uniaxial compression test, adopts a digital image acquisition and analysis system to position an initial crack position of a sample, and obtains displacement difference value change data of the region, introduces displacement difference value average fluctuation amplitude as a quantitative parameter for describing the degree of rock localized differential deformation, and determines the rock cracking stress strength threshold through a stress value corresponding to a sudden increase inflection point of the displacement difference value average fluctuation amplitude-time curve, so that the rock cracking stress threshold can be conveniently and accurately obtained, and a theoretical and experimental basis can be provided for the stability evaluation and control research of surrounding rock of underground engineering.

Description

Technical Field

[0001] This invention belongs to the field of rock mechanics and underground geotechnical engineering technology, specifically relating to a method for determining the rock crack initiation strength threshold based on localized displacement difference fluctuations. Background Technology

[0002] The initiation stress strength of rock refers to the stress intensity at which a new crack initiates and steadily propagates under axial compressive load. In underground rock engineering, the initiation stress strength is an important parameter for evaluating rock mass stability. Accurately determining the initiation stress strength of rock has significant theoretical and practical value for the prevention and control of disasters such as underground tunnel wall spalling, tunnel wall cracking, and coal wall spalling.

[0003] Currently, common methods for determining the rock crack initiation strength threshold include crack strain model calculation, acoustic emission parameter method, lateral strain combined with volumetric strain observation method, and moving point regression method. Among these, the crack strain model calculation method is significantly affected by the rock's elastic modulus E and Poisson's ratio ν, resulting in some error in the obtained crack initiation stress intensity. The acoustic emission method is susceptible to interference from external noise, rock structure, and mineral composition, leading to randomness in the obtained crack initiation stress intensity. The lateral strain combined with volumetric strain observation method and the moving point regression method rely on visual selection of characteristic inflection points; furthermore, due to the large amount of data during rock deformation and failure, key points are easily overlooked or missed, thus introducing subjectivity and errors in the obtained crack initiation strength results. In summary, while there are many methods for determining the rock crack initiation strength threshold, they all have certain limitations, such as ignoring the influence of local deformation and being prone to randomness and subjectivity.

[0004] Studies have shown that the damage state of rocks is closely related to the activity state of their internal defects. The essence of rock fracture and failure is that under external load, internal defects in the rock (such as microcracks, pores, joints, etc.) are compacted and developed into cracks, which eventually propagate into macroscopic fracture surfaces. Due to the presence of internal defects, rock deformation and failure exhibit significant localized deformation zones. The degree of differential deformation within these zones gradually increases with increasing load. When the rock reaches its crack initiation strength, cracks form. Subsequently, with further increases in load, the displacement difference between the two sides of the crack exhibits non-uniform fluctuation characteristics. This localized non-uniform deformation leads to the initiation and propagation of rock cracks. Therefore, based on the microcrack propagation law, by quantitatively characterizing and analyzing the localized displacement difference fluctuation characteristics of the region where the initial crack is located under load, the crack initiation strength threshold of the rock can be accurately obtained. Summary of the Invention

[0005] This invention addresses the problems of existing methods for determining the rock crack initiation stress threshold, such as the influence of slight local deformation and the tendency to generate randomness and strong subjectivity. It provides a method for determining the rock crack initiation stress threshold based on localized displacement difference fluctuations.

[0006] The present invention adopts the following technical solution: A method for determining the rock crack initiation strength threshold based on localized displacement difference fluctuations includes the following steps: The first step is to prepare samples from the rock mass to be tested and process them into standard samples. The second step is to spray black and white matte paint onto the surface of the standard rock sample to create a speckled sample with a white background and black spots. The third step is to place the speckled specimen on a pressure testing machine and apply prestress to compress it; The fourth step is to set up the digital image acquisition and analysis system, adjust the camera angle and light source intensity, and use a calibration plate to calibrate the instrument to ensure that the digital image acquisition and analysis system can acquire clear sample photos. The fifth step is to carry out a uniaxial compression test at a preset loading rate. While applying axial stress, the digital image acquisition and analysis system is turned on to record the full-field deformation of the sample surface. After the standard sample is destroyed, loading and image acquisition are stopped. The sixth step is to plot the axial stress-time curve based on the uniaxial compression deformation data of the specimen. Step 7: Based on the high-speed camera photos of the specimen failure morphology taken by the digital image acquisition and analysis system, locate the initial crack position of the specimen, and set up displacement monitoring nodes on both sides of the initial crack. Use the image analysis module of the digital image acquisition and analysis system to record the displacement difference data at the displacement monitoring nodes on both sides of the initial crack of the specimen during the entire experiment. Step 8: Based on the displacement difference data on both sides of the initial crack recorded by the image acquisition and analysis system, plot the displacement difference-time variation curve of the displacement monitoring nodes on both sides of the initial crack. The ninth step is to analyze the displacement difference-time variation curve, define and calculate the average fluctuation amplitude of the displacement difference on both sides of the initial crack in the rock, and plot the average fluctuation amplitude of the displacement difference-time curve. The stress value at the moment when the average fluctuation amplitude of the displacement difference-time curve suddenly increases is the determined crack initiation strength threshold of the rock.

[0007] Furthermore, the prestress mentioned in the third step is 100 kN.

[0008] Furthermore, the loading method for the uniaxial compression experiment described in step five is displacement control, with a loading rate of 0.1 mm / min and an image acquisition rate of 5 frames / s.

[0009] Furthermore, in step seven, the displacement monitoring nodes are located on both sides of the center of the initial crack, and the line connecting the displacement monitoring nodes on both sides is perpendicular to the tangent of the initial crack. The distance between the nodes on both sides is 8~10mm.

[0010] Furthermore, the displacements of the displacement differences are all radial displacements, that is, displacements perpendicular to the axial load direction.

[0011] Furthermore, the average fluctuation amplitude of the displacement difference is defined as the average value of the fluctuation amplitude of the displacement difference between the two displacement monitoring nodes on both sides of the initial crack in the rock per unit time. It is used to quantify the change and fluctuation characteristics of the displacement difference-time curve. The larger the value, the more intense the localized differential deformation in the area where the initial crack is located, and the stronger the crack expansion.

[0012] Furthermore, the formula for calculating the average fluctuation amplitude of the displacement difference is as follows: Where Rt represents the average fluctuation amplitude of the displacement difference between the two sides of the initial crack at time t, n is the number of frames captured by the image acquisition and analysis system per unit time, and Δx i+1 With Δx i These represent the radial displacement difference between the monitoring nodes on both sides of the initial crack recorded in the (i+1)th frame and the ith frame at time t.

[0013] Furthermore, the image acquisition and analysis system is a 3D-DIC system.

[0014] The beneficial effects of this invention are as follows: On the one hand, this invention uses a digital image acquisition and analysis system to capture and analyze the full-field deformation of rocks, enabling precise location of the initial crack area. On the other hand, by analyzing the localized deformation characteristics of the sample, this invention introduces the average fluctuation amplitude of displacement difference as a quantitative parameter to characterize the degree of localized differential deformation of rocks, and determines the rock crack initiation strength threshold based on the fluctuation law of localized displacement difference, thus alleviating the problems of strong subjectivity and large error in determining the crack initiation strength threshold in traditional technical solutions. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention; Figure 2 For the preparation of standard rock samples containing speckled inclusions; Figure 3 Layout diagram of displacement monitoring nodes; Figure 4 The displacement difference-time curve of the sample displacement monitoring node; Figure 5 The graphs show the average fluctuation range of displacement difference over time and the axial stress over time. Detailed Implementation

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] The first step involved testing the rock, identifying it as sandy mudstone. The rock was then processed using a wire cutter into standard cylindrical specimens with a diameter of 50 mm, a height of 100 mm, and a surface flatness within ±0.05 mm. Before the test, the specimens were painted to create a white-based, black-spotted sandy mudstone speckled specimen. Figure 2 As shown.

[0018] The second step involves placing the test sample on a pressure testing machine and applying a preload of 100KN to compress it. Then, a digital image acquisition and analysis system is set up, the camera angle and light source intensity are adjusted, and the instrument is calibrated using a calibration plate to ensure that the digital image acquisition system can acquire clear images of the sample. The digital image acquisition and analysis system is a 3D-DIC system.

[0019] The third step involves conducting a uniaxial compression test. An external axial load is applied while image acquisition is performed. Loading and image acquisition cease once the standard specimen fails. The loading method is displacement control, with a loading rate set to 0.1 mm / min and an image acquisition rate set to 5 frames / s.

[0020] The fourth step involves locating the initial crack position based on high-speed camera images of the specimen's failure morphology captured by the digital image acquisition system. Subsequently, displacement monitoring nodes are placed on both sides of the initial crack. The line connecting the displacement monitoring nodes on both sides of the initial crack is perpendicular to the tangent of the initial crack, and the distance between the nodes is 8 mm. The detailed node placement is shown in the figure below. Figure 3 As shown.

[0021] Fifth, the rock exhibits the Poisson effect, generating tensile stress within it while bearing axial loads. Since the tensile strength of the rock is much lower than its compressive strength, the initial failure of the sample is primarily tensile failure. Therefore, based on the evolution data of the radial displacement difference on both sides of the initial crack, a displacement difference-time curve for the displacement monitoring nodes is plotted, as shown below. Figure 4 As shown.

[0022] Step 6: Calculate the average fluctuation range of the displacement difference on both sides of the initial crack in the specimen. The calculation formula is as follows: Where Rt represents the average fluctuation amplitude of the displacement difference between the two sides of the initial crack at time t, n is the number of frames captured by the image acquisition and analysis system per unit time, which is taken as 5, and Δx i+1 With Δx i These represent the radial displacement difference between the monitoring nodes on both sides of the initial crack recorded in the (i+1)th frame and the ith frame at time t.

[0023] Step 7: Plot the axial stress-time curve and the average fluctuation amplitude of displacement difference-time curve on the same horizontal axis, as shown below. Figure 5 As shown, after the initial crack initiation, the average fluctuation amplitude of the displacement difference increases rapidly. The inflection point of the sudden increase in the average fluctuation amplitude of the displacement difference-time curve is located, and the corresponding rock stress intensity is obtained. The crack initiation strength threshold of this sample is found to be 31.26 MPa.

[0024] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. 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 present invention shall still fall within the scope of the present invention.

Claims

1. A method for determining the rock crack initiation strength threshold based on localized displacement difference fluctuations, characterized in that: Includes the following steps: The first step is to prepare samples from the rock mass to be tested and process them into standard samples. The second step is to spray black and white matte paint onto the surface of the standard rock sample to create a speckled sample with a white background and black spots. The third step is to place the speckled specimen on a pressure testing machine and apply prestress to compress it; The fourth step is to set up the digital image acquisition and analysis system, adjust the camera angle and light source intensity, and use a calibration plate to calibrate the instrument to ensure that the digital image acquisition and analysis system can acquire clear sample photos. The fifth step is to carry out a uniaxial compression test at a preset loading rate. While applying axial stress, the digital image acquisition and analysis system is turned on to record the full-field deformation of the sample surface. After the standard sample is destroyed, loading and image acquisition are stopped. The sixth step is to plot the axial stress-time curve based on the uniaxial compression deformation data of the specimen. Step 7: Based on the high-speed camera photos of the specimen failure morphology taken by the digital image acquisition and analysis system, locate the initial crack position of the specimen, and set up displacement monitoring nodes on both sides of the initial crack. Use the image analysis module of the digital image acquisition and analysis system to record the displacement difference data at the displacement monitoring nodes on both sides of the initial crack of the specimen during the entire experiment. The displacement monitoring nodes are located on both sides of the middle of the initial crack, and the line connecting the displacement monitoring nodes on both sides is perpendicular to the tangent of the initial crack. The distance between the nodes on both sides is 8~10mm. Step 8: Based on the displacement difference data on both sides of the initial crack recorded by the image acquisition and analysis system, plot the displacement difference-time variation curve of the displacement monitoring nodes on both sides of the initial crack. The ninth step is to analyze the displacement difference-time variation curve, define and calculate the average fluctuation amplitude of the displacement difference on both sides of the initial crack in the rock, and plot the average fluctuation amplitude of the displacement difference-time curve. The stress value at the moment corresponding to the sudden increase in the average fluctuation amplitude of the displacement difference-time curve is the determined crack initiation strength threshold of the rock. The displacements of the displacement differences are all radial displacements, that is, displacements perpendicular to the axial load direction; The average fluctuation amplitude of the displacement difference is defined as the average value of the fluctuation amplitude of the displacement difference between the two displacement monitoring nodes on both sides of the initial crack in the rock per unit time. It is used to quantify the change and fluctuation characteristics of the displacement difference-time curve. The larger the value, the more intense the localized differential deformation in the area where the initial crack is located, and the stronger the crack expansion. The formula for calculating the average fluctuation amplitude of the displacement difference is: Where Rt represents the average fluctuation amplitude of the displacement difference between the two sides of the initial crack at time t, n is the number of frames captured by the image acquisition and analysis system per unit time, and Δx i+1 With Δx i These represent the radial displacement difference between the monitoring nodes on both sides of the initial crack recorded in the (i+1)th frame and the ith frame at time t.

2. The method for determining the rock crack initiation strength threshold based on localized displacement difference fluctuation as described in claim 1, characterized in that: The prestress mentioned in the third step is 100 kN.

3. The method for determining the rock crack initiation strength threshold based on localized displacement difference fluctuation as described in claim 1, characterized in that: The loading method for the uniaxial compression experiment described in step 5 is displacement control, with a loading rate of 0.1 mm / min and an image acquisition rate of 5 frames / s.

4. The method for determining the rock crack initiation strength threshold based on localized displacement difference fluctuation as described in claim 1, characterized in that: The image acquisition and analysis system is a 3D-DIC system.

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