Method for determining crack initiation and damage stress threshold of brittle rock crack

Abstract

The invention discloses a method for determining crack initiation and damage stress thresholds of brittle rock cracks, which comprises the following steps: carrying out a rock conventional uniaxial / triaxial compression test to obtain rock axial stress and axial strain test data; drawing an axial stress-axial strain relation curve of the rock, and calculating the elastic modulus of the rock; calculating the axial strain of the rock crack; drawing a rock crack axial strain-axial strain relation curve; determining a crack initiation point according to the slope change of the crack axial strain-axial strain curve; a reference line is added, the difference value between the reference line and the corresponding point of the crack axial strain curve is calculated, and the position with the maximum difference value is the crack damage point. According to the method, the two characteristic stresses of the brittle rock can be quickly and accurately predicted, and a basis can be provided for design and optimization of surrounding rock support parameters of deep underground engineering.

Description

Technical Field

[0001] The present invention relates to a method for determining a stress threshold of crack initiation and damage in brittle rock, belonging to the technical field of deep underground engineering disaster prevention and control, and in particular to a method for determining a stress threshold of crack initiation and damage in brittle rock based on an axial strain-axial strain relationship curve of a rock crack. Background Art

[0002] In order to meet the needs of social development, deep underground projects such as deep tunnels, deep water diversion tunnels, and deep high-level radioactive waste storage have developed rapidly. These underground projects are mainly built in hard rock environments. Indoor tests have shown that hard rock is extremely brittle, and its deformation and failure are closely related to the expansion of its internal cracks. The deformation and failure process of brittle rock under compression can be divided into the crack closure stage, elastic stage, stable crack expansion stage, unstable crack expansion stage, and post-peak stage. The turning point stress between the elastic stage and the stable crack expansion stage is called the crack initiation stress, and the turning point stress between the stable crack expansion stage and the unstable crack expansion stage is called the crack damage stress. Rapidly and accurately predicting these two characteristic stresses of brittle rock is of great guiding significance for optimizing the support design of deep underground projects and maintaining the stability of their surrounding rocks.

[0003] At present, the main methods for determining the crack initiation and damage stress threshold of brittle rock are the crack volume strain method and the acoustic emission characteristic parameter method. The former not only requires measuring the axial deformation of the rock, but also uses a circumferential extensometer to measure its circumferential deformation, and then calculates its volume strain, and finally obtains its crack volume strain; the latter requires at least two acoustic emission probes to be installed on the rock surface in advance, and the acoustic emission signal is output through a dedicated acoustic emission demodulator. It can be seen that the above two methods require special instruments and equipment, have high requirements on laboratory hardware, and the process of obtaining the characteristic stress of brittle rock is relatively complicated. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for determining the crack initiation and damage stress threshold of brittle rock cracks. Based on the rock crack axial strain-axial strain relationship curve, a conventional single triaxial compression test of the rock is first carried out, and then the crack axial strain is calculated. Finally, the rock characteristic stress can be determined from the crack axial strain and axial strain relationship curve.

[0005] In order to solve the above technical problems, the technical solution of the present invention is: a method for determining the crack initiation and damage stress threshold of brittle rock, the innovation of which is that it includes the following steps:

[0006] S1. Carry out uniaxial and triaxial compression tests on brittle rocks to obtain rock axial stress and axial strain test data;

[0007] S2. Draw the rock axial stress-axial strain relationship curve and calculate the rock elastic modulus;

[0008] S3, calculate the axial strain of rock crack;

[0009] S4. Draw the relationship curve between axial strain and axial strain of rock crack;

[0010] S5. determining the crack initiation point according to the change in the slope of the crack axial strain-axial strain curve;

[0011] S6. Add a reference line and calculate the difference between the reference line and the corresponding point of the crack axial strain curve. The point with the largest difference is the crack damage point.

[0012] Preferably, in S1, the rock is cylindrical with dimensions of 50 mm in diameter and 100 mm in height.

[0013] Preferably, in S1, the uniaxial triaxial compression test adopts displacement control or stress control, and the loading rate is controlled so that the rock is in a quasi-static loading state.

[0014] Preferably, in S2, the elastic modulus is the ratio of the stress increment to the strain increment in the linear growth segment of the rock axial stress-axial strain curve.

[0015] Preferably, in S3, the calculation formula for the crack axial strain is:

[0016]

[0017] In the formula, is the axial strain of the crack; ε1 is the axial strain; σ1 is the maximum principal stress; σ3 is the minimum principal stress; E is the elastic modulus.

[0018] Preferably, in S4, the crack axial strain-axial strain relationship curve and the axial stress-axial strain relationship curve in S2 are plotted in the same figure, with the same abscissa and different ordinates.

[0019] Preferably, in S5, the specific process of determining the crack initiation point is:

[0020] Determination of the crack initiation point Under triaxial compression conditions of rock at low confining pressure, the changing trend of the crack axial strain-axial strain curve was observed, and it was found that the crack axial strain went through three stages with the increase of axial strain, firstly growing in a concave shape, then basically remaining unchanged, and finally growing in a concave shape; the slope of the crack axial strain-axial strain curve first gradually decreased from a positive value to 0, then maintained for a period of time, and finally the slope of the curve gradually increased from 0; the turning point where the slope of the curve began to increase from 0 was determined as the crack initiation point, and the axial stress corresponding to this point was the crack initiation stress.

[0021] Preferably, in S5, the crack initiation point is determined under triaxial compression conditions with high confining pressure on the rock. The axial strain of the crack goes through two stages as the axial strain increases, first remaining at 0 and then growing in a concave shape. The slope of the crack axial strain-axial strain curve first remains at 0 and then gradually increases. The turning point where the slope of the curve increases from 0 is determined as the crack initiation point, and the axial stress corresponding to this point is the crack initiation stress.

[0022] Preferably, in S6, the specific process of determining the crack damage point is:

[0023] On the crack axial strain-axial strain curve, a reference line is drawn by connecting the points corresponding to the crack initiation stress and the peak stress, and then the difference between the reference line and the ordinate at the corresponding abscissa on the curve is calculated. The point with the maximum difference is determined as the crack damage point, and the axial stress corresponding to this point is the crack damage stress.

[0024] The advantages of the present invention are that in the process of determining the crack initiation and damage stress threshold of brittle rock, the present invention only needs to measure the axial deformation of the rock, does not need to use other instruments to measure its circumferential deformation, and does not need to use acoustic emission equipment to obtain acoustic emission signals. The requirements for laboratory hardware are not high, and it can be completed in a general ordinary mechanics laboratory, and the calculation process is relatively simple. Therefore, the method for determining the crack initiation and damage stress threshold of brittle rock proposed by the present invention is simpler and has wider applicability.

[0025] Conduct conventional uniaxial and triaxial compression tests on rocks to obtain test data on axial stress and axial strain of rocks; draw the relationship curve between axial stress and axial strain of rocks and calculate the elastic modulus of rocks; calculate the axial strain of rock cracks; draw the relationship curve between axial strain and axial strain of rock cracks; determine the crack initiation point according to the change in the slope of the axial strain and axial strain curve of the cracks; add a reference line and calculate the difference between the reference line and the corresponding point of the axial strain curve of the cracks. The point with the largest difference is the crack damage point. The present invention can quickly and accurately predict the two characteristic stresses of brittle rocks and provide a basis for the design and optimization of surrounding rock support parameters for deep underground engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for describing the embodiments are briefly introduced below.

[0027] Figure 1 It is a schematic diagram of the overall process of a method for determining the crack initiation and damage stress threshold of brittle rock according to the present invention;

[0028] Figure 2It is a schematic diagram for determining the crack initiation point in a schematic diagram for determining the crack initiation and damage stress threshold of brittle coal rock at a confining pressure of 5 MPa in a method for determining the crack initiation and damage stress threshold of brittle rock of the present invention;

[0029] Figure 3 It is a schematic diagram for determining crack damage points in a schematic diagram for determining crack initiation and damage stress thresholds of brittle coal rock at a confining pressure of 5 MPa in a method for determining crack initiation and damage stress thresholds of brittle rock of the present invention;

[0030] Figure 4 This is a schematic diagram for determining the crack initiation point in a schematic diagram for determining the crack initiation and damage stress threshold of brittle coal rock at a confining pressure of 20 MPa in a method for determining the crack initiation and damage stress threshold of brittle rock of the present invention;

[0031] Figure 5 This is a schematic diagram for determining crack damage points in a schematic diagram for determining crack initiation and damage stress thresholds of brittle coal rock at a confining pressure of 20 MPa in a method for determining crack initiation and damage stress thresholds of brittle rock of the present invention. DETAILED DESCRIPTION

[0032] The method for determining the crack initiation and damage stress threshold of brittle rock in the present invention comprises the following steps:

[0033] S1. Carry out uniaxial and triaxial compression tests on brittle rocks to obtain rock axial stress and axial strain test data;

[0034] S2. Draw the rock axial stress-axial strain relationship curve and calculate the rock elastic modulus;

[0035] S3, calculate the axial strain of rock crack;

[0036] S4. Draw the relationship curve between axial strain and axial strain of rock crack;

[0037] S5. determining the crack initiation point according to the change in the slope of the crack axial strain-axial strain curve;

[0038] S6. Add a reference line and calculate the difference between the reference line and the corresponding point of the crack axial strain curve. The point with the largest difference is the crack damage point.

[0039] In the process of determining the crack initiation and damage stress threshold of brittle rock, the present invention only needs to measure the axial deformation of the rock, does not need to use other instruments to measure its circumferential deformation, and does not need to use acoustic emission equipment to obtain acoustic emission signals. The requirements for laboratory hardware are not high, and it can be completed in a general ordinary mechanics laboratory, and the calculation process is relatively simple. Therefore, the method for determining the crack initiation and damage stress threshold of brittle rock proposed by the present invention is simpler and has wider applicability.

[0040] Conduct conventional uniaxial and triaxial compression tests on rocks to obtain test data on axial stress and axial strain of rocks; draw the relationship curve between axial stress and axial strain of rocks and calculate the elastic modulus of rocks; calculate the axial strain of rock cracks; draw the relationship curve between axial strain and axial strain of rock cracks; determine the crack initiation point according to the change in the slope of the axial strain and axial strain curve of the cracks; add a reference line and calculate the difference between the reference line and the corresponding point of the axial strain curve of the cracks. The point with the largest difference is the crack damage point. The present invention can quickly and accurately predict the two characteristic stresses of brittle rocks and provide a basis for the design and optimization of surrounding rock support parameters for deep underground engineering.

[0041] Among them, the rock in S1 is cylindrical, with a diameter of 50 mm and a height of 100 mm. The uniaxial triaxial compression test adopts displacement control or stress control, and the loading rate should be controlled to make the rock in a quasi-static loading state. The elastic modulus in S2 is the ratio of the stress increment to the strain increment in the linear growth section of the rock axial stress-axial strain curve.

[0042] In S3, the calculation formula for the crack axial strain is:

[0043]

[0044] In the formula, is the axial strain of the crack; ε1 is the axial strain; σ1 is the maximum principal stress; σ3 is the minimum principal stress; E is the elastic modulus.

[0045] In S4, the crack axial strain-axial strain relationship curve and the axial stress-axial strain relationship curve in S2 are plotted in the same figure, with the same abscissa and different ordinates.

[0046] In S5, the specific process of determining the crack initiation point is as follows: the determination of the crack initiation point is to observe the change trend of the crack axial strain-axial strain curve under triaxial compression conditions with low confining pressure on the rock, and obtain that the crack axial strain goes through three stages with the increase of axial strain, firstly growing in a concave shape, then basically remaining unchanged, and finally growing in an upward concave shape; the slope of the crack axial strain-axial strain curve first gradually decreases from a positive value to 0, then maintains for a period of time, and finally the slope of the curve gradually increases from 0; the turning point where the slope of the curve starts to increase from 0 is determined as the crack initiation point, and the axial stress corresponding to this point is the crack initiation stress.

[0047] In S5, the determination of the crack initiation point is that under the triaxial compression condition of rock under high confining pressure, the axial strain of the crack goes through two stages with the increase of axial strain, first maintaining at 0, and then growing in a concave shape; the slope of the crack axial strain-axial strain curve first maintains at 0, and then gradually increases; the turning point where the slope of the curve starts to increase from 0 is determined as the crack initiation point, and the axial stress corresponding to this point is the crack initiation stress.

[0048] Confining pressure refers to the pressure exerted on a rock by the surrounding rock mass. The confining pressure of rocks deep underground is mainly caused by the weight of the overlying rocks and is often called static rock pressure. The confining pressure of crustal rocks increases with the increase of burial depth, and the two are generally linearly related.

[0049] Low confining pressure: refers to a smaller confining pressure value, usually caused by the weight of the overlying rock, but the pressure is smaller. High confining pressure: refers to a larger confining pressure value, also caused by the weight of the overlying rock, but the pressure is larger. The main difference between low confining pressure and high confining pressure lies in the size of the confining pressure and their impact on the strength and elastic-plastic characteristics of rock materials.

[0050] Under low confining pressure, the natural cracks inside the rock material are not completely closed, and the specimen is highly heterogeneous, resulting in a nonlinear growth in the stress-strain relationship at the initial stage of loading. Under high confining pressure, the natural cracks inside the rock specimen are basically completely closed before loading, and the specimen is highly homogeneous, so the stress-strain relationship at the initial stage of loading grows linearly, that is, it is elastic deformation.

[0051] In this application, different rock types correspond to different ranges of low and high confining pressures, and the ranges of low and high confining pressures are determined according to the rock type. For rocks with strong homogeneity and good integrity, there are only a small number of natural cracks inside, so a lower confining pressure can completely close the natural cracks inside before loading. For rocks with poor homogeneity and relatively broken rocks, there are a large number of natural cracks inside, so a higher confining pressure is required to completely close the natural cracks inside before loading.

[0052] In S6, the specific process of determining the crack damage point is as follows: on the crack axial strain-axial strain curve, a reference line is drawn by connecting the points corresponding to the crack initiation stress and the peak stress, and then the difference between the reference line and the ordinate at the corresponding abscissa on the curve is calculated, and the point with the maximum difference is determined as the crack damage point, and the axial stress corresponding to the point is the crack damage stress.

[0053] Example 1

[0054] The method for determining the crack initiation and damage stress threshold of brittle rock is as follows: Figure 1 This embodiment will introduce the specific content of each step in detail according to the step sequence of the method.

[0055] 1. Carry out conventional uniaxial and triaxial compression tests on brittle rocks to obtain rock axial stress and axial strain test data. In this embodiment, the experimental sample is brittle coal rock, which is processed into a cylindrical specimen with a size of φ50×100mm, a confining pressure of 5MPa, and an axial loading rate of 0.02mm / min.

[0056] 2. Draw the rock axial stress-axial strain relationship curve and calculate the rock elastic modulus. Since both stress thresholds occur in the pre-peak stage of rock deformation, this example only shows the axial stress-axial strain curve of brittle coal in the pre-peak stage, such as Figure 2 As shown in Figure 2, the elastic modulus of brittle coal rock is 4.22 GPa by calculating the ratio of stress increment to strain increment in the linear growth section of the stress-strain curve.

[0057] 3. Calculate the axial strain of the rock crack. The calculation formula for the axial strain of the crack in this embodiment is:

[0058]

[0059] In the formula, is the axial strain of the crack; ε1 is the axial strain; σ1 and σ3 are the maximum and minimum principal stresses respectively; E is the elastic modulus.

[0060] 4. Draw the rock crack axial strain-axial strain relationship curve. In this embodiment, the crack axial strain-axial strain relationship curve and the axial stress-axial strain relationship curve are drawn in the same figure, such as Figure 2 Shown in the middle curve DEAB.

[0061] 5. Determine the crack initiation point based on the change in the slope of the crack axial strain-axial strain curve. Figure 2 From the trend of the axial strain-axial strain curve of the medium crack, it can be seen that the axial strain of the crack goes through three stages with the increase of the axial strain, firstly it grows in a concave shape (DE segment), then it remains basically unchanged (EA segment), and finally it grows in a concave shape (AB segment). Therefore, the slope of the curve first gradually decreases from a positive value to 0, then it maintains for a period of time, and finally the slope of the curve gradually increases from 0. The turning point where the slope of the curve starts to increase from 0, that is, point A, is determined as the crack initiation point, and the axial stress corresponding to this point is the crack initiation stress.

[0062] 6. Add a reference line, calculate the difference between the reference line and the corresponding point of the crack axial strain curve, and the point with the largest difference is the crack damage point. Figure 2 Draw a reference line, i.e. line segment AB, at the points corresponding to the crack initiation stress and the peak stress on the axial strain-axial strain curve of the medium crack, and then calculate the difference between the line segment AB and the ordinate at the corresponding abscissa on the curve AB to obtain Figure 3 ,Will Figure 3 The point with the largest difference, i.e. point C, is determined as the crack damage point. Figure 2 The corresponding axial stress in is the crack damage stress.

[0063] Example 2

[0064] In Example 1, the confining pressure applied to the brittle rock is 5 MPa, which represents the method for determining the crack initiation and damage stress threshold of brittle rock under low confining pressure or uniaxial loading. For the case of higher confining pressure, the only difference is when determining the crack initiation point in step 5. The following takes the brittle coal rock under a confining pressure of 20 MPa as an example to introduce the specific content of each step in detail.

[0065] 1. Carry out conventional uniaxial and triaxial compression tests on brittle rocks to obtain rock axial stress and axial strain test data. In this embodiment, the experimental sample is brittle coal rock, which is processed into a cylindrical specimen with a size of φ50×100mm, a confining pressure of 20MPa, and an axial loading rate of 0.02mm / min.

[0066] 2. Draw the rock axial stress-axial strain relationship curve and calculate the rock elastic modulus. Since both stress thresholds occur in the pre-peak stage of rock deformation, this example only shows the axial stress-axial strain curve of brittle coal in the pre-peak stage, such as Figure 4 As shown in Figure 2, the elastic modulus of brittle coal rock is 5.38 GPa by calculating the ratio of stress increment to strain increment in the linear growth section of the stress-strain curve.

[0067] 3. Calculate the axial strain of the rock crack. The calculation formula for the axial strain of the crack in this embodiment is:

[0068]

[0069] In the formula, is the axial strain of the crack; ε1 is the axial strain; σ1 and σ3 are the maximum and minimum principal stresses respectively; E is the elastic modulus.

[0070] 4. Draw the rock crack axial strain-axial strain relationship curve. In this embodiment, the crack axial strain-axial strain relationship curve and the axial stress-axial strain relationship curve are drawn in the same figure, such as Figure 4 As shown in the middle curve EAB.

[0071] 5. Determine the crack initiation point based on the change in the slope of the crack axial strain-axial strain curve. Figure 4 From the change trend of the axial strain-axial strain curve of the medium crack, it can be seen that the axial strain of the crack only goes through two stages with the increase of the axial strain. First, it remains at 0 (EA segment), and then it grows concavely (AB segment). Therefore, the slope of the curve first remains at 0, and then gradually increases. The turning point where the slope of the curve increases from 0, that is, point A, is determined as the crack initiation point, and the axial stress corresponding to this point is the crack initiation stress.

[0072] 6. Add a reference line, calculate the difference between the reference line and the corresponding point of the crack axial strain curve, and the point with the largest difference is the crack damage point. Figure 4 Draw a reference line, i.e. line segment AB, at the points corresponding to the crack initiation stress and the peak stress on the axial strain-axial strain curve of the medium crack, and then calculate the difference between the line segment AB and the ordinate at the corresponding abscissa on the curve AB to obtain Figure 5 ,Will Figure 5 The point with the largest difference, i.e. point C, is determined as the crack damage point. Figure 4 The corresponding axial stress in is the crack damage stress.

[0073] It should be understood that the above description is for illustration and not for limitation. Many embodiments and many applications beyond the examples provided will be apparent to those skilled in the art upon reading the above description. Therefore, the scope of the present application should not be determined with reference to the above description, but should be determined with reference to the appended claims and the full scope of equivalents to which such claims are entitled. For the purpose of comprehensiveness, all articles and references, including disclosures of patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the preceding claims is not intended to be a waiver of the subject matter, nor should it be considered that the inventors did not consider the subject matter to be part of the disclosed inventive subject matter.

Claims

1. A method for determining the stress threshold of crack initiation and damage in brittle rock, characterized in that The steps include: S1. Carry out uniaxial and triaxial compression tests on brittle rocks to obtain rock axial stress and axial strain test data; S2. Draw the rock axial stress-axial strain relationship curve and calculate the rock elastic modulus; S3, calculate the axial strain of rock crack; S4. Draw the relationship curve between axial strain and axial strain of rock crack; S5. determining the crack initiation point according to the change in the slope of the crack axial strain-axial strain curve; S6. Add a reference line and calculate the difference between the reference line and the corresponding point of the crack axial strain curve. The point with the largest difference is the crack damage point.

2. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S1, the rock is cylindrical, with dimensions of 50 mm in diameter and 100 mm in height.

3. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S1, the uniaxial triaxial compression test adopts displacement control or stress control, and the loading rate is controlled so that the rock is in a quasi-static loading state.

4. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S2, the elastic modulus is the ratio of the stress increment to the strain increment in the linear growth section of the rock axial stress-axial strain curve.

5. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S3, the calculation formula of the crack axial strain is: In the formula, is the axial strain of the crack; ε1 is the axial strain; σ1 is the maximum principal stress; σ3 is the minimum principal stress; E is the elastic modulus.

6. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S4, the crack axial strain-axial strain relationship curve and the axial stress-axial strain relationship curve in S2 are plotted in the same figure, with the same abscissa and different ordinates.

7. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S5, the specific process of determining the crack initiation point is: Determination of the crack initiation point Under triaxial compression conditions of rock at low confining pressure, the changing trend of the crack axial strain-axial strain curve was observed, and it was found that the crack axial strain went through three stages with the increase of axial strain, firstly growing in a concave shape, then basically remaining unchanged, and finally growing in a concave shape; the slope of the crack axial strain-axial strain curve first gradually decreased from a positive value to 0, then maintained for a period of time, and finally the slope of the curve gradually increased from 0; the turning point where the slope of the curve began to increase from 0 was determined as the crack initiation point, and the axial stress corresponding to this point was the crack initiation stress.

8. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S5, the determination of the crack initiation point is that when the rock is under triaxial compression conditions with high confining pressure, the axial strain of the crack goes through two stages as the axial strain increases, first maintaining at 0 and then growing in a concave shape; the slope of the crack axial strain-axial strain curve first maintains at 0 and then gradually increases; the turning point where the slope of the curve starts to increase from 0 is determined as the crack initiation point, and the axial stress corresponding to this point is the crack initiation stress.

9. A method for determining crack initiation and damage stress thresholds of brittle rocks according to claim 1, characterized in that: In S6, the specific process of determining the crack damage point is: On the crack axial strain-axial strain curve, a reference line is drawn by connecting the points corresponding to the crack initiation stress and the peak stress, and then the difference between the reference line and the ordinate at the corresponding abscissa on the curve is calculated. The point with the maximum difference is determined as the crack damage point, and the axial stress corresponding to this point is the crack damage stress.

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