Rock uniaxial compression damage threshold determination method based on heavy mark range analysis

Abstract

The invention provides a rock uniaxial compression damage threshold determination method based on remarking range analysis, and the method comprises the steps: synchronously collecting rock acoustic emission signals in the process of carrying out a uniaxial compression test on rock, and obtaining a rock acoustic emission signal time sequence; analyzing the rock acoustic emission signal time sequence to obtain a Hurst index time sequence; the Hurst index time sequence is subjected to fitting, and a Hurst index change curve is obtained; the peak point of the Hurst index change curve is determined, and the rock loading stress corresponding to the peak point during the uniaxial compression test is the determined rock uniaxial compression damage threshold value. According to the method for determining the rock uniaxial compression damage threshold value based on the remarking range analysis, provided by the invention, through experimental verification, the determination precision of the rock damage threshold value can be improved, so that the requirements of high-precision application occasions are met.

Description

Technical Field

[0001] The invention belongs to the technical field of rock damage threshold determination, and specifically relates to a method for determining a rock uniaxial compression damage threshold based on recalibrated range analysis. Background Art

[0002] The rock damage threshold is the stress corresponding to the initial point where the rock begins to be damaged when loaded. Specifically, when the rock reaches the damage threshold, the internal microcracks accelerate and develop through the rock, and the rock enters the damage stage from the damage stage. At this time, the stress borne by the rock is the damage stress, that is, the rock damage threshold. The rock is subjected to stress during the rock damage stage, which is a key stage in the entire process of rock damage. Studying the rock damage threshold is of great significance to studying the entire process of rock damage.

[0003] Existing methods for determining rock damage thresholds generally have limited accuracy and cannot meet the requirements of high-precision applications. Summary of the invention

[0004] In view of the defects of the prior art, the present invention provides a method for determining the uniaxial compression damage threshold of rock based on recalibrated range analysis, which can effectively solve the above problems.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] The present invention provides a method for determining a rock uniaxial compression damage threshold based on rescaled range analysis, comprising the following steps:

[0007] Step S1, during a uniaxial compression test on rock, synchronously collecting rock acoustic emission signals to obtain a rock acoustic emission signal time series;

[0008] Step S2, analyzing the rock acoustic emission signal time series to obtain a Hurst exponent time series;

[0009] Step S3, fitting the Hurst exponent time series to obtain a Hurst exponent change curve;

[0010] Step S4, determining the peak point of the Hurst exponent variation curve, the rock loading stress during the uniaxial compression test corresponding to the peak point is the determined rock uniaxial compression damage threshold.

[0011] Preferably, in step S1, the rock acoustic emission signal is one or more of energy rate, cumulative energy, count rate and cumulative count.

[0012] Preferably, step S2 specifically comprises:

[0013] Step S2.1, the rock acoustic emission signal time series is expressed as: x = {x i}, i = 1, 2, ..., N; where: N is the number of rock acoustic emission signals in the rock acoustic emission signal time series; for the i-th rock acoustic emission signal x i , whose sampling time is t i ;

[0014] Step S2.2, setting a value set of the subsequence length n; wherein the subsequence length n is set to have a total of z values;

[0015] Step S2.3, for sampling time t i , the corresponding Hurst index H is obtained by the following method i :

[0016] Step S2.3.1, traverse the value set of subsequence length n; for each subsequence length n, execute steps S2.3.2 to S2.3.4;

[0017] Step S2.3.2, obtain sampling time t1 to sampling time t i The time series of rock acoustic emission signals within a certain time length is expressed as: [1-i] ={x1,…,x i};

[0018] Step S2.3.3: convert the rock acoustic emission signal time series x of length i into [1-i] , divided into M subsequences of length n, represented as: X1, X2, …, X M ;

[0019] For the subsequence X m , m=1,2,…,M, perform the following operations:

[0020] ①For subsequence X m , m=1,2,…,M, using formula (1), we can get the average value

[0021]

[0022] in:

[0023] x j,m Represents the subsequence X m The j-th rock acoustic emission signal in , j = 1, 2, ..., n;

[0024] ②For subsequence X m , m=1,2,…,M, using formula (2), we can get its standard deviation S m :

[0025]

[0026] ③For subsequence X m , using formula (3), we can get the j-th rock acoustic emission signal x j,m The corresponding cumulative deviation Y j,m :

[0027]

[0028] Where: x k,m Represents the subsequence X m The kth rock acoustic emission signal in , k = 1, 2, …, j;

[0029] This gives the subsequence X m The corresponding cumulative deviation time series Y m = {Y 1,m ,Y 2,m ,…,Y n,m};

[0030] Using formula (4), we get the subsequence X m The maximum deviation R m :

[0031] R m =max{Y 1,m ,Y 2,m ,…,Y n,m}-min{Y 1,m ,Y 2,m ,…,Y n,m} (4)

[0032] ④ Using formula (5), we get the subsequence X m Range (R / S) m :

[0033]

[0034] Step S2.3.4, therefore, for each subsequence X m , m=1,2,…,M, the corresponding range (R / S) is obtained m ; Using formula (6), we can get the average re-standardized range (R / S) of the current subsequence length n. n :

[0035]

[0036] Step S2.3.4, therefore, since the subsequence length n is set with z values, a total of z average re-scaled range values ​​(R / S) are obtained. n ;

[0037] The average rescaled range (R / S) is obtained from this n and the fitting curve of subsequence length n;

[0038] According to the fitting curve, the average rescaled range (R / S) shown in formula (7) is obtained: n The scaling relationship with the subsequence length n is:

[0039] (R / S) n =C×n H (7)

[0040] Where: C is the constant term of the function, H is the slope of the function, and is the fitting coefficient, which can be directly determined by fitting the curve;

[0041] Step S2.3.5, using formula (8), the average rescaled range (R / S) is obtained n Perform double logarithmic regression on n, and the slope of the function H is obtained, which is the sampling time t i The corresponding Hurst index H i ;

[0042] log(R / S) n =log(C)+Hlog(n) (8)

[0043] Step S2.4, if i=N, execute step S2.5; otherwise, set i=i+1 and return to step S2.3;

[0044] Step S2.5, therefore, for the rock acoustic emission signal time series x = {x i}, i = 1, 2, ..., N, the corresponding Hurst index at each sampling time is obtained, so that the Hurst index time series H = {H i},i=1,2,…,N.

[0045] The method for determining the rock uniaxial compression damage threshold based on re-calibrated range analysis provided by the present invention has the following advantages:

[0046] The rock uniaxial compression damage threshold determination method based on re-calibrated range analysis provided by the present invention has been verified by experiments to be able to improve the determination accuracy of the rock damage threshold, thereby meeting the requirements of high-precision application occasions. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A schematic flow chart of a method for determining a rock uniaxial compression damage threshold based on rescaled range analysis provided by the present invention;

[0048] Figure 2The test result diagram of the stress change curve LINE1, the energy change line LINE2 and the Hurst exponent change curve LINE3 based on the energy rate provided in the embodiment of the present invention. DETAILED DESCRIPTION

[0049] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0050] The present invention provides a method for determining the uniaxial compression damage threshold of rock based on rescaled range analysis. Acoustic emission monitoring is performed while performing a uniaxial compression test on the rock to obtain a time series of acoustic emission signals. The time series of acoustic emission signals can accurately reflect the through-development process of microcracks inside the rock during the rock loading process. Therefore, by analyzing the time series of acoustic emission signals, characteristic points at which the rock reaches the damage threshold and enters the damage stress stage can be obtained, thereby determining the damage threshold of the rock.

[0051] Furthermore, the present invention proposes a method for analyzing the time series of acoustic emission signals using a rescaled range analysis method, performing a rescaled range analysis on the time series of rock acoustic emission signals to obtain the Hurst index of the rock at different sampling times, and then obtaining a temporal variation curve of the Hurst index. The stress corresponding to the peak point of the Hurst index curve is the determined uniaxial compression damage threshold of the rock.

[0052] The rock uniaxial compression damage threshold determination method based on re-calibrated range analysis provided by the present invention has been verified by experiments to be able to improve the determination accuracy of the rock damage threshold, thereby meeting the requirements of high-precision applications.

[0053] See also Figure 1 The present invention provides a method for determining the rock uniaxial compression damage threshold based on rescaled range analysis, comprising the following steps:

[0054] Step S1, during a uniaxial compression test on rock, using an acoustic emission monitoring instrument to synchronously collect rock acoustic emission signals to obtain a rock acoustic emission signal time series;

[0055] In this step, the rock acoustic emission signal is one or more of energy rate, cumulative energy, count rate and cumulative count.

[0056] Step S2, analyzing the rock acoustic emission signal time series to obtain a Hurst exponent time series;

[0057] Step S3, fitting the Hurst exponent time series to obtain a Hurst exponent change curve;

[0058] Step S4, determining the peak point of the Hurst exponent variation curve, the rock loading stress during the uniaxial compression test corresponding to the peak point is the determined rock uniaxial compression damage threshold.

[0059] Specifically, the penetration and development of microcracks inside the rock determines the ultimate damage and destruction of the rock, that is, the penetration and development of microscopic fine cracks leads to the loss of macroscopic rock strength, and ultimately leads to the destruction of the rock. Therefore, by statistically analyzing the microcracks inside the rock and obtaining their changing laws in the time series, the characteristics of the rock at different stress stages can be analyzed. The phenomenon of changes in the internal stress of the material, rapid release of energy and generation of elastic waves is called acoustic emission. By using acoustic emission detection technology to monitor rocks, the energy changes inside the stressed rock can be expressed in the form of electrical signals. Further analysis of the changes in parameters such as energy and counts in the rock in the time series can obtain the generation, development and penetration of microcracks inside the rock, and then the uniaxial compression damage threshold of the rock can be determined.

[0060] In the present invention, a method for determining the uniaxial compression damage threshold of rock based on rescaled range analysis is provided. In particular, for step S2, the time series of the rock acoustic emission signal is analyzed to obtain the Hurst exponent time series, which is specifically:

[0061] Step S2.1, the rock acoustic emission signal time series is expressed as: x = {x i}, i = 1, 2, ..., N; where: N is the number of rock acoustic emission signals in the rock acoustic emission signal time series; for the i-th rock acoustic emission signal x i , whose sampling time is t i ;

[0062] Step S2.2, setting a value set of the subsequence length n; wherein the subsequence length n is set to have a total of z values;

[0063] Step S2.3, for sampling time t i , the corresponding Hurst index H is obtained by the following method i :

[0064] Step S2.3.1, traverse the value set of subsequence length n; for each subsequence length n, execute steps S2.3.2 to S2.3.4;

[0065] Step S2.3.2, obtain sampling time t1 to sampling time t i The time series of rock acoustic emission signals within a certain time length is expressed as: [1-i] ={x1,…,x i};

[0066] Step S2.3.3: convert the rock acoustic emission signal time series x of length i into [1-i] , divided into M subsequences of length n, represented as: X1, X2, …, X M ;

[0067] For the subsequence X m , m=1,2,…,M, perform the following operations:

[0068] ①For subsequence X m , m=1,2,…,M, using formula (1), we can get the average value

[0069]

[0070] in:

[0071] x j,m Represents the subsequence X m The j-th rock acoustic emission signal in , j = 1, 2, ..., n;

[0072] ②For subsequence X m , m=1,2,…,M, using formula (2), we can get its standard deviation S m :

[0073]

[0074] ③For subsequence X m , using formula (3), we can get the j-th rock acoustic emission signal x j,m The corresponding cumulative deviation Y j,m :

[0075]

[0076] Where: x k,m Represents the subsequence X m The kth rock acoustic emission signal in , k = 1, 2, …, j;

[0077] This gives the subsequence X m The corresponding cumulative deviation time series Y m = {Y 1,m ,Y 2,m ,…,Y n,m};

[0078] Using formula (4), we get the subsequence X m The maximum deviation R m :

[0079] R m =max{Y 1,m ,Y2,m ,…,Y n,m}-min{Y 1,m ,Y 2,m ,…,Y n,m} (4)

[0080] ④ Using formula (5), we get the subsequence X m Range (R / S) m :

[0081]

[0082] Step S2.3.4, therefore, for each subsequence X m , m=1,2,…,M, the corresponding range (R / S) is obtained m ; Using formula (6), we can get the average re-standardized range (R / S) of the current subsequence length n. n :

[0083]

[0084] Step S2.3.4, therefore, since the subsequence length n is set with z values, a total of z average re-scaled range values ​​(R / S) are obtained. n ;

[0085] The average rescaled range (R / S) is obtained from this n and the fitting curve of subsequence length n;

[0086] According to the fitting curve, the average rescaled range (R / S) shown in formula (7) is obtained: n The scaling relationship with the subsequence length n is:

[0087] (R / S) n =C×n H (7)

[0088] Where: C is the constant term of the function, H is the slope of the function, and is the fitting coefficient, which can be directly determined by fitting the curve;

[0089] Step S2.3.5, using formula (8), the average rescaled range (R / S) is obtained n Perform double logarithmic regression on n, and the slope of the function H is obtained, which is the sampling time t i The corresponding Hurst index H i ;

[0090] log(R / S) n =log(C)+Hlog(n) (8)

[0091] Step S2.4, if i=N, execute step S2.5; otherwise, set i=i+1 and return to step S2.3;

[0092] Step S2.5, therefore, for the rock acoustic emission signal time series x = {x i}, i = 1, 2, ..., N, the corresponding Hurst index at each sampling time is obtained, so that the Hurst index time series H = {H i}, i = 1, 2, ..., N. According to the present invention, the range of the Hurst index is (0, 1).

[0093] When the rock reaches the damage threshold during loading and enters the damage stage, the internal microcracks expand and penetrate until they are destroyed. Therefore, the present invention selects the rock loading stress point corresponding to the peak point of the Hurst index with the strongest long-term memory as the rock damage threshold.

[0094] The effect of a method for determining the rock uniaxial compression damage threshold based on re-calibrated range analysis provided by the present invention is verified as follows:

[0095] Reference method:

[0096] Taking the CVS method, which is currently the most commonly used method for determining rock damage threshold, as a reference, the CVS method determines the rock damage threshold in the following way:

[0097] The CVS method assumes that the crack volume strain remains unchanged in the linear elastic stage, so the starting point and end point of the flat section of the crack volume strain curve correspond to the closing stress and the crack initiation stress respectively. When the volume strain has an inflection point, it means that the rock changes from compression deformation to expansion deformation, that is, the peak point of the volume strain corresponds to the damage stress. Therefore, the damage threshold of the rock can be determined by the CVS method.

[0098] The crack volume strain calculation formula is as follows:

[0099] ε vc =ε v -ε ve

[0100] ε v =ε1+2ε3

[0101]

[0102] Where: vc , ε v and ε ve Volume strain, crack volume strain and elastic volume strain; ε1 and ε3 are axial and hoop strains, respectively; σ1 is axial stress, in MPa; E is elastic modulus, in GPa; μ is Poisson's ratio.

[0103] Test method:

[0104] 1. Carry out uniaxial compression test on granite. After the test, obtain its stress change curve LINE1 and energy change line LINE2;

[0105] By adopting the damage threshold determination method of the present invention, the energy rate of the rock acoustic emission signal is selected to obtain the Hurst exponent change curve LINE3 based on the energy rate.

[0106] Analysis of test results:

[0107] like Figure 2 Shown are test result diagrams of stress change curve LINE1, energy change line LINE2 and Hurst exponent change curve LINE3 based on energy rate.

[0108] right Figure 2 After analysis, we can draw the following conclusions:

[0109] Analyzing the stress variation curve LINE1, its stress peak point appears at point D (868, 142), that is, the stress peak appears at 868 seconds, and the value of the stress peak is 142 MPa.

[0110] The analysis of the Hurst exponent change curve LINE3 based on the energy rate shows that the peak value of the Hurst exponent appears at point A (737, 0.8961), that is, the peak value of the Hurst exponent appears at 737 seconds, and the value of the peak value of the Hurst exponent is 0.8961. It corresponds to point C (737, 115) on the stress change curve LINE1, that is, the damage threshold is determined to be 115MPa, which appears at 737 seconds.

[0111] The damage threshold position point determined by the traditional CVS method is point B (687, 104), that is, the damage threshold is determined to be 104 MPa, which occurs at 687 seconds.

[0112] By analyzing the energy change line LINE2, it can be determined that the starting point of its energy mutation is 842 seconds.

[0113] It can be seen that compared with the damage threshold determined by the traditional CVS method, the damage threshold determined by the present invention is 115MPa, which is closer to the stress peak value of 142MPa, and the occurrence time of the damage threshold determined by the present invention is 737 seconds, which is closer to the starting point of the energy mutation of 842 seconds. Therefore, the damage threshold determined by the present invention has better accuracy than the traditional CVS method.

[0114] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be considered as the scope of protection of the present invention.

Claims

1. A method for determining the uniaxial compression damage threshold of rock based on rescaled range analysis, characterized in that: The following steps are involved: Step S1, during a uniaxial compression test on rock, synchronously collecting rock acoustic emission signals to obtain a rock acoustic emission signal time series; Step S2, analyzing the rock acoustic emission signal time series to obtain a Hurst exponent time series; Step S3, fitting the Hurst exponent time series to obtain a Hurst exponent change curve; Step S4, determining the peak point of the Hurst exponent variation curve, the rock loading stress during the uniaxial compression test corresponding to the peak point is the determined rock uniaxial compression damage threshold.

2. The method for determining the rock uniaxial compression damage threshold based on rescaled range analysis according to claim 1 is characterized in that: In step S1, the rock acoustic emission signal is one or more of energy rate, cumulative energy, count rate and cumulative count.

3. The method for determining the rock uniaxial compression damage threshold based on rescaled range analysis according to claim 1 is characterized in that: Step S2 is specifically as follows: Step S2.1, the rock acoustic emission signal time series is expressed as: x = {x i }, i = 1, 2, ..., N; where: N is the number of rock acoustic emission signals in the rock acoustic emission signal time series; for the i-th rock acoustic emission signal x i , whose sampling time is t i ; Step S2.2, setting a value set of the subsequence length n; wherein the subsequence length n is set to have a total of z values; Step S2.3, for sampling time t i , the corresponding Hurst index H is obtained by the following method i : Step S2.3.1, traverse the value set of subsequence length n; for each subsequence length n, execute steps S2.3.2 to S2.3.4; Step S2.3.2, obtain sampling time t1 to sampling time t i The time series of rock acoustic emission signals within a certain time length is expressed as: [1-i] ={x1,…,x i }; Step S2.3.3: convert the rock acoustic emission signal time series x of length i into [1-i] , divided into M subsequences of length n, represented as: X1, X2, …, X M ; For the subsequence X m , m=1,2,…,M, perform the following operations: ①For subsequence X m , m=1,2,…,M, using formula (1), we can get the average value in: x j,m Represents the subsequence X m The j-th rock acoustic emission signal in , j = 1, 2, ..., n; ②For subsequence X m , m=1,2,…,M, using formula (2), we can get its standard deviation S m : ③For subsequence X m , using formula (3), we can get the j-th rock acoustic emission signal x j,m The corresponding cumulative deviation Y j,m : Where: x k,m Represents the subsequence X m The kth rock acoustic emission signal in , k = 1, 2, …, j; This gives the subsequence X m The corresponding cumulative deviation time series Y m = {Y 1,m ,Y 2,m ,…,Y n,m }; Using formula (4), we get the subsequence X m The maximum deviation R m : R m =max{Y 1,m ,AND 2,m ,…,AND n,m }-min{And 1,m ,AND 2,m ,…,AND n,m } (4) ④ Using formula (5), we get the subsequence X m Range (R / S) m : Step S2.3.4, therefore, for each subsequence X m , m=1,2,…,M, the corresponding range (R / S) is obtained m ; Using formula (6), we can get the average re-standardized range (R / S) of the current subsequence length n. n : Step S2.3.4, therefore, since the subsequence length n is set with z values, a total of z average re-scaled range values ​​(R / S) are obtained. n ; The average rescaled range (R / S) is obtained from this n and the fitting curve of subsequence length n; According to the fitting curve, the average rescaled range (R / S) shown in formula (7) is obtained: n The scaling relationship with the subsequence length n is: (R / S) n =C×n H (7) Where: C is the constant term of the function, H is the slope of the function, and is the fitting coefficient, which can be directly determined by fitting the curve; Step S2.3.5, using formula (8), the average rescaled range (R / S) is obtained n Perform double logarithmic regression on n, and the slope of the function H is obtained, which is the sampling time t i The corresponding Hurst index H i ; log(R / S) n =log(C)+Hlog(n) (8) Step S2.4, if i=N, execute step S2.5; otherwise, set i=i+1 and return to step S2.3; Step S2.5, therefore, for the rock acoustic emission signal time series x = {x i }, i = 1, 2, ..., N, the corresponding Hurst index at each sampling time is obtained, so that the Hurst index time series H = {H i },i=1,2,…,N.

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