CN112444448A - Rock compression microcrack expansion directionality evaluation method based on cluster analysis and information source entropy principle - Google Patents

Rock compression microcrack expansion directionality evaluation method based on cluster analysis and information source entropy principle Download PDF

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CN112444448A
CN112444448A CN202011283254.0A CN202011283254A CN112444448A CN 112444448 A CN112444448 A CN 112444448A CN 202011283254 A CN202011283254 A CN 202011283254A CN 112444448 A CN112444448 A CN 112444448A
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张正虎
胡李华
马天辉
李迎春
唐世斌
唐春安
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Abstract

A rock compression microcrack expansion directionality evaluation method based on cluster analysis and an information source entropy principle belongs to the field of rock mechanics and geotechnical engineering. Firstly, real-time acoustic emission monitoring of the deformation and damage process of the rock under the action of compressive load is carried out, the spatial coordinate information of an acoustic emission event is obtained, and a single-key group structure of an acoustic emission event sequence is established. Secondly, solving a single bond dip angle representing the microcrack propagation direction. Thirdly, counting all single-key dip angles of the acoustic emission event sequences with the number of N, calculating the spatial correlation directivity index of the acoustic emission event sequences, and calculating the information source entropy of the single-key dip angles. And finally, with the advancement of the loading time, a new matrix is established for the next acoustic emission event sequence, the steps are repeated, the spatial correlation directivity index and the information source entropy H in the whole rock deformation damage process are calculated, and the rock microcrack expansion directivity is evaluated in real time. The method can realize quantitative evaluation of crack propagation directionality in the rock deformation destruction process, and is convenient to solve.

Description

Rock compression microcrack expansion directionality evaluation method based on cluster analysis and information source entropy principle
Technical Field
The invention belongs to the field of rock mechanics and geotechnical engineering, relates to an evaluation method for a crack propagation path of a rock under the action of a compressive load, and particularly relates to an evaluation index and method suitable for the propagation directionality of a rock compressive microcrack.
Background
In tunnel excavation, mineral resource exploitation, water conservancy and hydropower engineering construction, the stability of surrounding rocks is of great importance. Rock destruction can lead to a series of geological disasters, such as rock burst, collapse and landslide. These disasters not only severely threaten engineering safety and service life, but also endanger the life safety of employees. Compared with artificial engineering materials such as concrete, cement mortar and the like, the rock is a typical heterogeneous and anisotropic natural geological material, and the damage evolution process is complex and difficult to predict. The initiation, expansion and accumulation of microcracks in the rock under the action of external load finally result in the macroscopic destruction of the rock. Therefore, the research on the expansion rule of the microcracks of the rocks under the action of external loads has important significance for understanding and predicting geological disasters related to rock fracture.
Quantitative investigation of rock fractures, particularly microcracks, is generally more difficult to achieve. As a passive non-destructive inspection method, acoustic emission techniques have been widely used to evaluate the rock micro-fracturing process. Many researchers study the spatial-temporal distribution and evolution rules of acoustic emission signals in the rock deformation and damage process, and mainly focus on the changes of the spatial positions and the number of the acoustic emission signals. However, the research on the microcrack propagation directionality of the pressed rock is less, and an effective characterization index and an effective evaluation method of the microcrack propagation directionality are not formed.
Disclosure of Invention
In view of the above, the invention provides a rock compression microcrack expansion directionality evaluation method based on cluster analysis and an information source entropy principle. The method is simple and convenient to operate, and can be used for quantitatively evaluating the microcrack expansion directionality of the rock under the action of the compressive load.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a method for evaluating the propagation directionality of the pressed microcracks of the rock comprises the following steps:
firstly, carrying out real-time acoustic emission monitoring on the deformation and damage process of the rock under the action of compressive load, and acquiring spatial coordinate information (x, y, z) of an acoustic emission event. For convenience in employing the following formula, it is suggested that the loading direction be defined as the z-axis.
And secondly, establishing a single-key group structure of the acoustic emission event sequence. A single-bond clustering analysis method, also called a nearest neighbor clustering algorithm, ensures that each acoustic emission event is connected with the event with the nearest distance. For an N number of acoustic emission event sequences, an N matrix D is defined1Each element in the matrix represents a spatiotemporal distance between a pair of acoustic emission events. Specifically, element d of row m and column nmnRepresenting a spatiotemporal distance between the mth acoustic emission event and the nth acoustic emission event as shown by:
Figure BDA0002781505200000021
wherein x, y, z represent the three-dimensional coordinates of the acoustic emission event; t and B are respectively occurrence time and space-time correlation coefficient.
If B is 0, the element dmnRepresenting the spatial distance between two events. To find the nearest neighbors of the ith event, we compare each element of the ith row. When element dijAt the minimum, the jth event is the nearest neighbor of the ith event. Connecting lines between ith and jth eventsThe wire is referred to as a single bond. After successively searching all events, establish D1The single bond structure of (1).
And thirdly, solving a single bond dip angle representing the expansion direction of the microcracks. Each single bond can be considered a space vector. Thus, vectors for the ith and jth events
Figure BDA0002781505200000022
Can be expressed as:
Figure BDA0002781505200000023
in the above formula Ax，Ay，AzRepresenting a spatial vector
Figure BDA0002781505200000024
Components in the x, y, z directions.
Calculating each space vector
Figure BDA0002781505200000025
Corresponding unit vector
Figure BDA0002781505200000026
Figure BDA0002781505200000027
Wherein a isx，ay，azRepresenting unit vectors
Figure BDA0002781505200000028
Components in the x, y, z directions.
The inclination angle (theta) of the single bond, which is defined as the angle between the unit vector and its projection on the xy plane, is used to characterize the microcrack propagation directionality, as shown in fig. 2. In this case, the inclination angle (θ) has a value range of
Figure BDA0002781505200000029
Due to the fact thatThe microcracks are symmetrical in propagation and the inclination angle is satisfied
Figure BDA00027815052000000210
Therefore, the tilt angle (θ) can be calculated by the following equation:
Figure BDA0002781505200000031
wherein r represents a unit vector
Figure BDA0002781505200000032
The projection length in the xy plane; | z | represents a unit vector
Figure BDA0002781505200000033
Length in z direction.
And fourthly, counting all single-key dip angles of the acoustic emission event sequence with the number N, and calculating a spatial correlation directivity index ([ xi ]).
First, the percentage of the inclination angle in different angle ranges is counted. The symbol psi is defined as the sum of the single bond cumulative tilt angles for tilt angles less than theta. Symbol psisumRepresents the sum of the tilt angles of all single bonds. Thus, the ratio ψ/ψsumTo normalize the cumulative tilt angle. Normalizing the cumulative tilt angle (psi/psi) by a goodness of fit testsum) The distribution with inclination angle (theta) follows the Weibull distribution. The distribution fitting function can be expressed as:
Figure BDA0002781505200000034
in the formula, eta represents a proportional parameter; γ represents a shape parameter.
The probability density function in the formula (5) is a probability that the inclination of a single bond is smaller than θ. The spatial correlation directivity index ([ xi ]) is the inclination at which the probability density function is equal to 0.5. That is, the inclination angle θ when the condition W (θ) is satisfied 0.5 is the spatial correlation directivity index (ξ).
And fifthly, calculating the information source entropy of the single-key dip angle. The source entropy H (theta) of the single-bond dip can be calculated by the formula (6-8):
Figure BDA0002781505200000035
Figure BDA0002781505200000036
Figure BDA0002781505200000037
in which P represents the probability, #iThe fingers are distributed in [ i delta theta, (i +1) delta theta]The sum of the single bond inclinations in the range, (i ═ 0,1,2,.., k). Δ θ is a pitch of the tilt angle, which is preset for grouping and counting the tilt angles, and can be arbitrarily selected, but should not be larger than 0.2. The symbol k is the maximum value of the inclination angle thetamaxDivided by the integer part of Δ θ.
Sixthly, as the loading time advances, a new N multiplied by N matrix D is established for the next acoustic emission event sequence with the number of N2Using the above-mentioned analysis matrix D1The method of (4), repeating steps two to five. Therefore, the spatial correlation directivity index (xi) and the information source entropy H in the whole rock deformation destruction process can be calculated, and the rock microcrack expansion directivity can be evaluated in real time.
The invention has the beneficial effects that: the representation indexes of the expansion directionality of the rock stressed microcracks are provided, the representation indexes comprise space-related directionality indexes and information source entropy, the chaos degree of the expansion direction change and the direction change of the microcracks can be represented, the quantitative evaluation of the expansion directionality of the cracks in the rock deformation and damage process is realized, the solution is convenient, and the method can be widely applied to the microscopic evaluation of the rock deformation and damage process under the action of compression load.
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FIG. 1 is a schematic flow chart of a rock compression microcrack expansion directionality evaluation method based on cluster analysis and an information source entropy principle, which is provided by the invention;
FIG. 2 is a schematic diagram illustrating single bond tilt angle definition;
FIG. 3 is a spatial distribution and single bond group architecture for an acoustic emission event sequence: (a) spatial distribution; (b) a single key group architecture;
FIG. 4 is a normalized cumulative tilt angle (psi/psi)sum) Obtaining a fitting function between the inclination angle (theta) and a space correlation directivity index (xi);
Detailed Description
In order to further explain the technical scheme of the invention, the invention is explained in detail by combining the attached drawings and the embodiment.
As shown in FIG. 1, the method for evaluating the propagation directionality of the microcracks under rock compression comprises the following steps:
(1) and (3) carrying out real-time acoustic emission monitoring on the deformation and damage process of the rock under the action of the compressive load, and acquiring the spatial coordinate information (x, y, z) of the acoustic emission event. In the embodiment, a uniaxial compression test of granite is adopted, real-time acoustic emission monitoring is carried out on the whole deformation and damage process, the space coordinates (x, y and z) of an acoustic emission event are obtained, and the z axis is the loading direction. The spatial distribution of the first 100 acoustic emission events under uniaxial loading is shown in FIG. 3 (a).
(2) A single bond group architecture of the acoustic emission event sequence is established. In this embodiment, the acoustic emission sequence length N is taken as 100, that is, a single-key group structure analysis is performed once every 100 acoustic emission events, and the rock compression microcrack propagation directionality is evaluated once. And (5) establishing a single-bond group structure of the acoustic emission event sequence by adopting the method of the step two. Fig. 3(b) shows the corresponding single key group architecture.
(3) And solving a single bond dip angle representing the microcrack expansion direction. And (4) calculating the single bond inclination angle by adopting a formula (2-4). The calculated single-key inclination angle of the embodiment is shown by the circular data points in FIG. 4.
(4) All single-key dip angles of the acoustic emission event sequence with the number N are counted, and a spatial correlation directivity index ([ xi ]) of the acoustic emission event sequence is calculated. Normalized cumulative inclination angle (ψ/ψ) of the present embodimentsum) The statistical relationship with the tilt angle (θ) is shown in fig. 4. Weibull distribution fitting function of
Figure BDA0002781505200000051
The spatial correlation directivity index ([ xi ]) is the inclination at which the probability density function is equal to 0.5. The spatial correlation directivity index (ξ) of the present embodiment is 0.9, as indicated by the rectangular dots in fig. 4.
(5) And calculating the information source entropy H of the single bond dip angle. The present embodiment calculates the source entropy H using equation (6-8). The tilt pitch (Δ θ) was set to 0.02 and the calculated source entropy was 3.5.
(6) And repeating the second step to the fifth step, and calculating to obtain the spatial correlation directivity index (xi) and the source entropy H of the acoustic emission event sequence with the number of 2 nd and 3 rd (corresponding to rock damage) and the number of n (corresponding to rock damage) as 100, thereby evaluating the rock microcrack expansion directivity in real time.
The above-mentioned embodiments only express the embodiments of the present invention, but not should be understood as the limitation of the scope of the invention patent, it should be noted that, for those skilled in the art, many variations and modifications can be made without departing from the concept of the present invention, and these all fall into the protection scope of the present invention.

Claims (3)

1. A rock compression microcrack expansion directionality evaluation method based on cluster analysis and an information source entropy principle is characterized by comprising the following steps:
firstly, carrying out real-time acoustic emission monitoring on a deformation and damage process of a rock under the action of a compressive load, acquiring spatial coordinate information (x, y, z) of an acoustic emission event, and defining a loading direction as a z axis;
secondly, establishing a single-key group structure of the acoustic emission event sequence;
for an N number of acoustic emission event sequences, an N matrix D is defined1Each element in the matrix represents a spatiotemporal distance between a pair of acoustic emission events; specifically, element d of row m and column nmnRepresenting a spatiotemporal distance between the mth acoustic emission event and the nth acoustic emission event;
if B is 0, the element dmnRepresenting the spatial distance between two events; for each element of the ith rowA comparison is made to find the nearest neighbor of the ith event: when element dijAt the minimum, the jth event is the nearest neighbor of the ith event; the straight line connecting the ith and jth events is called a single bond; after successively searching all events, establish D1The single bond architecture of (a);
thirdly, solving a single bond inclination angle representing the expansion direction of the microcracks;
each single key is considered as a space vector, a vector of the ith and jth events
Figure FDA0002781505190000011
Expressed as:
Figure FDA0002781505190000012
in the formula, Ax，Ay，AzRepresenting a spatial vector
Figure FDA0002781505190000013
Components in the x, y, z directions;
calculating each space vector
Figure FDA0002781505190000014
Corresponding unit vector
Figure FDA0002781505190000015
Figure FDA0002781505190000016
In the formula, ax，ay，azRepresenting unit vectors
Figure FDA0002781505190000017
Components in the x, y, z directions;
projecting unit vector on xy planeAn included angle between the shadows is defined as a single-bond dip angle (theta), and the dip angle is adopted to represent the microcrack expansion directionality; the microcracks are symmetrically expanded and the inclination angle is satisfied
Figure FDA0002781505190000018
And is calculated by the following formula:
Figure FDA0002781505190000021
wherein r represents a unit vector
Figure FDA0002781505190000022
The projection length in the xy plane; | z | represents a unit vector
Figure FDA0002781505190000023
A length in the z direction;
fourthly, counting all single-key dip angles of the acoustic emission event sequence with the number of N, and calculating a spatial correlation directivity index (xi) of the acoustic emission event sequence;
firstly, counting the percentage of the dip angle in different angle ranges; the symbol psi is defined as the sum of the single bond cumulative dips with dips less than theta; symbol psisumRepresents the sum of the inclination angles of all single bonds; thus, the ratio ψ/ψsumTo normalize the cumulative dip angle; normalizing the cumulative tilt angle (psi/psi) by a goodness of fit testsum) The distribution follows Weibull distribution along with the inclination angle (theta); the distribution fit function is expressed as:
Figure FDA0002781505190000024
in the formula, eta represents a proportional parameter; gamma represents a shape parameter;
the probability density function in the formula (5) refers to the probability that the inclination angle of a single bond is smaller than theta; the tilt angle θ when the condition W (θ) is satisfied 0.5 is the spatial correlation directivity index (ξ);
fifthly, calculating the information source entropy of the single-key dip angle;
the source entropy H (theta) of the single-bond dip angle is calculated by the formula (6-8):
Figure FDA0002781505190000025
Figure FDA0002781505190000026
Figure FDA0002781505190000027
wherein, P represents probability; psiiThe fingers are distributed in [ i delta theta, (i +1) delta theta](ii) the sum of the single bond inclinations in the range, (i ═ 0,1,2,. k); the symbol k is the maximum value of the inclination angle thetamaxDividing the integer part by delta theta, wherein the delta theta is a pitch of the dip angle and is a preset pitch for grouping and counting the dip angle;
sixthly, as the loading time advances, a new N multiplied by N matrix D is established for the next acoustic emission event sequence with the number of N2Using the above analysis matrix D1The method can calculate the spatial correlation directivity index (xi) and the information source entropy H in the whole rock deformation damage process by repeating the second step to the fifth step, and evaluates the rock microcrack expansion directivity in real time.
2. The method for evaluating the directionality of propagation of the microcracks under pressure of the rock according to claim 1, wherein d is a measure of the directionality of propagation of microcracks under pressure based on cluster analysis and source entropy principlemnAs shown in the following formula:
Figure FDA0002781505190000031
wherein x, y, z represent the three-dimensional coordinates of the acoustic emission event; t and B are respectively occurrence time and space-time correlation coefficient.
3. The method for evaluating the directionality of propagation of the microcracks under pressure of the rock according to claim 1, wherein Δ θ is not more than 0.2.
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