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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Dalian University of Technology
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Abstract

一种基于聚类分析和信源熵原理的岩石受压微裂纹扩展方向性评价方法，属于岩石力学与岩土工程领域。首先，进行岩石在压缩荷载作用下变形破坏过程的实时声发射监测，获取声发射事件的空间坐标信息，并建立声发射事件序列的单键群架构。其次，求解表征微裂纹扩展方向的单键倾角。再次，统计数量为N的声发射事件序列的所有单键倾角，计算其空间相关方向性指标，并计算单键倾角的信源熵。最后，随着加载时间的推进，对于下一个声发射事件序列再建立新的矩阵，重复上述步骤，计算整个岩石变形破坏过程中的空间相关方向性指标和信源熵H，实时地对岩石微裂纹扩展方向性进行评价。本发明能够实现岩石变形破坏过程中裂纹扩展方向性的定量评价，求解方便。

Figure 202011283254

The invention discloses a method for evaluating the propagation direction of micro-cracks under compression based on cluster analysis and the principle of source entropy, belonging to the fields of rock mechanics and geotechnical engineering. Firstly, the real-time acoustic emission monitoring of the deformation and failure process of rock under compressive load is carried out, the spatial coordinate information of acoustic emission events is obtained, and the single-key group structure of the acoustic emission event sequence is established. Second, solve for the single bond inclination that characterizes the direction of microcrack propagation. Thirdly, all single-bond inclinations of the acoustic emission event sequence with a statistical number of N are calculated, and their spatially correlated directivity indices are calculated, and the source entropy of the single-bond inclinations is calculated. Finally, as the loading time progresses, a new matrix is established for the next acoustic emission event sequence, and the above steps are repeated to calculate the spatially correlated directional index and the source entropy H during the entire rock deformation and failure process, and real-time analysis of the rock microstructure. Crack propagation directionality was evaluated. The invention can realize the quantitative evaluation of the crack propagation direction in the process of rock deformation and failure, and the solution is convenient.

Figure 202011283254

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.
Drawings
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)

1.一种基于聚类分析和信源熵原理的岩石受压微裂纹扩展方向性评价方法，其特征在于，包括以下步骤：1. a method for evaluating the directionality of micro-crack expansion under compression based on cluster analysis and source entropy principle, is characterized in that, comprises the following steps: 第一步，进行岩石在压缩荷载作用下变形破坏过程的实时声发射监测，获取声发射事件的空间坐标信息(x,y,z)，将加载方向定义为z轴；The first step is to carry out real-time acoustic emission monitoring of the deformation and failure process of the rock under the action of compressive load, obtain the spatial coordinate information (x, y, z) of the acoustic emission event, and define the loading direction as the z-axis; 第二步，建立声发射事件序列的单键群架构；The second step is to establish the single-key group structure of the acoustic emission event sequence; 对于一个数量为N的声发射事件序列，定义一个N×N的矩阵D1，矩阵中的每个元素表示一对声发射事件之间的时空距离；具体来说，第m行第n列的元素dmn表示第m个声发射事件和第n个声发射事件之间的时空距离；For a sequence of N acoustic emission events, an N×N matrix D 1 is defined, and each element in the matrix represents the space-time distance between a pair of acoustic emission events; specifically, the m-th row and n-th column of the The element dmn represents the space-time distance between the mth acoustic emission event and the nth acoustic emission event; 设B＝0，元素dmn表示两个事件之间的空间距离；对第i行的每个元素进行比较，寻找第i个事件的最近邻居：当元素dij最小时，第j个事件是第i个事件的最近邻居；连接第i个和第j个事件之间的直线称为一个单键；在逐次搜索所有事件之后，建立D1的单键架构；Let B=0, the element dmn represents the spatial distance between two events; compare each element in the i-th row to find the nearest neighbor of the i-th event: when the element d ij is the smallest, the j-th event is The nearest neighbor of the i-th event; the straight line connecting the i-th and j-th events is called a single bond; after successively searching all events, the single-bond architecture of D 1 is established; 第三步，求解表征微裂纹扩展方向的单键倾角；The third step is to solve the single bond inclination angle that characterizes the direction of microcrack propagation; 每个单键看作是一个空间向量，第i个和第j个事件的向量
Figure FDA0002781505190000011
表示为:Each single key is seen as a space vector, the vectors of the ith and jth events
Figure FDA0002781505190000011
Expressed as:
Figure FDA0002781505190000012
Figure FDA0002781505190000012
 式中，Ax，Ay，Az表示空间向量
Figure FDA0002781505190000013
在x、y、z方向上的分量；In the formula, A x , A y , A z represent the space vector
Figure FDA0002781505190000013
components in the x, y, z directions; 计算每个空间向量
Figure FDA0002781505190000014
对应的单位向量
Figure FDA0002781505190000015
Calculate each space vector
Figure FDA0002781505190000014
the corresponding unit vector
Figure FDA0002781505190000015
Figure FDA0002781505190000016
Figure FDA0002781505190000016
 式中，ax，ay，az表示单位向量
Figure FDA0002781505190000017
在x、y、z方向上的分量；In the formula, a x , a y , and a z represent the unit vector
Figure FDA0002781505190000017
components in the x, y, z directions; 将单位向量与其在xy平面的投影之间的夹角定义为单键的倾角(θ)，并采用倾角表征微裂纹扩展方向性；微裂纹扩展为对称的，倾角满足
Figure FDA0002781505190000018
并通过下式计算：The angle between the unit vector and its projection on the xy plane is defined as the inclination angle (θ) of the single bond, and the inclination angle is used to characterize the direction of microcrack propagation; the microcrack expansion is symmetrical, and the inclination angle satisfies
Figure FDA0002781505190000018
and calculated by the following formula:
Figure FDA0002781505190000021
Figure FDA0002781505190000021
 式中，r表示单位向量
Figure FDA0002781505190000022
在xy平面的投影长度；|z|表示单位向量
Figure FDA0002781505190000023
在z方向上的长度；where r is the unit vector
Figure FDA0002781505190000022
Projection length on the xy plane; |z| represents the unit vector
Figure FDA0002781505190000023
the length in the z direction; 第四步，统计数量为N的声发射事件序列的所有单键倾角，计算其空间相关方向性指标(ξ)；The fourth step is to calculate the spatial correlation directivity index (ξ) of all the single-bond inclination angles of the acoustic emission event sequence whose number is N; 首先，统计倾角在不同角度范围内的百分比；符号ψ定义为倾角小于θ的单键累积倾角之和；符号ψsum表示所有单键的倾角总和；因此，比值ψ/ψsum为归一化累积倾角；通过拟合优度检验，归一化累积倾角(ψ/ψsum)随倾角(θ)分布服从Weibull分布；分布拟合函数表示为:First, the percentage of inclination angles in different angular ranges is counted; the symbol ψ is defined as the sum of the cumulative inclination angles of single bonds with an inclination angle less than θ; the symbol ψ sum represents the sum of the inclination angles of all single bonds; therefore, the ratio ψ/ψ sum is the normalized cumulative Dip angle; through the goodness-of-fit test, the normalized cumulative dip angle (ψ/ψ sum ) follows the Weibull distribution along with the dip angle (θ); the distribution fitting function is expressed as:
Figure FDA0002781505190000024
Figure FDA0002781505190000024
 式中，η表示比例参数；γ表示形状参数；In the formula, η represents the scale parameter; γ represents the shape parameter; 公式(5)中的概率密度函数是指单键的倾角小于θ的概率；满足条件W(θ)＝0.5时的倾角θ即为空间相关方向性指标(ξ)；The probability density function in formula (5) refers to the probability that the inclination angle of a single bond is less than θ; the inclination angle θ when the condition W(θ)=0.5 is satisfied is the spatial correlation directivity index (ξ); 第五步，计算单键倾角的信源熵；The fifth step is to calculate the source entropy of the single bond inclination; 单键倾角的信源熵H(θ)通过公式(6-8)进行计算：The source entropy H(θ) of the single bond inclination is calculated by formula (6-8):
Figure FDA0002781505190000025
Figure FDA0002781505190000025
Figure FDA0002781505190000026
Figure FDA0002781505190000026
Figure FDA0002781505190000027
Figure FDA0002781505190000027
 式中，P表示概率；ψi指分布在[iΔθ,(i+1)Δθ]范围内的单键倾角之和，(i＝0,1,2,...,k)；符号k是倾角最大值θmax除以Δθ的整数部分，其中，Δθ为倾角间距，是为了将倾角分组统计而预先设定的间距；In the formula, P represents probability; ψ i refers to the sum of single bond inclination angles distributed in the range of [iΔθ,(i+1)Δθ], (i=0,1,2,...,k); the symbol k is The maximum inclination angle θ max is divided by the integer part of Δθ, where Δθ is the inclination angle interval, which is a preset interval for grouping statistics of inclination angles; 第六步，随着加载时间的推进，对于下一个数量为N的声发射事件序列，再建立一个新的N×N的矩阵D2，采用上述分析矩阵D1的方法，重复第二步到第五步，能够计算整个岩石变形破坏过程中的空间相关方向性指标(ξ)和信源熵H，实时地对岩石微裂纹扩展方向性进行评价。The sixth step, as the loading time progresses, for the next sequence of acoustic emission events with a number of N, a new N×N matrix D 2 is established, and the above-mentioned method of analyzing the matrix D 1 is used, and the second step to In the fifth step, the spatially related directional index (ξ) and the source entropy H of the entire rock deformation and failure process can be calculated, and the propagation direction of rock microcracks can be evaluated in real time. 2.根据权利要求1所述的一种基于聚类分析和信源熵原理的岩石受压微裂纹扩展方向性评价方法，其特征在于，所述的dmn如下式所示：2. a kind of rock compression micro-crack propagation direction evaluation method based on cluster analysis and source entropy principle according to claim 1, is characterized in that, described d mn is as follows:
Figure FDA0002781505190000031
Figure FDA0002781505190000031
 式中，x，y，z代表声发射事件的三维坐标；t和B分别为发生时间和时空相关系数。In the formula, x, y, z represent the three-dimensional coordinates of the acoustic emission event; t and B are the time and space-time correlation coefficients, respectively. 3.根据权利要求1所述的一种基于聚类分析和信源熵原理的岩石受压微裂纹扩展方向性评价方法，其特征在于，所述的Δθ不大于0.2。3 . The method for evaluating the directionality of micro-crack growth under compression based on cluster analysis and the principle of source entropy according to claim 1 , wherein the Δθ is not greater than 0.2. 4 .
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