Self-similarity recognition characteristics of acoustic emission in concrete fracture

Self-similarity identification characteristics of acoustic emission of concrete material fracture

      Abstract The concept of acoustic emission process is proposed by combining the research on material acoustic emission, mechanical process, and material fracture damage and other destructive processes. The self-similarity characteristic function for quantitatively investigating the acoustic emission process is given. On this basis, the self-similarity identification characteristics of acoustic emission of concrete specimen fracture are determined according to the three-point bending test of concrete specimens.
      Keywords concrete material, fracture, acoustic emission process, self-similarity, identification characteristics          1 Introduction 　　The experimental results show that the acoustic emission of multi-crack and multi-phase change composite materials such as concrete after being stressed is often generated by multiple acoustic emission sources at the same time. In this way, the measured acoustic emission signal is the superposition of multiple acoustic emission source signals. Therefore, it is very difficult to use signal analysis methods to establish the relationship between mechanical processes and acoustic emission parameters, and it is almost impossible to capture and track the original signal. Therefore, so far, the research on the relationship between acoustic emission and mechanical processes has only remained at the level of qualitative analysis. 　　Concrete contains many defects, cracks and microstructural inhomogeneities of different properties. The fracture process of concrete material is essentially a continuous process from primary cracks to microcracks and finally macroscopic fractures. Fracture mechanics uses the cracking of the main crack as the basis for judging the fracture of materials. Therefore, when using fracture mechanics theory to solve the fracture problem of concrete, a very important issue is how to determine the critical condition, that is, which state is the critical state of cracking in the above continuous process. 　　This paper changes the practice of only analyzing acoustic emission as a signal. On the basis of giving the definition of the acoustic emission process, it proposes to find the relationship between the mechanical process and the acoustic emission parameters from a nonlinear perspective. The self-similar characteristic function is given. Through experiments, the evolution law of the self-similarity of the acoustic emission process of the concrete specimen during the three-point bending process is analyzed, and then the acoustic emission self-similarity identification characteristics of the critical state of concrete fracture are obtained. The work of this paper aims to organically combine the study of acoustic emission with the study of mechanical processes and material failure processes, provide a new idea for the study of the fracture mechanism of concrete materials, and provide a quantitative basis for the application of acoustic emission technology in the stability evaluation and damage prediction of concrete structures.       2 Concept of acoustic emission process The 　　test results of acoustic emission rate and acoustic emission energy release rate of concrete test block (specification: 7cm×7cm×7cm, mix ratio: cement: sand: stone: water = 1:1.6:3.2:0.6, maximum aggregate particle size 1cm) under uniaxial compression. The values ​​of different parameters in different states show great randomness and discreteness. The 　　acoustic emission process of materials is usually expressed as a sequence of acoustic emission parameters. If the probability of the acoustic emission parameter x taking a certain value at time t in a mechanical process is e, then the acoustic emission process of the material can be expressed as a random process, that is,       x=X(e, t) (e∈Ω, t∈T)       where: x——acoustic emission parameter; 　　　e——probability value corresponding to state t, 0≤e≤1; 　　　T——total duration of the process; 　　　Ω——probability space; 　　　t——test time. It can also be a relative stress level or a relative strain level. Of course, T at this time is the limit relative stress or limit relative strain of the material. 　　As far as concrete materials are concerned, the probability e of an acoustic emission parameter taking a certain value in a certain state is affected by many factors at the same time, that is, it is a function of many random variables at the same time. Here, the probability e can be expressed as       e=f(m, t, h, c, …)       where: m is the characteristic parameter of the material itself; 　　　t is temperature; 　　　h is humidity; 　　　c is experimental conditions, etc. 　　Obviously, due to the variability, randomness, fuzziness and correlation between these factors, it is difficult or impossible to find an accurate expression to determine this probability. However, as a nonlinear process, since it is a concomitant process of the evolution of the internal structure of the material under load, it must contain the relevant characteristics of the mechanical process and the material evolution process at the same time. Therefore, we can examine and explore the nonlinear characteristics of the acoustic emission process from the perspective of nonlinear disciplines based on the structural characteristics of the material and through mechanical tests of the material. The following is a discussion on the self-similarity of the acoustic emission process of concrete materials based on the experiment.       3 Self-similarity characteristic function of acoustic emission process 　　Self-similarity means that after a thing or phenomenon is subdivided into smaller parts through several steps, each part is enlarged and compared with the original thing, and the two are still "similar", that is, the part and the whole are similar in form, function and information. The 　　test results of different acoustic emission parameters in different acoustic emission processes or different states of the same process have both obvious differences and certain similarities. Experiments have shown that not only is the distribution of acoustic emission sequences in the time domain fractal, but the distribution of acoustic emission events in space also has fractal characteristics [4]. The fractal characteristics also indicate that the acoustic emission process has self-similarity characteristics. In order to quantitatively 　　describe the degree of self-similarity of different acoustic emission processes of concrete materials and different stages of acoustic emission processes, and to examine the evolution law of self-similarity of acoustic emission processes, it is necessary to first establish a self-similarity characteristic function. 　　The degree of self-similarity between acoustic emission processes or acoustic emission states can be expressed by a self-similarity function. For the acoustic emission basic parameter sequence X={xi}, i=1, 2, …, n, it can be divided into m (m≤n) time zones according to a certain time interval (stress level), and the acoustic emission behavior represented by the acoustic emission basic parameter sequence segment in each time zone, such as the maximum acoustic emission rate, maximum amplitude, average acoustic emission rate, average amplitude, acoustic emission count, etc., can be calculated. In this way, we get a sample       Y={yi} with a capacity of m. 　　Then, we first take the first r elements in Y to form an r-dimensional "embedding space" and get the vector z1, that is,       z1={y1, y2, ..., yr}. 　　After that, we slide over time and get a vector for each data slide. In this way, we can find all the vectors zk: 　　　　　　　　　　　　　　zk={yk, yk+1, ..., yk+r-1} 　　　　　　　　　　　　　　k=1, 2, ..., m-r+1. 　　Take the first s zk values ​​and calculate the distance dij between (zi+zj) in turn, where i, j=1, 2, ..., k. Given the self-similarity ratio 1=1/ε, ε is a given scale, calculate how many point pairs have a distance less than ε, and find the proportion c of these point pairs to the total point pairs. By constantly changing the ε value, we can calculate several groups of c(ε) values ​​between 0 and 1, and then we can calculate the self-similarity coefficient μs. For h εj, j=1, 2, …, h, the definition       is: ∑ represents the sum from j=1 to j=h; 　　where μ is the Heaviside function, which is defined as       follows. The similarity between two processes or two states can be judged based on the size of μs. 　　The variation of the self-similarity coefficient of the acoustic emission process of concrete specimens under uniaxial compression with the relative stress level. It can be seen that the self-similarity of the acoustic emission process is different at different stress levels. Therefore, if appropriate r and s are selected, the self-similarity coefficient can be used as an identification feature for abnormal acoustic emission states. 



















 
















      The variation of coefficient with relative stress level
      4 The variation characteristics of self-similarity of acoustic emission process during the fracture of concrete materials
　　In order to study the self-similarity characteristics of acoustic emission during the fracture of concrete, a three-point bending test of a concrete beam with a cut in the middle was carried out.
　　The specimen size is 4cm×8cm×28cm, and the mix ratio is cement: sand: gravel: water = 1:1.35:3.15:0.55. The specimen is demoulded 24h after forming, and then soaked in water at 20°C for 7d, and then placed in a standard curing room for curing to 28d. A 4cm deep cut is prefabricated in the middle of the specimen. Before the experiment, the end of the cut is sawed with a hacksaw, and continuous loading is adopted. During the test, while conducting acoustic emission detection, the vertical displacement at the center of the beam is measured with a micrometer. The total gain of the acoustic emission detection is set to 100dB, of which the preamplifier is 40dB, the main amplifier is 60dB, and the threshold value is set to 32dB.
      Variation curve of the self-similarity coefficient of acoustic emission parameters at different stress levels
　　When the relative stress level reaches about 65%, the acoustic emission event count curve suddenly rises and the displacement increases sharply. At this time, the specimen reaches the critical state of fracture [6]. At this stress level, the self-similarity coefficient reaches a minimum value and then gradually recovers. The critical fracture of the specimen occurs in the process of recovering from the minimum value. Therefore, the minimum value of the self-similarity coefficient of the acoustic emission process indicates the arrival of macroscopic fracture. We express the acoustic emission self-similarity pattern of the material under the critical fracture state as the "minimum-recovery" type.
      5 Conclusion
　　(1) It can be considered that the mechanical process to which the material is subjected and the evolution process of the internal structure of the material are nonlinear processes that follow the same evolution mechanism and can be studied by acoustic emission.
　　(2) The self-similar characteristic function established can be used to quantitatively describe the degree of self-similarity of the acoustic emission process or different states in the acoustic emission process.
　　(3) The test results show that the degree of self-similarity of the corresponding acoustic emission process in different states during the three-point bending of the concrete specimen is different, that is, the degree of self-similarity of the acoustic emission process changes with the change of the stress state. The minimum value of the self-similarity coefficient of the acoustic emission process indicates the arrival of macroscopic fracture. Therefore, the acoustic emission self-similarity recognition mode exhibited by the concrete specimen in the critical fracture state is the "minimum-rebound" type.

Acoustic emission self-similarity identification characteristics of concrete material fracture
Release date: 2007-04-07 09:17:42
      Abstract The concept of acoustic emission process is proposed by combining the research on material acoustic emission, mechanical process, and material fracture damage and other destructive processes. The self-similarity characteristic function for quantitatively examining the acoustic emission process is given. On this basis, the acoustic emission self-similarity identification characteristics of concrete specimen fracture are determined according to the three-point bending test of concrete specimens.
      Keywords Concrete material, fracture, acoustic emission process, self-similarity, identification characteristics          1 Introduction 　　The experimental results show that the acoustic emission of multi-crack and multi-phase change composite materials such as concrete after being stressed is often generated by multiple acoustic emission sources at the same time. In this way, the measured acoustic emission signal is the superposition of multiple acoustic emission source signals. Therefore, it is very difficult to use signal analysis methods to establish the relationship between the mechanical process and the acoustic emission parameters, and it is almost impossible to capture and track the original signal. Therefore, so far, the research on the relationship between acoustic emission and mechanical process has only remained at the level of qualitative analysis. 　　Concrete contains many defects, cracks and microstructural inhomogeneities of different properties. The fracture process of concrete material is essentially a continuous process from primary cracks to microcracks and finally macroscopic fractures. Fracture mechanics uses the cracking of the main crack as the basis for judging the fracture of materials. Therefore, when using fracture mechanics theory to solve the fracture problem of concrete, a very important issue is how to determine the critical condition, that is, which state is the critical state of cracking in the above continuous process. 　　This paper changes the practice of only analyzing acoustic emission as a signal. On the basis of giving the definition of the acoustic emission process, it proposes to find the relationship between the mechanical process and the acoustic emission parameters from a nonlinear perspective. The self-similar characteristic function is given. Through experiments, the evolution law of the self-similarity of the acoustic emission process of the concrete specimen during the three-point bending process is analyzed, and then the acoustic emission self-similarity identification characteristics of the critical state of concrete fracture are obtained. The work of this paper aims to organically combine the study of acoustic emission with the study of mechanical processes and material failure processes, provide a new idea for the study of the fracture mechanism of concrete materials, and provide a quantitative basis for the application of acoustic emission technology in the stability evaluation and damage prediction of concrete structures.       2 Concept of acoustic emission process The 　　test results of acoustic emission rate and acoustic emission energy release rate of concrete test block (specification: 7cm×7cm×7cm, mix ratio: cement: sand: stone: water = 1:1.6:3.2:0.6, maximum aggregate particle size 1cm) under uniaxial compression. The values ​​of different parameters in different states show great randomness and discreteness. The 　　acoustic emission process of materials is usually expressed as a sequence of acoustic emission parameters. If the probability of the acoustic emission parameter x taking a certain value at time t in a mechanical process is e, then the acoustic emission process of the material can be expressed as a random process, that is,       x=X(e, t) (e∈Ω, t∈T)       where: x——acoustic emission parameter; 　　　e——probability value corresponding to state t, 0≤e≤1; 　　　T——total duration of the process; 　　　Ω——probability space; 　　　t——test time. It can also be a relative stress level or a relative strain level. Of course, T at this time is the limit relative stress or limit relative strain of the material. 　　As far as concrete materials are concerned, the probability e of an acoustic emission parameter taking a certain value in a certain state is affected by many factors at the same time, that is, it is a function of many random variables at the same time. Here, the probability e can be expressed as       e=f(m, t, h, c, …)       where: m is the characteristic parameter of the material itself; 　　　t is temperature; 　　　h is humidity; 　　　c is experimental conditions, etc. 　　Obviously, due to the variability, randomness, fuzziness and correlation between these factors, it is difficult or impossible to find an accurate expression to determine this probability. However, as a nonlinear process, since it is a concomitant process of the evolution of the internal structure of the material under load, it must contain the relevant characteristics of the mechanical process and the material evolution process at the same time. Therefore, we can examine and explore the nonlinear characteristics of the acoustic emission process from the perspective of nonlinear disciplines based on the structural characteristics of the material and through mechanical tests of the material. The following is a discussion on the self-similarity of the acoustic emission process of concrete materials based on the experiment.       3 Self-similarity characteristic function of acoustic emission process 　　Self-similarity means that after a thing or phenomenon is subdivided into smaller parts through several steps, each part is enlarged and compared with the original thing, and the two are still "similar", that is, the part and the whole are similar in form, function and information. The 　　test results of different acoustic emission parameters in different acoustic emission processes or different states of the same process have both obvious differences and certain similarities. Experiments have shown that not only is the distribution of acoustic emission sequences in the time domain fractal, but the distribution of acoustic emission events in space also has fractal characteristics [4]. The fractal characteristics also indicate that the acoustic emission process has self-similarity characteristics. In order to quantitatively 　　describe the degree of self-similarity of different acoustic emission processes of concrete materials and different stages of acoustic emission processes, and to examine the evolution law of self-similarity of acoustic emission processes, it is necessary to first establish a self-similarity characteristic function. 　　The degree of self-similarity between acoustic emission processes or acoustic emission states can be expressed by a self-similarity function. For the acoustic emission basic parameter sequence X={xi}, i=1, 2, …, n, it can be divided into m (m≤n) time zones according to a certain time interval (stress level), and the acoustic emission behavior represented by the acoustic emission basic parameter sequence segment in each time zone, such as the maximum acoustic emission rate, maximum amplitude, average acoustic emission rate, average amplitude, acoustic emission count, etc., can be calculated. In this way, we get a sample       Y={yi} with a capacity of m. 　　Then, we first take the first r elements in Y to form an r-dimensional "embedding space" and get the vector z1, that is,       z1={y1, y2, ..., yr}. 　　After that, we slide over time and get a vector for each data slide. In this way, we can find all the vectors zk: 　　　　　　　　　　　　　　zk={yk, yk+1, ..., yk+r-1} 　　　　　　　　　　　　　　k=1, 2, ..., m-r+1. 　　Take the first s zk values ​​and calculate the distance dij between (zi+zj) in turn, where i, j=1, 2, ..., k. Given the self-similarity ratio 1=1/ε, ε is a given scale, calculate how many point pairs have a distance less than ε, and find the proportion c of these point pairs to the total point pairs. By constantly changing the ε value, we can calculate several groups of c(ε) values ​​between 0 and 1, and then we can calculate the self-similarity coefficient μs. For h εj, j=1, 2, …, h, the definition       is: ∑ represents the sum from j=1 to j=h; 　　where μ is the Heaviside function, which is defined as       follows. The similarity between two processes or two states can be judged based on the size of μs. 



















 















　　The variation of the self-similarity coefficient of the acoustic emission process of the concrete specimen under uniaxial compression with the relative stress level. It can be seen that the degree of self-similarity of the acoustic emission process is different at different stress levels. Therefore, if appropriate r and s are selected, the self-similarity coefficient can be used as an identification feature of abnormal acoustic emission state.
      The variation of the coefficient with relative stress level
      4 The variation characteristics of the self-similarity of the acoustic emission process during the fracture of concrete materials
　　In order to study the self-similarity characteristics of acoustic emission during the fracture of concrete, a three-point bending test of a concrete beam with a cut in the middle was carried out.
　　The specimen size is 4cm×8cm×28cm, and the mix ratio is cement: sand: gravel: water = 1:1.35:3.15:0.55. The specimen is demolded 24h after forming, then soaked in water at 20°C for 7d, and then placed in a standard curing room for curing to 28d. A 4cm deep cut is prefabricated in the middle of the specimen. Before the experiment, the end of the cut is sawed with a hacksaw, and continuous loading is adopted. During the test, while conducting the acoustic emission test, the vertical displacement at the center of the beam was measured with a micrometer. The acoustic emission test was set to a total gain of 100 dB, including 40 dB for the preamplifier, 60 dB for the main amplifier, and a threshold value of 32 dB.
      The variation curve of the self-similarity coefficient of acoustic emission parameters at different stress levels
　　When the relative stress level reaches about 65%, the acoustic emission event count curve suddenly rises and the displacement increases sharply. At this time, the specimen reaches the critical state of fracture [6]. At this stress level, the self-similarity coefficient reaches a minimum value and then gradually recovers. The critical fracture of the specimen occurs in the process of recovering from the minimum value. Therefore, the minimum value of the self-similarity coefficient of the acoustic emission process indicates the arrival of macroscopic fracture. We express the acoustic emission self-similarity pattern of the material in the critical fracture state as the "minimum-recovery" type.
      5 Conclusion
　　(1) It can be considered that the mechanical process of the material and the evolution of the internal structure of the material are nonlinear processes that follow the same evolution mechanism and can be studied by acoustic emission.
　　(2) The established self-similar characteristic function can be used to quantitatively describe the acoustic emission process or the degree of self-similarity of different states in the acoustic emission process.
　　(3) The test results show that the degree of self-similarity of the corresponding acoustic emission process in different states during the three-point bending of the concrete specimen is different, that is, the degree of self-similarity of the acoustic emission process changes with the change of the stress state. The minimum value of the self-similarity coefficient of the acoustic emission process indicates the arrival of macroscopic fracture. Therefore, the acoustic emission self-similarity recognition mode exhibited by the concrete specimen in the critical fracture state is the "minimum-rebound" type.