Reinforced concrete bonding-slippage constitutive relation establishing method based on MFCC

Abstract

The invention discloses a reinforced concrete bonding-slippage constitutive relation establishing method based on MFCC, and belongs to the technical field of reinforcing steel bar and concrete bonding behavior analysis methods. The establishment method comprises the following steps: firstly, acquiring reinforced concrete parameters, a bonding-slip curve and acoustic emission characteristic parameters; secondly, extracting a plurality of MFCC characteristic parameters based on the amplitude parameters, drawing an MFCC characteristic pattern by combining the energy parameters, selecting # imgabs0 # MFCC characteristics, and dividing real damage stages of a bond-slip curve of the reinforced concrete by combining acoustic emission characteristic parameters; and finally, based on the obtained real damage stage, obtaining a bonding-sliding curve containing the effective real damage stage, and establishing a bonding-sliding constitutive model of the reinforced concrete by using data of the bonding-sliding curve containing the effective real damage stage. The establishment method can adapt to the influence of material parameters and express the real process of damage, and the process of establishing the model has high generalization force.

Description

Technical Field

[0001] The present invention belongs to the technical field of steel bar and concrete bonding behavior analysis methods, and specifically relates to a method for establishing a steel bar and concrete bonding-slip constitutive relationship based on MFCC (Mel Frequency Cepstral Coefficients). Background Art

[0002] As one of the most widely used composite materials in the construction process, reinforced concrete fully integrates the advantages of both concrete and steel bars. However, the premise for the joint work of steel bars and concrete is good bonding between the two, which is an interaction between steel bars and concrete to transfer stress and coordinate deformation. The bonding behavior of reinforced concrete is a manifestation of the ability of steel bars and concrete to work together, which directly affects the safety and durability of the structure. Therefore, it is very important to analyze the bonding behavior of reinforced concrete.

[0003] At present, many studies have been carried out on the bond-slip constitutive relationship of reinforced concrete, and the main forms can be divided into single-segment form and multi-segment form.

[0004] The single-stage form summarizes the bond-slip relationship of the rising section when bond damage occurs, which has advantages in the convergence of numerical calculations. For example, the study on the bond-slip constitutive model of the interface between plain round steel bars and concrete (Bulletin of the Chinese Ceramic Society, Vol. 36, No. 9, September 2017) established the bond-slip constitutive model of the interface between plain round steel bars and concrete using experimental results and theoretical analysis. However, this form simply expresses the bond-slip relationship in mathematical form, while weakening the true expression of the bond damage of steel bars and concrete, and there are errors in practical applications.

[0005] The multi-segment form divides the bond-slip relationship of the rising section when bond damage occurs, which can better reflect the failure mechanism of different bond failure modes and reflect the main distribution of bond stress at different stages of bond action. For example, the Chinese patent application "Method and system for establishing bond-slip constitutive model of steel bar and concrete after high temperature" (publication number 117542421A) provides a method for establishing a multi-segment bond-slip constitutive model after high temperature by using a calculation method of fitting and substituting multiple sets of formulas. For example, the literature "Research on the establishment method of bond-slip constitutive relationship of reinforced concrete" (Sichuan Building Science Research, Vol. 32, No. 1, February 2006) introduces equivalent strain and correction coefficient to provide a method for establishing bond-slip constitutive relationship of corroded steel bar and concrete. However, the ideal bond-slip relationship is a local bond-slip constitutive relationship applicable to any position on any long bond segment. Due to the uneven distribution of bond stress with bond length and the difficulty in measuring local bond performance parameters, the results of segmenting the multi-segment form according to test conditions are difficult to reflect the real damage.

[0006] In addition, the bond-slip constitutive relationship needs to accurately describe the characteristics of reinforced concrete. The above forms usually rely on specific test conditions. Although they can provide certain predictive capabilities, they have poor adaptability under complex conditions (such as different types of reinforced concrete material parameters) and cannot reflect the actual damage of reinforced concrete regarding bond-slip in real time, and cannot be fully applied in actual engineering.

[0007] Therefore, in engineering practice, how to generally cover the material parameters of different types of reinforced concrete to establish a bond-slip constitutive model that can reflect the real damage of reinforced concrete can provide a reference for the maintenance and reinforcement of reinforced concrete structures, which is of great significance for improving the structural life design method and reducing maintenance costs. Summary of the invention

[0008] In view of the problems existing in the above-mentioned prior art, the present invention provides a method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC, the purpose of which is to establish a bond-slip-constitutive model that can reflect the real damage of reinforced concrete in combination with acoustic emission technology, thereby providing an important basis for damage assessment of the bond interface between steel and concrete.

[0009] To achieve the above objectives, the present invention adopts the following technical solutions:

[0010] The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC includes the following steps:

[0011] Step S1, obtaining reinforced concrete parameters, a bond-slip curve of reinforced concrete and acoustic emission characteristic parameters, wherein the acoustic emission characteristic parameters include energy parameters, amplitude parameters, ring count, rise time and duration;

[0012] Step S2, extracting multiple MFCC feature parameters based on the amplitude parameter, drawing an MFCC feature map based on the extracted multiple MFCC feature parameters and energy parameters, and selecting the first MFCC features, combined with amplitude parameters, ring counts, rise time and duration, to classify the real damage stage of the bond-slip curve of the reinforced concrete parameters;

[0013] Step S3, based on the real damage stage of the bond-slip curve of the reinforced concrete parameters, a bond-slip curve containing an effective real damage stage is obtained, and the bond-slip constitutive model of the reinforced concrete parameters is established using data of the bond-slip curve containing the effective real damage stage.

[0014] Furthermore, the process of step S1 is:

[0015] Step S11, obtaining reinforced concrete parameters;

[0016] Step S12, a pull-out test is used to obtain the bond-slip curve of the reinforced concrete (i.e., the relationship curve between the bond stress and the slip amount between the steel bar and the concrete), and the acoustic emission technology is used for real-time monitoring during the pull-out test to obtain the acoustic emission characteristic parameters.

[0017] Furthermore, in step S1, the reinforced concrete parameters include steel bar parameters and concrete parameters, the steel bar parameters include one or more of steel bar type, steel bar chemical element composition, steel bar overall length, steel bar bonding length, and steel bar embedded concrete position, and the concrete parameters include one or more of concrete mix ratio, concrete size, concrete curing temperature, concrete curing humidity, and concrete curing time.

[0018] Furthermore, the process of step S2 is:

[0019] Step S21, pre-emphasize the amplitude parameter to obtain a pre-emphasized acoustic emission signal;

[0020] Step S22, dividing the pre-emphasized acoustic emission signal into frames, multiplying each frame of the pre-emphasized acoustic emission signal by a windowing function to obtain a framed windowed acoustic emission signal, converting the framed windowed acoustic emission signal from the time domain to the frequency domain by discrete Fourier transform, and calculating the signal power spectrum;

[0021] Step S23, passing the signal power spectrum through a set of Mel filters, defining the number of Mel filters, and calculating the logarithmic energy of the Mel filter output;

[0022] Step S24, using discrete cosine transform (DCT) to decorrelate and reduce the dimension of the logarithmic energy, and finally calculate and obtain multiple MFCC feature parameters;

[0023] Step S25, draw an MFCC feature map based on multiple MFCC feature parameters and energy parameters, select the first MFCC features;

[0024] Step S26, Select the first The maximum point of the fluctuation response of the MFCC feature is taken as the first point of the real damage stage of the reinforced concrete bond-slip curve. mutation points, , , where They are the amplitude parameter, ringing count, rise time and duration of the acoustic emission characteristic parameters. The mutation point of each stage (can be qualitatively determined based on the trend of acoustic emission characteristic parameters and the trend of adhesion-slip curve);

[0025] Step S27, dividing the real damage stage of the bond-slip curve of the reinforced concrete parameters based on the mutation point of the real damage stage of the bond-slip curve of the reinforced concrete.

[0026] Furthermore, in step S21, the formula for the pre-emphasis processing is:

[0027] ;

[0028] In the formula, Take 0.97, To pre-emphasize the acoustic emission signal, For the The amplitude of the sampling points, For the The amplitude of the sampling points, is a positive integer;

[0029] Step S22, the frame division formula is:

[0030] ;

[0031] In the formula, For the Frame pre-emphasis of AE signal, is a positive integer, is the frame shift, is the frame length;

[0032] The formula of the windowing function is:

[0033] ;

[0034] In the formula, For the Frame segmentation and windowing of acoustic emission signals, is the Hamming window coefficient, take 0.46;

[0035] The formula for the discrete Fourier transform is:

[0036] ;

[0037] ;

[0038] In the formula, is the signal power spectrum function, for No. The discrete Fourier transform of the values, is an imaginary unit, is a positive integer;

[0039] In step S23, the calculation formula of the logarithmic energy is:

[0040] ;

[0041] In the formula, Logarithmic energy No. values, For the The Mel filter transfer function values, is the total number of Mel filters;

[0042] In step S24, the calculation formula for decorrelation and dimensionality reduction is:

[0043] ;

[0044] In the formula, is the first parameter of MFCC feature coefficients, is the number of Mel cepstral coefficients, ranging from 12 to 24.

[0045] Further, in step S25, the The fluctuation response of the MFCC features is similar to the fluctuation of the energy parameter; further, the ≤12; in particular, further, the =1 or 2 (in most cases, the fluctuation responses of each MFCC feature are similar, and are also similar to the fluctuations of the energy parameter).

[0046] Furthermore, in step S27, based on the mutation point of the real damage stage of the reinforced concrete bond-slip curve and in combination with the trend of the reinforced concrete bond-slip curve, the real damage stage of the bond-slip curve of the reinforced concrete parameters is divided into a micro-slip stage (slope approaches 0), a linear rise stage (slope remains unchanged), a constrained development stage (slope decreases, does not approach 0), and a splitting-pullout degradation stage (slope decreases, with a tendency to approach 0).

[0047] It should be noted that as the bonding performance degrades, some of the real damage stages will merge and disappear. The micro-slip stage is composed of the ineffective slip caused by the test fixture and the very small slip at the beginning. In this stage, the bonding stress approaches 0, and only the slip increases. This stage does not participate in the establishment of the constitutive model.

[0048] Furthermore, the process of step S3 is:

[0049] Step S31, based on the real damage stage of the bond-slip curve of the reinforced concrete parameters, combined with the bond-slip curve of the reinforced concrete, by moving the coordinate origin, ignoring the micro-slip stage in the real damage stage, to obtain a bond-slip curve containing an effective real damage stage;

[0050] ;

[0051] ;

[0052] In the formula, For the The effective bond stress, For the The original bond stress, is the maximum bonding stress in the micro-slip stage, For the The effective slip amount, For the The original slip amount, is the maximum slip amount in the micro-slip stage;

[0053] Step S32, based on the bond-slip curve containing the effective real damage stage, establish the bond-slip constitutive model of the reinforced concrete parameters containing the correction coefficient:

[0054] ;

[0055] In the formula, Bond stress With slip The piecewise function of the variation, , , are the restraining strength, splitting strength and ultimate strength of reinforced concrete in the bond-slip process, , , , are the initial slip, restrained slip, splitting slip and limit slip in the bond-slip process of reinforced concrete, and All are bond stress correction factors;

[0056] Step S33, the data of the bond-slip curve containing the effective real damage stage is substituted into the model of step S32, and the matrix laboratory (MATLAB) is used to fit to obtain and ;

[0057] Step S34, establish and The expression is:

[0058] , ;

[0059] In the formula, To ignore the suppression strength before the micro-slip stage in the real damage stage, , , , All are undetermined coefficients;

[0060] , , , The value of τ is obtained by r ' , and Substitute into and The expression of is obtained by fitting using MATLAB;

[0061] Step S35: and Substituting into the model of step S32, the bond-slip constitutive model of the reinforced concrete parameters is obtained:

[0062] .

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] (1) The MFCC-based reinforced concrete bond-slip constitutive relationship establishment method of the present invention is established based on acoustic emission real-time monitoring technology. Compared with the existing bond-slip constitutive relationship establishment method, this method can adapt to the influence of material parameters, can express the real process of damage, and the process of establishing the model has strong generalization power, and has a wider range of applications in practical engineering.

[0065] (2) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC of the present invention divides the bond failure process of reinforced concrete into damage stages based on MFCC, and establishes the bond-slip constitutive model of reinforced concrete based on the divided stages. Compared with the stage division of the traditional model, the method can represent the real damage of reinforced concrete bond failure, the division stage is more accurate, and it can effectively describe the bond-slip behavior of steel bars and concrete, and it is more practical.

[0066] (3) The MFCC-based reinforced concrete bond-slip constitutive relationship establishment method of the present invention proposes a bond stress correction coefficient in the model based on the MFCC-divided stages, which can accurately express the bond stress value at the stage mutation point and can avoid the problem of non-convergence of calculations caused by sudden changes in bond strength in numerical calculations to a certain extent.

[0067] (4) The MFCC-based reinforced concrete bond-slip constitutive relationship establishment method of the present invention establishes an expression for the bond stress correction coefficient, which can effectively predict the bond-slip behavior of the same type of steel bars and concrete, and provide technical support for the damage assessment of various types of reinforced concrete bond interfaces, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0069] Figure 1 Schematic diagram of the real damage stage of the bond stress-slip curve of the reinforced concrete specimen of Example 1 of the present invention; in the figure, is the bonding stress, is the slip amount, They are the inhibition strength, splitting strength, ultimate strength and the inhibition strength before the micro-slip stage in the real damage stage of the bond-slip curve of the reinforced concrete specimen, , , , , They are the original initial slip, initial slip, suppressed slip, splitting slip and limit slip of the bond-slip curve of reinforced concrete specimens, respectively. Stage I', stage I, stage II and stage III are divided into micro-slip stage, linear rise stage, constraint development stage and splitting-pullout degradation stage.

[0070] Figure 2 1 and 2 are bond stress-slip curves of reinforced concrete specimens with different corrosion rates in Example 1 of the present invention; in the figure, (a) is a corrosion rate of 0%, (b) is a corrosion rate of 3%, (c) is a corrosion rate of 5%, and (d) is a corrosion rate of 8%.

[0071] Figure 3 1 is the stage division result of the acoustic emission characteristic parameters of the reinforced concrete specimen with a corrosion rate of 0% in Example 1 of the present invention; in the figure, (a) is the amplitude, (b) is the ringing count, (c) is the rise time, and (d) is the duration.

[0072] Figure 4 These are MFCC characteristic diagrams of the real damage stages of reinforced concrete specimens with different corrosion rates in Example 1 of the present invention. In the diagram, (a) is a corrosion rate of 0%, (b) is a corrosion rate of 3%, (c) is a corrosion rate of 5%, and (d) is a corrosion rate of 8%.

[0073] Figure 5 The results of dividing the real damage stages of the bond-slip curves of reinforced concrete specimens with different corrosion rates in Example 1 of the present invention; in the figure, (a) is a corrosion rate of 0%, (b) is a corrosion rate of 3%, (c) is a corrosion rate of 5%, and (d) is a corrosion rate of 8%. The star indicates that MFCC-1 The maximum point of the fluctuation response within the range. DETAILED DESCRIPTION

[0074] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below in conjunction with embodiments.

[0075] In the following examples, various processes and methods not described in detail are conventional methods known in the art. Unless otherwise specified, the materials, reagents, devices, instruments, equipment, etc. used in the following examples can be obtained from commercial sources.

[0076] Example 1

[0077] The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC is as follows:

[0078] Step S11, obtaining reinforced concrete parameters, the chemical element composition of the steel bars is shown in Table 1, and the concrete mix ratio is shown in Table 2:

[0079] Table 1 Chemical element composition of steel bars

[0080]

[0081] Table 2 Concrete mix ratio

[0082]

[0083] The concrete was vibrated into the mold, and the pulled specimens were demoulded and transferred to a curing room with a relative humidity of 95% and a temperature of 20°C±2°C for curing for 28 days. The concrete size of 100mm×100mm×200mm was adopted, and a HRB400 steel bar was vertically embedded in the central axis with an overall length of 420mm and a bonding length of 100mm. The electric corrosion method was used to simulate the corrosion environment, and reinforced concrete pull-out specimens with corrosion rates of 0%, 3%, 5%, and 8% were prepared, referred to as specimens.

[0084] Step S12, the pull-out test uses an electro-hydraulic servo fatigue testing machine (MTS) as the loading device. The range of the testing machine is ±200kN. The linear variable differential transformer (LVDT) is placed under the free end to continuously monitor and record the axial sliding deformation of the specimen. In the test, the test is considered to be over when the relative slip between the steel bar and the concrete reaches 10mm or the specimen is split and damaged. The same type of specimen was tested twice, and the damage of the two tests was different, so the changes in the bond-slip curve of the reinforced concrete and the acoustic emission characteristic parameters are also different. The bond-slip curve results of reinforced concrete are as follows Figure 2 shown.

[0085] Figure 2 (a) is the bond stress-slip curve of the reinforced concrete specimen with a corrosion rate of 0%, f0×0-1 represents the first test result of the specimen with a corrosion rate of 0%, and f0×0-2 represents the second test result of the specimen with a corrosion rate of 0%. Figure 2 (b) is the bond stress-slip curve of the reinforced concrete specimen with a corrosion rate of 3%, f0×3-1 represents the first test result of the specimen with a corrosion rate of 3%, and f0×3-2 represents the second test result of the specimen with a corrosion rate of 3%. Figure 2 (c) is the bond stress-slip curve of the reinforced concrete specimen with a corrosion rate of 5%, f0×5-1 represents the first test result of the specimen with a corrosion rate of 5%, and f0×5-2 represents the second test result of the specimen with a corrosion rate of 5%. Figure 2 (d) is the bond stress-slip curve of the reinforced concrete specimen with a corrosion rate of 8%, f0×8-1 represents the primary test result of the specimen with a corrosion rate of 8%, and f0×8-2 represents the secondary test result of the specimen with a corrosion rate of 8%.

[0086] Step S13, first process the test specimen, and use acoustic emission (AE) technology to monitor the loading process of the direct pull test. The SAEU2S acoustic emission test system is used in conjunction with the SR150 acoustic emission sensor. The threshold calibration of the acquisition system is 40dB, the peak definition time is set to 50μs, the hit definition time is set to 150μs, and the hit lock time is set to 300μs.

[0087] Step S21, pre-emphasize the amplitude parameter to obtain a pre-emphasized acoustic emission signal. The formula for pre-emphasis is:

[0088] ;

[0089] In the formula, Take 0.97, To pre-emphasize the acoustic emission signal, For the The amplitude of the sampling points, For the The amplitude of the sampling points, is a positive integer;

[0090] Step S22, dividing the pre-emphasized acoustic emission signal into frames, and the framing formula is:

[0091] ;

[0092] In the formula, For the Frame pre-emphasis of AE signal, is a positive integer, is the frame shift, is the frame length; the frame length of the specimens with corrosion rates of 0% and 3% is set to 20, and the frame shift is set to 10; the frame length of the specimens with corrosion rates of 5% and 8% is set to 10, and the frame shift is set to 5;

[0093] Multiply each frame of pre-emphasized AE signal by the windowing function to obtain a framed windowed AE signal. The formula of the windowing function is:

[0094] ;

[0095] In the formula, For the Frame segmentation and windowing of acoustic emission signals, is the Hamming window coefficient, take 0.46;

[0096] The framed and windowed acoustic emission signal is converted from the time domain to the frequency domain by discrete Fourier transform, and the signal power spectrum is calculated;

[0097] ;

[0098] ;

[0099] In the formula, is the signal power spectrum function, for No. The discrete Fourier transform of the values, is an imaginary unit, is a positive integer;

[0100] Step S23, pass the signal power spectrum through a group of Mel filters, define the number of Mel filters, calculate the logarithmic energy output by the Mel filters, and the calculation formula of the logarithmic energy is:

[0101] ;

[0102] In the formula, Logarithmic energy No. values, For the The Mel filter transfer function values, is the total number of Mel filters, =16.

[0103] Step S24, using discrete cosine transform to decorrelate and reduce the dimension of the logarithmic energy, and finally calculate the MFCC feature parameters. The calculation formula for decorrelation and dimensionality reduction is:

[0104] ;

[0105] In the formula, is the first parameter of MFCC feature coefficients, is the number of Mel-frequency cepstral coefficients, which is 12.

[0106] Step S25, based on multiple MFCC feature parameters and energy parameters, draw MFCC feature graphs. The MFCC feature graphs of reinforced concrete specimens with corrosion rates of 0%, 3%, 5%, and 8% are as follows: Figure 4 As shown in (a), (b), (c), and (d) (in the figure, MFCC-1, MFCC-2, MFCC-3, MFCC-4, MFCC-5, MFCC-6, MFCC-7, MFCC-8, MFCC-9, MFCC-10, MFCC-11, and MFCC-12 are the 1st to 12th MFCC feature parameters respectively);

[0107] Select the first MFCC feature, namely MFCC-1.

[0108] Step S26, Select the first The maximum point of the fluctuation response of the MFCC feature is taken as the first point of the real damage stage of the reinforced concrete bond-slip curve. mutation points, , , where They are the amplitude parameter, ringing count, rise time and duration of the acoustic emission characteristic parameters. The stage division of acoustic emission characteristic parameters takes the specimen with 0% corrosion rate as an example. The results are as follows: Figure 3 As shown in (a)-(d).

[0109] Step S27, based on the mutation point of the real damage of the bond-slip curve of the reinforced concrete and the trend of the bond-slip curve of the reinforced concrete, the real damage stage of the bond-slip curve of the reinforced concrete is divided. The schematic diagram of the real damage stage is as follows: Figure 1As shown in Figure 1, stage I', stage I, stage II, and stage III are divided into micro-slip stage (slope approaches 0), linear rising stage (slope remains unchanged), constraint development stage (slope decreases, does not approach 0), and splitting-pullout degradation stage (slope decreases, with a tendency to approach 0). The division results of the real damage stages of the bond-slip curves of reinforced concrete specimens with corrosion rates of 0%, 3%, 5%, and 8% are shown in Figure 1. Figure 5 As shown in (a), (b), (c) and (d).

[0110] Step S31, based on the mutation point of the real damage stage of the reinforced concrete parameter bond-slip curve, combined with the reinforced concrete bond-slip curve, by moving the coordinate origin, ignoring the micro-slip stage in the real damage stage, to obtain a bond-slip curve containing an effective real damage stage;

[0111] ;

[0112] ;

[0113] In the formula, For the The effective bond stress, For the The original bond stress, is the maximum bonding stress in the micro-slip stage, For the The effective slip amount, For the The original slip amount, is the maximum slip amount in the micro-slip stage;

[0114] Step S32, based on the bond-slip curve containing the effective real damage stage, establish the bond-slip constitutive model of the reinforced concrete parameters containing the correction coefficient:

[0115] ;

[0116] In the formula, Bond stress With slip The piecewise function of the variation, , , are the restraining strength, splitting strength and ultimate strength of reinforced concrete in the bond-slip process, , , , are the initial slip, restrained slip, splitting slip and limit slip in the bond-slip process of reinforced concrete, and Both are bond stress correction factors.

[0117] Step S33, substitute the data of the bond-slip curve containing the effective real damage stage into the bond-slip constitutive model of step S32, and use MATLAB to fit to obtain and , goodness of fit High, the results are shown in Table 3:

[0118] Table 3 Bond stress correction coefficient and stage division results

[0119]

[0120] Step S34, establish and The expression is:

[0121] , ;

[0122] In the formula, To ignore the suppression strength before the micro-slip stage in the real damage stage, , , , All are undetermined coefficients;

[0123] , , , The value of τ is obtained by r ' , and Substitute into and The expression of is obtained by fitting using MATLAB, and the goodness of fit is All above 0.9;

[0124] Step S35: and Substitute the bond-slip constitutive model of step S32 to obtain the bond-slip constitutive model of the reinforced concrete parameters:

[0125] .

[0126] The bonding damage process of the specimens in the secondary test is divided into stages in the same way to obtain Substituting it into the above formula, the bond-slip constitutive model of reinforced concrete specimens is obtained. The model data is compared with the test data, and the model accuracy is calculated. The formula is shown below, and the results are shown in Table 4:

[0127] ;

[0128] In the formula, is the model accuracy, For the Test bond stress, For the The bonding stress of the model, is the average value of the test bond stress.

[0129] Table 4 Model validation results

[0130]

[0131] Since the damage process of reinforced concrete with the same parameters in the test process is different, the damage stages need to be determined according to the specific damage results. The results are inconsistent. According to the divided stages, the bond-slip constitutive model is established. After substituting the bond-slip constitutive model of this type of reinforced concrete into the above formula, the obtained model data and test data are calculated with accuracy, which shows that the trends of the two data are very consistent, indicating that this method has high accuracy and reliability.

[0132] In summary, the method of the present invention can use acoustic emission technology to establish the bond-slip constitutive relationship of reinforced concrete. The stage division of the bond-slip process of reinforced concrete is realized by MFCC feature extraction, which can represent the real damage of reinforced concrete bond failure and the stage division is more accurate. In addition, the present invention has wide applicability and can be applied to the exploration of bond-slip behavior of reinforced concrete under complex conditions, and has strong practicality in practical engineering applications.

[0133] Obviously, the above embodiments are merely examples for clear explanation, and are not intended to limit the embodiments. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. The obvious changes or modifications derived from them are still within the protection scope of the invention.

Claims

1. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC is characterized by: The following steps are involved: Step S1, obtaining reinforced concrete parameters, a bond-slip curve of reinforced concrete and acoustic emission characteristic parameters, wherein the acoustic emission characteristic parameters include energy parameters, amplitude parameters, ring count, rise time and duration; Step S2, extracting multiple MFCC feature parameters based on the amplitude parameter, drawing an MFCC feature map based on the extracted multiple MFCC feature parameters and energy parameters, and selecting the first MFCC features, combined with amplitude parameters, ring counts, rise time and duration, to classify the real damage stage of the bond-slip curve of the reinforced concrete parameters; Step S3, based on the real damage stage of the bond-slip curve of the reinforced concrete parameters, a bond-slip curve containing an effective real damage stage is obtained, and the bond-slip constitutive model of the reinforced concrete parameters is established using data of the bond-slip curve containing the effective real damage stage.

2. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 1 is characterized in that: The process of step S1 is as follows: Step S11, obtaining reinforced concrete parameters; Step S12, a pull-out test is used to obtain the bond-slip curve of the reinforced concrete, and the acoustic emission technology is used for real-time monitoring during the pull-out test to obtain acoustic emission characteristic parameters.

3. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 1, characterized in that: In step S1, the reinforced concrete parameters include steel bar parameters and concrete parameters. The steel bar parameters include one or more of steel bar type, steel bar chemical element composition, steel bar overall length, steel bar bonding length, and steel bar embedded concrete position. The concrete parameters include one or more of concrete mix ratio, concrete size, concrete curing temperature, concrete curing humidity, and concrete curing time.

4. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 1, characterized in that: The process of step S2 is: Step S21, pre-emphasize the amplitude parameter to obtain a pre-emphasized acoustic emission signal; Step S22, dividing the pre-emphasized acoustic emission signal into frames, multiplying each frame of the pre-emphasized acoustic emission signal by a windowing function to obtain a framed windowed acoustic emission signal, converting the framed windowed acoustic emission signal from the time domain to the frequency domain by discrete Fourier transform, and calculating the signal power spectrum; Step S23, passing the signal power spectrum through a set of Mel filters, defining the number of Mel filters, and calculating the logarithmic energy of the Mel filter output; Step S24, using discrete cosine transform to decorrelate and reduce the dimension of the logarithmic energy, and finally calculating and obtaining a plurality of MFCC feature parameters; Step S25, draw an MFCC feature map based on multiple MFCC feature parameters and energy parameters, select the first MFCC features; Step S26, Select the first The maximum point of the fluctuation response of the MFCC feature is taken as the first point of the real damage stage of the reinforced concrete bond-slip curve. mutation points, , , where They are the amplitude parameter, ringing count, rise time and duration of the acoustic emission characteristic parameters. Phase mutation point; Step S27, dividing the real damage stage of the bond-slip curve of the reinforced concrete parameters based on the mutation point of the real damage stage of the bond-slip curve of the reinforced concrete.

5. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 4 is characterized in that: In step S21, the formula for the pre-emphasis processing is: ； In the formula, Take 0.97, To pre-emphasize the acoustic emission signal, For the The amplitude of the sampling points, For the The amplitude of the sampling points, is a positive integer; Step S22, the frame division formula is: ； In the formula, For the Frame pre-emphasis of acoustic emission signal, is a positive integer, is the frame shift, is the frame length; The formula of the windowing function is: ； In the formula, For the Frame segmentation and windowing of acoustic emission signals, is the Hamming window coefficient, take 0.46; The formula for the discrete Fourier transform is: ； ； In the formula, is the signal power spectrum function, for No. The discrete Fourier transform of the values, is an imaginary unit, is a positive integer; In step S23, the calculation formula of the logarithmic energy is: ； In the formula, Logarithmic energy No. values, For the The Mel filter transfer function values, is the total number of Mel filters; In step S24, the calculation formula for decorrelation and dimensionality reduction is: ； In the formula, is the first parameter of MFCC feature coefficients, is the number of Mel cepstral coefficients, ranging from 12 to 24.

6. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 4 is characterized in that: In step S25, the ≤12.

7. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 6, characterized in that: Said =1 or 2.

8. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 4, characterized in that: In step S27, based on the mutation point of the real damage stage of the bond-slip curve of the reinforced concrete and combined with the trend of the bond-slip curve of the reinforced concrete, the real damage stage of the bond-slip curve of the reinforced concrete parameters is divided into a micro-slip stage, a linear rise stage, a constrained development stage, and a splitting-pullout degradation stage.

9. The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC according to claim 1, characterized in that: The process of step S3 is as follows: Step S31, based on the real damage stage of the bond-slip curve of the reinforced concrete parameters, combined with the bond-slip curve of the reinforced concrete, by moving the coordinate origin, ignoring the micro-slip stage in the real damage stage, to obtain a bond-slip curve containing an effective real damage stage; ； ； In the formula, For the The effective bond stress, For the The original bond stress, is the maximum bonding stress in the micro-slip stage, For the The effective slip amount, For the The original slip amount, is the maximum slip amount in the micro-slip stage; Step S32, based on the bond-slip curve containing the effective real damage stage, establish the bond-slip constitutive model of the reinforced concrete parameters containing the correction coefficient: ； In the formula, Bond stress With slip The piecewise function of the variation, , , are the restraining strength, splitting strength and ultimate strength of reinforced concrete in the bond-slip process, , , , are the initial slip, restrained slip, splitting slip and limit slip in the bond-slip process of reinforced concrete, and All are bond stress correction factors; Step S33, substitute the data of the bond-slip curve containing the effective real damage stage into the model of step S32, and use the matrix laboratory to fit to obtain and ; Step S34, establish and The expression is: ， ； In the formula, To ignore the suppression strength before the micro-slip stage in the real damage stage, , , , All are undetermined coefficients; , , , The value of τ is obtained by r ' , and Substitute into and The expression for was obtained using the Matrix Lab fit; Step S35: and Substituting into the model of step S32, the bond-slip constitutive model of the reinforced concrete parameters is obtained: 。

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