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 and acoustic emission characteristic parameters in a reinforced concrete bonding failure process; then respectively drawing a time point-acoustic emission characteristic parameter curve and a time point-MFCC characteristic parameter curve, and taking the time point corresponding to the maximum downward fluctuation degree of the MFCC characteristic parameter in the time range as the first bonding failure stage division time point of the reinforced concrete; and finally, dividing a bonding-slip curve of the reinforced concrete parameters based on the division time points of the bonding failure stages, and establishing a bonding-slip constitutive model of the reinforced concrete parameters based on the obtained bonding-slip curve containing the effective real damage stages. 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] This invention belongs to the technical field of analysis methods for the bond behavior of steel bars and concrete, specifically relating to a method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC (Mehr frequency cepstral coefficients). Background Technology

[0002] Reinforced concrete, as one of the most widely used composite materials in construction, fully integrates the advantages of both concrete and steel reinforcement. However, the prerequisite for the joint operation of steel reinforcement and concrete is a good bond between them, which is an interaction between the steel reinforcement and concrete that transfers stress and coordinates deformation. The bond behavior of reinforced concrete reflects the collaborative working ability between steel reinforcement and concrete, and it directly affects the safety and durability of the structure. Therefore, analyzing the bond behavior of reinforced concrete is crucial.

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

[0004] The single-segment form summarizes the bond-slip relationship in the ascending segment 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 a bond-slip constitutive model of the interface between plain round steel bars and concrete using experimental results and theoretical analysis. However, this form only expresses the bond-slip relationship mathematically, weakening the true representation of bond damage in reinforced concrete, and thus introducing errors in practical applications.

[0005] The multi-segment form divides the bond-slip relationship in the ascending segment when bond damage occurs, which can better reflect the failure mechanism of different bond failure modes and show the main distribution of bond stress at different stages of the bond action. For example, the Chinese patent application "Method and System for Establishing Bond-Slip Constitutive Model of Steel Reinforcement and Concrete after High Temperature" (Publication No. 117542421A) provides a method for establishing a multi-segment bond-slip constitutive model after high temperature by using a calculation method that fits and substitutes multiple sets of formulas. Another example is the research on the establishment method of bond-slip constitutive relationship of reinforced concrete (Sichuan Building Science Research, Vol. 32, No. 1, February 2006), which introduces equivalent strain and correction coefficients to provide a method for establishing the bond-slip constitutive relationship of corroded reinforced concrete. However, the ideal bond-slip relationship is applicable to the local bond-slip constitutive relationship at any position on any bond segment of arbitrary length. Due to the non-uniformity of bond stress distribution with bond length and the difficulty in measuring local bond performance parameters, the results of the multi-segment form based on experimental conditions are difficult to reflect the true damage.

[0006] Furthermore, bond-slip constitutive relations require accurate description of the properties of reinforced concrete. The above forms usually depend on specific test conditions. Although they can provide some predictive ability, they are poorly adaptable to complex conditions (such as different types of reinforced concrete material parameters) and cannot reflect the real damage of reinforced concrete with respect to bond-slip in real time, thus they cannot be fully applied in practical engineering.

[0007] Therefore, in engineering practice, establishing a bond-slip constitutive model that comprehensively covers the parameters of different types of reinforced concrete materials and can reflect the actual damage of reinforced concrete can provide a reference for the maintenance and reinforcement of reinforced concrete structures. This is of great significance for improving structural life design methods and reducing maintenance costs. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a method for establishing bond-slip constitutive relations of reinforced concrete based on MFCC. The purpose is to establish a bond-slip constitutive model that can reflect the actual damage of reinforced concrete by combining acoustic emission technology, thus providing an important basis for damage assessment of the bond interface between steel bars and concrete.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: The method for establishing bond-slip constitutive relations of reinforced concrete based on MFCC includes the following steps: Step S1: Obtain the parameters of reinforced concrete and the time points in the process of bond failure of reinforced concrete, as well as the slip, bond stress and acoustic emission characteristic parameters corresponding to each time point. The acoustic emission characteristic parameters include amplitude parameters, ring count, rise time and duration. Step S2: Extract MFCC feature parameters based on amplitude parameters, and select 0th or 1st order MFCC feature parameters. Plot curves with time points as the abscissa and amplitude parameters, ring count, rise time, duration, and selected MFCC feature parameters as the ordinate, respectively, to obtain the curves of time point-amplitude parameters, time point-ring count, time point-rise time, time point-duration, and time point-MFCC feature parameters. On the curve of time point - MFCC characteristic parameters, the horizontal axis Within the time range, the time point corresponding to the maximum downward fluctuation of the MFCC characteristic parameters is taken as the first time point of the reinforced concrete. Divide the time points into stages of adhesion failure; The , ; In the formula, The curves representing time point versus amplitude parameter, time point versus ring count, time point versus rise time, and time point versus duration are respectively the first curves on these curves. Divide the time points into stages of adhesion failure. It is a positive integer; Step S3: Based on the slip and bond stress obtained in Step S1, plot the bond-slip curve of the reinforced concrete parameters, according to the data obtained in Step S2. The slip and bond stress corresponding to the time points of the bond failure stage of each reinforced concrete are divided, and the bond-slip curves of the reinforced concrete parameters are divided to obtain the bond-slip curves containing the effective real damage stage. Based on the bond-slip curves containing the effective real damage stage, a bond-slip constitutive model of the reinforced concrete parameters is established.

[0010] Preferably, the process of step S1 is as follows: Step S11: Obtain reinforced concrete parameters; Step S12 involves using a pull-out test and acoustic emission technology to monitor and obtain the time points in the process of bond failure of reinforced concrete, as well as the corresponding slip, bond stress and acoustic emission characteristic parameters at each time point.

[0011] Preferably, in step S1, the reinforced concrete parameters include steel reinforcement parameters and concrete parameters. The steel reinforcement parameters include one or more of the following: steel reinforcement type, steel reinforcement chemical composition, total steel reinforcement length, steel reinforcement bond length, and steel reinforcement embedment position in concrete. The concrete parameters include one or more of the following: concrete mix proportion, concrete dimensions, concrete curing temperature, concrete curing humidity, and concrete curing time.

[0012] Preferably, in step S2, the process of extracting MFCC feature parameters based on amplitude parameters is as follows: Step S21: The amplitude parameters are pre-emphasized to obtain a pre-emphasized acoustic emission signal; Step S22: The pre-emphasized acoustic emission signal is divided into frames, and each frame of the pre-emphasized acoustic emission signal is multiplied by a window function to obtain the framed windowed acoustic emission signal. The framed windowed acoustic emission signal is transformed from the time domain to the frequency domain by discrete Fourier transform, and the signal power spectrum is calculated. Step S23: Pass the signal power spectrum through a set of Mel filters, define the number of Mel filters, and calculate the logarithmic energy of the Mel filter output; Step S24: The logarithmic energy is decorrelated and reduced in dimensionality using discrete cosine transform, and the MFCC feature parameters are finally calculated.

[0013] More preferably, in step S21, the formula for the pre-emphasis processing is: ; In the formula, Take 0.97, For pre-emphasis acoustic emission signals, For the first The amplitude at each sampling point For the first The amplitude at each sampling point It is a positive integer; Step S22, the formula for frame division is: ; In the formula, For the first Frame pre-emphasized acoustic emission signal, It is a positive integer. The number of frame-shifted samples. Number of samples per frame length; The formula for the windowing function is: ; In the formula, For the first Frame-by-frame windowed acoustic signal transmission. The coefficient for the Hamming window is 0.46. The formula for the discrete Fourier transform is: ; ; In the formula, The power spectrum function of the signal. for The Discrete Fourier transform of each value The imaginary unit, It is a positive integer; In step S23, the formula for calculating the logarithmic energy is: ; In the formula, Logarithmic energy The One value, For the first The transfer function of the ______ Mel filter One value, The total number of Mel filters; In step S24, the calculation formulas for decorrelation and dimensionality reduction are as follows: ; In the formula, The first characteristic parameter of MFCC One coefficient, The number of Mel cepstral coefficients is 12-24.

[0014] Preferably, in step S2, the The curves based on time point-amplitude parameter, time point-ring count, time point-rise time, and time point-duration were obtained using the following methods: Step S251: Set the sliding window size of the curve's horizontal coordinate to 15 seconds and the sliding window movement step size to 0.02 seconds to obtain several sliding windows; Step S252: Calculate the mean value of the acoustic emission characteristic parameters corresponding to each of the two adjacent sliding windows. The calculation formula is as follows: In the formula, The mean values ​​of the acoustic emission characteristic parameters for the left sliding window. The mean values ​​of the acoustic emission characteristic parameters of the right sliding window. The first of the left sliding window Sample data of acoustic emission characteristic parameters, The first of the right sliding window Sample data of acoustic emission characteristic parameters, This represents the total number of sample data for acoustic emission characteristic parameters in the left sliding window. This represents the total number of sample data for acoustic emission characteristic parameters in the right sliding window; Step S253: Calculate the difference metric for all adjacent pairs of sliding windows. The calculation formula is as follows: In the formula, This is a measure of the difference between adjacent sliding windows; Step S254: When the difference metric value is greater than the recording threshold, record the difference metric value, the difference sample data, and the time point corresponding to the difference sample data. The recorded difference sample data is the first time point recorded in the left sliding window. Sample data of acoustic emission characteristic parameters, wherein the recording threshold is 0.2~0.5; Step S255: Arrange the recorded difference metrics according to the chronological order of the time points corresponding to the difference sample data. Calculate the difference between two adjacent time points. If the difference is greater than a time threshold, use the earlier time point corresponding to the difference as the last time point of the previous set, and use the later time point corresponding to the difference as the first time point of the next set (if the difference is greater than the time threshold, it is not used as a set division time point). Divide the recorded difference metrics according to this time point division. A set, wherein the time threshold is 2-3 seconds; Step S256: In each set, select the time point corresponding to the largest difference metric as the first point on the corresponding curve. The time points are divided into stages of adhesion failure.

[0015] Preferably, in step S3, the bond-slip curves of the divided reinforced concrete parameters include one or more of the following in chronological order: microslip stage, linear rise stage, constraint development stage, and splitting-pull-out deterioration stage. Furthermore, the slope of the bond-slip curve in the micro-slip stage is initially less than 0.001 and then gradually increases; the slope of the bond-slip curve in the linear rise stage changes within 5%; the slope of the bond-slip curve in the constraint development stage gradually decreases but eventually does not decrease less than 0.001; and the slope of the bond-slip curve in the splitting-pull-out deterioration stage gradually decreases and eventually decreases less than 0.001.

[0016] More preferably, in step S3, the bond-slip curve of the divided reinforced concrete parameters includes a micro-slip stage. By shifting the origin of the coordinate system, the micro-slip stage is ignored, resulting in a bond-slip curve containing the effective true damage stage. The expression for shifting the origin of the coordinate system is: ; ; In the formula, For the first One effective bond stress value, For the first The original bond stress value, This represents the maximum bond stress during the microslip stage. For the first One effective slip value For the first The original slip value This represents the maximum slip value during the microslip stage.

[0017] More preferably, step S3, the method for establishing a bond-slip constitutive model of reinforced concrete parameters based on bond-slip curves containing effective real damage stages, includes: Step S31: Based on the bond-slip curve containing the effective true damage stage, establish a bond-slip constitutive model of the reinforced concrete parameters with correction coefficients: ; In the formula, For adhesive stress With slip A piecewise function that changes. , , These represent the maximum bond stresses in the linear rise phase, constraint development phase, and splitting-pull-out degradation phase of the bond-slip curves containing the effective true damage phase, respectively. , , , These represent the maximum slip amounts in the microslip stage, linear rise stage, constraint development stage, and splitting-pull-out degradation stage of the bond-slip curve containing the effective true damage stage, respectively. and All are adhesive stress correction factors; Step S32: Substitute the data from the bond-slip curves containing the effective true damage stage into the model from step S32, and use matrix laboratory fitting to obtain... and ; Step S33, establish and The expression: , ; In the formula, To ignore the maximum bond stress in the linearly rising phase before the microslip stage in the bond-slip curve containing the effective true damage stage, , , , All are undetermined coefficients; , , , The value will be obtained by , and Substitute into and The expression was obtained using matrix lab fitting; Step S34, will and Substituting into the model of step S32, the bond-slip constitutive model of the reinforced concrete parameters is obtained: .

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC of the present invention is based on the real-time acoustic emission monitoring technology. Compared with the existing bond-slip constitutive relationship establishment method, this method can adapt to the influence of material parameters, express the real process of damage, and the model establishment process has a strong generalization ability and a wider range of applications in actual engineering.

[0019] (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 a bond-slip constitutive model of reinforced concrete based on the stage division. Compared with the stage division of the traditional model, the present invention can represent the real damage of bond failure of reinforced concrete, the stage division is more accurate, and it can effectively describe the bond-slip behavior of steel bars and concrete, and has stronger practicality.

[0020] (3) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC of the present invention proposes a bond stress correction coefficient in the model based on the stages divided by MFCC, which can accurately express the bond stress value at the stage change point and can avoid the problem of non-convergence of calculation due to the sudden change of bond strength in numerical calculation to a certain extent.

[0021] (4) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC 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 provides technical support for the assessment of bond interface damage of various types of reinforced concrete. It has a wide range of applications. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used 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 those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 The figure shows the results of dividing the bond failure stage of reinforced concrete specimens with different corrosion rates in Example 1 of the present invention into time points; in the figure, (a) represents a corrosion rate of 0%, (b) represents a corrosion rate of 3%, (c) represents a corrosion rate of 5%, and (d) represents a corrosion rate of 8%; the star represents the horizontal axis. The time point corresponding to the maximum downward fluctuation of the MFCC characteristic parameters within the time range is the time point for dividing the bond failure stage of reinforced concrete; the intersection of stage I', stage I, stage II, and stage III on the curves of time point-amplitude parameter, time point-ring count, time point-rise time, and time point-duration is the time point for dividing the bond failure stage of the corresponding curve.

[0024] Figure 2 The figure shows the bond-slip curves of reinforced concrete specimens with different corrosion rates in Example 1 of the present invention; in the figure, (a) represents a corrosion rate of 0%, (b) represents a corrosion rate of 3%, (c) represents a corrosion rate of 5%, and (d) represents a corrosion rate of 8%.

[0025] Figure 3 This is a schematic diagram showing the result of dividing the bond-slip curves of reinforced concrete parameters according to Embodiment 1 of the present invention; in the figure, For bonding stress, For slip, These represent the inhibition strength, splitting strength, ultimate strength, and inhibition strength before the micro-slip stage (ignoring the actual damage stage) of the bond-slip curves of reinforced concrete specimens, respectively. 、 , , , The bond-slip curves of reinforced concrete specimens are represented by the original initial slip, initial slip, suppressed slip, splitting slip, and ultimate slip. Stages I', I, II, and III are divided into micro-slip stage, linear rise stage, constrained development stage, and splitting-pull-out deterioration stage. Detailed Implementation

[0026] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to embodiments.

[0027] In the following embodiments, various processes and methods not described in detail are conventional methods known in the art. Unless otherwise specified, the materials, reagents, apparatus, instruments, equipment, etc., used in the following embodiments are commercially available.

[0028] Example 1 The method for establishing bond-slip constitutive relations of reinforced concrete based on MFCC is as follows: Step S1: Step S11: Obtain the parameters of the reinforced concrete. The chemical element composition of the steel reinforcement is shown in Table 1, and the concrete mix design is shown in Table 2. Table 1 Chemical elemental composition of steel reinforcement Table 2 Concrete Mix Proportions Concrete was vibrated into the mold, and the pulled-out specimens were demolded and transferred to a curing room with a relative humidity of 95% and a temperature of 20℃±2℃ for 28 days. Concrete specimens with dimensions of 100mm×100mm×200mm were used, with an HRB400 steel bar vertically embedded in the central axis, resulting in a total length of 420mm and a bond length of 100mm. An electro-corrosion method was used to simulate a corrosion environment, and reinforced concrete pull-out specimens with corrosion rates of 0%, 3%, 5%, and 8% were prepared (hereinafter referred to as specimens). Two tests were conducted on the same type of specimen; the damage in the two tests was different, therefore the changes in slip, bond stress, and acoustic emission characteristic parameters of the reinforced concrete at each time point were also different. The two specimens were treated separately using the same method.

[0029] Step S12 involves conducting a pull-out test and using acoustic emission (AE) technology to monitor and acquire the time points in the bond failure process of reinforced concrete, as well as the corresponding slip, bond stress, and acoustic emission characteristic parameters at each time point. An electro-hydraulic servo fatigue testing machine (MTS) with a range of ±200 kN was used as the loading device for the pull-out test. A linear variable differential transformer (LVDT) was placed below the free end to continuously monitor and record the axial sliding deformation of the specimen. The test was considered complete when the relative slip between the steel reinforcement and concrete reached 10 mm or when the specimen showed splitting failure. Simultaneously, acoustic emission (AE) technology was used to monitor the loading process of the direct pull-out test. The SAEU2S acoustic emission testing system was used in conjunction with the SR150 acoustic emission sensor. The threshold calibration of the acquisition system was set to 40 dB, the peak definition time was set to 50 μs, the hit definition time was set to 150 μs, and the hit lock time was set to 300 μs.

[0030] Step S2: Step S21: Pre-emphasize the amplitude parameters to obtain the pre-emphasized acoustic emission signal. The formula for pre-emphasis processing is: ; In the formula, Take 0.97, For pre-emphasis acoustic emission signals, For the first The amplitude at each sampling point For the first The amplitude at each sampling point It is a positive integer.

[0031] Step S22: The pre-emphasized acoustic emission signal is divided into frames, and the framing formula is as follows: ; In the formula, For the first Frame pre-emphasized acoustic emission signal, It is a positive integer. The number of frame-shifted samples. The number of samples for frame length is set to 20 for specimens with corrosion rates of 0% and 3%, and 10 for specimens with frame shift. The number of samples for frame length is set to 10 for specimens with corrosion rates of 5% and 8%, and 5 for specimens with frame shift. Multiply the pre-emphasized acoustic emission signal of each frame by a windowing function to obtain the frame-by-frame windowed acoustic emission signal. The formula for the windowing function is: ; In the formula, For the first Frame-by-frame windowed acoustic signal transmission. The coefficient for the Hamming window is 0.46. The framed windowed acoustic transmission signal is converted from the time domain to the frequency domain by using discrete Fourier transform, and the signal power spectrum is calculated. ; ; In the formula, The power spectrum function of the signal. for The Discrete Fourier transform of each value The imaginary unit, It is a positive integer.

[0032] Step S23: Pass the signal power spectrum through a set of Mel filters, define the number of Mel filters, and calculate the logarithmic energy of the Mel filter output. The formula for calculating the logarithmic energy is: ; In the formula, Logarithmic energy The One value, For the first The transfer function of the ______ Mel filter One value, The total number of Mel filters, =16.

[0033] Step S24: The logarithmic energy is decorrelated and reduced in dimension using discrete cosine transform, and the MFCC feature parameters are finally calculated. The formulas for decorrelation and dimension reduction are as follows: ; In the formula, The first characteristic parameter of MFCC One coefficient, The number of Mel cepstral coefficients is 12.

[0034] In step S25, the first-order MFCC characteristic parameters are selected, and curves are plotted with time point as the abscissa and amplitude parameter, ring count, rise time, duration and selected MFCC characteristic parameters as the ordinate, respectively, to obtain the curves of time point-amplitude parameter, time point-ring count, time point-rise time, time point-duration and time point-MFCC characteristic parameters. The curves based on time point-amplitude parameters, time point-ring count, time point-rise time, and time point-duration are obtained using the following methods. : Step S251: Set the sliding window size of the curve's horizontal coordinate to 15 seconds and the sliding window movement step size to 0.02 seconds to obtain several sliding windows; Step S252: Calculate the mean value of the acoustic emission characteristic parameters corresponding to each of the two adjacent sliding windows. The calculation formula is as follows: In the formula, The mean values ​​of the acoustic emission characteristic parameters for the left sliding window. The mean values ​​of the acoustic emission characteristic parameters of the right sliding window. The first of the left sliding window Sample data of acoustic emission characteristic parameters, The first of the right sliding window Sample data of acoustic emission characteristic parameters, This represents the total number of sample data for acoustic emission characteristic parameters in the left sliding window. This represents the total number of sample data for acoustic emission characteristic parameters in the right sliding window; Step S253: Calculate the difference metric for all adjacent pairs of sliding windows. The calculation formula is as follows: In the formula, This is a measure of the difference between adjacent sliding windows; Step S254: When the difference metric value is greater than the recording threshold, record the difference metric value, the difference sample data, and the time point corresponding to the difference sample data. The difference sample data is the time point in the left sliding window. Sample data of acoustic emission characteristic parameters, wherein the recording threshold is 0.2; Step S255: Arrange the recorded difference measurement values ​​according to the chronological order of the time points corresponding to the difference sample data. Calculate the difference between two adjacent time points. When the difference is greater than a time threshold, use the earlier time point corresponding to the difference as the last time point of the previous set, and the later time point corresponding to the difference as the first time point of the next set. Divide the recorded difference measurement values ​​according to this time point division. A set, wherein the time threshold is 2 seconds; Step S256: In each set, select the time point corresponding to the largest difference metric as the first point on the corresponding curve. The time points are divided into stages of adhesion failure.

[0035] Step S26, on the curve of time point - MFCC characteristic parameters, the horizontal axis Within the time range, the time point corresponding to the maximum downward fluctuation of the MFCC characteristic parameters is taken as the first time point of the reinforced concrete. Divide the time points into stages of adhesion failure; The , ; In the formula, The curves representing time point versus amplitude parameter, time point versus ring count, time point versus rise time, and time point versus duration are respectively the first curves on these curves. Divide the time points into stages of adhesion failure. It is a positive integer; The stages of the curves for specimens with corrosion rates of 0%, 3%, 5%, and 8% are determined based on the time points of the bond failure stage, as shown in the figure. Figure 1 As shown in Table 3, the results of dividing the time points for the bonding failure stage are as follows.

[0036] Table 3. Time points for dividing the bond failure stage

[0037] Step S3: Step S31: Based on the slip and bond stress obtained in step S1, plot the bond-slip curves of the reinforced concrete parameters. The bond-slip curve results of the reinforced concrete are as follows: Figure 2 As shown, Figure 2 In Figure (a), the bond-slip curves of the reinforced concrete specimen with a corrosion rate of 0% are shown. f0×0-1 represents the result of the first test of the specimen with a corrosion rate of 0%, and f0×0-2 represents the result of the second test of the specimen with a corrosion rate of 0%. Figure 2 In Figure (b), the bond-slip curves of the reinforced concrete specimen with a corrosion rate of 3% are shown. f0×3-1 represents the result of the first test of the specimen with a corrosion rate of 3%, and f0×3-2 represents the result of the second test of the specimen with a corrosion rate of 3%. Figure 2 In the middle (c), the bond-slip curves of the reinforced concrete specimen with a corrosion rate of 5% are shown. f0×5-1 represents the result of the first test of the specimen with a corrosion rate of 5%, and f0×5-2 represents the result of the second test of the specimen with a corrosion rate of 5%. Figure 2 In the middle (d), the bond-slip curve of the reinforced concrete specimen with a corrosion rate of 8% is shown. f0×8-1 represents the result of the first test of the specimen with a corrosion rate of 8%, and f0×8-2 represents the result of the second test of the specimen with a corrosion rate of 8%.

[0038] Step S32: Based on the slip amount and bond stress corresponding to the time points of the bond failure stage obtained in step S2, divide the bond-slip curves of the reinforced concrete parameters, as follows: Figure 3 As shown, the bond-slip curves of the divided reinforced concrete parameters include one or more of the following in chronological order: microslip stage (stage I'), linear rise stage (stage I), constrained development stage (stage II), and splitting-pull-out deterioration stage (stage III). Furthermore, the slope of the bond-slip curve in the micro-slip stage is initially less than 0.001 and then gradually increases; the slope of the bond-slip curve in the linear rise stage changes within 5%; the slope of the bond-slip curve in the constraint development stage gradually decreases but eventually does not decrease less than 0.001; and the slope of the bond-slip curve in the splitting-pull-out deterioration stage gradually decreases and eventually decreases less than 0.001.

[0039] Step S33: The bond-slip curves of the divided reinforced concrete parameters include the micro-slip stage. By shifting the origin of the coordinate system, the micro-slip stage is ignored, resulting in a bond-slip curve containing the effective true damage stage. The expression for shifting the origin of the coordinate system is: ; ; In the formula, For the first One effective bond stress value, For the first The original bond stress value, This represents the maximum bond stress during the microslip stage. For the first One effective slip value For the first The original slip value This represents the maximum slip value during the microslip stage; If there is no micro-slip stage, the bond-slip curves of the reinforced concrete parameters are derived by dividing the time points corresponding to the slip amount and bond stress at the bond failure stages obtained in step S2. These curves contain the effective true damage stage. and It is 0.

[0040] Step S34: Based on the bond-slip curve containing the effective true damage stage, establish a bond-slip constitutive model of the reinforced concrete parameters including correction coefficients: ; In the formula, For adhesive stress With slip A piecewise function that changes. , , These are the maximum bond stresses (which can be denoted as inhibition strength, splitting strength, and ultimate strength) in the bond-slip curve containing the effective true damage stage, namely the linear rising stage, the constraint development stage, and the splitting-pull-out deterioration stage. , , , These are the maximum slip amounts (which can be denoted as initial slip, suppressed slip, splitting slip, and ultimate slip) in the bond-slip curve containing the effective real damage stage, namely the micro-slip stage, linear rise stage, constrained development stage, and splitting-pull-out deterioration stage. and All are adhesive stress correction factors.

[0041] Step S35: Substitute the data from the bond-slip curves containing the effective actual damage stage into the model from step S34, and use Matrix Laboratory (MATLAB) to fit the model. and goodness of fit The results are shown in Table 4: Table 4. Bond stress correction factor and stage division results

[0042] Establish and The expression: , ; In the formula, To ignore the maximum bond stress in the linearly rising phase before the micro-slip stage in the bond-slip curve containing the effective true damage stage, , , , All are undetermined coefficients; , , , The value will be obtained by , and Substitute into and The expression was obtained by fitting using MATLAB, and the goodness of fit was... All are above 0.9.

[0043] Step S36, will and Substituting these parameters into the model from step S34, we obtain the bond-slip constitutive model for the reinforced concrete parameters: .

[0044] The bonding damage process of the specimens in the secondary test was divided into stages using the same method, and the results were determined. Substituting these values ​​into the above formula yields the bond-slip constitutive model of the reinforced concrete specimen. The model data is then compared with the experimental data to calculate the model accuracy. The formula is shown below, and the results are presented in Table 5. ; In the formula, For model accuracy, For the first The bond stress of each test, For the first The model's bond stress, This represents the average value of the bond stress tested.

[0045] Table 5 Model Validation Results

[0046] Because the damage process of reinforced concrete with the same test parameters is different, the division of damage stages needs to be determined based on the specific damage results for each test of concrete with the same parameters. The results are inconsistent. A bond-slip constitutive model is established based on the defined stages. Substituting the data into the bond-slip constitutive model of this type of reinforced concrete in the above formula, the model data and experimental data, after accuracy calculation, show that the trends of the two data are very consistent, indicating that this method has high accuracy and reliability.

[0047] In summary, the method described in this invention can establish the bond-slip constitutive relationship of reinforced concrete using acoustic emission technology. The use of MFCC feature extraction enables the stage division of the bond-slip process in reinforced concrete, which can represent the true damage of bond failure and provides more accurate stage division. Furthermore, this invention has broad applicability and can be applied to the exploration of bond-slip behavior in reinforced concrete under complex conditions, demonstrating strong practicality in engineering applications.

[0048] Obviously, the above embodiments are merely examples for clear illustration and are not intended to limit the embodiments. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all embodiments here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for establishing a bond-slip constitutive relationship of reinforced concrete based on MFCC, characterized in that, The method comprises the following steps: Step S1, obtaining the parameters of reinforced concrete and the time points in the bonding failure process of reinforced concrete, and the corresponding slip amount, bonding stress and acoustic emission characteristic parameters at each time point; Step S2, extracting the MFCC characteristic parameters based on the amplitude parameters, and selecting the 0th or 1st order MFCC characteristic parameters, drawing curves with the time points as the horizontal coordinates and the amplitude parameters, the ringing count, the rise time, the duration and the selected MFCC characteristic parameters as the vertical coordinates respectively to obtain the curve of the time points-amplitude parameters, the curve of the time points-ringing count, the curve of the time points-rise time, the curve of the time points-duration and the curve of the time points-MFCC characteristic parameters; In the curve of the time point-MFCC feature parameters, the horizontal coordinate The time range is taken as the time point corresponding to the maximum downward fluctuation of the MFCC feature parameters to divide the time point of the first bond failure stage of reinforced concrete. The , ; wherein are the first are the first is a positive integer; Step S3, based on the slip amount and the bond stress obtained in step S1, the bond-slip curve of the reinforced concrete parameter is drawn, and the bond-slip curve of the reinforced concrete parameter is divided according to the slip amount and the bond stress corresponding to the bond failure stage division time point obtained in step S2, the bond-slip curve containing the effective real damage stage is obtained, and the bond-slip constitutive model of the reinforced concrete parameter is established based on the bond-slip curve containing the effective real damage stage. Step S3, based on the slip amount and the bond stress obtained in step S1, the bond-slip curve of the reinforced concrete parameter is drawn, and the bond-slip curve of the reinforced concrete parameter is divided according to the slip amount and the bond stress corresponding to the bond failure stage division time point obtained in step S2, the bond-slip curve containing the effective real damage stage is obtained, and the bond-slip constitutive model of the reinforced concrete parameter is established based on the bond-slip curve containing the effective real damage stage.

2. The method for establishing a bond-slip constitutive relation of reinforced concrete based on MFCC according to claim 1, characterized in that, The process of step S1 is as follows: Step S11, obtaining the parameters of reinforced concrete; Step S12, obtaining the time points in the bonding failure process of reinforced concrete and the corresponding slip amount, bonding stress and acoustic emission characteristic parameters at each time point by using the pull-out test and real-time monitoring of acoustic emission technology.

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

4. The method for establishing the bond-slip constitutive relation of reinforced concrete based on MFCC according to claim 1, characterized in that, In step S2, the process of extracting the MFCC characteristic parameters based on the amplitude parameters is as follows: Step S21, pre-emphasizing the amplitude parameters to obtain pre-emphasized acoustic emission signals; Step S22, framing the pre-emphasized acoustic emission signals, multiplying each frame of pre-emphasized acoustic emission signals by a window function to obtain framed and windowed acoustic emission signals, and converting the framed and windowed acoustic emission signals from time domain to frequency domain through discrete Fourier transform to calculate 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 log energy output by the mel filters; Step S24, using discrete cosine transform to decorrelate and reduce the dimension of the log energy to finally calculate the MFCC characteristic parameters.

5. The method for establishing the bond-slip constitutive relation of reinforced concrete based on MFCC according to claim 4, characterized in that, In step S21, the formula of pre-emphasizing is as follows: ； wherein taking 0.97, is a pre-emphasized acoustic emission signal, is the amplitude of the sample point, is the amplitude of the sample point, is a positive integer; In step S22, the formula of framing is as follows: ； wherein is the first frame pre-emphasized acoustic emission signal, is a positive integer, is the number of frame shift samples, is the number of frame length samples; The formula of the window function is as follows: ； wherein is the first frame the frame windowed acoustic emission signal, is the Hamming window coefficient, taken as 0.46; The formula of the discrete Fourier transform is as follows: ； ； wherein is a signal power spectral function, is the discrete Fourier transform of the first values of the second is the imaginary unit, is a positive integer; In step S23, the calculation formula of the log energy is as follows: ； wherein log energy th value, th value of the th mel filter transfer function, total number of mel filters; In step S24, the calculation formula of the decorrelation and dimension reduction is as follows: ； wherein is the number of MFCC feature parameters, is the number of coefficients of the MFCC feature parameters, is the number of mel-cepstral coefficients, taken to be 12-24.

6. The method for establishing a bond-slip constitutive relation of reinforced concrete based on MFCC according to claim 1, characterized in that, In step S2, the The curves based on the time point-amplitude parameter, the time point-ringing count, the time point-rise time and the time point-duration, respectively, are obtained by the following methods: Step S251, setting the size of the sliding window of the horizontal coordinates of the curve to 15 seconds and the moving step of the sliding window to 0.02 seconds to obtain a plurality of sliding windows; Step S252, calculating the mean values of the acoustic emission characteristic parameters corresponding to each of the adjacent two sliding windows, and the calculation formula is as follows: In the formula, is the average of the acoustic emission characteristic parameters of the left sliding window, is the average of the acoustic emission characteristic parameters of the right sliding window, is the first acoustic emission characteristic parameter sample data of the left sliding window, is the first acoustic emission characteristic parameter sample data of the right sliding window, is the first acoustic emission characteristic parameter sample data of the left sliding window, is the first acoustic emission characteristic parameter sample data of the right sliding window, is the total number of sample data of the acoustic emission characteristic parameters in the left sliding window, is the total number of sample data of the acoustic emission characteristic parameters in the right sliding window. Step S253, calculating the difference measure values of all adjacent two sliding windows, and the calculation formula is as follows: wherein is a difference measure value for adjacent sliding windows; Step S254, when the difference measure value is greater than the record threshold value, record the difference measure value, the difference sample data and the time point corresponding to the difference sample data, the recorded difference sample data is the first acoustic emission characteristic parameter sample data in the left sliding window, and the record threshold value is 0.2-0.

5. Step S255, arrange the recorded difference metric values according to the time points corresponding to the difference sample data in chronological order, calculate the difference value of two adjacent time points, when the difference value is greater than a time threshold, take the previous time point corresponding to the difference value as the last time point of the previous set, take the latter time point corresponding to the difference value as the first time point of the next set, and divide the recorded difference metric values into sets according to the division of the time points, and the time threshold is 2-3 seconds. Step S256, selects the time point corresponding to the largest difference measure value in each set as the first bond failure stage division time point on the corresponding curve.

7. The method for establishing a bond-slip constitutive relation of reinforced concrete based on MFCC according to claim 1, characterized in that, The divided bond-slip curve of the reinforced concrete parameter comprises one or more of a micro-slip stage, a linear rising stage, a constraint development stage, and a splitting-pullout deterioration stage in time sequence; The slope of the bond-slip curve of the micro-slip stage is initially less than 0.001 and gradually increases, the slope of the bond-slip curve of the linear rising stage varies within 5%, the slope of the bond-slip curve of the constraint development stage gradually decreases but is finally not less than 0.001, and the slope of the bond-slip curve of the splitting-pullout deterioration stage gradually decreases and is finally less than 0.

001.

8. The method for establishing a bond-slip constitutive relation of reinforced concrete based on MFCC according to claim 7, characterized in that, The divided bond-slip curve of the reinforced concrete parameter comprises a micro-slip stage, the micro-slip stage is ignored by moving the coordinate origin to obtain a bond-slip curve containing an effective real damage stage, and the expression of the moving coordinate origin is: ； ； wherein is the effective bond stress value, is the first is the original bond stress value, is the first is the maximum bond stress in the micro-slip regime, is the effective slip value, is the first is the original slip value, is the first is the maximum slip value in the micro-slip regime.

9. The method for establishing a bond-slip constitutive relation of reinforced concrete based on MFCC according to claim 8, characterized in that, The method for establishing the bond-slip constitutive model of the reinforced concrete parameter based on the bond-slip curve containing the effective real damage stage comprises: The method for establishing the bond-slip constitutive model of the reinforced concrete parameter based on the bond-slip curve containing the effective real damage stage comprises: The method for establishing the bond-slip constitutive model of the reinforced concrete parameter based on the bond-slip curve containing the effective real damage stage comprises: ； wherein is the bond stress is the slip is a piecewise function of the slip, , , is the maximum bond stress in the linear rising stage, the constraint development stage and the splitting-pullout degradation stage of the bond-slip curve with the effective real damage stage, respectively, , , , is the maximum slip in the micro-slip stage, the linear rising stage, the constraint development stage and the splitting-pullout degradation stage of the bond-slip curve with the effective real damage stage, respectively, and are the bond stress correction factors. Step S32, the data containing the cohesive-slippage curve of the effective real damage stage is substituted into the model of step S32, and the matrix laboratory fitting is used to obtain and ; Step S33, establishing and the expression: ， ； wherein is the maximum cohesive stress to neglect the linear rising stage before the micro-slip stage in the cohesive- slip curve containing the effective real damage stage, , , , are undetermined coefficients; , , , The value will be obtained by , and Substitute into and The expression was obtained using matrix lab fitting; Step S34, will and Substituting these parameters into the model from step S32, we obtain the bond-slip constitutive model for the reinforced concrete parameters: 。

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