Method for establishing bond-slip constitutive relation of reinforced concrete based on mfcc

Abstract

The method for establishing the bond-slip constitutive relation of reinforced concrete based on MFCC belongs to the technical field of analysis method of bond behavior of reinforced concrete. The method for establishing the method, first, obtains the parameters of reinforced concrete and the acoustic emission characteristic parameters in the bond failure process of reinforced concrete; then, respectively draws the time point-acoustic emission characteristic parameter curve and the time point-MFCC characteristic parameter curve, and takes the time point corresponding to the maximum downward fluctuation degree of the MFCC characteristic parameters in the time range as the first bond failure stage division time point of the reinforced concrete; finally, divides the bond-slip curve of the parameters of the reinforced concrete based on the first bond failure stage division time point, and establishes the bond-slip constitutive model of the parameters of the reinforced concrete based on the obtained bond-slip curve containing the effective real damage stage. The method for establishing can adapt to the influence of material parameters, express the real process of damage, and the process of establishing the model has strong generalization ability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of analysis method of steel and concrete bonding behavior, and particularly relates to a method for establishing a steel and concrete bonding-slip constitutive relationship based on MFCC (Mel Frequency Cepstral Coefficient). BACKGROUND

[0002] As one of the composite materials widely used in the construction process, steel reinforced concrete fully integrates the advantages of concrete and steel. However, the premise of the joint work of steel and concrete is the good bonding effect between them, which is a kind of interaction between steel and concrete to transfer stress and coordinate deformation. The bonding behavior of steel reinforced concrete is a manifestation of the collaborative work capability between steel and concrete, which directly affects the safety and durability of the structure, so it is very important to analyze the bonding behavior of steel reinforced concrete.

[0003] At present, many studies have been conducted on the bonding-slip constitutive relationship of steel reinforced concrete, which can be divided into single-section form and multi-section form.

[0004] The single-section form summarizes the bonding-slip relationship of the rising section when bonding damage occurs, which has an advantage in the convergence of numerical calculation. For example, the article "Study on Bond-Slip Constitutive Model of Plain Round Steel Bar and Concrete Interface" (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 bar and concrete by using experimental results and theoretical analysis. However, this form only expresses the bonding-slip relationship from a mathematical form, which weakens the real expression of the bonding damage of steel reinforced concrete, and there is an error in practical application.

[0005] The multi-section form divides the bonding-slip relationship of the rising section when bonding damage occurs, which can better reflect the damage mechanism of different bonding damage modes and reflect the main distribution of bonding stress in different stages of bonding effect. For example, the patent application "Method and system for establishing bond-slip constitutive model of steel bar and concrete after high temperature" (Publication No. 117542421A) provides a method for establishing a multi-section bond-slip constitutive model after high temperature by using a calculation method of fitting multiple formulas. For example, the article "Study on the establishment method of bond-slip constitutive relationship of steel reinforced concrete" (Sichuan Building Science Research, Vol. 32, No. 1, February 2006) introduces equivalent strain and correction coefficient to provide a method for establishing the bond-slip constitutive relationship of corroded steel reinforced concrete. However, the ideal bond-slip relationship is a local bond-slip constitutive relationship applicable to any position on the bonding section of any length. Due to the uneven distribution of bonding stress along the bonding length and the difficulty in measuring local bonding performance parameters, the multi-section form cannot reflect the real damage according to the segmented results of the test conditions.

[0006] In addition, the bond-slip constitutive relationship needs to accurately describe the characteristics of reinforced concrete, the above forms usually depend on specific test conditions, although it can provide certain prediction ability, but under complex conditions (such as different types of reinforced concrete material parameters) adaptability is poor, and also cannot reflect the real damage of reinforced concrete about bond-slip, and cannot be fully applied in practical engineering.

[0007] Therefore, in engineering practice, how to generally cover different types of reinforced concrete material parameters 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, and is of great significance for improving the structure life design method and reducing maintenance cost. SUMMARY

[0008] In view of the problems existing in the prior art, the present application provides a method for establishing a bond-slip constitutive relationship of reinforced concrete based on MFCC, which aims to establish a bond-slip constitutive model that can reflect the real damage of reinforced concrete by combining acoustic emission technology, and provide an important basis for damage evaluation of the bond interface between steel and concrete.

[0009] To achieve the above purpose, the application adopts the following technical solutions:

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

[0011] Step S1, obtaining reinforced concrete parameters and time points in the bond failure process of reinforced concrete, and corresponding slip, bond stress and acoustic emission characteristic parameters at each time point, the acoustic emission characteristic parameters including amplitude parameter, ringing count, rise time and duration;

[0012] Step S2, extracting MFCC characteristic parameters based on the amplitude parameter, and selecting the 0th or 1st order MFCC characteristic parameters, drawing curves with time points as abscissa and amplitude parameters, ringing counts, rise times, durations and selected MFCC characteristic parameters as ordinate respectively, to obtain the curves of time point-amplitude parameter, time point-ringing count, time point-rise time, time point-duration and time point-MFCC characteristic parameter;

[0013] In the curve of time point-MFCC characteristic parameter, the abscissa The time point corresponding to the maximum downward fluctuation degree of the MFCC characteristic parameter in the time range of the abscissa is taken as the division time point of the first bond failure stage of reinforced concrete;

[0014] The , ;

[0015] 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;

[0016] 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.

[0017] Preferably, the process of step S1 is as follows:

[0018] Step S11: Obtain reinforced concrete parameters;

[0019] 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.

[0020] 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.

[0021] Preferably, in step S2, the process of extracting MFCC feature parameters based on amplitude parameters is as follows:

[0022] Step S21: The amplitude parameters are pre-emphasized to obtain a pre-emphasized acoustic emission signal;

[0023] 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.

[0024] 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;

[0025] Step S24, the log energy is de-correlated and reduced in dimension using a discrete cosine transform, and finally MFCC feature parameters are calculated.

[0026] More preferably, in step S21, the formula of the pre-emphasis processing is:

[0027] ;

[0028] In the formula, Take 0.97, is the pre-emphasis acoustic emission signal, is the amplitude of the i-th sampling point, is the amplitude of the i-th sampling point, is a positive integer; Step S22, the formula of the frame is:

[0029] ;

[0030] In the formula, is the i-th frame pre-emphasis acoustic emission signal,

[0031] 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:

[0032] ;

[0033] ;

[0034] In the formula, is the i-th frame frame windowed acoustic emission signal, is a Hamming window coefficient, take 0.46; The formula of the discrete Fourier transform is:

[0035]

[0036] ;

[0037] ; In the formula,

[0038] is the signal power spectrum function, is the discrete Fourier transform of the i-th value of is an imaginary unit, is a positive integer; In step S23, the formula for calculating the log energy is:

[0039] ​​​​​

[0040] ;

[0041] wherein, is the logarithmic energy of the first value, is the first value of the Mel filter transfer function, is the first value of the Mel filter transfer function,

[0042] In step S24, the calculation formula of the decorrelation and dimension reduction is:

[0043] ;

[0044] wherein, is the first coefficient of the MFCC feature parameter, is the number of the Mel frequency cepstral coefficient, taking 12-24.

[0045] Preferably, in step S2, the is respectively obtained based on the curve of the time point-amplitude parameter, the curve of the time point-ring count, the curve of the time point-rise time, and the curve of the time point-duration by the following method:

[0046] In step S251, the size of the sliding window of the curve abscissa is set to 15 seconds, and the moving step length of the sliding window is 0.02 seconds, to obtain a plurality of sliding windows.

[0047] In step S252, the mean value of the acoustic emission feature parameter corresponding to each of the adjacent two sliding windows is calculated, and the calculation formula is:

[0048]

[0049] wherein, is the mean value of the acoustic emission feature parameter of the left sliding window, is the mean value of the acoustic emission feature parameter of the right sliding window, is the first acoustic emission feature parameter sample data of the left sliding window, is the first acoustic emission feature parameter sample data of the right sliding window, is the total number of the sample data of the acoustic emission feature parameter in the left sliding window, is the total number of the sample data of the acoustic emission feature parameter in the right sliding window;

[0050] In step S253, the difference measure value of all adjacent two sliding windows is calculated, and the calculation formula is:

[0051]

[0052] wherein, is a difference measure value of adjacent sliding windows;

[0053] Step S254, when the difference measure value is greater than a record threshold, 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 is 0.2-0.5;

[0054] Step S255, arrange the recorded difference measure values in the order of the time points corresponding to the difference sample data, calculate the difference value of two adjacent time points, when the difference value is greater than a time threshold, take the former time point corresponding to the difference value as the last time point of the previous set, and take the latter time point corresponding to the difference value as the first time point of the next set (the difference value greater than the time threshold is not taken as a set division time point), divide the recorded difference measure values into sets according to the division of the time points, and the time threshold is 2-3 seconds;

[0055] Step S256, select the time point corresponding to the maximum difference measure value in each set as the first bond failure stage division time point on the corresponding curve.

[0056] Preferably, step S3, the divided bond-slip curve of the reinforced concrete parameter includes one or more of the micro-slip stage, the linear rise stage, the constraint development stage and the splitting-pullout degradation stage in time sequence;

[0057] and the bond-slip curve slope of the micro-slip stage is initially less than 0.001 and gradually increases, the bond-slip curve slope of the linear rise stage changes within 5%, the bond-slip curve slope of the constraint development stage gradually decreases but is finally not less than 0.001, and the bond-slip curve slope of the splitting-pullout degradation stage gradually decreases and is finally less than 0.001.

[0058] More preferably, step S3, the divided bond-slip curve of the reinforced concrete parameter includes the micro-slip stage, the micro-slip stage is ignored by moving the coordinate origin to obtain a bond-slip curve containing the effective real damage stage, and the expression of the moving coordinate origin mode is:

[0059] ;

[0060] ;

[0061] wherein, is the effective bond stress value, is the original bond stress value, is the maximum bond stress in the micro-slip stage, is the effective slip value, is the original slip value, is the maximum slip value in the micro-slip stage.

[0062] More preferably, the method of establishing a bond-slip constitutive model of the reinforced concrete parameters based on the bond-slip curve containing the effective real damage stage in step S3 comprises:

[0063] Step S31, based on the bond-slip curve containing the effective real damage stage, establishing the bond-slip constitutive model of the reinforced concrete parameters containing correction coefficients:

[0064] ;

[0065] wherein, is a piecewise function of the bond stress varying with the slip, , , , are the maximum bond stresses in the linear rising stage, the constraint development stage and the splitting-pullout degradation stage of the bond-slip curve containing the effective real damage stage, respectively, , , , are the maximum slips in the micro-slip stage, the linear rising stage, the constraint development stage and the splitting-pullout degradation stage of the bond-slip curve containing the effective real damage stage, respectively, and are the bond stress correction coefficients;

[0066] Step S32, substituting the data of the bond-slip curve containing the effective real damage stage into the model in step S32, and using matrix laboratory fitting to obtain and ;

[0067] Step S33, establishing the expressions of and :

[0068] , ;

[0069] In the formula, is the maximum bond stress of the linear rising stage before the micro-slip stage in the bond-slip curve containing the effective real damage stage, 、 、 、 are undetermined coefficients;

[0070] 、 、 、 The numerical value of is obtained by substituting 、 and into the expression of and , and is obtained by using matrix laboratory fitting;

[0071] In step S34, and are substituted into the model in step S32 to obtain the bond-slip constitutive model of the reinforced concrete parameter:

[0072] .

[0073] Compared with the prior art, the beneficial effects of the present application are:

[0074] (1) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC can adapt to the influence of material parameters, can express the real process of damage, has strong generalization ability in the process of model establishment, and has a wider application range in actual engineering compared with the existing method for establishing the bond-slip constitutive relationship.

[0075] (2) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC divides the damage stages of the bond failure process of reinforced concrete based on MFCC, establishes the bond-slip constitutive model of reinforced concrete based on the divided stages, and can represent the real damage of the bond failure of reinforced concrete compared with the stage division of the traditional model, the stage division is more accurate, can effectively describe the bond-slip behavior of the reinforced concrete, and has stronger practicability.

[0076] (3) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC proposes a bond stress correction coefficient in the model based on the stages divided by MFCC, can accurately express the bond stress value of the stage mutation point, and can avoid the problem of calculation divergence caused by the sudden change of bond strength in numerical calculation to a certain extent.

[0077] ​​(4) The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC can effectively predict the bond-slip behavior of the same type of reinforced concrete, provides technical support for the damage evaluation of various types of reinforced concrete bond interfaces, and has a wide application range. BRIEF DESCRIPTION OF DRAWINGS

[0078] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0079] Figure 1 The results of dividing the time points of the bond failure stage of the reinforced concrete specimens with different corrosion rates in Example 1 of the present application; in the figure, (a) is the corrosion rate of 0%, (b) is the corrosion rate of 3%, (c) is the corrosion rate of 5%, and (d) is the corrosion rate of 8%; the star indicates the time point corresponding to the maximum downward fluctuation degree of the MFCC characteristic parameter in the time range of the horizontal coordinate The time point corresponding to the maximum downward fluctuation degree of the MFCC characteristic parameter in the time range of the horizontal coordinate

[0080] Figure 2 The bond-slip curves of the reinforced concrete specimens with different corrosion rates in Example 1 of the present application; in the figure, (a) is the corrosion rate of 0%, (b) is the corrosion rate of 3%, (c) is the corrosion rate of 5%, and (d) is the corrosion rate of 8%.

[0081] Figure 3 The schematic diagram of the division results of the bond-slip curves of the reinforced concrete parameters in Example 1 of the present application; in the figure, The bond stress, The slip amount, The suppression strength, splitting strength, ultimate strength and suppression strength before the micro-slip stage in the real damage stage of the bond-slip curve of the reinforced concrete specimen, 、 , , , The original initial slip amount, initial slip amount, slip inhibition amount, splitting slip amount and ultimate slip amount of the bond-slip curve of the reinforced concrete test piece, stage I', stage I, stage II and stage III are divided into micro-slip stage, linear rising stage, constraint development stage and splitting-pulling-out deterioration stage. DETAILED DESCRIPTION

[0082] In order to make the technical personnel in the art better understand the technical solutions of the present application, the present application will be further described in detail below in combination with embodiments.

[0083] In the following examples, various processes and methods not described in detail are conventional methods known in the art. The materials, reagents, devices, instruments, equipment, etc. used in the following examples can be obtained from commercial channels if not otherwise specified.

[0084] Example 1

[0085] The method for establishing the bond-slip constitutive relationship of reinforced concrete based on MFCC is as follows:

[0086] Step S1:

[0087] In step S11, the parameters of reinforced concrete are obtained. The chemical element composition of the steel bar is shown in Table 1, and the concrete mixing ratio is shown in Table 2:

[0088] Table 1 Chemical element composition of steel bar

[0089]

[0090] Table 2 Concrete mixing ratio

[0091]

[0092] The concrete is vibrated into the mold, the test sample is demolded and transferred to a curing room with a relative humidity of 95% and a temperature of 20℃±2℃ for curing for 28 days. The size of the concrete is 100mm×100mm×200mm, a HRB400 steel bar is vertically embedded in the center axis, the total length is 420mm, and the bonding length is 100mm. The electric corrosion method is used to simulate the corrosion environment, and reinforced concrete pull-out test pieces with corrosion rates of 0%, 3%, 5% and 8% are prepared, which are referred to as test pieces. The same type of test pieces are tested twice, and the damage of the two tests is different, so the slip amount, bond stress and acoustic emission characteristic parameters at each time point of the reinforced concrete are also different. Two test pieces are treated, and the treatment method is the same.

[0093] 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 exhibited 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.

[0094] Step S2:

[0095] Step S21: Pre-emphasize the amplitude parameters to obtain the pre-emphasized acoustic emission signal. The formula for pre-emphasis processing is:

[0096] ;

[0097] 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.

[0098] Step S22: The pre-emphasized acoustic emission signal is divided into frames, and the framing formula is as follows:

[0099] ;

[0100] 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.

[0101] 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:

[0102] ;

[0103] In the formula, For the first Frame-by-frame windowed acoustic transmission signal. The coefficient for the Hamming window is 0.46.

[0104] 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.

[0105] ;

[0106] ;

[0107] 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.

[0108] 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:

[0109] ;

[0110] 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.

[0111] 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:

[0112] ;

[0113] In the formula, The first characteristic parameter of MFCC One coefficient, The number of Mel cepstral coefficients is 12.

[0114] 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.

[0115] 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. :

[0116] 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;

[0117] 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:

[0118]

[0119] 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;

[0120] Step S253: Calculate the difference metric for all adjacent pairs of sliding windows. The calculation formula is as follows:

[0121]

[0122] In the formula, This is a measure of the difference between adjacent sliding windows;

[0123] 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;

[0124] 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 the time threshold value, take the former 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 value is 2 seconds;

[0125] Step S256, select the time point corresponding to the maximum difference metric value in each set as the first bond failure stage division time point on the corresponding curve.

[0126] Step S26, on the curve of the time point-MFCC feature parameter, take the time point corresponding to the maximum downward fluctuation degree of the MFCC feature parameter within the time range of the horizontal coordinate as the first bond failure stage division time point of the reinforced concrete;

[0127] The , ;

[0128] In the formula, is the first bond failure stage division time point on the curve of the time point-amplitude parameter, the curve of the time point- ringing count, the curve of the time point-rising time and the curve of the time point-duration, is a positive integer;

[0129] The curves divided by the bond failure stage division time points of the specimens with corrosion rates of 0%, 3%, 5% and 8% are shown in Figure 1 , and the bond failure stage division time point results are shown in Table 3.

[0130] Table 3 Bond failure stage division time point

[0131]

[0132] Step S3:

[0133] Step S31, draw the bond-slip curve of the reinforced concrete parameter based on the slip amount and the bond stress obtained in step S1, and the bond-slip curve result of the reinforced concrete is shown in Figure 2 , Figure 2 In the formula (a), the bond-slip curve of the reinforced concrete specimen with a corrosion rate of 0% is shown, f0x0-1 represents the first test result of the specimen with a corrosion rate of 0%, and f0x0-2 represents the second test result of the specimen with a corrosion rate of 0%, Figure 2In 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%.

[0134] 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).

[0135] 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.

[0136] 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:

[0137] ;

[0138] ;

[0139] 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;

[0140] 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.

[0141] 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:

[0142] ;

[0143] In the formula, For bond 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.

[0144] 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:

[0145] Table 4. Bond stress correction factor and stage division results

[0146]

[0147] Establish and The expression:

[0148] , ;

[0149] wherein, is the maximum bond stress ignoring the linear rising stage before the micro-slip stage in the bond-slip curve containing the effective real damage stage, 、 、 、 are undetermined coefficients;

[0150] 、 、 、 The values of 、 and are obtained by substituting and into the expressions of , and the goodness of fit is higher than 0.9 using MATLAB fitting.

[0151] Step S36, substituting and into the model of step S34, to obtain the bond-slip constitutive model of the reinforced concrete parameters:

[0152] .

[0153] The bond damage process of the specimens in the second test is divided into stages in the same way, and is obtained and substituted into the above formula to obtain the bond-slip constitutive model of the reinforced concrete specimens. The model data is compared with the test data, the model accuracy is calculated, and the formula is as follows, and the results are shown in Table 5:

[0154] ;

[0155] wherein, is the model accuracy, is the bond stress of the th test, is the bond stress of the th model, is the average value of the test bond stress.

[0156] Table 5 Model verification results

[0157]

[0158] Since the damage processes of the reinforced concrete with the same parameters are different in the test process, the damage stages need to be determined according to the specific damage results. The damage stages of the same parameter concrete in each test The results are inconsistent. According to the stage division, the bond-slip constitutive model is established After the bond-slip constitutive model of the type of reinforced concrete is substituted into the above formula, the model data obtained is very close to the trend of the test data after accuracy calculation, indicating that the method has high accuracy and reliability.

[0159] In summary, the method can realize the establishment of the bond-slip constitutive relationship of reinforced concrete by using acoustic emission technology. The stage division of the bond-slip process of reinforced concrete is realized by using the MFCC feature extraction, which can represent the real damage of the bond failure of reinforced concrete, and the stage division is more accurate. In addition, the application has wide applicability and can be applied to the exploration of the bond-slip behavior of reinforced concrete under complex conditions, and has strong practicality in engineering practical application.

[0160] Obviously, the above embodiments are only examples for clearly illustrating, but not limitation. For ordinary skilled in the art, on the basis of the above description, other different forms of changes or variations can also be made. Here, it is not necessary and impossible to enumerate all the embodiments. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

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 concrete mix ratio, 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 MFCC feature parameters, is the number of MFCC feature parameters, 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 relationship 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 into the model of step S32, the bond-slip constitutive model of the reinforced concrete parameters is obtained: 。

Images