Detection method for crack depth of directional conductive fiber reinforced concrete beam

Abstract

The invention discloses a directional conductive fiber reinforced concrete beam crack depth detection method, which comprises the following steps of: when directional conductive fiber reinforced concrete is damaged due to load, performing current excitation through a delimited area, and judging a damaged area of a component by utilizing potential response through a resistance method. Under the condition that a crack generation area is known, only the equivalent longitudinal resistance in the area is subjected to inversion by using fewer measurement resources, the result of the crack length can be obtained, and the scheme can also identify the maximum depth in a plurality of cracks when the plurality of cracks are generated in the area. The equivalent electrical model of the composite fixed-value resistor and the variable resistor does not directly depend on test piece material parameters, so that the method can be suitable for materials such as oriented wire fiber reinforced concrete and the like.

Description

Technical Field

[0001] The invention belongs to the field of conductive fiber reinforced concrete beam crack detection, and in particular relates to a method for detecting the crack depth of a directional conductive fiber reinforced concrete beam. Background Art

[0002] Resistance or voltage measurement is an effective method for detecting cracks in conductive fiber reinforced concrete. However, due to individual differences between conductive fiber reinforced concrete specimens and the bridging effect of the conductive fibers in the matrix after cracking, the law of change of the interface resistance between the fiber and the matrix during the cracking process is unstable, making it difficult to formulate a unified quantitative evaluation standard.

[0003] The use of electrical impedance imaging technology can achieve comprehensive damage detection of concrete beams, but this technology has high requirements on the location and number of electrode arrangements, requires multiple excitations, and processes a large amount of potential information, which increases the complexity and computational burden of detection. This method is only applicable to isotropic conductive concrete materials and cannot be applied to conductive concrete reinforced with directional fibers. Summary of the invention

[0004] To solve the above problems, we proposed a method for detecting the crack depth of oriented conductive fiber reinforced concrete beams.

[0005] The technical solution of the present invention is as follows:

[0006] A preparation method for a method for detecting crack depth of a directional conductive fiber reinforced concrete beam comprises the following steps:

[0007] Step 1, n electrodes are evenly arranged along the axial direction on the upper surface and the lower surface of the conductive fiber reinforced concrete specimen, wherein one electrode is arranged at each of the four corners of the conductive fiber reinforced concrete specimen;

[0008] Step 2, establishing an initial equivalent electrical model corresponding to the conductive fiber reinforced concrete specimen, and establishing a resistor network according to the arrangement of the electrodes, wherein the resistor grid is a grid-shaped grid composed of multiple rows of longitudinal resistors and multiple columns of transverse resistors, and the resistance value of the longitudinal resistor changes with the cracking of the conductive fiber reinforced concrete specimen; the resistance value of the transverse resistor is fixed and does not change with the cracking of the conductive fiber reinforced concrete specimen; wherein each electrode is correspondingly provided with a column of transverse resistors, a longitudinal resistor is provided between two transverse resistors, and the number of longitudinal resistors is set according to needs, and the more the number, the higher the detection accuracy;

[0009] Step 3, before the cracks are generated, any two electrodes are selected from the four electrodes at the four corners of the conductive fiber reinforced concrete specimen for excitation, and four combined excitation modes can be obtained. The order of the four combined excitation modes is determined as an excitation scheme, and the electrodes on the conductive fiber reinforced concrete specimen are excited according to the excitation scheme. The potentials of n electrodes on the conductive fiber reinforced concrete specimen are collected, and a set of response voltage vector data is obtained for each excitation. Four sets of response voltage vector data are obtained for four excitations, and the four sets of response voltage vector data are combined into a 1×4n total vector V0;

[0010] Step 4: Set the initial values ​​of the longitudinal resistance and the transverse resistance, and iteratively update the values ​​of the longitudinal resistance and the transverse resistance through the inversion algorithm, so that the residual between the experimental measurement value V0 of the potential and the model calculation value u(R) is minimized, and then the pre-crack equivalent value of each longitudinal resistance and transverse resistance is obtained;

[0011] Step 5: After the cracks are generated, the conductive fiber reinforced concrete specimen is excited again using the excitation scheme in step 3 to collect response voltage data;

[0012] Step 6: Compare the response voltage vector data before and after the crack is generated under the same excitation mode, and obtain the crack generation area according to the change of the potential difference;

[0013] Step 7: Set the value of each transverse resistor to the corresponding pre-crack equivalent value, set the value of the longitudinal resistance in the non-crack area to the corresponding pre-crack equivalent value, and perform inversion iteration on the value of the longitudinal resistance in the crack area according to the response voltage data after the crack is generated obtained in step 5 to obtain the post-crack equivalent value of each longitudinal resistance in the crack area, compare the post-crack equivalent value of each longitudinal resistance in the crack area with the pre-crack equivalent value of the corresponding longitudinal resistance, obtain the position of the longitudinal resistance where the resistance value changes, and then determine the crack depth.

[0014] Furthermore, in step 1, the number of electrodes on the upper surface and the lower surface of the conductive fiber reinforced concrete specimen is the same and the positions correspond one to one.

[0015] Furthermore, in step 6, any one of the four combined excitation modes in the excitation scheme is selected to calculate the crack generation area.

[0016] The present invention has the following beneficial technical effects:

[0017] The method of the present invention can perform current excitation by demarcating an area when directional conductive fiber reinforced concrete is damaged by load, and use the resistance method and the potential response to determine the damaged area of ​​the component. Under the condition that the crack generation area is known, less measurement resources are used to invert only the longitudinal resistance in the area, and the result of the crack length can be obtained. When multiple cracks are generated in the area, this solution can also identify the maximum depth of multiple cracks.

[0018] In view of the problem that it is difficult to formulate a unified quantitative evaluation standard due to individual differences in non-homogeneous composite materials such as steel fiber reinforced cement-based composite materials, the present invention determines the crack depth based on whether the resistivity has changed, and identifies the crack depth based on the size of the equivalent resistance change area obtained by inversion. The detection result does not depend on the specific value of the material performance parameter (such as the resistivity of the material), and is therefore not affected by the non-uniformity and individual differences of the material performance. It can be applied to materials such as directional conductor fiber reinforced concrete and has strong adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the specimen area division;

[0020] Figure 2 Schematic diagram of the arrangement of electrodes on the specimen;

[0021] Figure 3 is a schematic diagram of the equivalent electrical model;

[0022] Figure 4 Schematic diagram of the crack depth identification process. DETAILED DESCRIPTION

[0023] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0024] (1) Electrode arrangement, such as Figure 1 As shown in Figure 2, the upper and lower surfaces of the specimen are divided into multiple areas according to the size and accuracy requirements of the specimen, such as Figure 1 As shown, Q represents the divided area. First, the surface of the specimen is polished to ensure flatness and smoothness. Alcohol is used to clean the surface residue and dust. Tapes are pasted on both sides of the position where the electrodes need to be arranged to limit the effective area of ​​the conductive silver glue. The conductive silver glue is used to connect the wire to the cement matrix. The schematic diagram of the electrode arrangement is shown in Figure 2 As shown, positions 1 to 4 are used for current excitation.

[0025] (2) Incentive Collection Scheme

[0026] Conduct current excitation at points 1 and 2 and collect potential u1 (1) 、u2(1) ,……u n (1) ;

[0027] Conduct current excitation at points 3 and 4 and collect potential u1 (2) 、u2 (2) ,……u n (2) ;

[0028] Conduct current excitation at points 1 and 3 and collect potential u1 (3) 、u2 (3) ,……u n (3) ;

[0029] Conduct current excitation at points 2 and 4 and collect potential u1 (4) 、u2 (4) ,……u n (4) .

[0030] All potentials are combined into a 1×4n vector V0.

[0031] (3) Establishing the initial equivalent electrical model

[0032] According to the area divided by the test piece during the electrode arrangement, the following Figure 2 The resistor network shown in the figure has white components as longitudinal resistors, whose values ​​change with cracking; black components as transverse resistors, whose values ​​are considered unchanged after cracks appear in the specimen. The initial value of the resistor is adjusted, and the corresponding response voltage vector u(R) is calculated through the same excitation acquisition method.

[0033] (4) Inversion method

[0034] The following is a brief explanation using the Newton-Raphson method as an example.

[0035] The main idea of ​​the algorithm is to minimize the residual between the potential measurement value v0 and the potential calculation value u(R) by iterating the longitudinal resistance and the transverse resistance. The objective function is usually taken as

[0036]

[0037] The purpose of inversion is to find a unit resistance distribution that minimizes the above objective function.

[0038] Taking the derivative of f(R) with respect to R, we have

[0039] f'(R)=[u'(R)] T [u(R)-v0] (2)

[0040] where u'(R) is called the Jacobian matrix and is defined as

[0041]

[0042] where u i (R) is the potential corresponding to the i-th measuring level, R j is the resistance value of the jth resistor.

[0043] Perform Taylor series expansion on f'(R) and retain the linear terms, and we get

[0044] f'≈f'(R k )+f”(R k )ΔR k (4)

[0045] Where k is the number of iterations,

[0046] ΔR k =R k+1 -R k (5)

[0047] f”(R k ) is the Hessian matrix, which can be approximated as

[0048] f”(R k )=[u'(R k )] T u'(R k ) (6)

[0049] Substituting equations (2) and (6) into the right side of equation (4) and setting it equal to 0, we can obtain

[0050] ΔR k =-[[u'(R k )] T u'(R k )] -1 [u'(R k )] T [u(R k )-v0] (7)

[0051] Therefore, the iteration formula is

[0052] R k+1 =R k +ΔR k (8)

[0053] Based on the above ideas, the inversion algorithm process of the resistance vector R can be established as follows:

[0054] ①Given the initial value R 0 , calculate the value corresponding to R0 The potential distribution u(R 0 ) and the corresponding objective function value f(R 0 );

[0055] ②Number of iterations k = 1;

[0056] ③Judge whether the objective function value is less than the preset value, or the number of iterations reaches the preset value. If yes, the iteration is terminated; if not, continue;

[0057] ③ Find the Jacobian matrix and Hessian matrix;

[0058] ④Calculate ΔR k , and let R k+1 =R k +ΔR k ;

[0059] ⑤ Calculate the value corresponding to R k+1 The potential distribution u(R k+1 ), calculate the objective function value f(R k+1 );

[0060] ⑦Iteration number k=k+1. Go to ③;

[0061] Among them, the calculated value u(R 0 ) and u(R k+1 ) is solved by using Kirchhoff’s law.

[0062] (5) Crack detection

[0063] Crack detection is divided into two processes: crack area identification and crack depth identification.

[0064] For crack area identification, such as Figure 3 As shown in the figure, Q represents the divided area. Before and after the crack is generated, current excitation is given to the electrodes at both ends (electrodes 1 and 2), and the potential at the electrodes in each area is collected. According to the voltage on each area (V1, V2...V m ) to determine the crack area Q k .

[0065] After the crack area is determined, the sample is repeatedly excited with current according to the excitation scheme of step (2). The longitudinal resistance value of the crack area is inverted and reconstructed using the obtained electrode potential data. The Jacobian matrix is ​​solved with the longitudinal resistance of the crack area (set as x×y), that is, R j =(R 11 ,R 12 ,R 13 ,…,R xy ), the change in longitudinal resistance in the crack region ΔR can be obtained by inversionk , to determine the location of the changed longitudinal resistance, such as Figure 4 As shown, if the longitudinal resistance value in the dotted area changes, the crack depth is determined to be w corresponding thereto.

[0066] The above is an example of the best implementation of the present invention, and the parts not described in detail are common knowledge of ordinary technicians in the field. The protection scope of the present invention shall be based on the content of the claims, and any equivalent transformation based on the technical enlightenment of the present invention is also within the protection scope of the present invention.

Claims

1. A method for preparing a method for detecting crack depth of a directional conductive fiber reinforced concrete beam, characterized in that: The following steps are involved: Step 1, n electrodes are evenly arranged along the axial direction on the upper surface and the lower surface of the conductive fiber reinforced concrete specimen, wherein one electrode is arranged at each of the four corners of the conductive fiber reinforced concrete specimen; Step 2, establishing an initial equivalent electrical model corresponding to the conductive fiber reinforced concrete specimen, and establishing a resistor network according to the arrangement of the electrodes, wherein the resistor grid is a grid-shaped grid composed of multiple rows of longitudinal resistors and multiple columns of transverse resistors, and the resistance value of the longitudinal resistor changes with the cracking of the conductive fiber reinforced concrete specimen; the resistance value of the transverse resistor is fixed and does not change with the cracking of the conductive fiber reinforced concrete specimen; wherein each electrode is correspondingly provided with a column of transverse resistors, a longitudinal resistor is provided between two transverse resistors, and the number of longitudinal resistors is set according to needs, and the more the number, the higher the detection accuracy; Step 3, before the cracks are generated, any two electrodes are selected from the four electrodes at the four corners of the conductive fiber reinforced concrete specimen for excitation, and four combined excitation modes can be obtained. The order of the four combined excitation modes is determined as an excitation scheme, and the electrodes on the conductive fiber reinforced concrete specimen are excited according to the excitation scheme. The potentials of n electrodes on the conductive fiber reinforced concrete specimen are collected, and a set of response voltage vector data is obtained for each excitation. Four sets of response voltage vector data are obtained for four excitations, and the four sets of response voltage vector data are combined into a 1×4n total vector V0; Step 4: Set the initial values ​​of the longitudinal resistance and the transverse resistance, and iteratively update the values ​​of the longitudinal resistance and the transverse resistance through the inversion algorithm, so that the residual between the experimental measurement value V0 of the potential and the model calculation value u(R) is minimized, and then the pre-crack equivalent value of each longitudinal resistance and transverse resistance is obtained; Step 5: After the cracks are generated, the conductive fiber reinforced concrete specimen is excited again using the excitation scheme in step 3 to collect response voltage data; Step 6: Compare the response voltage vector data before and after the crack is generated under the same excitation mode, and obtain the crack generation area according to the change of the potential difference; Step 7: Set the value of each transverse resistor to the corresponding pre-crack equivalent value, set the value of the longitudinal resistance in the non-crack area to the corresponding pre-crack equivalent value, and perform inversion iteration on the value of the longitudinal resistance in the crack area according to the response voltage data after the crack is generated obtained in step 5 to obtain the post-crack equivalent value of each longitudinal resistance in the crack area, compare the post-crack equivalent value of each longitudinal resistance in the crack area with the pre-crack equivalent value of the corresponding longitudinal resistance, obtain the position of the longitudinal resistance where the resistance value changes, and then determine the crack depth.

2. The preparation method of the method for detecting crack depth of oriented conductive fiber reinforced concrete beam according to claim 1, characterized in that: In the step 1, the number of electrodes on the upper surface and the lower surface of the conductive fiber reinforced concrete specimen is the same and the positions correspond one to one.

3. The preparation method of the method for detecting crack depth of oriented conductive fiber reinforced concrete beam according to claim 1, characterized in that: In step 6, any one of the four combined excitation modes in the excitation scheme is selected to calculate the crack generation area.

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