A method and system for analyzing mechanical properties of CFRP grid reinforced concrete

Abstract

The application provides a mechanical property analysis method and system of CFRP grid reinforced concrete, parameters and loading schemes of a stress analysis model of a CFRP grid concrete beam are acquired, a linear softening model is used for a CFRP grid and a concrete interface bonding slip relationship; a known beam with the same height and bearing external bending moment is constructed; in a first stage with a crack bottom width less than a critical crack width, load, crack parameters and stress distribution characteristics in a crack expansion process are calculated according to geometric characteristics, concrete characteristics and CFRP characteristics of the known beam; in a second stage with the crack bottom width greater than or equal to the critical crack width, a force balance equation is described, a relationship between the crack bottom width and the compressive stress of the top of the section is defined, and the load, crack parameters and stress distribution characteristics in the crack expansion process are calculated. The application considers post-cracking tensile stress in the concrete, bonding slip behavior between the CFRP and the concrete, and the result is accurate.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge engineering, and particularly relates to a mechanical property analysis method and system of CFRP grid reinforced concrete. BACKGROUND

[0002] The statements in this section merely provide background information related to the application and do not necessarily constitute prior art.

[0003] Fiber reinforced composite material (FRP) is a composite material composed of reinforcing fibers and polymer matrix. Due to the advantages of light weight, high strength, good corrosion resistance, good fatigue resistance and the like, FRP is widely used in the reinforcement and reinforcement of concrete structures to effectively improve the tensile strength and crack resistance of the structure, and to improve the durability and prolong the service life of the structure.

[0004] Although some scholars have carried out research on FRP reinforced concrete structures with cracks, these researches are mostly focused on the crack resistance analysis of the structure by externally attaching FRP, and usually use carbon fiber reinforced polymer (CFRP) for external reinforcement. Considering the problem of steel corrosion in bridge, tunnel and other engineering, embedded CFRP reinforced concrete beam has become a powerful trend in future structure development. It is urgent to propose an effective calculation method for the performance and fracture characteristics of the embedded CFRP reinforced beam under the condition of existing cracks. SUMMARY

[0005] In order to solve the above problems, the application provides a mechanical property analysis method and system of CFRP grid reinforced concrete. The application predicts the stress performance of the CFRP grid concrete beam based on a fracture analysis model, which considers the post-cracking tensile stress in the concrete, the bonding and sliding behavior between CFRP and concrete, and the analysis result is accurate.

[0006] According to some embodiments, the application adopts the following technical scheme:

[0007] A mechanical property analysis method of CFRP grid reinforced concrete, comprising the following steps:

[0008] Obtaining the basic parameters and loading scheme of the stress analysis model of the CFRP grid concrete beam, and adopting a linear softening model for the bonding and sliding relationship between the CFRP grid and the concrete interface;

[0009] Constructing a known beam with the same height and bearing external bending moment;

[0010] In the first stage, when the crack width is less than the critical crack width, the load, crack parameters and stress distribution characteristics during the crack propagation are calculated according to the known geometric characteristics of the beam, the concrete characteristics and the CFRP characteristics;

[0011] In the second stage, when the crack width is greater than or equal to the critical crack width, the force balance equation is described, and the relationship between the crack width and the compressive stress at the top of the section is defined, and the load, crack parameters and stress distribution characteristics during the crack propagation are calculated.

[0012] As an alternative embodiment, the basic parameters include size parameters, concrete parameters and joint parameters.

[0013] As an alternative embodiment, the CFRP mesh concrete beam stress analysis model is provided with a CFRP mesh horizontally penetrating in the concrete beam, a loading force is arranged at the top center of the CFRP mesh concrete beam, a test piece is arranged at the bottom of the CFRP mesh concrete beam, the height of the CFRP mesh concrete beam is H, the width is b, the span is L, the height of the test piece is a0, the height of the CFRP mesh from the bottom is c, and the elastic modulus of the CFRP mesh is E f , and the area is A f .

[0014] As an alternative embodiment, the known beam is a rectangular RC beam with a width of b, a beam height of H (effective depth d) and bearing external bending moment M, and it is assumed that the compressive stress at the top of the beam will not reach the compressive strength of the concrete.

[0015] As an alternative embodiment, in the first stage, the cross section, crack geometry and parameters are obtained: d = a ′ +s+t;

[0016] In the formula: a ′ =a-c, a is the crack length, c is the thickness of the protective layer, the value is H-d, s is the distance from the visible crack tip to the neutral axis, and t is the depth of the compression zone;

[0017] According to the cohesive model, the tensile stress at the crack tip is equal to f t , and according to the plane section assumption outside the cracking zone, the compressive stress σ c at the top of the section and the tensile strength of the concrete are:

[0018] CMOD is defined as the opening distance of the crack bottom, and the force balance in the x direction at the crack interface is considered,

[0019] Where SF is the CFRP tension.

[0020] As an alternative embodiment, in the first stage, when the CFRP remains elastic, the CFRP tension SF is determined as:

[0021]

[0022] The interfacial bond strength of the FRP concrete is τ max , and the variable λ el is expressed as:

[0023]

[0024] The critical crack width is Cr, and the expression of CMOD is:

[0025]

[0026] For each assumed value of the crack length a, the related values of s, t, σ c , CMOD and SF are determined, and the load, crack parameter and stress distribution characteristics in the crack propagation process are obtained by solving the above equations, with the known geometric characteristics of the beam, the concrete characteristics and the CFRP characteristics.

[0027] As an alternative embodiment, the moment is:

[0028]

[0029] As an alternative embodiment, in the second stage, the force balance equation is described as:

[0030]

[0031] When CMOD>Cr, the relationship between CMOD and σc can be defined as:

[0032]

[0033] By solving, the load, crack parameter and stress distribution characteristics in the crack propagation process are obtained.

[0034] As an alternative embodiment, in each step, the value of CMOD should be compared with the value of the maximum allowable slip s max of the FRP and the concrete respectively, and if CMOD exceeds twice the value of s max , the failure of the beam is caused by the slip of the CFRP.

[0035] As an alternative embodiment, the moment is:

[0036]

[0037] A mechanical performance analysis system of a CFRP mesh reinforced concrete comprises:

[0038] The data acquisition module is used for acquiring basic parameters and loading schemes of the CFRP mesh concrete beam stress analysis model, and a linear softening model is used for the CFRP mesh and the concrete interface bonding slip relationship.

[0039] The known beam model construction module is used for constructing a known beam with the same height and bearing external bending moment.

[0040] The first calculation module is used for calculating the load, crack parameter and stress distribution characteristics in the crack expansion process according to the geometric characteristics, concrete characteristics and CFRP characteristics of the known beam in the first stage that the crack bottom width is less than the critical crack width.

[0041] The second calculation module is used for calculating the load, crack parameter and stress distribution characteristics in the crack expansion process by describing the force balance equation and defining the relationship between the crack bottom width and the compressive stress of the top section of the cross section in the second stage that the crack bottom width is greater than or equal to the critical crack width.

[0042] Compared with the prior art, the beneficial effects of the present application are:

[0043] The calculation process of the present application comprehensively considers different local phenomena to more accurately describe the initiation and expansion of cracks, consider the post-cracking tensile stress in the concrete, and the bonding slip behavior between the CFRP and the concrete. The present application can realize the prediction of the type I crack length development and crack opening displacement of the CFRP mesh concrete three-point bending specimen.

[0044] The analysis method of the CFRP reinforced concrete proposed in the present application obtains the theoretical prediction results and the test results that are matched, and the method can be used in the cracking analysis of actual concrete engineering.

[0045] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the following preferred embodiments are described in detail below, and the accompanying drawings are described as follows. BRIEF DESCRIPTION OF DRAWINGS

[0046] The drawings accompanying the specification of the present application form a part of the present application, and the schematic embodiments of the present application and the description thereof are used to explain the present application, and do not constitute an improper limitation on the present application.

[0047] Figure 1 The loading schematic diagram of the reinforced concrete beam specimen established by the present application;

[0048] Figure 2 The size schematic diagram of the reinforced concrete beam established by the present application;

[0049] Figure 3 The interface bonding slip relationship of the CFRP and the concrete established by the present application;

[0050] Figure 4 Stress distribution diagrams of different crack development stages established for the present application, wherein (a) is CMOD

[0051] Figure 5 P-CMOD comparison diagram of plain concrete sample established for the present application;

[0052] Figure 6 P-CMOD comparison diagram of CFRP mesh concrete sample established for the present application. DETAILED DESCRIPTION

[0053] The present application will be further described below in conjunction with the accompanying drawings and examples.

[0054] It should be noted that the following detailed description is illustrative only and is intended to provide further description of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application pertains.

[0055] It should be noted that the terms used herein are only intended to describe specific embodiments and are not intended to limit exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should be further understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of the features, steps, operations, devices, components and / or combinations thereof.

[0056] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0057] Embodiment One

[0058] A mechanical property analysis method of CFRP mesh reinforced concrete, comprising the following steps:

[0059] Step 1, determine the basic parameters of the constructed finite element model, including size parameters, concrete parameters and joint parameters, etc. Adopt the loading scheme as shown in Figure 1 The model size is as shown in Figure 2 The CFRP mesh concrete beam stress analysis model is provided with a CFRP mesh in the horizontal through of the concrete beam, the top center of the CFRP mesh concrete beam is provided with a loading force, the bottom of the CFRP mesh concrete beam is provided with a test piece, the height of the CFRP mesh concrete beam is H, the width is b, the span is L, the height of the test piece is a0, and the height of the CFRP mesh from the bottom surface is c.

[0060] The bond-slip relationship between CFRP and concrete is assumed to be linearly softening, as shown in Fig. 1. Figure 3

[0061] Step 2, Consider a rectangular RC beam with width b, height H, effective depth d, and subjected to external bending moment M, as shown in Fig. 2. It is assumed that the amount of CFRP used for crack resistance is not large enough to cause compressive stress at the top of the beam to reach the compressive strength of concrete. The formulation of the model considers two stages of behavior. The first stage is when the crack width is less than the critical crack width Cr, and the second stage is when the crack width is greater than or equal to the critical crack width Cr. Figure 2

[0062] Step 3, Theoretical analysis of the first stage, based on the cross-section, crack geometry, and parameters shown in Fig. 3(a), gives: Figure 4

[0063] d = a ′ + s + t (5)

[0064] where: a ′ = a - c; a is the crack length; c is the cover thickness, which is H - d; s is the distance from the visible crack tip to the neutral axis; t is the depth of the compression zone.

[0065] According to the cohesive model, the tensile stress at the crack tip is equal to the tensile strength of concrete f t . From the plane section assumption outside the cracking zone, the compressive stress σ c at the top of the section and the tensile strength of concrete are:

[0066]

[0067] Considering the balance of forces in the x-direction at the crack interface,

[0068]

[0069] where: SF is the CFRP tensile force.

[0070] When the CFRP remains elastic, the elastic force SF is determined as:

[0071]

[0072] λ el is expressed as:

[0073]

[0074] The expression for CMOD is:

[0075]

[0076] ​​​For each assumed value of crack length a, the values of s, t, σ c , CMOD and SF can be determined. The geometric properties of the beam (H, d, b, c), the concrete properties (f c , f t , C r , E c ) and the CFRP properties (s max , τ max , E f , A f ) are known. The load, crack parameters, stress distribution characteristics during the crack propagation can be solved by solving equations (6), (7), (8), (9) and (10).

[0077] The moment is:

[0078]

[0079] Step 4, Theoretical analysis of the second phase, at the beginning of the second phase, CMOD exceeds Cr and the beam cannot withstand any tensile stress at the bottom of the concrete fibers. The stress transfer in the second phase is similar to the first phase, except for the loss of tensile strength of the concrete and the subsequent beginning of tensile softening. At CMOD = Cr and CMOD > Cr, according to (b) shown in Figure 4 , the force balance equation can be described as:

[0080]

[0081] When CMOD > Cr, the relationship between CMOD and σc can be defined as:

[0082]

[0083] The load, crack parameters, stress distribution characteristics during the crack propagation can be solved by solving equations (6), (7), (8), (9), (12) and (13). In each step, the value of COD should be compared with the value of smax, respectively. If the COD exceeds twice the value of smax, the failure of the beam is due to the slip of the CFRP.

[0084] The moment is:

[0085]

[0086] For each assumed value of crack length a, the values of s, t, σ c , CMOD and SF can be determined. The geometric properties of the beam (H, d, b, c), the concrete properties (f c , f t , C r , Ec ) and CFRP properties (s max , t max , E s , n, A s ). By solving equations (6), (7), (8), (9) and (10), the load, crack parameters, stress distribution characteristics during the crack propagation process can be solved.

[0087] In the above solution, the solution of transcendental equations can be divided into the following steps:

[0088] (1) First assume the crack length a, then s can be obtained through equation (5), which can be expressed as a function of t.

[0089] (2) Further according to formula (6), σ c can be made as a function of t.

[0090] (3) According to formula (8), after a is given, SF will have a fixed calculation result.

[0091] (4) According to formula (10), a result about CMOD can be obtained, which can be expressed as a function of t.

[0092] (5) Finally, according to the force balance equation formula (7), t can be solved by optimization algorithm.

[0093] (6) With the solution of t, all variables, including the bending moment M of formula (11), will also be solved.

[0094] (7) Repeat steps (1) to (6), add the discrimination condition CMOD < Cr, and the whole process results of the first stage bending moment and crack opening width can be solved.

[0095] The end discrimination condition of the second stage analysis. That is, the maximum calculation result of CMOD divided by 2 cannot exceed Smax in Figure 3 . Because if it exceeds Smax, all FRP will be completely stripped, resulting in invalid force and bending moment balance equation.

[0096] In the second stage, for each assumed value of crack length a, the related values of s, t, σ c , CMOD and SF can be determined. Given the geometric properties of the beam (H, d, b, c), concrete properties (f c , f t , C r , E c ) and CFRP properties (s max , t max , E s , n, A sBy solving equations (6), (7), (8), (9), (12) and (13), the load, crack parameters and stress distribution characteristics during crack propagation can be obtained.

[0097] The solution to the transcendental equations above can be broken down into the following steps:

[0098] (1) Based on the final crack length obtained in step 3, add an increment to obtain the assumed crack length a, and then s can be obtained through equation (5), where s can be expressed as a function of t.

[0099] (2) Further according to formula (6), σ can be made c It is a function of t.

[0100] (3) According to formula (8), once a is given, SF will have a fixed calculation result.

[0101] (4) From formula (13), we can obtain a result about CMOD, which can be expressed as a function of t.

[0102] (5) Then, based on the force balance equation formula (12), t can be solved by an optimization algorithm.

[0103] (6) Once the solution for t is obtained, all variables, including the bending moment M in formula (13), will also be solved.

[0104] (7) Repeat steps (1) to (6), adding the criterion CMOD≥Cr, to solve for the bending moment and crack opening width in the second stage. However, it is worth noting that this calculation also requires an additional control condition: the maximum calculated result at CMOD, after being divided by 2, cannot exceed [the specified value]. Figure 3 The maximum value is Smax. This is because if Smax is exceeded, all FRP will completely peel off, causing the force and moment balance equations to fail.

[0105] The solution results for plain concrete cut-joint beams are as follows: Figure 5 As shown, the solution results for the CFRP mesh slotted beam are as follows: Figure 6 As shown in the figure, the analytical method for CFRP-reinforced concrete proposed in this invention yields a good match between theoretical predictions and experimental results, and this method can be used in crack analysis of actual concrete engineering projects. Here, "Test" refers to the experimental results, and "Theory" refers to the theoretical prediction results.

[0106] In summary, the present application predicts the mechanical performance of CFRP (Carbon Fiber Reinforced Polymer) meshed concrete beams based on a fracture analysis model. The model is a closed-form solution that incorporates different local phenomena to more accurately describe the initiation and propagation of cracks. The fracture analysis model includes the post-cracking tensile stress in concrete, the bond-slip behavior between CFRP and concrete. The model can predict the development of mode-I crack length and crack opening displacement of CFRP meshed concrete three-point bending specimens.

[0107] The present application carries out 7-day and 14-day test tests of 12 samples, and the calculation results are in good agreement with the test results. The research results show that the P-CMOD curve of the plain concrete beam presents a typical single-peak curve. After the first peak point, the plain concrete beam loses stability and the crack opens rapidly. The P-CMOD curve of the CFRP reinforced beam also shows a downward segment due to the sudden release of local fracture energy. However, due to the bonding force between the CFRP mesh and the concrete, the mesh begins to repeatedly develop its tensile strength, and the P-CMOD curve appears a second rising segment, reaching a second peak point. Subsequently, the CFRP-concrete interface undergoes bond-slip softening, and thereafter, with the increase of the crack opening displacement, the load presents a small amplitude fluctuation state and can maintain a certain load level.

[0108] Embodiment two

[0109] A mechanical performance analysis system of CFRP mesh reinforced concrete, comprising:

[0110] A data acquisition module is configured to acquire basic parameters and loading schemes of a stress analysis model of a CFRP meshed concrete beam, and a linear softening model is used for the bond-slip relationship between the CFRP mesh and the concrete interface.

[0111] A known beam model construction module is configured to construct a known beam with the same height and subjected to an external bending moment.

[0112] A first calculation module is configured to calculate the load, crack parameters and stress distribution characteristics in the crack propagation process according to the geometric characteristics, concrete characteristics and CFRP characteristics of the known beam in a first stage when the crack bottom width is less than the critical crack width.

[0113] A second calculation module is configured to describe the force balance equation and define the relationship between the crack bottom width and the compressive stress at the top of the section in a second stage when the crack bottom width is greater than or equal to the critical crack width, and calculate the load, crack parameters and stress distribution characteristics in the crack propagation process.

[0114] The above merely describes the preferred embodiments of the present application and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made by those skilled in the art without departing from the spirit and principle of the present application shall fall within the protection scope of the present application.

Claims

1. A method for analyzing the mechanical properties of CFRP mesh-reinforced concrete, characterized in that, Includes the following steps: The basic parameters and loading scheme of the stress analysis model of CFRP mesh concrete beam are obtained. The bond-slip relationship between CFRP mesh and concrete interface is adopted using a linear softening model. Construct a known beam of the same height that is subjected to external bending moment; In the first stage, when the width at the bottom of the crack is less than the critical crack width, the load, crack parameters, and stress distribution characteristics during the crack propagation process are calculated based on the known geometric properties of the beam, concrete properties, and CFRP properties. In the second stage, where the width at the bottom of the crack is greater than or equal to the critical crack width, the force balance equations are described as follows: ； Where SF is the CFRP tensile force, b is the width of the CFRP mesh concrete beam, a is the crack length, ft is the tensile strength of the concrete, s is the distance from the visible crack tip to the neutral axis, and t is the depth of the compression zone. Where CMOD is the critical crack width, and CMOD is the opening distance at the crack base. This represents the compressive stress at the top of the cross section; When CMOD > Cr, the relationship between CMOD and σc can be defined as: ； Where c is the thickness of the protective layer. =ac, Ec is the elastic modulus of concrete; By solving the problem, we can obtain the load, crack parameters, and stress distribution characteristics during the crack propagation process.

2. The method for analyzing the mechanical properties of CFRP mesh-reinforced concrete as described in claim 1, characterized in that, The basic parameters include dimensional parameters, concrete parameters, and joint cutting parameters.

3. The method for analyzing the mechanical properties of CFRP mesh-reinforced concrete as described in claim 1, characterized in that, The stress analysis model of the CFRP mesh concrete beam consists of a horizontally continuous CFRP mesh in the concrete beam. A loading force is applied at the top center of the CFRP mesh concrete beam, and a specimen is placed at the bottom of the CFRP mesh concrete beam. The height of the CFRP mesh concrete beam is H, the width is b, the span is L, the specimen height is a0, the height of the CFRP mesh from the bottom surface is c, and the elastic modulus E of the CFRP mesh is... f Area A f .

4. The method for analyzing the mechanical properties of CFRP mesh-reinforced concrete as described in claim 1, characterized in that, The known beam is a rectangular RC beam with a width of b, a height of H, an effective depth of d, and subjected to an external bending moment M. It is assumed that the compressive stress at the top of the beam will not reach the compressive strength of the concrete.

5. The method for analyzing the mechanical properties of CFRP mesh-reinforced concrete as described in claim 1, characterized in that, in In the first stage, the cross-section, crack geometry, and parameters are obtained as follows: ； In the formula: =ac, where a is the crack length, c is the protective layer thickness (value Hd), s is the distance from the visible crack tip to the neutral axis, and t is the depth of the compression zone; According to the cohesive model, the tensile stress at the crack tip is equal to f. t Starting from the assumption of a plane section outside the cracked zone, the compressive stress σ at the top of the section... c The tensile strength of concrete is: ； Consider the force balance in the x-direction at the crack interface: ； Where SF is the CFRP tensile force and b is the width of the CFRP grid concrete beam; When the CFRP remains elastic, the CFRP tensile force SF is determined as follows: ； in, The maximum allowable slip value, For interfacial bond strength, denoted as , where is the contact perimeter between the reinforcing steel bars and the surrounding concrete in the CFRP mesh concrete beam, and n is the number of reinforcing steel bars in the CFRP mesh concrete beam. variable λ el The expression is: ； in, The area of ​​the CFRP mesh. The elastic modulus of the CFRP mesh; Define CMOD as the opening distance at the bottom of the crack, and the expression for CMOD is: ； in, This refers to the elastic modulus of concrete. The critical crack width; For each assumed value of crack length a, determine s, t, σ c Given the relevant values ​​of CMOD and SF, the geometric properties of the beam, the properties of the concrete, and the properties of CFRP, the load, crack parameters, and stress distribution characteristics during crack propagation can be obtained by solving the above equations.

6. The method for analyzing the mechanical properties of CFRP mesh-reinforced concrete as described in claim 5, characterized in that the torque is: 。 7. The method for analyzing the mechanical properties of CFRP mesh-reinforced concrete as described in claim 1, characterized in that, The CMOD value should be correlated with the maximum allowable slip value of FRP and concrete, respectively. max The values ​​are compared, if CMOD exceeds s max If the beam's failure is twice that of the CFRP, then the failure is due to CFRP slippage.

8. A method for analyzing the mechanical properties of CFRP mesh-reinforced concrete as described in claim 1 or 7, characterized in that the torque is: 。 9. A mechanical property analysis system for CFRP mesh-reinforced concrete, characterized in that, include: The data acquisition module is used to acquire the basic parameters and loading scheme of the stress analysis model of CFRP mesh concrete beam. The bond-slip relationship between CFRP mesh and concrete interface adopts a linear softening model. The known beam model building module is used to construct known beams of the same height that are subjected to external bending moments; The first calculation module is used to calculate the load, crack parameters, and stress distribution characteristics during the crack propagation process in the first stage, when the crack bottom width is less than the critical crack width, based on the known geometric properties of the beam, concrete properties, and CFRP properties. The second calculation module, used in the second stage where the crack bottom width is greater than or equal to the critical crack width, describes the force balance equations, specifically: ； Where SF is the CFRP tensile force, b is the width of the CFRP mesh concrete beam, a is the crack length, ft is the tensile strength of the concrete, s is the distance from the visible crack tip to the neutral axis, and t is the depth of the compression zone. Where CMOD is the critical crack width, and CMOD is the opening distance at the crack base. This represents the compressive stress at the top of the cross section; When CMOD > Cr, the relationship between CMOD and σc can be defined as: ； Where c is the thickness of the protective layer. =ac, Ec is the elastic modulus of concrete; By solving the problem, we can obtain the load, crack parameters, and stress distribution characteristics during the crack propagation process.

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