Method and system for analyzing mechanical properties of CFRP (carbon fiber reinforced plastic) grid reinforced concrete

Abstract

The invention provides a mechanical property analysis method and system for CFRP grid reinforced concrete, parameters and a loading scheme of a CFRP grid concrete beam stress analysis model are obtained, and a linear softening model is adopted for the bond-slip relation between a CFRP grid and a concrete interface; constructing known beams which have the same height and bear external bending moment; at the first stage that the width of the bottom of the crack is smaller than the critical crack width, the load, crack parameters and stress distribution characteristics in the crack expansion process are calculated according to the known geometric characteristics of the beam, the concrete characteristics and the CFRP characteristics; and in the second stage that the crack bottom width is larger than or equal to the critical crack width, a force balance equation is described, the relation between the crack bottom width and the pressure stress of the section top is defined, and the load, crack parameters and stress distribution characteristics in the crack expansion process are obtained through calculation. According to the method, the post-cracking tensile stress in the concrete and the bonding slippage behavior between the CFRP and the concrete are considered, and the result is accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a mechanical property analysis method and system of CFRP grid reinforced concrete. Background Art

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

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

[0004] Although some scholars have conducted research on FRP reinforcement of cracked concrete structures, these studies mostly focus on the analysis of the crack resistance of external FRP, and usually use carbon fiber reinforced composite material CFRP (Carbon Fiber Reinforced Polymer) for external reinforcement. Considering that in bridges, tunnels and other projects, in order to solve the problem of steel corrosion, embedded CFRP reinforced concrete beams have become a powerful trend in the development of future structures. It is urgent to propose an effective calculation method for the performance and fracture characteristics of embedded CFRP reinforced beams under existing crack conditions. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a mechanical property analysis method and system for CFRP grid reinforced concrete. The present invention predicts the mechanical performance of CFRP grid concrete beams based on a fracture analysis model. The fracture analysis model takes into account the post-cracking tensile stress in concrete and the bond-slip behavior between CFRP and concrete, and the analysis result is accurate.

[0006] According to some embodiments, the present invention adopts the following technical solutions:

[0007] A method for analyzing the mechanical properties of CFRP grid reinforced concrete comprises the following steps:

[0008] The basic parameters and loading scheme of the CFRP mesh concrete beam stress analysis model are obtained, and the linear softening model is used for the bond-slip relationship between the CFRP mesh and concrete interface;

[0009] Construct a known beam of the same height and subjected to an external bending moment;

[0010] In the first stage when the crack bottom width is less than the critical crack width, the load, crack parameters and stress distribution characteristics during the crack extension process are calculated based on the known geometric characteristics of the beam, concrete characteristics and CFRP characteristics.

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

[0012] As an optional implementation, the basic parameters include size parameters, concrete parameters and cutting parameters.

[0013] As an optional implementation, the CFRP grid concrete beam stress analysis model is a concrete beam with a CFRP grid horizontally penetrated, a loading force is set at the top center of the CFRP grid concrete beam, a test piece is set at the bottom of the CFRP grid concrete beam, the height of the CFRP grid concrete beam is H, the width is b, the span is L, the test piece height is a0, and the height of the CFRP grid from the bottom surface is c. The elastic modulus E of the FRP grid f , area 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 subjected to an 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] Where: a ′ = ac, a is the crack length, c is the protective layer thickness, its value is Hd, 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 , starting from the assumption of a flat section outside the cracking zone, the compressive stress σ at the top of the section c And the tensile strength of concrete is:

[0018] Define CMOD as the opening distance at the bottom of the crack, considering the balance of forces in the x-direction at the crack interface.

[0019] Wherein, 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 FRP concrete is τ max , variable λ el The expression is:

[0023]

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

[0025]

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

[0027] As an alternative embodiment, the torque 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 problem, the load, crack parameters and stress distribution characteristics during the crack propagation process are obtained.

[0034] As an alternative embodiment, in each step, the value of CMOD should be respectively related to the maximum allowable slip value s of FRP and concrete. max If CMOD exceeds s max If the load is twice as large as that of the beam, the failure of the beam is caused by the slip of CFRP.

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

[0036]

[0037] A mechanical properties analysis system for CFRP grid reinforced concrete, comprising:

[0038] Data acquisition module, used to obtain the basic parameters and loading scheme of the CFRP mesh concrete beam stress analysis model. The bond-slip relationship between the CFRP mesh and concrete interface adopts a linear softening model;

[0039] A known beam model building module is used to build known beams of the same height and subjected to external bending moments;

[0040] The first calculation module is used to calculate the load, crack parameters and stress distribution characteristics during the crack extension process according to the known geometric characteristics of the beam, concrete characteristics and CFRP characteristics in the first stage when the crack bottom width is less than the critical crack width;

[0041] The second calculation module is used to describe the force balance equation in the second stage when the crack bottom width is greater than or equal to the critical crack width, and to define the relationship between the crack bottom width and the compressive stress at the top of the cross section, so as to calculate the load, crack parameters and stress distribution characteristics during the crack expansion process.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The calculation process of the present invention integrates different local phenomena to more accurately describe the initiation and propagation of cracks, taking into account the post-cracking tensile stress in concrete and the bond-slip behavior between CFRP and concrete. It can predict parameters such as the length development of type I cracks and crack opening displacement of CFRP grid concrete three-point bending specimens.

[0044] The analysis method for CFRP reinforced concrete proposed in the present invention obtains theoretical prediction results that are relatively consistent with the test results, and the method is useful in crack analysis of actual concrete engineering.

[0045] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0047] Figure 1 A schematic diagram of loading a reinforced concrete beam specimen established by the present invention;

[0048] Figure 2 A schematic diagram of the dimensions of the reinforced concrete beam established for the present invention;

[0049] Figure 3 The interfacial bond-slip relationship between CFRP and concrete established by the present invention;

[0050] Figure 4 The stress distribution diagrams for different crack development stages established for the present invention, where (a) is CMOD < Cr and (b) is CMOD ≥ Cr;

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

[0052] Figure 6 The P-CMOD comparison diagram of the CFRP grid concrete sample established for the present invention. Detailed implementation manners

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

[0054] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanations of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

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

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

[0057] Embodiment 1

[0058] A method for analyzing the mechanical properties of CFRP grid-reinforced concrete, comprising the following steps:

[0059] Step 1, determining the basic parameters of the established finite element model, including size parameters, concrete parameters, and cut joint parameters, etc. Adopt the loading scheme as shown in Figure 1 , and the model size is as shown in Figure 2 , that is, the mechanical analysis model of the CFRP grid concrete beam is that a CFRP grid is horizontally penetrated in the concrete beam, a loading force is arranged at the center of the top of the CFRP grid concrete beam, a specimen is arranged at the bottom of the CFRP grid concrete beam, the height of the CFRP grid concrete beam is H, the width is b, the span is L, the height of the specimen is a0, and the height of the CFRP grid from the bottom surface is c.

[0060] The bond-slip relationship between CFRP and concrete interface adopts a linear softening model, such as Figure 3 shown.

[0061] Step 2: Consider a rectangular RC beam with width b, beam height H, effective depth d, and subjected to external bending moment M, such as Figure 2 As shown. Considering that the reinforcement for crack resistance will not be configured with a lot of CFRP. Therefore, it is assumed that the compressive stress at the top of the beam will not reach the compressive strength of the concrete. The model formula considers two stages of behavior. In the first stage, the crack bottom width is less than the critical crack width Cr, and in the second stage, the crack bottom width is greater than or equal to the critical crack width Cr.

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

[0063] d=a ′ +s+t(5)

[0064] Where: a ′ =ac; a is the crack length; c is the protective layer thickness, whose value is Hd; 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 concrete tensile strength f t Based on the assumption of a flat section outside the cracking zone, the compressive stress σ at the top of the section is c And the tensile strength of concrete is:

[0066]

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

[0068]

[0069] Where: SF is the CFRP tension.

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

[0071]

[0072] λ el The expression is:

[0073]

[0074] The CMOD expression is:

[0075]

[0076] In the first stage, for each assumed value of the crack length a, s, t, σ can be determined c , CMOD and SF. c 、f t , C r 、E c ) and CFRP properties (s max , τ max 、E f , A f ). By solving equations (6), (7), (8), (9) and (10), the load, crack parameters and stress distribution characteristics during the crack propagation process can be obtained.

[0077] The torque is:

[0078]

[0079] Step 4, Theoretical analysis of the second stage, at the beginning of the second stage, CMOD exceeds Cr and the beam with concrete bottom fibers cannot withstand any tensile stress. The stress transfer in the second stage is similar to the first stage, except that the concrete tensile strength is lost and the tensile softening begins. When CMOD = Cr and CMOD>Cr, according to Figure 4 As shown in (b), 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] By solving equations (6), (7), (8), (9), (12) and (13), the load, crack parameters and stress distribution characteristics during the crack propagation process can be obtained. In each step, the value of COD should be compared with the value of smax. If COD exceeds twice the value of smax, the failure of the beam is due to CFRP slip.

[0084] The torque is:

[0085]

[0086] In the first stage, for each assumed value of the crack length a, s, t, σ can be determined c , CMOD and SF. c 、f t , C r 、Ec ) and CFRP properties (s max , τ max , E s , n, A s ). By solving equations (6), (7), (8), (9) and (10), the load, crack parameters, and stress distribution characteristics during crack propagation can be obtained.

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

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

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

[0090] (3) From formula (8), when a is given, SF will have a fixed calculation result.

[0091] (4) From formula (10), a result regarding CMOD can be obtained, and CMOD can be expressed as a function of t.

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

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

[0094] (7) Repeat steps (1) to (6), and by adding the discriminant condition CMOD < Cr, the full-process results of the bending moment and crack opening width in the first stage can be solved.

[0095] The end discriminant condition for the second-stage analysis. That is, after dividing the maximum calculation result at CMOD by 2, it cannot exceed Figure 3 Smax in. Because, if it exceeds Smax, then all FRP will be completely peeled off, resulting in the failure of the force and bending moment balance equations.

[0096] In the second stage, for each assumed value of the crack length a, the relevant 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 , τ max , E s , n, A s). By solving equations (6), (7), (8), (9), (12) and (13), the load, crack parameters and stress distribution characteristics during the crack propagation process can be obtained.

[0097] In the above solution, the solution of the transcendental equation can be decomposed into the following steps:

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

[0099] (2 According to formula (6), we can make σ c is a function of t.

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

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

[0102] (5)Finally, according to the force balance equation (12), t can be solved by the optimization algorithm.

[0103] (6) With the solution of t, all variables, including the bending moment M in formula (13), can also be solved.

[0104] (7) Repeat steps (1) to (6) and add the judgment condition CMOD ≥ Cr to solve the full process results of the bending moment and crack opening width in the second stage. However, it is worth noting that this calculation also requires the addition of a control condition, that is, the maximum calculation result at CMOD cannot exceed 0.0000 after being divided by 2. Figure 3 Because if Smax is exceeded, all FRP will be completely peeled off, causing the force and moment equilibrium equations to fail.

[0105] The solution results of plain concrete slotted beams are as follows Figure 5 As shown in the figure, the solution results of the CFRP mesh slotted beam are as follows: Figure 6 As shown. It can be seen that the analysis method of CFRP reinforced concrete proposed in the present invention obtains theoretical prediction results that are relatively consistent with the test results, and this method is useful in crack analysis of actual concrete engineering. Test refers to the test results, and Theory refers to the theoretical prediction results.

[0106] In summary, the present invention predicts the mechanical properties of CFRP (Carbon Fiber Reinforced Polymer) grid concrete beams based on the fracture analysis model. The model is a closed solution that integrates 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 and the bond-slip behavior between CFRP and concrete. The model can predict parameters such as the length development of type I cracks and crack opening displacement of CFRP grid concrete three-point bending specimens.

[0107] The present invention carried out 7-day and 14-day experimental tests on 12 samples, and the calculation results were in good agreement with the experimental 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 becomes unstable and the crack opens rapidly. The P-CMOD curve of the CFRP reinforced beam also shows a descending section due to the sudden release of local fracture energy. However, due to the bonding force between the CFRP grid and the concrete, the grid begins to repeatedly exert its tensile strength, and the P-CMOD curve shows a second ascending section and reaches the second peak point. Subsequently, the CFRP-concrete interface undergoes bonding slip softening, and thereafter, as the crack opening displacement increases, the load fluctuates slightly and can maintain a certain load level.

[0108] Embodiment 2

[0109] A mechanical properties analysis system for CFRP grid reinforced concrete, comprising:

[0110] Data acquisition module, used to obtain the basic parameters and loading scheme of the CFRP mesh concrete beam stress analysis model. The bond-slip relationship between the CFRP mesh and concrete interface adopts a linear softening model;

[0111] A known beam model building module is used to build known beams of the same height and subjected to external bending moments;

[0112] The first calculation module is used to calculate the load, crack parameters and stress distribution characteristics during the crack extension process according to the known geometric characteristics of the beam, concrete characteristics and CFRP characteristics in the first stage when the crack bottom width is less than the critical crack width;

[0113] The second calculation module is used to describe the force balance equation in the second stage when the crack bottom width is greater than or equal to the critical crack width, and to define the relationship between the crack bottom width and the compressive stress at the top of the cross section, so as to calculate the load, crack parameters and stress distribution characteristics during the crack expansion process.

[0114] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made by those skilled in the art within the spirit and principle of the present invention without creative labor shall be included in the protection scope of the present invention.

Claims

1. A method for analyzing the mechanical properties of CFRP grid reinforced concrete, characterized in that: The following steps are involved: The basic parameters and loading scheme of the CFRP mesh concrete beam stress analysis model are obtained, and the linear softening model is used for the bond-slip relationship between the CFRP mesh and concrete interface; Construct a known beam of the same height and subjected to an external bending moment; In the first stage when the crack bottom width is less than the critical crack width, the load, crack parameters and stress distribution characteristics during the crack extension process are calculated based on the known geometric characteristics of the beam, concrete characteristics and CFRP characteristics. In the second stage when the crack bottom width is greater than or equal to the critical crack width, the force balance equation is described, and the relationship between the crack bottom width and the compressive stress at the top of the section is defined. The load, crack parameters and stress distribution characteristics during the crack extension process are calculated.

2. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 1, characterized in that: The basic parameters include size parameters, concrete parameters and cutting parameters.

3. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 1, characterized in that: The stress analysis model of the CFRP grid concrete beam is that a CFRP grid is horizontally arranged in the concrete beam, a loading force is arranged at the top center of the CFRP grid concrete beam, a test piece is arranged at the bottom of the CFRP grid concrete beam, the height of the CFRP grid 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 grid from the bottom surface is c. The elastic modulus E of the FRP grid f , area A f .

4. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 1, characterized in that: The known beam is a rectangular RC beam with a width of b, a beam height of H, an effective depth of d and subjected to an 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.

5. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 1, characterized in that In the first stage, the cross section, crack geometry and parameters are obtained: d = a ′ +s+t; Where: a ′ = ac, a is the crack length, c is the protective layer thickness, its value is 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 flat section outside the cracking zone, the compressive stress σ at the top of the section c And the tensile strength of concrete is: Consider the balance of forces in the x-direction at the crack interface: Wherein, SF is the CFRP tension; When CFRP remains elastic, the CFRP tension SF is determined as: Variable λ el The expression is: Define CMOD as the opening distance at the bottom of the crack. The expression of CMOD is: For each assumed value of the crack length a, determine s, t, σ c , CMOD and SF, the geometric characteristics of the beam, the characteristics of concrete and CFRP are known, and the load, crack parameters and stress distribution characteristics during the crack propagation process are obtained by solving the above equations.

6. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 5, characterized in that the moment is:

7. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 1, characterized in that In the second stage, the force balance equation is described as: When CMOD>Cr, the relationship between CMOD and σc can be defined as: By solving the problem, the load, crack parameters and stress distribution characteristics during the crack propagation process are obtained.

8. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 7, characterized in that: The value of CMOD should be equal to the maximum allowable slip value s of FRP and concrete respectively. max If CMOD exceeds s max If the load is twice as large as that of the beam, the failure of the beam is caused by the slip of CFRP.

9. A method for analyzing mechanical properties of CFRP grid reinforced concrete as claimed in claim 7 or 8, characterized in that the moment is:

10. A mechanical properties analysis system for CFRP grid reinforced concrete, characterized in that: include: Data acquisition module, used to obtain the basic parameters and loading scheme of the CFRP mesh concrete beam stress analysis model. The bond-slip relationship between the CFRP mesh and concrete interface adopts a linear softening model; A known beam model building module is used to build known beams of the same height and subjected to external bending moments; The first calculation module is used to calculate the load, crack parameters and stress distribution characteristics during the crack extension process according to the known geometric characteristics of the beam, concrete characteristics and CFRP characteristics in the first stage when the crack bottom width is less than the critical crack width; The second calculation module is used to describe the force balance equation in the second stage when the crack bottom width is greater than or equal to the critical crack width, and to define the relationship between the crack bottom width and the compressive stress at the top of the cross section, so as to calculate the load, crack parameters and stress distribution characteristics during the crack expansion process.

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