Constitutive relation of bond-slip between FRP and concrete and method for calculating load-displacement curve

Abstract

This invention provides a method for calculating the bond-slip constitutive model and load-displacement curve of the FRP-concrete interface. The bond-slip constitutive model calculation method includes: obtaining the basic parameters of the FRP-concrete interface after high temperature; and obtaining the fracture energy G of the FRP-concrete interface at room temperature. f,0 And the ductility coefficient B0; based on the basic parameters and fracture energy G f,0 Calculate the interfacial fracture energy G of FRP-concrete after high temperature. f,T Based on the ductility coefficient B0, calculate the ductility coefficient B at the FRP-high temperature concrete interface. T According to the interfacial fracture energy G of FRP-concrete after high temperature f,T And ductility coefficient B T This invention calculates the bond-slip constitutive model of the FRP-concrete interface after high temperature. The method presented in this invention has high reliability and a simple calculation process, which will help promote the application of external FRP reinforcement in high-temperature damaged concrete structures.

Description

Technical Field

[0001] This invention relates to the field of FRP-concrete interface technology, specifically to a method for calculating the bond-slip constitutive model and load-displacement curve of an FRP-concrete interface. Background Technology

[0002] Reinforced concrete structures can often be reused after fire through reinforcement and repair, offering significant advantages over large-scale demolition and reconstruction, such as lower cost and less pollution. Traditional concrete structure reinforcement methods include increasing the cross-section and encasing the structure in steel, but these methods generally suffer from drawbacks such as cumbersome procedures, long construction periods, increased weight, encroachment on usable space, and poor durability. In contrast, fiber-reinforced polymer (FRP) composites offer significant advantages such as high specific strength, high specific modulus, and strong corrosion and fatigue resistance. They have been widely used in civil engineering for nearly thirty years and are an ideal material for reinforcing and repairing concrete after high temperatures. The construction process is very simple: typically, the concrete surface is first impregnated with epoxy resin, then FRP fabric is attached, and an epoxy resin layer is evenly applied to each layer of FRP fabric. Finally, the structure is ready for use after the resin has fully cured.

[0003] In the design of FRP-reinforced concrete structures, the interfacial properties between FRP and concrete are a key factor affecting the structural mechanical properties. This is because when FRP and concrete are subjected to joint stress, relative slippage occurs between them, leading to interfacial shear stress. Currently, the interfacial properties of FRP-concrete at room temperature have been systematically studied, and relatively mature design methods have been developed. However, for the FRP-concrete interface after high temperatures, there is still a lack of calculation methods for the interfacial bond-slip constitutive model and load-displacement curves. This has become a challenge in the design of reinforced structures, hindering the widespread application of external FRP reinforcement methods in fire- or high-temperature-exposed concrete structures.

[0004] The search revealed:

[0005] Chinese invention patent application CN113901545A discloses a method for establishing a bond-slip constitutive model of an FRP-reinforced ECC member, comprising the following steps: Step 1, establishing a preliminary constitutive model, the calculation formula of which includes bond strength τ, slip s, maximum bond strength τm, the corresponding rebar slip sm, and curve shape adjustment parameters M and N; Step 2, establishing the relationship between τm, sm and FRP rebar diameter, FRP rebar stress, and fiber content in ECC material; Step 3, establishing the relationship between curve shape adjustment parameters M and N and FRP rebar diameter, FRP rebar stress, and fiber content in ECC material; Step 4, establishing the bond-slip constitutive model of the FRP-reinforced ECC member. However, the method in this patent still cannot obtain the interfacial properties between FRP and high-temperature concrete. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a simple and clear method for calculating the bond-slip constitutive model and load-displacement curve of the FRP-concrete interface.

[0007] According to one aspect of the present invention, a constitutive method for calculating the bond-slip structure of an FRP-concrete interface is provided, the method comprising:

[0008] Obtain the basic parameters of the FRP-concrete interface after high temperature;

[0009] Obtain the fracture energy G at the FRP-concrete interface at room temperature f,0 And the ductility coefficient B0;

[0010] Based on the aforementioned basic parameters and fracture energy G f,0 Calculate the interfacial fracture energy G of FRP-concrete after high temperature. f,T ;

[0011] Calculate the ductility coefficient B at the FRP-concrete interface after high temperature based on the ductility coefficient B0. T ;

[0012] According to the interfacial fracture energy G of FRP-concrete after high temperature f,T And ductility coefficient B T Calculate the bond-slip constitutive model of the FRP-concrete interface after high temperature.

[0013] Furthermore, the acquisition of basic parameters of the FRP-concrete interface after high temperature includes parameters of the concrete base and parameters of the external FRP.

[0014] Furthermore, the parameters of the concrete base include: the tensile strength f of the concrete at room temperature. t , width of concrete base b cand the thickness t of the concrete base c ;

[0015] The parameters of the externally bonded FRP include: the elastic modulus E of the FRP. f The width b of the FRP f And the thickness t of FRP f .

[0016] Furthermore, the fracture energy G at the FRP-concrete interface at room temperature is obtained. f,0 And the ductility coefficient B0, where the fracture energy G f,0 The calculation formula is:

[0017]

[0018] in,

[0019] Furthermore, the calculation of the interfacial fracture energy G of FRP-concrete after high temperature is... f,T Among them, the interfacial fracture energy G f,T The calculation formula is:

[0020]

[0021] Where T is the maximum temperature experienced by the concrete.

[0022] Furthermore, the calculation of the ductility coefficient B of the FRP-concrete interface after high temperature is... T Among them, the interface ductility coefficient B T The calculation formula is:

[0023]

[0024] Furthermore, the calculation formula for the bond-slip constitutive model of the FRP-concrete interface after high temperature is as follows:

[0025]

[0026] Where, τ f,T σ represents the shear stress at the FRP-concrete interface after high temperature, in MPa; s represents the relative slip at the FRP-concrete interface after high temperature, in mm.

[0027] According to another aspect of the present invention, a method for calculating the load-displacement curve of an FRP-concrete interface is provided, the method comprising:

[0028] The bond-slip constitutive model of the FRP-concrete interface was calculated using the above-mentioned method.

[0029] Obtain the elastic modulus E of concrete at room temperature c,0 And calculate the elastic modulus E of the concrete after high temperature. c,T ;

[0030] Based on the elastic modulus E of the concrete after high temperature c,T Based on the bond-slip constitutive model of the FRP-concrete interface after high temperature, the load-slip curve of the FRP-concrete interface after high temperature is calculated.

[0031] Furthermore, the elastic modulus E of concrete at room temperature c,0 The elastic modulus E of concrete after high temperature can be measured by static compressive elasticity test or calculated by concrete compressive strength test value. c,T Among them, the elastic modulus E of concrete after high temperature c,T The calculation formula is:

[0032]

[0033] Where T is the maximum temperature experienced by the concrete.

[0034] Furthermore, the calculation formula for the load-slip curve of the FRP-concrete interface after high temperature is as follows: when the bond length is sufficiently long.

[0035]

[0036] Where P is the tensile force at the loading end, and Δ is the displacement at the loading end.

[0037] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0038] The method for calculating the bond-slip constitutive model and load-displacement curve of the FRP-concrete interface provided by this invention fully considers the effects of high temperature on the concrete material itself, as well as on the fracture energy and ductility coefficient of the FRP-concrete interface. The calculation results can be obtained with only the basic geometric parameters and the material parameters at room temperature. The calculation process is simple and has high reliability. The accuracy of the method is verified by the load-displacement curve test data of the single shear test of FRP-strengthened concrete after high temperature in the literature. Attached Figure Description

[0039] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0040] Figure 1 This is a constitutive model of the bond-slip interface between FRP and high-temperature concrete in an embodiment of the present invention;

[0041] Figure 2 This is a comparison chart of the predicted and measured values ​​of the FRP-high temperature concrete interface load-displacement curve in an embodiment of the present invention. Detailed Implementation

[0042] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0043] This invention provides a constitutive calculation method for bond-slip at the FRP-concrete interface. This method relates to the FRP-concrete interface after high-temperature treatment, and includes:

[0044] Step 1: Obtain the basic parameters of the FRP-concrete interface after high temperature;

[0045] Obtain the basic parameters of the FRP-concrete interface after high temperature, including the parameters of the concrete base and the parameters of the external FRP.

[0046] The parameters of the concrete base include: the tensile strength f of the concrete at room temperature. t , width of concrete base b c and the thickness t of the concrete base c The tensile strength f of concrete at room temperature t It can be measured by tensile testing or calculated from the concrete compressive strength test value.

[0047] The parameters for externally bonded FRP include: the elastic modulus E of the FRP. f The width b of the FRP f And the thickness t of FRP f .

[0048] Step 2: Obtain the fracture energy G at the FRP-concrete interface at room temperature. f,0 And the ductility coefficient B0;

[0049] Obtain the FRP-concrete interface parameters at room temperature, i.e., the fracture energy G. f,0 And the ductility coefficient B0, where the fracture energy G f,0 The calculation formula is:

[0050]

[0051] in,

[0052] B0 adopts the recommended value for FRP fabric overlay using the ordinary wet bonding method, given by Dai Jianguo et al. in "Development of the Nonlinear BondStress–Slip Model of Fiber Reinforced Plastics Sheet–Concrete Interfaces with a Simple Method", which has been widely adopted by the academic community.

[0053] Step 3, based on the basic parameters and fracture energy G f,0 Calculate the interfacial fracture energy G of FRP-concrete after high temperature. f,T ;

[0054] Calculate the interfacial fracture energy G of FRP-concrete after high temperature. f,T Among them, the interfacial fracture energy G f,T The calculation formula is:

[0055]

[0056] Where T is the maximum temperature experienced by the concrete.

[0057] Step 4: Calculate the ductility coefficient B at the FRP-high-temperature concrete interface based on the ductility coefficient B0. T ;

[0058] Calculate the interfacial ductility coefficient B of FRP-concrete after high temperature. T Among them, the interface ductility coefficient B T The calculation formula is:

[0059]

[0060] Step 5, based on the interfacial fracture energy G of FRP-concrete after high temperature. f,T And ductility coefficient B T Calculate the bond-slip constitutive model of the FRP-concrete interface after high temperature.

[0061] Calculate the bond-slip constitutive model of the FRP-concrete interface after high temperature. The formula for calculating the bond-slip constitutive model of the FRP-concrete interface after high temperature is as follows:

[0062]

[0063] Where, τ f,T σ represents the shear stress at the FRP-concrete interface after high temperature, in MPa; s represents the relative slip at the FRP-concrete interface after high temperature, in mm.

[0064] Another embodiment of the present invention provides a method for calculating the load-displacement curve of the FRP-concrete interface, the method comprising:

[0065] S1. Calculate the bond-slip constitutive model of FRP-concrete interface using the above-mentioned FRP-concrete interface bond-slip constitutive model calculation method;

[0066] S2. Obtain the elastic modulus E of concrete at room temperature. c,0 And calculate the elastic modulus E of the concrete after high temperature. c,T ;

[0067] Elastic modulus E of concrete at room temperature c,0 It can be obtained through static compressive modulus of elasticity test or calculated from concrete compressive strength test value.

[0068] Calculate the elastic modulus E of concrete after high temperature. c,T Among them, the elastic modulus E of concrete after high temperature c,T The calculation formula is:

[0069]

[0070] Where T is the maximum temperature experienced by the concrete.

[0071] S3. Based on the elastic modulus E of concrete after high temperature. c,T Based on the bond-slip constitutive model of the FRP-concrete interface after high temperature, the load-displacement curve of the FRP-concrete interface after high temperature is calculated.

[0072] In the interfacial mechanical analysis of FRP-concrete, the interfacial bond-slip constitutive model obtained in step S1 is substituted into the governing equations, and a boundary condition with one end free is introduced to solve for the interfacial mechanical behavior of FRP-concrete, ultimately obtaining the interfacial load-displacement curve. When the bond length is sufficiently long, the calculation formula for the FRP-concrete interface load-displacement curve after high temperature is as follows:

[0073]

[0074] Where P is the tensile force at the loading end, Δ is the displacement at the loading end, and A T and α T The method for determining the value is as follows:

[0075]

[0076]

[0077] The basic parameter in the above formula is b. c t c E f b fThe results are obtained in step S1 during the calculation of the bond-slip constitutive model of the FRP-concrete interface after high temperature.

[0078] The method for calculating the bond-slip constitutive model and load-displacement curve of the FRP-concrete interface after high temperature provided in this invention fully considers the effects of high temperature on the concrete material itself, as well as on the fracture energy and ductility coefficient of the FRP-concrete interface, by using geometric parameters and mechanical property parameters at room temperature. It can calculate the bond-slip constitutive model of the FRP-concrete interface after high temperature and further calculate the load-displacement curve. It has high reliability and a simple calculation process, which helps to promote the application of external FRP reinforcement method in high-temperature damaged concrete structures.

[0079] Using the literature "Inquiry into bond behavior of CFRP sheets to concrete exposed to elevated temperatures – Experimental & analytical evaluation" as a comparison, and employing the same EBR48 series specimens from the single shear test of FRP-strengthened high-temperature concrete as described in that literature, the constitutive calculation method for the bond-slip interface between FRP and high-temperature concrete includes the following steps:

[0080] Step 1: Determine the basic parameters of the FRP-concrete interface after high temperature, including:

[0081] (1) Parameters of the concrete base:

[0082] ① Elastic modulus E of concrete at room temperature c,0 =35364MPa, obtained from the concrete cylinder compressive strength test value f' c =55.9MPa and the formula recommended by the American Concrete Institute (ACI) 318-19 standard. Calculation yielded;

[0083] ② Tensile strength f of concrete at room temperature t = 3.96 MPa, passing the compressive strength test value f' of concrete cylinder c =55.9MPa and the formula f recommended by the International Federation of Concrete Soil and Water Concrete (IFSC) Model Code 2010 standard. t =0.3(f') c -8) 2 / 3 Calculation yielded;

[0084] ③ Width b of concrete base c =150mm;

[0085] ④ Concrete base thickness t c =150mm;

[0086] (2) Parameters of external FRP:

[0087] ① The elastic modulus E of FRP f =238000MPa;

[0088] ② The width b of the FRP f =48mm;

[0089] ③ The thickness t of FRP f =0.131mm;

[0090] Step 2: Determine the FRP-concrete interface parameters at room temperature, i.e., the fracture energy G. f,0 And the ductility coefficient B0;

[0091]

[0092]

[0093] B0 = 10.4

[0094] B0 is the recommended value for applying FRP fabric using the ordinary wet bonding method.

[0095] Step 3: Calculate the elastic modulus E of the concrete after high temperature. c,T According to E c,0 =35364MPa and E was calculated c,300 E c,400 and E c,500 The corresponding values ​​are 18177 MPa, 12093 MPa, and 8150 MPa.

[0096] Step 4: Calculate the interfacial fracture energy G of FRP-concrete after high temperature. f，T According to G f，0 =0.753 N / mm and G was calculated f,300 G f,400 and G f,500 The values ​​are 1.135 N / mm, 1.091 N / mm, and 0.924 N / mm, respectively.

[0097] Step 5: Calculate the ductility coefficient B of the FRP-concrete interface after high temperature. T According to B0 = 10.4 and Calculation yields B 300 B 400 and B 500 The values ​​are 5.91, 5.41, and 5.37, respectively.

[0098] Step 6: Calculate the bond-slip constitutive model of the FRP-concrete interface after high temperature, and apply the above concrete interface fracture energy G. f,T and interface ductility coefficient B T Substitution get:

[0099]

[0100]

[0101]

[0102]

[0103] Based on the calculation results, the constitutive model of bond-slip at the FRP-concrete interface after high temperature is obtained as follows: Figure 1 As shown.

[0104] The method for calculating the load-displacement curve of the FRP-concrete interface after high temperature includes: calculating the bond-slip constitutive model of the FRP-concrete interface after high temperature using the above method; and calculating the load-slip curve of the FRP-concrete interface after high temperature based on the bond-slip constitutive model of the FRP-concrete interface after high temperature.

[0105] When the bond length is long enough, the formula for calculating the load-displacement curve of the FRP-concrete interface after high temperature is:

[0106]

[0107]

[0108]

[0109] Based on the existing data and the three formulas above, we can calculate the following in sequence:

[0110] ①α0, α 300 α 400 α 500 The values ​​are 0.0019, 0.0037, 0.0055, and 0.0082, respectively.

[0111] ②A0, A 300 A 400 A 500 The values ​​are 0.0070, 0.0085, 0.0084, and 0.0077, respectively.

[0112] ③Calculate α as described above T and A T Substitution The predicted values ​​of the load-displacement curve are as follows:

[0113] Ignoring the effect of high temperature: P = 10390(1-e -10.4Δ );

[0114] After 300℃: P=12950(1-e -5.91Δ );

[0115] After 400℃: P=12490(1-e -5.41Δ );

[0116] After 500℃: P=11480(1-e -5.31Δ );

[0117] The comparison figure of predicted and measured values ​​of FRP-concrete interface load-displacement curve after high temperature is shown in the figure below. Figure 2 As shown in the figure, the line graph represents the predicted value, and the scatter plot represents the measured values ​​of the load-displacement curve test data of FRP-strengthened high-temperature concrete from the single shear test in the literature "Inquiry into bond behavior of CFRP sheets to concrete exposed to elevated temperatures – Experimental & analytical evaluation". The cross, rhombus, and triangle shapes are from specimens EBR48-300-2, EBR48-400-1, and EBR48-500-2, respectively, representing the interfacial mechanical behavior of FRP-concrete after high temperatures of 300℃, 400℃, and 500℃. The figure shows that the measured values ​​of the load-displacement curve are close to the predicted values, indicating that this method can accurately characterize the influence of high temperature on the interfacial mechanical behavior of FRP-concrete through the interfacial bond-slip constitutive model and key parameters after high temperatures, proving the accuracy of the method.

[0118] The method for calculating the bond-slip constitutive model and load-displacement curve of the FRP-concrete interface provided in the above embodiments fully considers the effects of high temperature on the concrete material itself, as well as on the fracture energy and ductility coefficient of the FRP-concrete interface. The calculation results can be obtained with only the basic geometric parameters and the material parameters at room temperature. The calculation process is simple and has high reliability. The accuracy of the method has been verified by experiments in the literature.

[0119] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention. The above preferred features can be used in any combination without conflict.

Claims

1. A method for calculating a FRP-concrete interfacial bond slip constitutive equation, characterized by, include: Obtain the basic parameters of the FRP-concrete interface after high temperature, wherein the basic parameters include the parameters of the concrete base and the parameters of the external FRP; the parameters of the concrete base include: the tensile strength f of the concrete at room temperature. t , width of concrete base b c and the thickness t of the concrete base c The parameters of the externally bonded FRP include: the elastic modulus E of the FRP. f The width b of the FRP f And the thickness t of FRP f The tensile strength of concrete at room temperature (f) t Measured by tensile testing or calculated by concrete compressive strength test values; Obtain the fracture energy G at the FRP-concrete interface at room temperature f,0 And the ductility coefficient B0, where the fracture energy G f,0 The calculation formula is: wherein Based on the aforementioned basic parameters and fracture energy G f,0 Calculate the interfacial fracture energy G of FRP-concrete after high temperature. f,T Among them, the interfacial fracture energy G f,T The calculation formula is: Where T is the maximum temperature experienced by the concrete; According to the ductility coefficient B0, the FRP-high temperature concrete interface ductility coefficient B is calculated T Wherein, the interface ductility coefficient B T The calculation formula is: According to the interfacial fracture energy G of FRP-concrete after high temperature f,T And ductility coefficient B T Calculate the bond-slip constitutive model of the FRP-concrete interface after high temperature.

2. The FRP-concrete interfacial bond-slip constitutive calculation method according to claim 1, characterized by, The calculation formula for the bond-slip constitutive model of the FRP-concrete interface after high temperature is as follows: Where, τ f,T σ represents the shear stress at the FRP-concrete interface after high temperature, in MPa; s represents the relative slip at the FRP-concrete interface after high temperature, in mm.

3. A method for calculating an FRP-concrete interfacial load-displacement curve, characterized by, include: Calculate the bond-slip constitutive model of the FRP-concrete interface using the method described in claim 1 or 2; Obtain the elastic modulus E of concrete at room temperature c,0 And calculate the elastic modulus E of the concrete after high temperature. c,T ; Based on the elastic modulus E of the concrete after high temperature c,T Based on the bond-slip constitutive model of the FRP-concrete interface after high temperature, the load-slip curve of the FRP-concrete interface after high temperature is calculated.

4. The FRP-concrete interfacial load-displacement curve calculation method according to claim 3, characterized by, The calculation of the elastic modulus E of concrete after high temperature c,T Among them, the elastic modulus E of concrete after high temperature c,T The calculation formula is: Where T is the maximum temperature experienced by the concrete.

5. The FRP-concrete interfacial load-displacement curve calculation method according to claim 3, characterized by, The calculation formula for the load-slip curve of the FRP-concrete interface after high temperature is as follows: When the bond length is sufficiently long, the calculation formula for the load-slip curve of the FRP-concrete interface after high temperature is: wherein P is the load end tension, and Δ is the load end displacement,

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