Concrete bond-slip constitutive model and calculation method of anchorage length

Abstract

The application discloses a concrete bonding slip constitutive model and a calculation method of anchorage length, and comprises the following steps: measuring the bonding stress between basalt rib and super high performance concrete through a pull-out test; based on an existing theoretical model, and by comprehensively analyzing test data, a bonding slip constitutive model suitable for basalt rib hybrid steel fiber super high performance concrete is established; based on bonding slip mechanism analysis, a correction coefficient is introduced to correct the calculation formula of the bonding slip constitutive model of basalt rib hybrid steel fiber super high performance concrete; by substituting test results, fitting coefficients are solved, and the calculation formula of the bonding slip constitutive model of basalt rib hybrid steel fiber super high performance concrete is obtained; and according to relevant basic anchorage length design specifications, a suggested formula of the basic anchorage length of basalt rib hybrid steel fiber super high performance concrete is provided.

Description

Technical Field

[0001] This invention relates to the field of basalt-reinforced steel fiber reinforced ultra-high performance concrete technology, and particularly to a concrete bond-slip constitutive model and a method for calculating anchorage length. Background Technology

[0002] With the continuous expansion of the engineering field, people have increasingly higher requirements for the comprehensive performance of concrete structures. Ordinary reinforced concrete structures, due to their poor durability and low strength, can no longer fully meet the needs of engineering in harsh environments. Basalt Fiber Reinforced Plastic (BFRP) reinforcement, as a new type of composite material with excellent corrosion resistance and tensile strength, can effectively solve the durability and strength problems caused by steel corrosion. However, basalt reinforcement has a low elastic modulus and poor plasticity, which can easily cause brittle failure of concrete structures. Ultra-High Performance Concrete (UHPC) has excellent physical and mechanical properties and can make up for the defects of basalt reinforcement. However, the high cost of UHPC restricts its application in the engineering field.

[0003] This invention attempts to partially replace industrial steel fiber (ISF) in UHPC raw materials with inexpensive and environmentally friendly recycled tire steel fiber (RTSF). Based on this, a basalt-reinforced hybrid steel fiber ultra-high performance concrete structure system is constructed, combining the excellent properties of all three. This novel concrete structure not only effectively improves the mechanical properties of materials but also saves construction costs, aligning with the current development concepts of resource recycling and environmental protection.

[0004] In novel structural systems like basalt-reinforced ultra-high performance concrete (UHVDC) with steel fibers, the two materials, basalt reinforcement and UHVDC with completely different properties, can work together primarily through the bond stress between them. To ensure good performance of this new structural system, prevent bond failure, fully utilize the high strength of the basalt reinforcement, and guarantee a good bond between the two, a thorough understanding of their bond properties is necessary. Summary of the Invention

[0005] The purpose of this invention is to provide a concrete bond-slip constitutive model and a method for calculating anchorage length, so as to solve one or more technical problems existing in the prior art, and at least provide a beneficial option or create conditions.

[0006] The technical solution adopted to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a concrete bond-slip constitutive model and a method for calculating anchorage length, including:

[0008] S1 obtained the bond stress and bond slip curves of basalt-reinforced steel fiber ultra-high performance concrete by conducting bond performance tests on basalt-reinforced steel fiber ultra-high performance concrete specimens.

[0009] S2 compares the bond-slip curve of basalt-reinforced steel fiber-reinforced ultra-high performance concrete with the bond-slip curve of existing concrete bond-slip theoretical models;

[0010] S3, based on the bond-slip mechanism analysis, introduces a correction coefficient to modify the calculation formula of the bond-slip constitutive model of basalt-reinforced steel fiber ultra-high performance concrete;

[0011] Based on the test results of the bonding performance of basalt-reinforced steel fiber ultra-high performance concrete components, S4 solves the fitting coefficient and obtains the calculation formula of the bond-slip constitutive model of basalt-reinforced steel fiber ultra-high performance concrete.

[0012] Based on relevant basic anchorage length design specifications, S5 proposes a suggested formula for the basic anchorage length of basalt-reinforced steel fiber reinforced ultra-high performance concrete.

[0013] As a further improvement to the above technical solution, in step S2, the existing concrete bond-slip theoretical models include: the CMR model and the BFRP reinforcement alkali-induced concrete bond-slip constitutive model; wherein,

[0014] The CMR model is an accurate model for the rising phase of the bond-slip curve, and its calculation formula is as follows:

[0015]

[0016] In the formula: —Ultimate bond strength;

[0017] , — Corrected parameters obtained by fitting experimental data.

[0018] The BFRP-reinforced alkali-induced concrete bond-slip constitutive model includes a micro-slip stage, a slip stage, a descent stage, and a residual stage, and its calculation formula is as follows:

[0019] Microslip stage:

[0020] Slip phase:

[0021] Descent phase:

[0022] Residual stage:

[0023] In the formula: , , —Initial bond strength, ultimate bond strength, residual bond strength;

[0024] , , —— , , The corresponding slip amount;

[0025] , , , , , , —Parameters determined based on experimental results;

[0026] e-exponential function.

[0027] As a further improvement to the above technical solution, the calculation formula for the constitutive model of basalt-reinforced steel fiber ultra-high performance concrete bond-slip full-stage in step S3 is as follows:

[0028] Ascent Phase:

[0029] Descent phase:

[0030] Residual stage:

[0031] In the formula: , —Ultimate bond strength, residual bond strength;

[0032] , —— , The corresponding slip amount;

[0033] , , , , , , , —Parameters determined based on experimental results;

[0034] e-exponential function.

[0035] As a further improvement to the above technical solution, step S4 specifically includes the following steps:

[0036] Based on the test results of the bond performance of basalt-reinforced steel fiber reinforced ultra-high performance concrete members, S41 calculates the parameters corresponding to each concrete member. , , , , , , , The value;

[0037] S42 takes the average value of the corresponding parameters of multiple concrete components and substitutes the obtained average value into the correction formula in step S3 to obtain the calculation formula of the bond-slip constitutive model of basalt-reinforced steel fiber ultra-high performance concrete:

[0038] Ascent Phase:

[0039] Descent phase:

[0040] Residual stage:

[0041]

[0042] In the formula: , —Ultimate bond strength, residual bond strength;

[0043] , —— , The corresponding slip amount;

[0044] e-exponential function.

[0045] As a further improvement to the above technical solution, in step S5, the existing basic anchorage length design specification is ACI440.1R-03, which recommends using the following formula to predict the bond strength and anchorage length of FRP reinforced concrete structures:

[0046]

[0047]

[0048] In the formula: —Ultimate bond strength (MPa); ——FRP bar diameter mm;

[0049] —Concrete compressive strength (MPa); —Basic anchorage length (mm);

[0050] — Tensile strength of FRP reinforcement (MPa).

[0051] , —Parameters determined based on experimental results.

[0052] As a further improvement to the above technical solution, in step S5, based on relevant basic anchorage length design specifications, a suggested formula for the basic anchorage length of basalt-reinforced steel fiber reinforced ultra-high performance concrete is proposed:

[0053]

[0054] In the formula: —Basic anchorage length (mm); ——BFRP bar diameter mm;

[0055] —Ultimate tensile strength of BFRP reinforcement (MPa);

[0056] —UHPC cube compressive strength (MPa).

[0057] The beneficial effects of this invention are:

[0058] Compared with existing technologies, the present invention provides a concrete bond-slip constitutive model and a method for calculating anchorage length, which can significantly improve the accuracy of bond-slip calculation results for basalt-reinforced steel fiber reinforced ultra-high performance concrete. Specifically, it has the following beneficial effects:

[0059] 1. The calculation formulas of the existing theoretical model are modified. Based on the analysis of the bond-slip mechanism, the calculation formulas for all stages are modified, which increases the applicability of the model and improves the accuracy of the bond-slip constitutive model of basalt-reinforced steel fiber ultra-high performance concrete.

[0060] 2. Addressing the problems existing in current ordinary reinforced concrete structures, this paper proposes using lightweight, high-strength, corrosion-resistant, and fatigue-resistant basalt reinforcement to replace steel bars; ultra-high performance concrete with superior durability and tensile strength to replace ordinary concrete; and steel fibers recycled from waste tires to replace ordinary industrial steel fibers. By combining the excellent properties of these three materials and leveraging their strengths to compensate for their weaknesses, a novel composite structure—basalt-reinforced hybrid steel fiber ultra-high performance concrete—is established. This concrete structure not only improves the mechanical properties of the materials but also saves construction costs, aligning with current concepts of resource recycling and environmental protection, and providing guidance for engineering practice. Attached Figure Description

[0061] The present invention will be further described below with reference to the accompanying drawings and embodiments;

[0062] Figure 1 A flowchart is provided for a concrete bond-slip constitutive model and a method for calculating anchorage length;

[0063] Figure 2 Schematic diagram of the pull-out specimen;

[0064] Figure 3 Bond slip curves of pull-out specimens at various bond lengths;

[0065] Figure 4 Bond slip curves of pull-out specimens at various bond lengths;

[0066] Figure 5 CMR model;

[0067] Figure 6 BFRP reinforcement alkali-induced concrete bond-slip constitutive model;

[0068] Figure 7 BFRP-UHPC bond-slip constitutive model;

[0069] Figure 8 Experimental curves and corresponding fitted curves;

[0070] Figure 9 Experimental curves and corresponding fitted curves. Detailed Implementation

[0071] This section will describe in detail specific embodiments of the present invention. Preferred embodiments of the present invention are shown in the accompanying drawings. The purpose of the drawings is to supplement the textual description with graphics, so that people can intuitively and vividly understand each technical feature and overall technical solution of the present invention, but they should not be construed as limiting the scope of protection of the present invention.

[0072] In the description of this invention, if there are words such as "several", they mean one or more, "multiple" means two or more, "greater than", "less than", "exceeding" etc. are understood to exclude the number itself, and "above", "below", "within" etc. are understood to include the number itself.

[0073] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0074] This invention provides a concrete bond-slip constitutive model and a method for calculating anchorage length. To clarify the purpose and concept of this invention, the following will be illustrated in conjunction with the embodiments. Figures 1 to 9 The method provided by this invention will be further described and illustrated below. It should be understood that the following embodiments are for illustrative purposes only and do not limit the scope of protection of this invention.

[0075] This embodiment designed 30 sets of pull-out tests on basalt-reinforced steel fiber reinforced ultra-high performance concrete, with 3 specimens in each set. Based on these tests, calculations were performed using the bond-slip constitutive model calculation formula given by existing theories to solve for the values ​​of various fitting parameters, resulting in a modified bond-slip constitutive model calculation formula for basalt-reinforced steel fiber reinforced ultra-high performance concrete. Based on relevant basic anchorage length design specifications, a recommended formula for the basic anchorage length of basalt-reinforced steel fiber reinforced ultra-high performance concrete structures was proposed.

[0076] The following is a detailed description of the experiments used in the examples:

[0077] (1) Test materials

[0078] Quartz sand: Natural quartz sand is selected, with a particle size range of 40-80 mesh.

[0079] Cement: PO42.5 ordinary Portland cement meeting the standard requirements is selected. Its main chemical composition is shown in Table 1.

[0080] Table 1 Chemical composition of PO42.5 ordinary Portland cement

[0081]

[0082] Mineral powder: S95 grade mineral powder is used, with a specific surface area greater than 400 m². 2 / g, chemical composition is shown in Table 2.

[0083] Table 2 Chemical composition of mineral powder

[0084]

[0085] Silica fume: The silica fume used is produced by Huangshi Huaxin Cement Plant. The main chemical component of silica fume is SiO2, with a content exceeding 90%. Silica fume can play a good filling role in ultra-high performance concrete and has strong pozzolanic activity. It can undergo a secondary hydration reaction with Ca(OH)2 to generate CSH gel, which is beneficial to enhancing the density and strength of concrete. The specific chemical composition of silica fume is shown in Table 3.

[0086] Table 3 Chemical composition of silica fume

[0087]

[0088] Water: Ordinary tap water from Wuhan is used.

[0089] Water-reducing agent: Select a polycarboxylate high-efficiency water-reducing agent with a water reduction rate of greater than 35%.

[0090] Industrial steel fiber (ISF): High-strength micro-copper-plated steel fiber with uniform diameter and similar length is used. Its physical and mechanical properties are shown in Table 4.

[0091] Table 4 Physical and mechanical properties of industrial steel fibers

[0092]

[0093] Waste tire steel fiber (RTSF): Waste tire steel fiber produced by Jintai Environmental Protection Company in Xiangyang, Hubei Province. The physical and mechanical properties of RTSF are shown in Table 2-5.

[0094] Table 5 Physical and mechanical properties of RTSF

[0095]

[0096] Basalt reinforcement: The basalt reinforcement used in this invention is produced by Jiangsu Lvcaigu Company and comes in three diameters: 12mm, 14mm and 16mm, and two surface types: deep thread type and sand-adhesive type.

[0097] Based on the results of the previous adaptation test by the research group, the matrix mix ratio of UHPC was determined. Since this paper considers the influence of the total steel fiber content and the ratio of waste tire steel fiber to industrial steel fiber on the bonding performance of the component, the following seven UHPC mix ratios were set, as shown in Table 6.

[0098] Table 6 UHPC mix proportions (kg / m³) 3 )

[0099]

[0100] Note: "IU" represents industrial steel fiber ultra-high performance concrete, "HU" represents hybrid steel fiber ultra-high performance concrete, "RU" represents waste steel fiber ultra-high performance concrete, and "U" represents ultra-high performance concrete without added steel fibers; "2-1" indicates that the content of waste steel fibers is 2% and the content of industrial steel fibers is 1%.

[0101] (2) Specimen design

[0102] Four specifications of BFRP bars were selected for this experiment: deep-threaded BFRP bars with diameters of 12mm, 14mm, and 16mm, and sand-bonded BFRP bars with a diameter of 14mm. Seven mix proportions of ultra-high performance concrete were selected, and detailed mix proportions can be found in Table 6.

[0103] This experiment used the RTSF-ISF incorporation ratio, RTSF dosage, BFRP bar diameter, BFRP bar surface morphology, BFRP bar bond length, concrete cover thickness, and concrete strength (age) as experimental variables. Thirty sets of pull-out tests were set up, with three 150mm×150mm×150mm cubic specimens in each set, to study the influence of these seven factors on the bonding performance of the component. The experimental design is shown in Table 7.

[0104] Table 7 Pull-out test data

[0105]

[0106] Note: In the specimen numbers, "12, 14, 16" represent the diameter of the BFRP bar; "2-1" indicates that the volumetric content of waste steel fiber is 2% and the volumetric content of industrial steel fiber is 1%; "A" represents deep thread type BFRP bar, and "B" represents sand-bonded type BFRP bar; "4d, 6d, 8d" represent the bonding length, where d is the diameter of the corresponding BFRP bar; "7T" and "14T" represent the curing time of 7 days and 14 days, respectively; and "d, 2d, 3d, 4d" in the last four groups represent the thickness of the concrete protective layer.

[0107] One end of the BFRP reinforcement needs to be anchored with a steel sleeve to prevent shear damage from the universal testing machine fixtures, which would affect the test. The anchorage length is 300mm. A suitably sized PVC pipe is used to sleeve the BFRP reinforcement; the bond length between the BFRP reinforcement and the UHPC is controlled by adjusting the length of the PVC pipe. Schematic diagrams of the center pull-out specimen and the eccentric pull-out specimen are shown below. Figure 2 .

[0108] This experiment used displacement loading at a loading rate of 0.6 mm / min. The experiment could be terminated if any of the following four conditions occurred during the experiment:

[0109] (1) The specimen underwent splitting failure;

[0110] (2) BFRP reinforcement fracture;

[0111] (3) BFRP reinforcement pulled out;

[0112] (4) The load value does not change much, and the load-displacement curve is a horizontal line.

[0113] (3) Test results

[0114] The pull-out test results of basalt reinforcement and hybrid steel fiber ultra-high performance concrete are shown in Table 8. Due to the large number of specimens tested, the result of the specimen in each group that was closest to the average ultimate bond strength was selected, and the bond-slip curve of that specimen was used for analysis. The bond-slip curves of pull-out specimens with different bond lengths in this test are shown in Table 8. Figure 3 and Figure 4 As shown.

[0115] Table 8 Pull-out test data

[0116]

[0117] (4) Bonded-slip constitutive model

[0118] The constitutive model was established based on a large amount of experimental data. The experimental results were analyzed, the experimental curves were divided into segments, and finally the patterns were summarized and expressed using mathematical formulas. At present, the bond-slip constitutive models with high consistency in the bond-slip curves of the pull-out specimens in this experiment include: the CMR model and the bond-slip constitutive model of BFRP-reinforced alkali-activated concrete.

[0119] (1) CMR model

[0120] Since practical engineering mainly considers the rising phase of the bond-slip curve, this rising segment is more important than other phases. Therefore, Cosenza et al. proposed an accurate model specifically for the rising phase of the bond-slip curve, called the CMR model, such as... Figure 5 As shown. Its expression is:

[0121] (1)

[0122] In the formula: —Ultimate bond strength;

[0123] , — Corrected parameters obtained by fitting experimental data.

[0124] (2) Constitutive model of bond-slip concrete induced by BFRP reinforcement and alkali

[0125] Experiments revealed that the bond-slip curve of BFRP-reinforced concrete structures is actually nonlinear in the descending phase. Therefore, the descending phase of the model proposed by Hao Qingduo was modified, and a bond-slip constitutive model more suitable for BFRP-reinforced concrete structures was proposed. (See...) Figure 6 Its expression is:

[0126] Microslip stage: (2a)

[0127] Slip phase: (2b)

[0128] Descent phase: (2c)

[0129] Residual stage: (2d)

[0130] In the formula: , , —Initial bond strength, ultimate bond strength, residual bond strength;

[0131] , , —— , , The corresponding slip amount;

[0132] , , , , , , —Parameters determined based on experimental results.

[0133] Since pull-out specimens, exhibiting the most typical bond failure mode, effectively reflect the entire bond-slip process between BFRP reinforcement and UHPC, this experiment compared the bond-slip curves of such specimens with the aforementioned model. Overall, the model showed a high degree of agreement with the BFRP reinforcement-alkali-induced concrete bond-slip constitutive model. After fitting, the model showed the highest fit with the CMR model; however, since the curve fitted by the CMR model was not closed, this paper made certain modifications to the CMR model. Based on the above theoretical models and the experimental data from this experiment, a bond-slip constitutive model that best fits the BFRP reinforcement-UHPC structure is proposed. Figure 7 .

[0134] The bond-slip constitutive model of BFRP-UHPC reinforcement is divided into three stages: (1) the rising stage, corresponding to segment OA, in which the slip is relatively small, but the bond stress rises rapidly; (2) the falling stage, corresponding to segment AB, in which the curve begins to show a non-linear decline; and (3) the residual stage, corresponding to segment BC, in which the curve exhibits a sinusoidal fluctuation. The expression of the bond-slip constitutive model of BFRP-UHPC reinforcement is:

[0135] Ascent Phase: (3a)

[0136] Descent phase: (3b)

[0137] Residual stage: (3c)

[0138] In the formula: , —Ultimate bond strength, residual bond strength;

[0139] , —— , The corresponding slip amount;

[0140] , , , , , , , —Parameters determined based on experimental results;

[0141] e-exponential function.

[0142] In this experiment, a total of 20 groups of specimens experienced pull-out failure. The RTSF-ISF incorporation ratio had little effect on the bond-slip curve of the specimens, while the sand-bonded BFRP reinforcement significantly weakened the bond performance of the BFRP reinforcement UHPC structure. In practical applications, this type of BFRP reinforcement should be avoided as much as possible. Therefore, the bond-slip curves of the following 8 groups of specimens were selected to verify the established model. The test data of each specimen are shown in Table 9.

[0143] Table 9 Test data for each specimen

[0144]

[0145] The values ​​at points A and B of each group of specimens were substituted into the formula to obtain the values ​​of each parameter, as shown in Table 10.

[0146] Table 10 Fitting parameter values

[0147]

[0148] Take the average value of the fitting parameters for each specimen and substitute it into the above formula.

[0149] Therefore, the calculation formula for the bond-slip constitutive model of basalt-reinforced steel fiber ultra-high performance concrete is:

[0150] Slip phase: (4a)

[0151] Descent phase: (4b)

[0152] Residual stage:

[0153] (4c)

[0154] In the formula: , —Ultimate bond strength, residual bond strength;

[0155] , —— , The corresponding slip amount;

[0156] e-exponential function.

[0157] The values ​​of the correction coefficients for each curve were determined based on the bond performance tests of basalt-reinforced steel fiber reinforced ultra-high performance concrete specimens. The curve correction coefficients for each concrete specimen were calculated using MATLAB software. , , , , , , , The value.

[0158] Specifically, it is to Figure 7 The bond-slip curves obtained from the bond performance tests of basalt-reinforced steel fiber reinforced ultra-high performance concrete specimens are stored in MATLAB software. A universal testing machine can measure the bond stress τ and the corresponding slip s at each point on the curve. Simultaneously, the constitutive model formula for the entire bond-slip process of basalt-reinforced steel fiber reinforced ultra-high performance concrete proposed in this invention (i.e., the modified formula in step S42) and the ultimate bond stress corresponding to the termination point of the rising segment in Table 9 are also included. and the ultimate bond stress Corresponding slip Values, and the bond stress at the descent segment cutoff point in Table 9. and the bond stress Corresponding slip The values ​​are stored in MATLAB. The modified formula in step S42 is fitted in MATLAB software, and the curve correction coefficient corresponding to each concrete specimen is obtained using MATLAB software. , , , , , , , The value; take the curve correction coefficient corresponding to multiple concrete specimens. Take the average value average value average value average value average value average value average value The average value is shown in Table 10. The average value is 0.73. The average value is 0.57. The average value is 0.056. The average value is 2.26. The average value is 12.04. The average value is 0.21. The average value is 0.75. The average value is 7.89. Substituting the average value into the correction formula in step S42, we can obtain the calculation formula for the bond-slip constitutive model of basalt-reinforced steel fiber ultra-high performance concrete.

[0159] The bond-slip theoretical curves and experimental curves of basalt-reinforced steel fiber reinforced ultra-high performance concrete were compared. Figure 8 and Figure 9 It can be seen that the deviation between the theoretical curve and the experimental curve in the rising segment of each specimen is within 2%, and the deviation between the theoretical curve and the experimental curve in the falling segment and the residual segment is within 0.5%. Moreover, the ultimate bond strength and residual bond strength of the theoretical curve are in complete agreement with the experimental curve, and the error values ​​are all within acceptable ranges. The overall agreement is high, indicating that the proposed bond-slip constitutive model can well describe the entire bond-slip process of basalt-reinforced steel fiber ultra-high performance concrete.

[0160] (5) Anchorage length design

[0161] The minimum bond anchorage length corresponding to the ultimate tensile strength of the reinforcing bar is called the basic anchorage length. Determining the basic anchorage length allows the strength of the reinforcing bar to be fully utilized in the concrete, preventing the structure from losing its performance due to bond failure. Therefore, determining the basic anchorage length of BFRP bars in UHPC is of great significance for the design and application of this type of structure.

[0162] Based on ACI 440.1R-03, published by the American Concrete Institute in 2003, this standard recommends using the following formula to predict the bond strength and anchorage length of FRP-reinforced concrete structures:

[0163] (5a)

[0164] (5b)

[0165] In the formula: —Ultimate bond strength (MPa); ——FRP bar diameter (mm);

[0166] — Concrete compressive strength (MPa); —Basic anchorage length (mm);

[0167] — Tensile strength of FRP reinforcement (MPa).

[0168] , —Parameters determined based on experimental results.

[0169] The above specifications provide basic anchorage length prediction formulas, but whether they can be applied to the actual situation of BFRP-reinforced UHPC structures needs to be verified by starting with the ultimate bond strength.

[0170] The formula for calculating the tensile load of reinforcing bars is:

[0171] (6)

[0172] In the formula: —Ultimate tensile strength of reinforcing steel (MPa); — Reinforcing bar diameter (mm).

[0173] Assuming the bond stress is uniformly distributed along the bond length, the formula for calculating the ultimate bond force is:

[0174] (7)

[0175] In the formula: — Reinforcing bar diameter (mm); —Basic anchorage length (mm);

[0176] — Ultimate bond stress (MPa).

[0177] make The formula for calculating the basic anchorage length is obtained as follows:

[0178] (8)

[0179] In the formula: the meaning of each parameter is the same as in formulas (6) and (7).

[0180] Equation (8) shows that the basic anchorage length is inversely proportional to the ultimate bond strength, which means that the greater the ultimate bond strength of the component, the smaller the basic anchorage length.

[0181] The standard formula (5) does not impose restrictions on certain values, and its parameters... , The design was determined through experimental results, making it suitable for various structures. Although the specification only considers the effects of concrete strength and reinforcement diameter, analysis of experimental results suggests that in practical applications of BFRP-reinforced UHPC structures, sand-bonded BFRP reinforcement should be avoided, the total volumetric steel fiber content should be maintained at around 2%-3%, and the protective layer thickness should be... The above has almost no impact on the bonding performance of the structure, so this specification can predict the basic anchorage length of BFRP-reinforced UHPC structures relatively well.

[0182] Due to the standard formula (5) The compressive strength of a concrete cylinder is converted to the compressive strength of a concrete cube. The conversion formula is:

[0183] (9)

[0184] Substituting into the standard formula (5), we get:

[0185] (10)

[0186] In the formula: —Parameters determined based on experimental results; ——BFRP bar diameter (mm).

[0187] Equation (5b) is actually derived from equations (5a) and (8). Therefore, substituting equation (10) into equation (8) yields a new basic anchorage length formula:

[0188] (11)

[0189] Substituting the relevant data from this experiment into equation (10), we can obtain... The values ​​are shown in Table 11.

[0190] Table 11 Parameters Calculation results

[0191]

[0192] From equation (11), we can see that the parameter The smaller the value, the larger the basic anchorage length. Based on structural safety considerations, [the following is likely an error and requires more context:] Taking a conservative value of 29.6, and substituting this value into equation (11), we can obtain the basic anchorage length formula for BFRP-reinforced UHPC structures:

[0193] (12)

[0194] In the formula: —Basic anchorage length (mm); ——BFRP bar diameter (mm);

[0195] —Ultimate tensile strength of BFRP reinforcement (MPa);

[0196] —UHPC cube compressive strength (MPa).

[0197] Finally, it should be noted that the contents not described in detail in this specification belong to the prior art known to those skilled in the art. The above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating a concrete bond-slip constitutive model and anchorage length, characterized by, The application relates to a method for determining the bond-slip constitutive model of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC), which comprises the following steps: S1: obtaining the bond stress and bond-slip curve of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC) through the bond performance test of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC) specimens; S2: comparing the bond-slip curve of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC) with the bond-slip curve of existing concrete bond-slip theoretical models; S3: based on the bond-slip mechanism analysis, introducing a correction coefficient to correct the calculation formula of the bond-slip constitutive model of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC), wherein the calculation formula of the bond-slip constitutive model of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC) in the step S3 is as follows: Rising phase: wherein, ; Rising phase: wherein, ; residual phase: wherein, ; In the formulae: represents the ultimate bond strength, represents the residual bond strength; representing the corresponding slip amount, representing the corresponding slip amount; , , , , , , , are parameters determined from the test results; e represents an exponential function; S4: based on the bond performance test results of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC) components, solving the fitting coefficient, and obtaining the calculation formula of the bond-slip constitutive model of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC); S5: according to the relevant basic anchorage length design specification, the application provides a basic anchorage length formula of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC).

2. The method according to claim 1, wherein The step S4 specifically comprises the following steps: S41 based on the test results of the bonding performance of basalt fiber reinforced hybrid steel fiber reinforced concrete members, the corresponding parameters of each concrete member are obtained 、 、 、 、 、 、 、 the numerical value of S42: taking the average value of the corresponding parameters of a plurality of concrete components, and substituting the obtained average value into the correction formula in the step S3 to obtain the calculation formula of the bond-slip constitutive model of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC): Rising phase: wherein, ; Rising phase: wherein, ; residual stage: wherein ; In the formulae: represents the ultimate bond strength, represents the residual bond strength; indicates the corresponding slip amount, indicates the corresponding slip amount; e represents an exponential function.

3. The method according to claim 1, wherein, In the step S5, according to the relevant basic anchorage length design specification, the application provides a basic anchorage length formula of basalt fiber reinforced polymer (BFRP) and steel fiber reinforced polymer (SRP) hybrid fiber reinforced ultra-high performance concrete (UHPC). In the formulae: represents the basic anchorage length, with the unit of mm; represents the diameter of the BFRP tendon, with the unit of mm; BFRP tendon ultimate tensile strength, in MPa; and BFRP tendon ultimate tensile strength, in MPa; and represents the compressive strength of the UHPC cube, in MPa.

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