A method for calculating the bond-slip constitutive relationship of ultra-high performance concrete and steel

Abstract

The application discloses a kind of super high performance concrete and the bond slip constitutive relation calculation method of reinforcing steel, comprising the following steps: according to structural design and concrete mix proportion, the bond length of pulling test in pulling reinforcing steel, the thickness of the protective layer of reinforcing steel and the compressive strength of concrete are determined, and pulling test is carried out;According to the pulling test result, the influence of the selection of pulling test test parameters on bond stress, reinforcing steel bond strength and peak slip is obtained, and the corresponding function relationship is established, according to the test results, the curve of bond stress change with position is obtained by calculation and drawing, and the function relationship of bond stress change with position is obtained by regression;Establish the function expression of the bond slip constitutive relation of super high performance concrete and reinforcing steel.The bond stress when reinforcing steel slips can be accurately reflected by the application, the prediction result is accurate, and the practicality is strong.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of the bond-slip constitutive relationship of ultra-high performance concrete, and particularly relates to a bond-slip constitutive relationship calculation method of ultra-high performance concrete and steel bars. BACKGROUND

[0002] Ultra-high performance concrete is a fiber reinforced cementitious composite material with high strength, high toughness, high durability and high fluidity, and has super strong bond performance with steel bars, so that the bond length of the lapped steel bars can be greatly shortened, and the ultra-high performance concrete is widely applied in bridge engineering bridge deck wet joint connection, and node connection in fabricated building structure. The steel bars only need a small straight anchorage length to meet the stress requirements of the structure, reduce the site wet operation, and improve the construction efficiency.

[0003] For a concrete structure, the joint work of steel bars and concrete is an important guarantee for the stress performance of the reinforced concrete. The bond between the steel bars and the concrete reflects the cooperative performance between the materials in the structure or the component, which can be represented by the bond-slip constitutive relationship between the two. The strength of the concrete, the bond length of the steel bars, the thickness of the protective layer of the steel bars, the stirrup ratio and other factors will all affect the bond-slip performance of the steel bars and the concrete.

[0004] At present, the following related technologies exist in the research on the bond-slip constitutive relationship:

[0005] (1) Foreign scholars Bae et al. found based on the pull-out test that the bond strength decreases in the increasing range of the steel fiber volume fraction from 0% to 1% and then to 2%; Alkaysi et al. believed that the bond strength of UHPC increases rapidly at the early age, and the bond strength can reach 75% of the final strength at the age of 7 days.

[0006] (Content cited from: Bae BI, Choi HK, Choi CS. Bond stress between conventional reinforcement and steel fibre reinforced reactive powder concrete[J]. Construction and Building Materials, 2016, 112:825-835).

[0007] (2) Domestic scholar Deng Zongcai et al. studied the influence of steel bar embedded length, steel bar cover thickness, steel bar diameter, RPC strength and steel fiber volume fraction on the bonding performance of RPC through 54 center drawing, 6 cubic eccentric drawing, 6 prismatic center drawing and 6 plate center drawing anchorage test block system, established the formula to calculate the bond length of critical steel bar, and fitted the relationship between ultimate bond stress and steel bar cover thickness, relative embedded length (content from: Deng Zongcai, Yuan Changxing. Experimental study on the bonding performance of high-strength steel and reactive powder concrete [J]. Journal of Civil Engineering, 2014, 47(3): Ultra-high performance concrete and steel bond-slip constitutive relationship calculation method 69-78).

[0008] (3) Gao Danying et al. studied the bonding performance of steel bar and steel fiber concrete of different strength based on the pull-out test of steel bar and steel fiber concrete local bonding test block with internal strain gauges, and proposed a three-segment bond-slip constitutive model (content from: Gao Danying, Chen Gang, Hadi Muhammad Najib Sadraddin, et al. Bond-slip performance and relationship model of steel bar and steel fiber concrete [J]. Journal of Building Structures, 2015, 36(07): 132-139).

[0009] (4) An Mingzhe et al. studied the influence of deformed steel bar diameter and steel bar bond length on the bonding performance of reactive powder concrete (RPC), and proposed a bond-slip constitutive model of deformed steel bar and RPC, but the constitutive model only has an ascending segment and cannot reflect the whole curve of bond-slip during steel bar pull-out (content from: An Mingzhe, Zhang Meng. Experimental study on the bonding performance of deformed steel bar and reactive powder concrete [J]. China Railway Science, 2007, 28(2): 50-54).

[0010] (5) Jia Fangfang proposed a four-segment steel bar and reactive powder concrete constitutive model through beam test and pull-out test, pointed out that the characteristic parameters in the constitutive model are related to the bond length of steel bar and the cover thickness of steel bar, but did not give specific calculation formula (content from: Jia Fangfang. Experimental study on the bonding performance of steel bar and reactive powder concrete [D]. Beijing: Beijing Jiaotong University, 2013).

[0011] (6) Mechanical anchorage is also one of the important ways to improve the bond-slip performance of steel-concrete. Liu Lixin et al. carried out the pull-out test of HRB500 hot-rolled ribbed steel bars with concrete specimens with two mechanical anchorage methods of welding symmetrical short steel bars at the end and anchoring plates at the end. The research shows that the cracking load and the ultimate load of the mechanical anchorage test block with transverse steel bars are quite different, showing a certain ductility, and the improvement effect of mechanical anchorage is obvious. Wang Hong et al. carried out the pull-out test on two batches of test blocks with four mechanical anchorage forms of hook, upset, welded anchor and welded anchor plate, and analyzed the role and stress failure mechanism of anchor head and ordinary section, reliability analysis and bond length of basic steel bars.

[0012] In summary, with the popularization and application of ultra-high performance concrete, more and more scholars have invested in the research on the mechanical properties of ultra-high performance concrete. The bond-slip constitutive relationship between ultra-high performance concrete and steel is the basic theoretical basis for studying the bearing capacity and seismic performance of ultra-high performance concrete structure, and is also the basis for structure finite element numerical calculation.

[0013] The existing research results on the bond-slip constitutive relationship between ultra-high performance concrete and steel mainly have the following problems:

[0014] (1) The constitutive relationship is incomplete, only the rising segment of the curve.

[0015] (2) Only the relationship between average bond stress and slip is considered, and the bond distribution stress of the steel in the anchoring section cannot be accurately reflected.

[0016] (3) The specific calculation formula of the shape parameter of the bond-slip constitutive model curve is not given, which leads to inaccurate model curve and poor practicability.

[0017] (4) Only the bond-slip performance of straight anchoring steel is considered, and the thick anchoring steel of the pier is not involved. SUMMARY

[0018] (1) The technical problem to be solved

[0019] Based on this, the present application provides a bond-slip constitutive relationship calculation method for ultra-high performance concrete and steel, which aims to solve the technical problems in the prior art that the research results on the bond-slip constitutive relationship between ultra-high performance concrete and steel cannot accurately reflect the bond stress when the steel slips and have poor practicability.

[0020] (2) Technical scheme

[0021] To solve the above technical problems, the present application provides a bond-slip constitutive relationship calculation method for ultra-high performance concrete and steel, comprising the following steps:

[0022] Step 1: According to the structural design and the concrete mix proportion, the bond length of the pull-out steel bar, the cover thickness of the steel bar and the concrete compressive strength of the concrete test piece in the pull-out test are determined, and the pull-out test is carried out;

[0023] Step 2: According to the pull-out test results, the influence of the bond length of the steel bar, the cover thickness of the steel bar and the concrete compressive strength of the concrete test piece on the bond strength is obtained, and a function relationship formula of the bond strength of the steel bar is established;

[0024] Step 3: According to the pull-out test results, the influence of the bond length of the steel bar, the cover thickness of the steel bar and the concrete compressive strength of the concrete test piece on the peak slip is obtained, and a function relationship formula of the peak slip of the steel bar is established;

[0025] Step 4: According to the pull-out test results, the test bond-slip curve is obtained, and according to the test bond-slip curve, the average bond stress-slip curve and the function relationship formula including the rising section and the falling section are obtained by regression Determine the influence degree of the bond length of the steel bar and the cover thickness of the steel bar on the rising section and the falling section of the curve;

[0026] Step 5: According to the pull-out test results, the test bond length of the steel bar is obtained, the bond stress curve with the position change is calculated and drawn, and the function relationship formula ψ(x) of the bond stress with the position change is obtained by regression;

[0027] Step 6: The bond-slip constitutive relationship τ(S) of the ultra-high performance concrete and the steel bar is established, and the function expression is as follows:

[0028] Preferably, in step 4, the method for obtaining the bond-slip curve is as follows: in the pull-out test, the test data of the steel bar pull-out load and the steel bar slip amount are collected, then the steel bar pull-out load directly obtained by the test is converted into the average bond stress of the steel bar, and the curve obtained by taking the slip amount as the horizontal coordinate and the average bond stress as the vertical coordinate is the bond-slip curve.

[0029] Preferably, the calculation formula for converting the steel bar pull-out load directly obtained by the test into the average bond stress of the steel bar is as follows:

[0030]

[0031] Wherein: is the average bond stress; F is the steel bar pull-out load; d is the diameter of the pull-out steel bar; L is the bond length of the steel bar; π is the circular constant.

[0032] Preferably, the pull-out test is performed using a pull-out test loading device. The pull-out test loading device includes the pull-out reinforcing bar. Symmetrically arranged upper and lower grooves are provided on opposite sides of the reinforcing bar along its length. A lower strain gauge is bonded to the upper groove, and an upper strain gauge is bonded to the lower groove. Multiple upper strain gauges are equidistantly arranged, as are multiple lower strain gauges. The upper and lower strain gauges are staggered along the length of the pull-out reinforcing bar. Epoxy resin is poured into the upper and lower grooves of the reinforcing bar, respectively. The pull-out test loading device also includes two... Two plastic tubes are spaced apart. A concrete specimen is cast outside the pull-out reinforcing bar and the plastic tubes. The pull-out reinforcing bar between the two plastic tubes is the bonding section, which is directly bonded to the concrete specimen. A clamp is provided on the upper part of the pull-out reinforcing bar, and a displacement gauge for measuring the slippage of the reinforcing bar is clamped at each end of the clamp. The concrete specimen is placed on a reaction frame, which is an integral frame structure. A through-hole load sensor for recording the pull-out load of the reinforcing bar is provided at the bottom of the concrete specimen. A ball joint for clamping a tensile testing machine is provided at the top of the reaction frame. The lower part of the pull-out reinforcing bar passes through the reaction frame. The tensile testing machine applies the load by pulling the lower part of the pull-out reinforcing bar.

[0033] Preferably, in the pull-out test of step 1, the diameter of the pull-out reinforcing bar is d, the thickness of the protective layer of the reinforcing bar is 1d-4d, the bond length of the pull-out reinforcing bar is 1d-10d, the compressive strength of the concrete specimen is 80MPa-150MPa, and the form of the end of the pull-out reinforcing bar includes straight type and thickened type.

[0034] Preferably, in step 2, the functional relationship of the steel bar bond strength is:

[0035]

[0036] Where: τ u λ is the bond strength of the reinforcing bar, λ is the pull-out end shape factor of the reinforcing bar, L is the bond length of the reinforcing bar, d is the diameter of the pull-out reinforcing bar, C is the protective layer thickness of the reinforcing bar, and f is the tensile strength of the reinforcing bar. c It refers to the compressive strength of concrete;

[0037] When the pulled-out reinforcement is straight, λ is taken as 1; when the pulled-out reinforcement is thickened, λ is calculated according to the following formula:

[0038]

[0039] Where: L is the bond length of the reinforcing bar, and d is the diameter of the pulled-out reinforcing bar.

[0040] Preferably, in step 3, the function relationship of the peak slip of the steel bar is:

[0041]

[0042] Wherein: S u is the peak slip of the steel bar, η is the shape coefficient of the end of the steel bar at the peak slip, L is the bond length of the steel bar, d is the diameter of the steel bar, and C is the thickness of the protective layer of the steel bar.

[0043] When the steel bar is flat, η is 1; when the steel bar is thick, η is calculated according to the following formula:

[0044]

[0045] Wherein: L is the bond length of the steel bar, and d is the diameter of the steel bar.

[0046] Preferably, in step 4, the average bond stress-slip curve and the function relationship are:

[0047]

[0048] Wherein: is the average bond stress, τ u is the bond strength, S u is the peak slip, S is the slip of the steel bar, α is the influence parameter of the rising section of the curve, and β is the influence parameter of the descending section of the curve.

[0049] Preferably, the influence parameters α and β of the rising section and the descending section of the bond slip curve are determined by the bond length of the steel bar and the thickness of the protective layer of the steel bar, and the calculation formula is:

[0050]

[0051]

[0052] Wherein: L is the bond length of the steel bar, d is the diameter of the steel bar, and C is the thickness of the protective layer of the steel bar.

[0053] Preferably, in step 5, the function relationship ψ(x) of the bond stress changing with the position is related to the ratio of the bond length of the steel bar to the diameter of the steel bar, and the function relationship is a quintic polynomial:

[0054]

[0055] Wherein: x is the length of the stress measurement point from the end of the steel bar anchor, L is the bond length of the steel bar, P1, P2, P3, P4, and P5 are undetermined coefficients, which are obtained by regression fitting of test data.

[0056] (III) Beneficial Effects

[0057] The beneficial effects of the present application compared with the prior art include:

[0058] The present application calculates the function relationship between the average bond stress of the steel bar and the slip and the model curve by considering the influence of the bond length of the steel bar, the thickness of the protective layer of the steel bar, and the strength grade of the concrete. Based on the stress distribution law in the bond section of the steel bar, a function relationship between the bond stress and the position in the bond section of the steel bar is established. The product of the function relationship between the average bond stress and the slip and the function relationship between the bond stress and the position is used to represent the bond-slip constitutive relationship between the ultra-high performance concrete and the steel bar. The constitutive relationship calculation method provided by the present application can accurately reflect the bond stress when the steel bar slips, and the prediction result is accurate and practical.

[0059] In the bond-slip constitutive relationship calculation method of the ultra-high performance concrete and the steel bar, the constitutive relationship curve is the full bond-slip curve, and the comprehensive influence of factors such as the bond length of the steel bar, the thickness of the protective layer of the steel bar, and the strength grade of the concrete is considered. The shape parameters of the bond-slip constitutive model curve are given in the specific calculation formula. The influence of the position relationship in the anchoring section of the steel bar on the bond stress is considered, and the bond-slip constitutive relationship curve of the ultra-high performance concrete and the steel bar can be accurately, comprehensively, quantitatively, and effectively predicted. BRIEF DESCRIPTION OF DRAWINGS

[0060] The features and advantages of the present application will be more clearly understood through reference to the accompanying drawings, which are schematic and should not be understood to limit the present application in any way, in which:

[0061] Figure 1 For the present application embodiment: schematic diagram of the steel bar drawing with a slot and a strain gauge arranged in the slot.

[0062] Figure 2 For the present application embodiment: schematic diagram of the structure of the straight steel bar drawing test specimen.

[0063] Figure 3 For the present application embodiment: schematic diagram of the structure of the thick steel bar drawing test specimen.

[0064] Figure 4 For the present application embodiment: schematic diagram of the structure of the steel bar drawing test block loading device.

[0065] Figure 5 For the present application embodiment: comparison diagram of the bond-slip curves of 120MPa ultra-high performance concrete in the drawing test.

[0066] Figure 6Figure 1 is a comparison chart of the bond-slip curves of 100MPa ultra-high performance concrete in the pull-out test of the embodiment of the present application.

[0067] Figure 7 Figure 2 is a comparison chart of the test data curve and the fitting curve of the bond stress change with position of 120MPa ultra-high performance concrete under the cover thickness of 2d steel bars in the pull-out test of the embodiment of the present application.

[0068] Figure 8 Figure 3 is a comparison chart of the bond-slip test curve in the cited document and the bond-slip constitutive relationship curve calculated by the present application.

[0069] Figure 9 Figure 4 is a side view of the present application. Figure 1

[0070] Explanation of reference signs:

[0071] 1. Straight type pull-out steel bar, 2. Steel bar thread, 3. Lower strain gauge, 4. Upper strain gauge, 5. Upper groove of steel bar, 6. Lower groove of steel bar, 7. Concrete test piece, 8. PVC pipe, 9. Thick type pull-out steel bar, 10. Welded steel bar, 11. Thick end of the steel bar, 12. Displacement meter, 13. Clamp, 14. Bonding section, 15. Spherical hinge, 16. Through load sensor, 17. Counterforce frame. DETAILED DESCRIPTION

[0072] In order to make the above objectives, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings. In the following description, a large number of specific details are set forth in order to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the concept of the present application, so the present application is not limited to the specific embodiments disclosed below.

[0073] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "connected", "connected" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected, it can be directly connected, or it can be indirectly connected through an intermediate medium, it can be the internal communication of two elements, or it can be "driven connection", that is, through various suitable ways such as belt drive, gear drive or chain wheel drive, etc. For ordinary skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0074] The specific embodiments of the present application will be described below with reference to the accompanying drawings. Figures 1-9 The present application further describes a method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and steel bars.

[0075] ​The application discloses a kind of super high performance concrete and the calculation method of bond slip constitutive relation of reinforcing bar, comprising the following steps:

[0076] Step 1: according to the structure design and concrete mix proportion, the bond length of the pull-out test in the pull-out test, the cover thickness of reinforcing bar and the concrete compressive strength of concrete test piece are determined, and the pull-out test is carried out.

[0077] Step 2: according to the pull-out test result, the influence of the bond length of reinforcing bar, the cover thickness of reinforcing bar and the concrete compressive strength of concrete test piece on bond strength is obtained, and the function relationship formula of reinforcing bar bond strength is established.

[0078] Step 3: according to the pull-out test result, the influence of the bond length of reinforcing bar, the cover thickness of reinforcing bar and the concrete compressive strength of concrete test piece on peak slip is obtained, and the function relationship formula of reinforcing bar peak slip is established.

[0079] Step 4: according to the pull-out test result, the test bond slip curve is obtained, and the average bond stress-slip curve and function relationship formula containing rising section and descending section are obtained by regression according to the test bond slip curve The influence degree of the bond length of reinforcing bar and the cover thickness of reinforcing bar on the rising section and the descending section of the curve is determined.

[0080] Step 5: according to the pull-out test result, the test bond length steel strain data is obtained, the curve of bond stress change with position is calculated and drawn, and the function relationship formula ψ (x) of bond stress change with position is obtained by regression.

[0081] Step 6: the bond slip constitutive relationship τ (S) of super high performance concrete and reinforcing bar is established, and the function expression is as follows:

[0082] According to the specific embodiment of the application, in step 4, the method for obtaining the bond slip curve is as follows: in the pull-out test, the test data of reinforcing bar pull-out load and reinforcing bar slip amount are collected, then the reinforcing bar pull-out load directly obtained by the test is converted into the average bond stress of reinforcing bar, and the curve obtained by taking the slip amount as the horizontal coordinate and the average bond stress as the vertical coordinate is the bond slip curve.

[0083] According to the specific embodiment of the application, the calculation formula for converting the reinforcing bar pull-out load directly obtained by the test into the average bond stress of reinforcing bar is as follows:

[0084]

[0085] Wherein: The average bond stress is F; F is the reinforcing bar pull-out load; d is the diameter of the pull-out reinforcing bar; L is the bond length of reinforcing bar; π is the circular constant.

[0086] More specifically, the plastic tube is a PVC tube 8, and in a specific implementation, a tensile testing machine clamps the upper ball hinge 15 to fix the counter-force frame 17, the lower bottom surface of the pull-out test block is placed on the through-load sensor 16, the tensile testing machine applies a load through the lower part of the pull-out reinforcing bar 1, the slippage of the pull-out reinforcing bar 1 is measured by two displacement meters 12 clamped by the upper clamp 13 of the pull-out reinforcing bar 1, and the average of the two displacement meters 12 is taken to offset the error caused by the imbalance of the displacement meter 12. During the test loading process, the pull-out load, the slippage of the reinforcing bar, and the strain of the reinforcing bar are collected by the data acquisition system, and the three are one-to-one corresponding.

[0087] More specifically, please refer to Figure 1 and Figure 9 The manufacturing method of the pull-out test loading device is as follows: the two sides of the pull-out reinforcing bar 1 are provided with reinforcing bar threads 2, the upper reinforcing bar groove 5 and the lower reinforcing bar groove 6 are respectively arranged in the middle non-threaded area of the pull-out reinforcing bar 1, and two symmetrical grooves are milled in the middle non-threaded area of the reinforcing bar threads 2 on the two sides of the pull-out reinforcing bar 1 along the length direction of the pull-out reinforcing bar 1, which are respectively the upper reinforcing bar groove 5 and the lower reinforcing bar groove 6, the depth of the groove is 2 mm, and the width is 4 mm.

[0088] In a specific implementation, the number and distance of strain gauges are designed according to the bond length of the reinforcing bar, the strain gauges are pasted in the upper reinforcing bar groove 55 and the lower reinforcing bar groove 66 of the reinforcing bar at equal intervals, the strain gauges are fixed in the strain gauge groove (the upper reinforcing bar groove 5 and the lower reinforcing bar groove 6) by using 502 glue, after the glue is dry, the whole groove is filled with epoxy resin, and the filling height of the epoxy resin is flush with the surface of the pull-out reinforcing bar 1.

[0089] Based on the pull-out test, the stress of the reinforcing bar in the bond section 14 is collected by the data acquisition system.

[0090] According to the specific implementation of the present application, in the pull-out test of step 1, the diameter of the pull-out reinforcing bar is d, the thickness of the protective layer of the reinforcing bar is 1d-4d, the bond length of the reinforcing bar is 1d-10d, the compressive strength of the concrete test piece is 80MPa-150MPa, and the form of the end of the pull-out reinforcing bar includes flat type and thick type.

[0091] According to the specific implementation of the present application, in the pull-out test of step 1, the diameter of the pull-out reinforcing bar 1 is d, the thickness of the protective layer of the reinforcing bar of the pull-out reinforcing bar 1 is 1d-4d, the bond length of the reinforcing bar of the pull-out reinforcing bar 1 is 1d-10d, the compressive strength of the concrete test piece 7 is 80MPa-150MPa, and the form of the end of the pull-out reinforcing bar 1 includes flat type and thick type.

[0092] More specifically, the forms of the end of the anchoring steel bar of the piling type include hydraulic piling, single-sided welding steel bar, double-sided welding steel bar, and bolt anchoring head. The concrete applied in the pull-out test is: ultra-high performance concrete with a compressive strength exceeding 120 MPa, reactive powder concrete with a compressive strength exceeding 100 MPa, or fiber high-strength concrete with a compressive strength exceeding 80 MPa.

[0093] More specifically, the end of the piling type steel bar is shown in the schematic diagram as Figure 3 The end 11 of the pull-out steel bar 9 is piling by a hydraulic piling machine, the length of the piling end is d (d is the diameter of the pull-out steel bar), the diameter of the piling end is d+4 mm, a steel bar 10 with a length of 50-80 mm and a diameter of d-4 mm is welded to the piling end of the steel bar, the steel bar 10 acts as a clamp to clamp the displacement meter to measure the slip of the steel bar, and the non-bonding section of the lower part of the pull-out steel bar is controlled by a PVC plastic pipe 8. The upper part of the pull-out steel bar 9 is directly bonded with the concrete 7 from the piling end to the PVC plastic pipe 8 to form a bonding section 14.

[0094] According to the specific embodiment of the present application, in step 2, the function relationship of the bond strength of the steel bar is:

[0095]

[0096] Wherein τ u is the bond strength of the steel bar, λ is the shape coefficient of the end of the pull-out steel bar, L is the bonding length of the steel bar, d is the diameter of the pull-out steel bar, C is the thickness of the protective layer of the steel bar, and f c is the compressive strength of the concrete.

[0097] When the pull-out steel bar is flat, λ is 1; when the pull-out steel bar is of the piling type, λ is calculated according to the following formula:

[0098]

[0099] Wherein L is the bonding length of the steel bar, and d is the diameter of the pull-out steel bar.

[0100] According to the specific embodiment of the present application, in step 3, the function relationship of the peak slip of the steel bar is:

[0101]

[0102] Wherein S u is the peak slip of the steel bar, η is the shape coefficient of the end of the pull-out steel bar, L is the bonding length of the steel bar, d is the diameter of the pull-out steel bar, and C is the thickness of the protective layer of the steel bar.

[0103] When the pull-out steel bar is flat, η is 1; when the pull-out steel bar is of the piling type, η is calculated according to the following formula:

[0104]

[0105] Wherein: L is the bond length of the steel bar, d is the diameter of the drawn steel bar.

[0106] According to the specific embodiment of the present application, in step 4, the average bond stress-slip curve and the functional relationship are as follows:

[0107]

[0108] Wherein: is the average bond stress, τ u is the bond strength, S u is the peak slip, S is the slip amount of the steel bar, a is the influence parameter of the rising section of the curve, and β is the influence parameter of the descending section of the curve.

[0109] According to the specific embodiment of the present application, the influence parameters a and β of the rising section and the descending section of the bond-slip curve are determined by the bond length of the steel bar and the cover thickness of the steel bar, and the calculation formula is as follows:

[0110]

[0111]

[0112] Wherein: L is the bond length of the steel bar, d is the diameter of the drawn steel bar, and C is the cover thickness of the steel bar.

[0113] According to the specific embodiment of the present application, in step 5, the functional relationship ψ(x) of the bond stress changing with the position is related to the ratio of the bond length of the steel bar and the diameter of the drawn steel bar, and the functional relationship is a quintic polynomial:

[0114]

[0115] Wherein: x is the length of the stress measurement point from the end of the steel bar anchor, L is the bond length of the steel bar, P1, P2, P3, P4, and P5 are undetermined coefficients, which are obtained by regression fitting of the test data.

[0116] According to the specific embodiment of the present application, the drawing test is completed by using a drawing test loading device, the drawing test loading device comprises a drawing steel bar 1, opposite sides of the length direction of the drawing steel bar 1 are symmetrically provided with a steel bar upper groove 5 and a steel bar lower groove 6, a lower strain gauge 3 is bonded in the steel bar upper groove 5, and an upper strain gauge 4 is bonded in the steel bar lower groove 6, the number of the upper strain gauges 4 is multiple, and the multiple upper strain gauges 4 are equidistantly arranged, the number of the lower strain gauges 3 is multiple, and the multiple lower strain gauges 3 are equidistantly arranged, the upper strain gauges 4 and the lower strain gauges 3 are staggered arranged in the length direction of the drawing steel bar 1, and epoxy resin is poured in the steel bar upper groove 5 and the steel bar lower groove 6 respectively, the drawing test loading device further comprises two plastic tubes which are respectively sleeved on the drawing flat steel bar 1, the two plastic tubes are arranged at intervals, the flat drawing steel bar 1 and the plastic tubes are externally poured with a concrete test piece 7, the plastic tubes are PVC tubes 8, the drawing steel bar 1 between the two plastic tubes is a bonding section 13, and the bonding section 13 is directly bonded with the concrete test piece 7; a plastic tube is arranged at the lower part of a thick end drawing steel bar 9, the concrete test piece 7 is externally poured from the thick end drawing steel bar to the plastic tube, the plastic tube is a PVC tube 8, the drawing steel bar 9 between the thick end and the plastic tube is the bonding section 13, and the bonding section 13 is directly bonded with the concrete test piece 7. A clamp 13 is arranged at the upper part, two displacement meters 12 for measuring the steel bar slip amount are respectively clamped at the two ends of the clamp 13, the concrete test piece 7 is arranged on a counterforce frame 17 which is a frame structure as a whole, a through load sensor 16 for recording the steel bar drawing load is arranged at the bottom of the concrete test piece 7, a spherical hinge 15 for clamping of a tension testing machine is arranged at the top of the counterforce frame 17, the lower part of the drawing steel bar 1 penetrates through the counterforce frame 17, and the tension testing machine realizes the load application through the lower part of the drawing steel bar 1.

[0117] The present application is further described below in combination with test data:

[0118] 1. Ultra-high performance concrete raw materials and mix proportion

[0119] The preparation of test blocks: three different strength concretes are used to prepare the concrete test piece 7. One is an ultra-high performance concrete with a concrete strength grade of 120 MPa, one is an ultra-high performance concrete with a concrete strength grade of 100 MPa, and one is an ultra-high performance concrete with a concrete strength grade of 80 MPa. The raw materials include: fine aggregate is quartz sand and quartz powder, wherein: the particle size of the quartz sand is 20-40 mesh, and the particle size of the quartz powder is 140-200 mesh; the cement is PO42.5 ordinary portland cement; the fly ash is grade II fly ash; the average particle size of the silica fume is 0.1-0.2 μm, the SiO2 content is not less than 92%, the water reducing agent is liquid polycarboxylic acid water reducing agent, and the water reducing rate is 30%; the fiber is flat copper-plated steel fiber, and the length-diameter ratio is 67.

[0120] Table 1: Ultra-high performance concrete mix proportion (kg / m 3 )

[0121]

[0122] 2. Test parameter design

[0123] The test was carried out according to the concrete strength grade of 120 MPa, 100 MPa and 80 MPa, and the reinforcement cover thickness was set to 2d and 4d, wherein the reinforcement end of 120 MPa and 100 MPa was flat, and the bonding length of the reinforcement was 2d, 3d, 4d, 5d and 6d respectively; the reinforcement end of 80 MPa was thick, and the bonding length of the reinforcement was 3d, 4d, 5d, 6d and 7d respectively. The test block parameter design is shown in Table 2.

[0124] Table 2: Test parameter design

[0125]

[0126] 3. Test method

[0127] The size of the test block is a cube of 150mmx150mmx150mm, and the length of the unbonding section 13 is controlled by the PVC plastic sleeve 8 at both ends of the pulled reinforcement 1. A plurality of strain gauges are used to measure the reinforcement strain. The test block is made as shown in Figure 2 and Figure 3 The test uses a WA-1000B type electro-hydraulic universal testing machine to load, takes the displacement of the free end of the reinforcement as the slip, and measures the displacement of the reinforcement upper clamp 13 by the two displacement meters 12; the load sensor is set at the bottom of the test block to record the pulling load. The test loading system is in accordance with the standard of "Test methods for concrete structures", and the force control loading mode is adopted, the control force should be slow and smooth to ensure the accuracy of the test, the rate control is 0.1-0.15KN / s, and the test block loading is shown in Figure 4 .

[0128] 4. Test results

[0129] The test block number is: U-L-C, U represents the concrete strength grade; L represents the bonding length of the reinforcement; C represents the cover thickness of the reinforcement. The test results are shown in Table 3 as follows.

[0130] Table 3: Test results

[0131]

[0132] 5. Comparison of test results

[0133] The comparison of the bond-slip constitutive relationship model curve of ultra-high performance concrete and steel under different bonding lengths of different steels and different cover thicknesses of the steels is shown in Figure 5 , Figure 6 , wherein Figure 5The bond-slip curve of 120 MPa ultra-high performance concrete, Figure 6 The bond-slip curve of 100 MPa ultra-high performance concrete.

[0134] The parameters of the bond length of the tested steel bar, the thickness of the protective layer of the steel bar and the strength grade are substituted into the bond-slip constitutive relationship curve calculation formula of the ultra-high performance concrete and the steel bar:

[0135]

[0136] The comparison of the formula calculation results and the test data is shown in Table 4, wherein τ u is the test value of the bond strength, τ cu is the calculation value of the bond strength; S u is the test value of the peak slip, and S cu is the calculation value of the peak slip.

[0137] Table 4: Comparison of calculation results

[0138]

[0139] The test data of the 120 MPa ultra-high performance concrete are substituted into the function relationship formula of the bond stress of the steel bar changing with the position, the undetermined coefficients of the position function are shown in Table 5, and the comparison of the test curve of the bond stress of the steel bar changing with the position and the calculation formula curve is shown in Table 5. Figure 7

[0140]

[0141] Table 5: Undetermined coefficients of the position function

[0142]

[0143] As shown in Figure 4 and Figure 5 , the calculation constitutive relationship curve of the ultra-high performance concrete and the steel bar is in good agreement with the test curve; the test data of the related literatures (the specific literatures are explained in the following part) are selected, the calculation method of the bond-slip constitutive relationship of the ultra-high performance concrete and the steel bar is provided, the comparison of the calculation constitutive relationship curve and the literature test data curve is shown in Figure 8 , the curves are in good agreement, and it is proved that the method is reliable.

[0144] It should be noted that the content of the above-mentioned "selecting the related literatures" is as follows:

[0145] Jia Fangfang. Experimental study on bond performance of steel bar and reactive powder concrete [D]. Beijing: Beijing Jiaotong University, 2013.

[0146] ​Zhao CH, Li HQ, Deng KL. Experimental study on bond performance between steel bar and ultra-high performance concrete with coarse aggregate[J]. Journal of Southwest Jiaotong University, 2019, 54(05):937-944.

[0147] Cheng DH, Fan YX, Wang YS. Bond-slip constitutive model of RC active powder concrete with steel bars[J]. Journal of Jilin University(Engineering Version), 2021, 51(04):1317-1330.

[0148] Xie L. Experimental study on bending and bond performance of steel fiber reinforced high strength concrete[D]. Zhengzhou: Zhengzhou University, 2003:3858.

[0149] Although the embodiments of the present application are described in conjunction with the drawings, various modifications and changes can be made by those skilled in the art without departing from the spirit and scope of the present application, and such modifications and changes fall within the scope defined by the appended claims.

Claims

1. A method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel, characterized in that, Includes the following steps: Step 1: Based on the structural design and concrete mix proportion, determine the bond length of the pulled-out steel bars, the thickness of the concrete cover, and the concrete compressive strength of the concrete specimens for the pull-out test, and then conduct the pull-out test. Step 2: Based on the pull-out test results, the effects of the bond length of the reinforcing bar, the thickness of the concrete cover, the end type of the reinforcing bar, and the compressive strength of the concrete specimen on the bond strength are obtained, and a functional relationship for the bond strength of the reinforcing bar is established; In Step 2, the functional relationship for the bond strength of the reinforcing bar is: Where: τ u λ is the bond strength of the reinforcing bar, λ is the pull-out end shape factor of the reinforcing bar, L is the bond length of the reinforcing bar, d is the diameter of the pull-out reinforcing bar, C is the protective layer thickness of the reinforcing bar, and f is the tensile strength of the reinforcing bar. c It refers to the compressive strength of concrete; When the pulled-out reinforcement is straight, λ is taken as 1; when the pulled-out reinforcement is thickened, λ is calculated according to the following formula: Where: L is the bond length of the reinforcing bar, and d is the diameter of the pull-out reinforcing bar; Step 3: Based on the pull-out test results, obtain the influence of the bond length of the reinforcing bar, the thickness of the protective layer of the reinforcing bar, the end form of the reinforcing bar, and the compressive strength of the concrete specimen on the peak slip, and establish the functional relationship of the peak slip of the reinforcing bar. In step 3, the functional relationship of the peak slip of the reinforcing bar is: Wherein: S u η is the peak slip of the reinforcing bar, η is the peak slip pull-out end shape factor of the reinforcing bar, L is the bond length of the reinforcing bar, d is the diameter of the pull-out reinforcing bar, and C is the protective layer thickness of the reinforcing bar. When the pulled-out reinforcing bar is straight, η is taken as 1; when the pulled-out reinforcing bar is thickened, η is calculated according to the following formula: Where: L is the bond length of the reinforcing bar, and d is the diameter of the pull-out reinforcing bar; Step 4: Based on the pull-out test results, obtain the test bond-slip curve. Based on the test bond-slip curve, regress to obtain the average bond stress-slip curve and functional relationship, which includes the rising and falling segments. Determine the degree of influence of the bond length of the reinforcing bars and the thickness of the concrete cover on the ascending and descending sections of the curve; Step 5: Based on the pull-out test results, obtain the strain data of the steel bar in the bonded section of the test, calculate and plot the curve of bond stress as a function of position, and regress to obtain the functional relationship ψ(x) of bond stress as a function of position. Step 6: Establish the bond-slip constitutive relation τ(S) between ultra-high performance concrete and reinforcing steel, with the following functional expression:

2. The method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel according to claim 1, characterized in that, In step 4, the method for obtaining the bond-slip curve is as follows: In the pull-out test, the test data of the pull-out load and the slip of the steel bar are collected. Then, the pull-out load of the steel bar obtained directly from the test is converted into the average bond stress of the steel bar. The curve obtained by plotting the slip on the horizontal axis and the average bond stress on the vertical axis is the bond-slip curve.

3. The method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel according to claim 2, characterized in that, The formula for converting the pull-out load of the steel bars obtained directly from the experiment into the average bond stress of the steel bars is as follows: in: denoted as average bond stress; F is the pull-out load of the steel bar; d is the diameter of the pulled-out steel bar; L is the bond length of the steel bar; and π is pi.

4. The method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel according to claim 3, characterized in that, The pull-out test is performed using a pull-out test loading device, which includes the pull-out reinforcing bar. The reinforcing bar has symmetrical upper and lower grooves on opposite sides along its length. A lower strain gauge is bonded to the upper groove, and an upper strain gauge is bonded to the lower groove. Multiple upper strain gauges are equidistantly arranged, as are multiple lower strain gauges. The upper and lower strain gauges are staggered along the length of the reinforcing bar. Epoxy resin is poured into the upper and lower grooves of the reinforcing bar, respectively. The pull-out test loading device also includes two plastic... The system comprises two plastic tubes spaced apart, with a concrete specimen cast outside the pull-out reinforcing bar and the plastic tubes. The pull-out reinforcing bar between the two plastic tubes forms the bonding section, which is directly bonded to the concrete specimen. A clamp is provided on the upper part of the pull-out reinforcing bar, with a displacement gauge for measuring the slippage of the reinforcing bar held at each end of the clamp. The concrete specimen is placed on a reaction frame, which is an integral frame structure. A through-hole load sensor for recording the pull-out load of the reinforcing bar is provided at the bottom of the concrete specimen. A ball joint for clamping a tensile testing machine is provided at the top of the reaction frame. The lower part of the pull-out reinforcing bar passes through the reaction frame, and the tensile testing machine applies the load by pulling the lower part of the pull-out reinforcing bar.

5. The method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel according to claim 1, characterized in that, In the pull-out test of step 1, the diameter of the pull-out steel bar is d, the thickness of the protective layer of the steel bar is 1d-4d, the bond length of the pull-out steel bar is 1d-10d, the compressive strength of the concrete specimen is 80MPa-150MPa, and the end form of the pull-out steel bar includes straight type and thickened type.

6. The method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel according to claim 1, characterized in that, In step 4, the average bond stress-slip curve and functional relationship are as follows: in: For the average bond stress, τ u For bond strength, S u For peak slip, S is the amount of rebar slip, α is the influence parameter of the rising segment of the curve, and β is the influence parameter of the falling segment of the curve.

7. The method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel according to claim 6, characterized in that, The influence parameters α (ascending segment) and β (descending segment) of the bond-slip curve are jointly determined by the bond length of the reinforcing bar and the thickness of the concrete cover. Their calculation formulas are as follows: Where: L is the bond length of the reinforcing bar, d is the diameter of the pulled-out reinforcing bar, and C is the thickness of the protective layer of the reinforcing bar.

8. The method for calculating the bond-slip constitutive relationship between ultra-high performance concrete and reinforcing steel according to claim 1, characterized in that, In step 5, the functional relationship ψ(x) of bond stress as a function of location is related to the ratio of the bond length of the rebar to the diameter of the pulled-out rebar, and its functional relationship is a univariate fifth-degree polynomial: Where: x is the length of the stress measuring point from the end of the rebar anchorage, L is the bond length of the rebar, and P1, P2, P3, P4, and P5 are undetermined coefficients obtained by regression fitting of experimental data.

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