Simulation method for bending resistance of interface between cast-in-situ concrete joint and bridge deck of widened bridge

Abstract

The application discloses a kind of simulation methods of anti-bending performance of interface between cast-in-situ concrete joint and bridge deck of widening bridge, including design macroscopic mechanics model, the macroscopic mechanics model is divided into three stages: (1) the first stage is elastic stage, corresponding to the case that wet joint interface does not crack under the action of bending moment;(2) the second stage is normal use stage, corresponding to the case that wet joint interface cracks under the action of bending moment, but the tensile reinforcement does not yield;(3) the third stage is yield stage, corresponding to the case that wet joint tensile reinforcement yields.The application can simulate the anti-bending performance of interface between cast-in-situ concrete joint and precast bridge deck of widening bridge, effectively reduce the calculation load and calculation time, and significantly improve the convergence of calculation, and can be applied to large-scale widening bridge engineering design.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering, specifically relating to a method for simulating the bending performance of the interface between cast-in-place concrete joints and precast bridge decks in widened bridges. Background Technology

[0002] With the rapid development of my country's economy, the original design standards of early-built highway bridges can no longer meet the increasing traffic demands, necessitating widening and reconstruction. In bridge widening and reconstruction projects, a new bridge is first constructed on one side of the existing bridge (the new bridge can be cast in place using scaffolding at the bridge site, or prefabricated in a factory and transported to the site for hoisting). Then, the bridge decks of the new and old bridges are connected using cast-in-place concrete wet joints, as shown in the attached diagram. Figure 1 As shown. Because the concrete wet joints and the bridge deck concrete on both sides are poured in batches, the interface between the wet joints and the bridge deck (hereinafter referred to as "wet joint interface") is a "weak" link in the widened bridge structure, and cracking is prone to occur during the operation of the bridge structure (as shown in the attached diagram). Figure 2 (As shown), it affects structural safety and service life.

[0003] Currently, scholars have conducted research on the mechanical properties of wet joints in concrete of widened bridges. The research methods include: (1) experimental research; (2) three-dimensional finite element numerical simulation. Among them, determining the mechanical properties of wet joints through experimental research requires a large amount of experimental funding and has a long implementation period; while the three-dimensional finite element model is affected by material and geometric nonlinearity, making calculation and modeling more difficult, and the calculation process may encounter convergence problems. Therefore, it is necessary to propose a method for simulating the bending performance of the interface between the cast-in-place concrete joint and the bridge deck of widened bridges, which is suitable for simulating the performance of the interface between the concrete wet joint and the bridge deck and can be applied to the design of large-scale widened bridge projects. Summary of the Invention

[0004] Based on existing experimental results on the bending resistance of wet joints in widened bridges, the purpose of this invention is to provide a method for simulating the bending resistance of the interface between the cast-in-place concrete joint and the bridge deck of a widened bridge. This method can simulate the bending resistance of the interface between the concrete wet joint and the bridge deck, effectively reduce the computational load and computation time, and significantly improve the convergence of the calculation.

[0005] The technical solution adopted by this invention to solve its technical problem is: a method for simulating the bending performance of the interface between the cast-in-place concrete joint and the bridge deck of a widened bridge, including the design of a macroscopic mechanical model, which is divided into three stages:

[0006] (1) The first stage is the elastic stage, which corresponds to the situation where cracks do not occur at the interface of the wet joint under bending moment.

[0007] (2) The second stage is the normal use stage, which corresponds to the situation where the wet joint interface cracks under bending moment, but the tensile reinforcement does not yield.

[0008] (3) The third stage is the yielding stage, which corresponds to the yielding of the tensile reinforcement in the wet joint;

[0009] The macroscopic mechanical model is expressed as follows:

[0010]

[0011] In the formula: M is the bending moment borne by the interface; The interface rotation angle is defined by k1, k2, and k3, which represent the interface rotation stiffness during the elastic, normal use, and yield stages, respectively; M represents the interface rotation stiffness during these stages. cr M is the cracking moment of the interface; y The yield moment of the interface; For the cracked corner of the interface; This is the yield angle of the interface.

[0012] Optionally, when the bending moment reaches the cracking bending moment M at the wet joint interface... cr At that time, the elastic phase ends;

[0013] The interface rotational stiffness k1 in the elastic stage is expressed as:

[0014]

[0015] In the formula: E u I is the elastic modulus of the concrete material at the wet joint; L is the moment of inertia of the wet joint section; and L is the span of the wet joint.

[0016] Optionally, the cracking moment M of the interface cr Represented as:

[0017] M cr =2Sf b (3)

[0018] In the formula: S is the area moment of the portion of the wet joint equivalent section above (or below) the centroidal axis about the centroidal axis; f b This refers to the bond strength at the wet joint interface.

[0019] Optionally, when the bending moment reaches the yield bending moment M at the wet joint interface... y At this time, the normal use phase ends;

[0020] The interface rotational stiffness k2 during normal use is expressed as:

[0021]

[0022] Where: I0 is the equivalent moment of inertia of the wet joint section under the condition that the interface is not cracked; I cr The moment of inertia of the wet joint section is calculated under the condition of interface cracking.

[0023] Optionally, the yield moment M of the interface y Represented as:

[0024] M y =f cu ·b·x·(h0-0.5x) (5)

[0025] In the formula: f cu denoted as , where b is the compressive strength of the bridge deck concrete material; b is the width of the concrete wet joint considered in the calculation; x is the height of the compression zone at the wet joint interface; and h0 is the effective height of the wet joint interface.

[0026] Furthermore, the effective height h0 of the wet joint interface is expressed as:

[0027] h0 = ha s (6)

[0028] In the formula, h is the height of the wet joint interface; a s This is the distance between the center of the tensile reinforcement in the wet joint and the edge of the tension zone.

[0029] Compared with the prior art, the beneficial effects of the technical solution provided by the present invention are:

[0030] This invention is based on macroscopic bending moment-curvature The relationship curve fills the gap in the simulation method (model) of macroscopic mechanical properties of widened concrete joints. Compared with three-dimensional finite element numerical simulation, the macroscopic mechanical model proposed in this invention can effectively reduce the computational load and computation time, and significantly improve the convergence of the calculation, making it suitable for engineering design of large-scale widened bridges. Attached Figure Description

[0031] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0032] Figure 1 A schematic diagram showing the location of the cast-in-place concrete joints in a bridge being widened.

[0033] Figure 2 Common defects at wet joints of cast-in-place concrete used for widening bridges include: interface cracking and water seepage.

[0034] Figure 3 A schematic diagram of the macroscopic mechanical model of the interface of the wet joint of cast-in-place concrete in a bridge to be widened;

[0035] Figure 4 This is a schematic diagram illustrating the principle of the four-point bending experiment.

[0036] Figure 5 Schematic diagram for designing concrete wet joint specimens (unit: mm);

[0037] Figure 6 Schematic diagram of reinforcement design for concrete wet joint specimens (unit: mm);

[0038] Figure 7 A schematic diagram of the four-point bending test apparatus for concrete wet joint specimens.

[0039] Figure 8 A schematic diagram of the displacement sensor arrangement for a four-point bending test of a concrete wet joint specimen (unit: mm);

[0040] Figure 9 The vertical force-interface opening width relationship curve for a four-point bending test of a concrete wet joint specimen;

[0041] Figure 10 The vertical force-mid-span deflection curves for four-point bending tests on concrete wet joint specimens;

[0042] Figure 11 The bending moment diagram of the concrete wet joint specimen under external load and unit bending moment at the interface is shown.

[0043] Figure 12 The moment of inertia I of the cross section after cracking at the wet joint interface cr Calculation diagram;

[0044] Figure 13 A schematic diagram of the calibration method for the macroscopic mechanical model parameter k3 of the wet joint interface;

[0045] Figure 14 A schematic diagram of finite element modeling for a wet joint specimen;

[0046] Figure 15 A comparison is made between the vertical force-mid-span deflection curves calculated using the finite element model and the experimental results. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0048] A method for simulating the flexural performance of the interface between cast-in-place concrete joints and bridge deck in a widened bridge includes designing a macroscopic mechanical model. Specifically, this macroscopic mechanical model is a piecewise linear interface rotation-bending moment constitutive relationship, as shown in the attached figure. Figure 3 As shown.

[0049] From the appendix Figure 3 It can be seen that the macroscopic mechanical model is divided into three stages: (1) The first stage is the elastic stage, which corresponds to the case where the interface of the wet joint does not crack under the action of bending moment; (2) The second stage is the normal use stage, which corresponds to the case where the interface of the wet joint cracks under the action of bending moment, but the tensile steel does not yield; (3) The third stage is the yielding stage, which corresponds to the case where the tensile steel of the wet joint yields.

[0050] The mathematical expression for this macroscopic mechanical model is as follows:

[0051]

[0052] In the formula: M is the bending moment borne by the interface; The interface rotation angle is defined by k1, k2, and k3, which represent the interface rotation stiffness during the elastic, normal use, and yield stages, respectively; M represents the interface rotation stiffness during these stages. cr M is the cracking moment of the interface; y The yield moment of the interface; For the cracked corner of the interface; This is the yield angle of the interface.

[0053] From the appendix Figure 3 It can be seen that in the elastic stage, the elastic rotational stiffness of the wet joint interface is k1. When the bending moment reaches the cracking bending moment M of the wet joint interface... cr At this point, the elastic phase ends. The interface rotational stiffness k1 during the elastic phase can be defined by formula (2):

[0054]

[0055] In the formula: E u I is the elastic modulus of the concrete material at the wet joint; L is the moment of inertia of the wet joint section; and L is the span of the wet joint.

[0056] Among them, the cracking bending moment M cr Referring to formulas (6.5.2-3) and (6.5.2-8) in the "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG3362-2018), the result can be calculated according to formula (3):

[0057] M cr =2Sf b (3)

[0058] In the formula: S is the area moment of the portion of the wet joint equivalent section above (or below) the centroidal axis about the centroidal axis; f bThe bond strength at the wet joint interface can be determined by the direct tension test as described in the reference (Semendary, A., Svecova, D. (2020) Factors affecting bond between precast concrete and cast in place ultra high performance concrete (UHPC). Engineering Structures. 216: 110746.).

[0059] From the appendix Figure 3 It can be seen that during normal use, the rotational stiffness of the wet joint interface is k. ２ When the bending moment reaches the yield bending moment M at the wet joint interface y At this point, the normal use phase ends. The interface rotational stiffness k2 during the normal use phase can be determined by formula (4):

[0060]

[0061] Where: I0 is the equivalent moment of inertia of the wet joint section under the condition that the interface is not cracked; I cr The moment of inertia of the wet joint section is calculated under the condition of interface cracking.

[0062] Among them, the yield bending moment M y Calculate according to formula (5):

[0063] M y =f cu ·b·x·(h0-0.5x) (5)

[0064] In the formula: f cu denoted as , where is the compressive strength of the bridge deck concrete material; , where is the width of the wet joint considered in the calculation; , where is the height of the compression zone at the wet joint interface; and , where is the effective height of the wet joint interface, calculated according to the following formula:

[0065] h0 = ha s (6)

[0066] Where: h is the height of the wet joint interface; a s This is the distance between the center of the tensile reinforcement in the wet joint and the edge of the tension zone.

[0067] From the appendix Figure 3 It can be seen that during the yielding stage, the rotational stiffness of the wet joint interface is k3, and when the bending moment reaches the ultimate bending moment M of the wet joint interface... u At that time, the wet joint interface was damaged.

[0068] Among them, the interfacial rotational stiffness k3 and the ultimate bending moment M during the yielding stage u The opening speed of the wet joint interface after the tensile reinforcement yields is related to the bond strength at the wet joint interface. The greater the bond strength, the greater the opening speed of the interface with increasing load. The interface rotational stiffness k3 and ultimate bending moment M at the yield stage are related. u The smaller the value, the more accurate the calibration can be based on the results of the wet joint bending test.

[0069] Example 1:

[0070] Using the macroscopic mechanical model of the wet joint interface proposed in this invention, the results of a four-point bending test on a concrete wet joint specimen were simulated to illustrate the model effect of the macroscopic mechanical model.

[0071] First, let's explain the principle of the four-point bending test, such as... Figure 4 As shown, a cast-in-place concrete wet joint specimen is supported on the ground using roller supports, forming simply supported boundary conditions. Specifically, vertical and horizontal displacements are constrained at one support point, while vertical displacement is constrained at the other. A vertical force is applied at the midpoint of a load distribution beam, which is placed in the middle of the wet joint specimen and connected to it via roller supports. Thus, the vertical force P is decomposed into two symmetrical vertical forces through the load distribution beam. Apply to wet joint specimens.

[0072] At this point, the bending moment diagram and shear force diagram of the wet joint specimen are as follows: Figure 4 As shown, assuming the distance between the roller support of the wet joint specimen and the roller support of the loading distribution beam is d1, the distance between the roller support of the loading distribution beam and the interface between the wet joint and the precast section is d2, and the span of the wet joint is c, then according to the bending moment diagram and shear force diagram, a "pure bending section" is formed between the two roller supports of the loading distribution beam. That is, the specimen in this section only bears the action of bending moment and not the action of shear force. The expression for bending moment M is: If the interface between the wet joint and the precast section is located in the pure bending zone, the bending (pure bending) performance of the interface can be simulated by a four-point bending test.

[0073] First, let's explain the design of the wet joint specimen in the four-point bending test, such as... Figure 5 As shown, the wet joint specimen consists of ordinary concrete (NSC) precast sections at both ends and an ultra-high strength concrete (UHPC) wet joint in the middle. The dimensions of the wet joint specimen are as follows: Figure 5 As shown.

[0074] The reinforcement details of the wet joint specimen are as follows: Figure 6 As shown, the longitudinal reinforcement (main reinforcement) uses HRB400 grade steel bars with a diameter of 12mm; the stirrups use HRB400 grade steel bars with a diameter of 6mm and a spacing of 150mm.

[0075] A four-point bending test was performed on the wet joint specimens. The test setup was as follows: Figure 7 As shown, the wet joint specimen is supported on the ground by roller supports, which are used to simulate simply supported boundary conditions. The hydraulic jack applies vertical force to the loading distribution beam through the reaction frame, and then transfers the vertical force to the wet joint specimen through the loading distribution beam.

[0076] Displacement sensors were evenly distributed on both sides of the UHPC wet joint section of the wet joint specimen to measure the interface opening during loading; a displacement sensor was also placed at the midpoint of the wet joint specimen, such as... Figure 8 As shown, this is used to measure the deflection of wet joint specimens during loading.

[0077] The vertical force-wet joint interface opening width relationship curve obtained from the four-point bending experiment is shown below. Figure 9 As shown, the vertical force-mid-span deflection curve of the specimen is as follows: Figure 10 As shown. By Figure 9 It can be seen that the right side of the wet joint specimen opened during the experimental loading process, while the left side of the wet joint specimen did not show obvious opening. This is because, according to... Figure 6 The specimen reinforcement configuration shows that there are three main reinforcement bars on the left interface and only two main reinforcement bars on the right interface. Therefore, during the experimental loading process, the main reinforcement bars on the right interface will yield in tension before the main reinforcement bars on the left interface, resulting in the right interface showing obvious opening earlier.

[0078] Depend on Figure 9 It can be seen that the turning point of accelerated opening of the right interface of the wet joint specimen is when the vertical force is 73kN, at which point the tensile reinforcement yields. Correspondingly, observe... Figure 10 It can be seen that the mid-span deflection of the wet joint specimen also begins to increase sharply when the vertical force is 73kN. Therefore, the yield force P of the wet joint specimen can be determined. y，test =73kN, in addition, observe Figure 10 It can be seen that when the vertical force is applied to 131.4 kN, the vertical force begins to decrease. Therefore, the ultimate load P of the wet joint specimen is... u，test =131.4kN.

[0079] Based on the above experimental phenomena, the macroscopic mechanical model described in formula (1) is used to simulate the vertical force-interface opening width relationship curve and the vertical force-mid-span deflection relationship curve of the wet joint specimen.

[0080] First, determine the rotational stiffness k1 in the elastic stage of the macroscopic mechanical model. Then, plot the bending moment diagrams of the wet joint specimen under external load and the bending moment diagram when a unit bending moment is applied at the joint, respectively. Figure 11In the figure (where d1 is the distance from the roller supports on both sides of the wet joint specimen to the roller supports on both sides of the loading distribution beam; d2 is the distance between the roller supports of the loading distribution beam and the two boundaries of the wet joint specimen; and c is the span of the wet joint), the rotation angle at the interface can be obtained using the graphical method:

[0081]

[0082] In the formula: E u I is the elastic modulus of the concrete material at the wet joint; I is the moment of inertia of the wet joint section; P is the vertical force applied by the actuator.

[0083] according to Figure 11 The bending moment at the wet joint interface under the external load shown in (a) is: Therefore, the rotational stiffness k1 of the wet joint interface in the elastic stage can be calculated according to the following formula:

[0084]

[0085] The cracking moment at the wet joint interface is calculated according to formula (3), where the bond strength f at the wet joint interface is... b Based on the direct tension test in Semindary and Svecova (2020), the average bond strength between the UHPC wet joint and the NSC precast section after 28 days of curing is 3.15 MPa. Therefore, in this invention, f b The value is taken as 3.15 MPa.

[0086] During normal use, the interface rotation stiffness k2 after the wet joint interface cracks can be calculated according to formula (4), where the moment of inertia I0 of the wet joint equivalent section when the interface is not cracked can be calculated by the following formula:

[0087]

[0088] Where: b is the width of the wet joint specimen; h is the height of the interface of the wet joint specimen; a s is the distance between the center of the tensile reinforcement in the wet joint and the edge of the tension zone; n is the ratio of the elastic modulus of the concrete and the reinforcement in the wet joint; A s This refers to the area of ​​the tensile reinforcement.

[0089] Calculate the equivalent moment of inertia I of the wet joint under the condition of interface cracking. cr At that time, assuming that the tensile zone concrete ceases to function after interface cracking, as shown in the attached... Figure 12 As shown. Based on the principle that the area moments of the compression zone and tension zone relative to the neutral axis are equal, the height x of the compression zone at the interface is... cr It can be calculated using the following formula:

[0090]

[0091] In the formula: A s The area of ​​the tension reinforcement is A (due to symmetrical reinforcement, the area of ​​the compression reinforcement is also A). s ).

[0092] The height x of the interface pressure zone is calculated according to formula (10). cr Subsequently, the equivalent moment of inertia I of the wet joint under interface cracking conditions... cr It can be calculated using the following formula:

[0093]

[0094] During normal use, the yield moment M at the interface is... y It can be calculated using formula (5);

[0095] During the yielding stage, the ultimate bending moment M at the interface is... u Based on the experimental results, calibration is performed, and the following is set:

[0096]

[0097] During the yielding stage, the rotational stiffness k3 of the interface is calibrated based on experimental results. (See attached diagram) Figure 13 As shown, the vertical force (P)-mid-span deflection relationship curve obtained from the experiment is expressed using the formula... The moment (M) at the wet joint interface is converted into a mid-span deflection curve. Then, the rotational stiffness k3 of the interface is made close to the yield moment M. y，test The subsequent curve has an approximate slope of k. 3，test .

[0098] Based on the results of material property tests (referencing GB / T50081-2002 "Standard for Test Methods of Mechanical Properties of Ordinary Concrete" and GB / T31387-2015 "Reactive Powder Concrete"), or referring to the values ​​in relevant specifications (such as "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362-2018)), the basic properties of concrete and steel reinforcement materials can be obtained. In this implementation case, the elastic modulus E of the wet joint UHPC material is... u =42100MPa, elastic modulus E of precast NSC material c =36500MPa, yield strength f of tensile steel reinforcement y =435MPa, interface height h=200mm, distance a between the center of the tensile reinforcement and the edge of the tension zone in the wet joint. s =36mm, area of ​​reinforcing steel bars in tension and compression zones (symmetrical reinforcement) A s =226.2mm2 The parameters of the macroscopic mechanical model can then be determined as shown in Table 1.

[0099] Table 1. Parameter values ​​for the macroscopic mechanical model of the wet joint interface.

[0100] <![CDATA[k1]]> kN·m / rad <![CDATA[6.55×10 4 ]]> <![CDATA[k2]]> kN·m / rad <![CDATA[7.05×10 3 ]]> <![CDATA[k3]]> kN·m / rad <![CDATA[1.2×10 2 ]]> <![CDATA[M cr ]]> kN·m 9.95 <![CDATA[M y ]]> kN·m 15.9 <![CDATA[M u ]]> kN·m 26.28

[0101] The finite element model created in the ABAUQS finite element software is shown in the attached figure. Figure 14 As shown. Since the experimental results (as mentioned above) show that the tensile reinforcement on the left side of the wet joint specimen did not yield during loading and the interface did not show obvious opening, the interface mechanical model was only established on the right side of the UHPC wet joint (Formula (1)). The NSC precast section and the UHPC wet joint in the wet joint specimen were simulated using two-dimensional beam elements. The longitudinal reinforcing bars were embedded in the beam section using the *rebar keyword.

[0102] A comparison between the vertical force-mid-span deflection curves calculated by the finite element model and the experimental results is attached. Figure 15 As shown, by appendix Figure 15 It can be seen that the macroscopic mechanical model of the interface in this invention can simulate the bending performance of wet joint specimens relatively accurately.

[0103] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for simulating the flexural performance of the interface between a cast-in-situ concrete joint and a bridge deck slab of a widened bridge, characterized in that, This includes designing a macroscopic mechanical model, which is divided into three stages: (1) The first stage is the elastic stage, which corresponds to the situation where no cracking occurs at the interface of the wet joint under bending moment; (2) The second stage is the normal use stage, which corresponds to the situation where the wet joint interface cracks under bending moment, but the tensile reinforcement does not yield. (3) The third stage is the yielding stage, which corresponds to the yielding of the tensile reinforcement in the wet joint; The macroscopic mechanical model is expressed as follows: ， In the formula: The bending moment borne by the interface; For the corner of the interface; , , These are the interface rotational stiffnesses for the elastic stage, normal use stage, and yield stage, respectively. The cracking moment of the interface; The yield moment of the interface; This refers to the cracked corner of the interface; For the yield angle of the interface; When the bending moment reaches the cracking bending moment at the wet joint interface At that time, the elastic phase ends; The interface rotational stiffness in the elastic phase Represented as: ， In the formula: The elastic modulus of the concrete material at the wet joint; The moment of inertia of the wet joint section; The span of the wet joint; The cracking moment of the interface Represented as: ， In the formula: The area moment of the portion of the cross-section above or below the centroidal axis of the wet joint about the centroidal axis; The bonding strength of the wet joint interface; When the bending moment reaches the yield bending moment at the wet joint interface At this time, the normal use phase ends; Interface rotational stiffness during normal use Represented as: ， In the formula: The equivalent moment of inertia of the wet joint section is calculated when the interface is not cracked. The moment of inertia of the wet joint section is calculated under the condition of interface cracking.

2. The method for simulating the flexural performance of the interface between the cast-in-place concrete joint and the bridge deck of a widened bridge according to claim 1, characterized in that, The yield moment of the interface Represented as: ， In the formula: The compressive strength of the bridge deck concrete material; The width of the wet concrete joint considered in the calculation; This refers to the height of the pressure zone at the wet joint interface; This refers to the effective height of the wet joint interface.

3. The method for simulating the flexural performance of the interface between the cast-in-place concrete joint and the bridge deck of a widened bridge according to claim 2, is characterized in that... The effective height of the wet joint interface Represented as: ， In the formula: The height of the wet joint interface; This is the distance between the center of the tensile reinforcement in the wet joint and the edge of the tension zone.

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