CN114254534A - Concrete constitutive model calculation method based on steel bar three-dimensional reinforcement effect - Google Patents

Concrete constitutive model calculation method based on steel bar three-dimensional reinforcement effect Download PDF

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CN114254534A
CN114254534A CN202111521882.2A CN202111521882A CN114254534A CN 114254534 A CN114254534 A CN 114254534A CN 202111521882 A CN202111521882 A CN 202111521882A CN 114254534 A CN114254534 A CN 114254534A
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李顺龙
崔洪涛
李忠龙
郭亚朋
王鑫
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Abstract

A concrete constitutive model calculation method based on a steel bar three-dimensional reinforcement effect relates to a modeling method for nonlinear damage of a reinforced concrete bridge. Acquiring the mechanical properties of the concrete and the reinforcing steel bar; establishing a single-axis stressed reinforced concrete cubic unit, decomposing the single-axis stressed reinforced concrete cubic unit into a one-dimensional axial stress unit and a two-dimensional normal stress unit, respectively calculating the reinforcement coefficient of the reinforced concrete and obtaining the elastic modulus; respectively correcting tensile and compressive stress-strain curves of the reinforced concrete cubic units stressed by the single shaft, and correcting damage evolution parameters to obtain corrected constitutive relation curves; the method is applied to establishing a three-dimensional entity nonlinear finite element model in a finite element, and calculating the plastic damage and the bearing capacity of the reinforced concrete structure. The reinforcement coefficient of the steel bar to the concrete is considered, and the corrected reinforced concrete constitutive model is provided, so that the ultimate bearing capacity of the actual bridge can be efficiently and accurately evaluated.

Description

Concrete constitutive model calculation method based on steel bar three-dimensional reinforcement effect
Technical Field
The invention relates to a modeling method for nonlinear damage of a reinforced concrete bridge, in particular to a concrete constitutive model calculation method based on a steel bar three-dimensional reinforcement effect, and belongs to the technical field of bridge engineering mechanical property analysis.
Background
The bridge, as a key component of modern traffic infrastructure, occupies an important strategic position in national and regional economic development. In recent years, more and more reinforced concrete bridges are built and enter a service state, so that the traffic and transportation efficiency of China is greatly improved, and the rapid increase of economy is promoted.
The mastering of the ultimate bearing capacity and safety margin of the bridge is a necessary condition before the bridge is put into use in a large scale and is an important precondition for ensuring the safe driving of vehicles. For the research of the safety performance of the bridge structure, the method widely adopted at present is a destructive experiment of a reduced scale test piece completed in a laboratory, but is limited by the randomness of the performance of the concrete material and the size effect of the structure, and the conclusion obtained through the reduced scale test piece in the laboratory is difficult to be directly applied to the safety performance evaluation of the actual bridge structure. In the experiment based on the actual bridge, whether a static loading mode or a dynamic loading mode is adopted, the emphasis is placed on researching whether the reinforced concrete bridge meets the design requirement in the operation period, if the ultimate bearing capacity and the safety margin of the bridge are to be accurately mastered, the destructive test based on the actual bridge is the most direct method, but the method is limited by high test cost, the safety of the field test is difficult to guarantee, and the like, and the research on the destructive test of the actual bridge is less at present.
In recent years, with the development of computer science and technology, numerical simulation analysis by using finite elements becomes an effective auxiliary means for researching the mechanical behavior of the reinforced concrete bridge. Researchers at home and abroad also improve the traditional simulation method in terms of unit types, constraint modes, material constitutive relations and the like, but still have some inevitable defects for the damage analysis of large reinforced concrete bridges: firstly, the common steel bar framework is complicated in structure, and steel bars in different positions and different arrangement modes are different in specification, so that finite element modeling is very complicated; secondly, after the concrete enters the plasticity stage, the stress instability phenomenon generated by the sharp decline of the stress-strain curve can greatly increase the convergence difficulty in the calculation process, and the calculation hardware and time cost can also be greatly improved. Therefore, a modeling method capable of efficiently and accurately calculating the nonlinear damage of the large-size reinforced concrete bridge is established, is used for evaluating the ultimate bearing capacity of the actual bridge, and is a difficult problem to be solved at present.
Disclosure of Invention
The invention provides a concrete constitutive model calculation method based on a steel bar three-dimensional reinforcement effect, which aims to solve the problems that the existing reinforced concrete constitutive model cannot be well suitable for simulating the nonlinear failure behavior of a large-volume reinforced concrete bridge structure, the modeling process is complex, and the calculation cost is extremely high.
In order to achieve the purpose, the invention adopts the following technical scheme: a concrete constitutive model calculation method based on a steel bar three-dimensional reinforcement effect comprises the following steps:
step 1: acquiring the mechanical properties of the concrete and the steel bar in the structure;
step 2: the method comprises the following steps of establishing a reinforced concrete cube unit stressed by a single shaft, taking concrete as a base material, taking reinforcing steel bars as an auxiliary reinforcing effect material, assuming that the reinforcing effect of the reinforcing steel bars is uniformly dispersed into the concrete to form a three-dimensional orthogonal unit, decomposing the three-dimensional orthogonal unit into a one-dimensional axial stress unit and a two-dimensional normal stress unit, respectively calculating the reinforcing coefficient of the reinforcing steel bars to the concrete, and obtaining the elastic modulus of the reinforced concrete cube unit stressed by the single shaft:
Figure BDA0003407805980000033
wherein, k is the three-dimensional reinforcing factor of the steel bar
κ＝κ1+κ2-1＝(α-1)es1+κ21/[(1-es2)κ21+es2]
α＝Es/EconIs the ratio of the modulus of elasticity of the steel bar to the concrete, kappa1Is a one-dimensional reinforcing coefficient, k2Is a two-dimensional reinforcement factor, κ21Reinforcement ratio for the reinforcement layer, es1Reinforcement ratio of one-dimensional axial force unit, es2The reinforcement ratio of the two-dimensional normal stress unit is obtained;
and step 3: correcting tensile and compressive stress-strain curves of the reinforced concrete cubic units stressed by the single shaft respectively, considering equation constraint conditions of tensile peak stress and reinforcing steel bar yield stress when correcting the tensile stress-strain curve, considering constraint of reinforcing steel bars on the concrete units when correcting the compressive stress-strain curve, and correcting damage evolution parameters to obtain a corrected constitutive relation curve on the basis of concrete structure design specifications (GB50010-2010) on the assumption that reinforcing steel bar damage does not occur and the reinforcing steel bars and the concrete do not slide relatively in the concrete cracking process:
the evolution parameters of the tensile damage are calculated according to the following formula:
Figure BDA0003407805980000031
the evolution parameters of the compression damage are calculated according to the following formula:
Figure BDA0003407805980000034
tensile stress sigmatCalculated according to the following formula:
Figure BDA0003407805980000032
compressive stress sigmacCalculated according to the following formula:
Figure BDA0003407805980000041
Figure BDA0003407805980000042
in the formula E0The initial elastic modulus of plain concrete is 0.075 rhos/ds，ρsReinforcement ratio for reinforcing bars, dsIs the diameter of the steel bar, ftFor tensile peak stress,. epsilontTensile strain, epsilon, of reinforced concrete cubic unit stressed for a single axiscCompressive strain, f, of a single-axis stressed reinforced concrete cubic unitc'cTo constrain the peak compressive stress of the concrete,. epsilonccIs fc'cCorresponding compressive strain, EsecCore concrete elastic modulus;
and 4, step 4: and applying the corrected constitutive relation curve to a finite element, establishing a three-dimensional entity nonlinear finite element model, and calculating the plastic damage and the bearing capacity of the reinforced concrete structure.
Compared with the prior art, the invention has the beneficial effects that: aiming at the problems of high cost of computing hardware and time and difficult convergence of the computing process when a reinforced concrete constitutive model used in a finite element program is used for computing a large-sized reinforced concrete bridge at present, the modeling simulation method capable of efficiently and accurately carrying out nonlinear damage on the large-sized reinforced concrete bridge is provided, the concrete is used as a base material, the steel bars are used as auxiliary reinforcing effect materials, a three-dimensional orthogonal unit is established and decomposed into a one-dimensional axial force bearing unit and a two-dimensional normal force bearing unit, the reinforcing coefficient of the steel bars to the concrete is considered, meanwhile, a corrected reinforced concrete constitutive model is provided, the ultimate bearing capacity of the reinforced concrete bridge can be accurately evaluated only by means of the existing computer hardware level, the time cost and the waste of hardware resources are effectively controlled, and the safety condition of the actual bridge service state can be known.
Drawings
FIG. 1 is an exploded schematic view of a single-axis stressed reinforced concrete cubic unit built in accordance with the present invention;
FIG. 2(a) is a diagram showing a real object of a box girder as a test object in the example of the present invention;
FIG. 2(b) is a vertical sectional layout view of FIG. 2 (a);
FIG. 2(c) is a cross-sectional layout view of FIG. 2 (a);
FIG. 3 is a schematic illustration of a test loading position in an embodiment of the present invention;
FIG. 4 is a schematic diagram of a sensor arrangement in an embodiment of the invention;
FIG. 5 is a constitutive graph of an embodiment of the invention;
FIG. 6 is a finite element model diagram of a prestressed concrete box girder according to an embodiment of the present invention;
FIG. 7(a) is a deflection versus load curve analyzed in an embodiment of the present invention;
FIG. 7(b) is a graph of beam end displacement versus load analyzed in an embodiment of the present invention;
FIG. 8 is a graph comparing results of a cross-mid-bed strain test and finite element calculations in an embodiment of the present invention;
FIG. 9(a) is a graph comparing finite element simulated crack propagation to observed cracks from field testing, where K is 1.6;
FIG. 9(b) is a graph comparing finite element simulated crack propagation to observed cracks from field tests, where K is 1.8;
fig. 9(c) is a graph comparing finite element simulated crack propagation to the crack observed in the field test, where K is 2.0.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
A concrete constitutive model calculation method based on a steel bar three-dimensional reinforcement effect comprises the following steps:
step 1: the mechanical properties of the concrete and the steel bars in the structure are obtained, and the method can be based on the mechanical property test of the test piece or the actual structure detection and the like.
Specifically, the process for testing the mechanical properties of the concrete and the steel bar comprises the following steps:
step 1.1, performing an axial compression strength test on a concrete sample with a cubic length of 150mm according to specification standard of concrete physical mechanical property test method (GB/T50081-2019), performing a static compression elastic modulus test on the concrete sample with a prism with a side length of 150mm x 300mm, and detecting the mechanical property of the concrete material by using methods such as a rebound test on an actual structure when test conditions are not met;
step 1.2, according to the specification "part 1 of the metal material tensile test: the room temperature test method (GB/T228.1-2010) is used for testing the mechanical properties of the material of the steel bar test piece, and when the test condition is not met, the yield strength and the elastic modulus of the steel bar can be obtained according to the design specification (TB10092-2017) of the concrete structure of the railway bridge and culvert.
Step 2: the method comprises the steps of establishing a single-shaft stressed reinforced concrete cubic unit, taking concrete as a base material, taking reinforcing steel bars as an auxiliary reinforcing effect material, assuming that the reinforcing effect of the reinforcing steel bars is uniformly dispersed into the concrete to form a three-dimensional orthogonal unit, decomposing the three-dimensional orthogonal unit into a one-dimensional axial stress unit and a two-dimensional normal stress unit, respectively calculating the reinforcing coefficient of the reinforcing steel bars to the concrete, and obtaining the elastic modulus of the single-shaft stressed reinforced concrete cubic unit.
Specifically, the process for establishing the reinforced concrete cubic unit stressed by the single shaft comprises the following steps:
step 2.1, a steel bar framework is formed by longitudinal steel bars and transverse stirrups in the structure, the steel bars can be considered to exist in concrete in a three-dimensional orthogonal mode, the concrete is used as a base material, the steel bars are used as an auxiliary reinforcing effect material, a single-shaft stressed reinforced concrete cubic unit is defined, and a three-dimensional orthogonal unit is formed by assuming that one of three orthogonal steel bars is in a stress direction (z direction) and the normal direction of a plane (xy plane) formed by the other two steel bars is the same as the stress direction;
2.2, assuming that the reinforcing steel bars are uniformly distributed and stressed in the concrete, dispersing the reinforcing effect of the reinforcing steel bars into the concrete, and decomposing the three-dimensional orthogonal unit into a one-dimensional axial stress unit and a two-dimensional normal stress unit based on a homogenization theory, as shown in fig. 1;
step 2.3, assuming that the steel bars and the concrete in the one-dimensional axial stress unit conform to the deformation coordination hypothesis, the elastic modulus of the one-dimensional axial stress unit after the steel bars play a reinforcing effect can be expressed as:
E1＝(1-es1)Econ+es1Es＝[(1-es1)+es1α]Econ＝κ1Econ
in the formula, E1Is the elastic modulus of a one-dimensional axial force unit, es1The reinforcement ratio of one-dimensional axial stress unit, alpha ═ Es/EconIs the ratio of the modulus of elasticity of the steel bar to the concrete, kappa1The reinforcement coefficient of the one-dimensional steel bar;
and 2.4, dispersing the steel bars of the two-dimensional normal stress unit to a reinforced surface, forming a part of the two-dimensional normal stress unit in a reinforced surface form, wherein the reinforced surface and the concrete layer have the same stress state according to the equal stress hypothesis, and the elastic modulus of the two-dimensional normal stress unit can be expressed as follows:
E2＝κ21/[(1-es2)κ21+es2]Econ＝κ2Econ
in the formula, E2Is the elastic modulus of a two-dimensional normal force-bearing unit, es2Reinforcement ratio, κ, for a two-dimensional normal force-bearing unit2Is a two-dimensional reinforcement factor, κ21Distributing reinforcement rate for the reinforcement layer;
and 2.5, superposing the effects of the decomposed one-dimensional axial stress unit and the two-dimensional normal stress unit, wherein the three-dimensional reinforcing steel bar strengthening coefficient is calculated according to the following formula because the concrete effect is repeatedly considered in the calculation process:
κ＝κ1+κ2-1＝(α-1)es1+κ21/[(1-es2)κ21+es2]
the elastic modulus calculation formula of the reinforced concrete cubic unit stressed by the single shaft is as follows:
Figure BDA0003407805980000071
and step 3: correcting tensile and compressive stress-strain curves of the reinforced concrete cubic units stressed by the single shaft respectively, considering equation constraint conditions of tensile peak stress and reinforcing steel bar yield stress when correcting the tensile stress-strain curve, considering constraint of the reinforcing steel bars on the concrete units when correcting the compressive stress-strain curve, and correcting damage evolution parameters to obtain a corrected constitutive relation curve on the premise that no reinforcing steel bar damage occurs and no relative slip occurs between the reinforcing steel bars and the concrete in a concrete cracking process based on concrete structure design specifications (GB 50010-2010).
Specifically, the calculation process of the constitutive relation curve of the uniaxially stressed reinforced concrete cubic unit after correction is as follows:
step 3.1, the failure mechanism of the reinforced concrete mainly shows tensile cracking and compressive fracture, when the concrete is damaged, the damage degree is expressed by a damage coefficient, and the concrete uniaxial tensile effective stress and the concrete uniaxial compressive effective stress are respectively as follows:
Figure BDA0003407805980000081
Figure BDA0003407805980000082
wherein t and c represent the tensile and compressive states of the concrete, respectively,
Figure BDA0003407805980000083
and
Figure BDA0003407805980000084
for equivalent plastic strain, E0Is the initial modulus of elasticity of plain concrete, dtAnd dcThe concrete damage evolution parameters are selected, the value range is 0-1, 0 represents a nondestructive state, and 1 represents complete damage;
and 3.2, for the single-shaft tensioned reinforced concrete cubic unit, if the reinforcing steel bars and the concrete are linearly superposed according to the reinforcing steel bar distribution ratio, the descending section of the stress-strain curve still has obvious tension instability phenomenon, and the nonlinear analysis of the large-volume prestressed concrete box girder still cannot be performedtCalculated according to the following formula:
Figure BDA0003407805980000085
for the reinforced concrete cubic unit with the single shaft pressed, the transverse stirrups provide lateral constraint force for concrete, and the compression resistance of the whole structure is greatly improvedcCalculated according to the following formula:
Figure BDA0003407805980000091
Figure BDA0003407805980000092
where θ is 0.075 ρs/ds，ρsReinforcement ratio for reinforcing bars, dsIs the diameter of the steel bar, ftFor tensile peak stress,. epsilontIs a single shaftStressed reinforced concrete cubic unit tensile strain, epsiloncCompressive strain, f, of a single-axis stressed reinforced concrete cubic unitc'cTo constrain the peak compressive stress of the concrete,. epsilonccIs fc'cCorresponding compressive strain, EsecCore concrete elastic modulus;
step 3.3, combining concrete structure design specifications (GB50010-2010) and the allowance equivalence principle, and assuming that tensile damage of the steel bars is not considered in the cracking process of the concrete, calculating tensile damage evolution parameters of the reinforced concrete cubic unit under the single-shaft stress according to the following formula:
Figure BDA0003407805980000093
step 3.4, considering the constraint action of the transverse stirrups on the concrete and the reinforcement action of the reinforcing steel bars on the concrete units, the concrete is not damaged in the compression and crushing process, and the compression damage evolution parameters of the reinforced concrete cubic unit under the single-shaft stress are calculated according to the following formula:
Figure BDA0003407805980000094
and 4, step 4: and applying the corrected constitutive relation curve to a finite element, establishing a three-dimensional entity nonlinear finite element model, and calculating the plastic damage and the bearing capacity of the reinforced concrete structure.
Specifically, the process of establishing the three-dimensional entity nonlinear finite element model is as follows:
step 4.1, establishing a three-dimensional nonlinear finite element model by using ABAQUS, simulating a single-shaft stressed reinforced concrete cubic unit by using a three-dimensional eight-node linear reduction unit (C3D8R), and simulating a prestressed steel strand by using a three-dimensional truss unit (T3D2) when the structure is a prestressed system, wherein the material performance is based on actual test data and a double-fold model is adopted;
and 4.2, applying the corrected constitutive relation curve obtained based on the steps to an ABAQUS finite element software CDP model, and applying load or displacement constraint to the built reinforced concrete beam to calculate the structural plastic damage and the bearing capacity.
Examples
The present embodiment is illustrated by combining the results of the foot scale prestressed concrete box girder failure test and the ABAQUS finite element model numerical simulation analysis.
The test object is a single-box single-chamber prestressed concrete simply-supported box girder, the total length of the box girder is 32.6m, the calculated span is 31.3m, the height of the girder is 3.25m, the width of the bridge deck is 12.6m, the box girder object is shown in fig. 2(a), the longitudinal section design drawing of the box girder is shown in fig. 2(b), the cross section design drawing is shown in fig. 2(C), the central line of a support is positioned below a web plate of a bottom plate at the end of the girder and is 0.65m away from the end of the girder, the transverse distance of the central lines of two supports at the end of the girder is 4.4m, the box girder material adopts concrete with the strength grade of C50 and reinforcing steel bars with the model of HRB400, the reinforcement rate of longitudinal reinforcing steel bars at the cross-middle section is e10.54%, transverse stirrup reinforcement ratio e2＝16％。
The box girder loading device comprises a box girder loading device, a box girder reaction frame loading device, a box girder web plate loading device and a box girder loading device, wherein the box girder loading device is used for loading the box girder, 10 loading positions are arranged at a top plate above the box girder web plate, a loading coefficient K is used for representing a loading grade in a test (the loading coefficient K is the ratio of bending moment borne by a girder body span in the loading test to design bending moment), the loading grade of a failure test is far beyond the K of a conventional bending test to be 1.2 grade, the loading grade of the test is set to be 2.55 grade, and the bearing capacity limit state and the safety margin of the box girder are researched.
The test loading position and the single top load are shown in fig. 3, the sensor arrangement scheme is shown in fig. 4, strain sensors and displacement sensors (including a vertical displacement meter and a longitudinal displacement meter) are all arranged below a box girder bottom plate, the strain sensors are arranged below a box girder central line and a web plate between a midspan and 1/4 and used for measuring the strain of the box girder bottom plate before cracking, and the displacement sensors are arranged at the midspan, 1/4 midspan and the beam end of a sliding support and used for respectively testing midspan deflection, 1/4 midspan deflection and beam end longitudinal displacement.
Step 1: according to the specification of Standard for testing method of physical and mechanical Properties of concrete (GB/T50081-2019), the material properties of the concrete sample are performedTest, average compressive Strength σ of 28d curing age test specimensc66.2MPa, modulus of elasticity Econ47.2GPa, the performance parameters of the steel bar material are determined according to part 1 of a metal material tensile test: tensile test is carried out on HRB400 steel bars by a room temperature test method (GB/T228.1-2010), and the elastic modulus Es＝2.0×105MPa, yield strength Ry473.37MPa, peak stress Rm＝648.55MPa。
Step 2: the cross-section longitudinal steel bars are used as the steel bars of the one-dimensional axial stress unit, the transverse stirrups are used as the stress steel bars of the two-dimensional normal unit, and the calculation results of the three-dimensional steel bar reinforcement coefficient and the elasticity modulus of the single-axis stressed reinforced concrete cubic unit are as follows:
κ＝(α-1)es1+κ21/[(1-es2)κ21+es2]＝1.090
E＝κEcon＝1.090×47200MPa＝51441MPa。
and step 3: based on the laboratory mechanical property test data of the concrete member material and the modified reinforced concrete constitutive model provided by the invention, a tensile stress-strain curve, a tensile damage evolution parameter-strain curve, a compressive stress-strain curve and a compressive damage evolution parameter-strain curve are respectively calculated, as shown in fig. 5.
And 4, step 4: based on actual test data of material performance and the constitutive relation of the reinforced concrete, a three-dimensional entity nonlinear finite element model is established in ABAQUS, a reinforced concrete cube unit stressed by a single shaft is simulated by a three-dimensional eight-node linear reduction unit (C3D8R), the size of a grid is about 20cm, the grid of the cross section of a box girder is further refined by considering that the C3D8R unit only comprises one integral point at the center of the unit, so that the hourglass problem of the C3D8R unit in the calculation process is solved, a prestressed steel strand is simulated by a three-dimensional truss unit (T3D2), and the finite element model component and the grid of the prestressed concrete box girder are divided as shown in figure 6 by adopting a double-fold line model and a prestressed concrete box girder finite element model component based on the actual test data of material performance.
And analyzing the mid-span deflection, 1/4 mid-span deflection and beam end longitudinal displacement based on the field failure test result and the finite element model analysis result. The relation curve of deflection and load is shown in fig. 7(a), the integral deformation can be divided into a linear elastic stage and a plastic stage, and the maximum value of mid-span deflection is close to 140 mm; the beam end displacement versus load curve is shown in fig. 7(b), and when loaded to the maximum load, the beam end displacement reaches 73 mm. The field test result is well matched with the finite element model calculation result, and the accuracy of the reinforced concrete constitutive model provided by the invention is verified. For example, as shown in fig. 8, the results of the midspan base plate strain test and the finite element calculation are approximately linear in relation to each other before the structure cracks, the test values of the sensors at the center line of the box girder and the lower edge of the web plate show an obvious shear hysteresis effect, and the actually measured strain is well matched with the results of the finite element calculation. In the process of numerical simulation by using ABAQUS, concrete cracking can be indirectly represented by using concrete plastic damage, and the concrete is generally considered to be in a cracking state when the concrete plastic damage value (SDEG) reaches above 0.5. The finite element model calculation of the reinforced concrete damage and the field test observation of the cracking condition of each load level are shown in fig. 9, and the crack development conditions are approximately the same, which also shows that the reinforced concrete constitutive model provided by the invention has better effect in simulating the crack development.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (5)

1. A concrete constitutive model calculation method based on a steel bar three-dimensional reinforcement effect is characterized by comprising the following steps: the calculation method comprises the following steps:
step 1: acquiring the mechanical properties of the concrete and the steel bar in the structure;
step 2: the method comprises the following steps of establishing a reinforced concrete cube unit stressed by a single shaft, taking concrete as a base material, taking reinforcing steel bars as an auxiliary reinforcing effect material, assuming that the reinforcing effect of the reinforcing steel bars is uniformly dispersed into the concrete to form a three-dimensional orthogonal unit, decomposing the three-dimensional orthogonal unit into a one-dimensional axial stress unit and a two-dimensional normal stress unit, respectively calculating the reinforcing coefficient of the reinforcing steel bars to the concrete, and obtaining the elastic modulus of the reinforced concrete cube unit stressed by the single shaft:
Figure FDA0003407805970000012
wherein, k is the three-dimensional reinforcing factor of the steel bar
κ＝κ1+κ2-1＝(α-1)es1+κ21/[(1-es2)κ21+es2]
α＝Es/EconIs the ratio of the modulus of elasticity of the steel bar to the concrete, kappa1Is a one-dimensional reinforcing coefficient, k2Is a two-dimensional reinforcement factor, κ21Reinforcement ratio for the reinforcement layer, es1Reinforcement ratio of one-dimensional axial force unit, es2The reinforcement ratio of the two-dimensional normal stress unit is obtained;
and step 3: correcting tensile and compressive stress-strain curves of the reinforced concrete cubic units stressed by the single shaft respectively, considering equation constraint conditions of tensile peak stress and reinforcing steel bar yield stress when correcting the tensile stress-strain curve, considering constraint of reinforcing steel bars on the concrete units when correcting the compressive stress-strain curve, and correcting damage evolution parameters to obtain a corrected constitutive relation curve on the basis of concrete structure design specifications (GB50010-2010) on the assumption that reinforcing steel bar damage does not occur and the reinforcing steel bars and the concrete do not slide relatively in the concrete cracking process:
the evolution parameters of the tensile damage are calculated according to the following formula:
Figure FDA0003407805970000011
the evolution parameters of the compression damage are calculated according to the following formula:
Figure FDA0003407805970000021
tensile stress sigmatCalculated according to the following formula:
Figure FDA0003407805970000022
compressive stress sigmacCalculated according to the following formula:
Figure FDA0003407805970000023
Figure FDA0003407805970000024
in the formula E0The initial elastic modulus of plain concrete is 0.075 rhos/ds，ρsReinforcement ratio for reinforcing bars, dsIs the diameter of the steel bar, ftFor tensile peak stress,. epsilontTensile strain, epsilon, of reinforced concrete cubic unit stressed for a single axiscCompressive strain, f, of a single-axis stressed reinforced concrete cubic unitc'cTo constrain the peak compressive stress of the concrete,. epsilonccIs fc'cCorresponding pressure responseChange, EsecCore concrete elastic modulus;
and 4, step 4: and applying the corrected constitutive relation curve to a finite element, establishing a three-dimensional entity nonlinear finite element model, and calculating the plastic damage and the bearing capacity of the reinforced concrete structure.
2. The concrete constitutive model calculation method based on the steel bar three-dimensional reinforcement effect according to claim 1, wherein: in the step 1, the concrete is subjected to an axial compression strength test according to the specification "test method standard for physical and mechanical properties of concrete" (GB/T50081-2019), and simultaneously a static compression elastic modulus test is performed, or a resilience test is performed on an actual structure to detect the mechanical properties of the concrete, and the reinforcing steel bars are subjected to a metal material tensile test part 1: the room temperature test method (GB/T228.1-2010) is used for testing the mechanical properties of materials, or the yield strength and the elastic modulus of the steel bars are taken according to the design specifications of the concrete structures of the bridges and culverts of railways (TB 10092-2017).
3. The concrete constitutive model calculation method based on the steel bar three-dimensional reinforcement effect according to claim 1, wherein: the process for establishing the reinforced concrete cubic unit stressed by the single shaft in the step 2 is as follows:
step 2.1, a steel bar framework is formed by longitudinal steel bars and transverse stirrups in the structure, the steel bars are considered to exist in the concrete in a three-dimensional orthogonal mode, and a three-dimensional orthogonal unit is formed on the assumption that one of three orthogonal steel bars is in the stress direction, and the normal direction of a plane formed by the other two steel bars is the same as the stress direction;
2.2, decomposing the three-dimensional orthogonal unit into a one-dimensional axial stress unit and a two-dimensional normal stress unit based on a homogenization theory;
step 2.3, assuming that the steel bars and the concrete in the one-dimensional axial stress unit conform to the deformation coordination hypothesis, the elastic modulus of the one-dimensional axial stress unit after the steel bars play a reinforcing effect can be expressed as:
E1＝(1-es1)Econ+es1Es＝[(1-es1)+es1α]Econ＝κ1Econ
in the formula, E1Is the elastic modulus of a one-dimensional axial force unit, es1The reinforcement ratio of one-dimensional axial stress unit, alpha ═ Es/EconIs the ratio of the modulus of elasticity of the steel bar to the concrete, kappa1The reinforcement coefficient of the one-dimensional steel bar;
and 2.4, dispersing the steel bars of the two-dimensional normal force-bearing unit to a reinforced surface, forming a part of the two-dimensional normal force-bearing unit in a reinforced surface form, and according to the equal stress hypothesis, expressing the elastic modulus of the two-dimensional normal force-bearing unit as follows:
E2＝κ21/[(1-es2)κ21+es2]Econ＝κ2Econ
in the formula, E2Is the elastic modulus of a two-dimensional normal force-bearing unit, es2Reinforcement ratio, κ, for a two-dimensional normal force-bearing unit2Is a two-dimensional reinforcement factor, κ21Distributing reinforcement rate for the reinforcement layer;
step 2.5, superposing the decomposed one-dimensional axial stress unit and two-dimensional normal stress unit effects, and calculating the three-dimensional reinforcing steel bar reinforcing coefficient according to the following formula:
κ＝κ1+κ2-1＝(α-1)es1+κ21/[(1-es2)κ21+es2]
the elastic modulus calculation formula of the reinforced concrete cubic unit stressed by the single shaft is as follows:
Figure FDA0003407805970000048
4. the concrete constitutive model calculation method based on the steel bar three-dimensional reinforcement effect according to claim 3, wherein: the calculation process of the corrected constitutive relation curve of the reinforced concrete cubic unit stressed by the single shaft in the step 3 is as follows:
step 3.1, the failure mechanism of the reinforced concrete mainly shows tensile cracking and compressive fracture, when the concrete is damaged, the damage degree is expressed by a damage coefficient, and the concrete uniaxial tensile effective stress and the concrete uniaxial compressive effective stress are respectively as follows:
Figure FDA0003407805970000041
Figure FDA0003407805970000042
wherein t and c represent the tensile and compressive states of the concrete, respectively,
Figure FDA0003407805970000043
and
Figure FDA0003407805970000044
for equivalent plastic strain, E0Is the initial modulus of elasticity of plain concrete, dtAnd dcThe concrete damage evolution parameters are selected, the value range is 0-1, 0 represents a nondestructive state, and 1 represents complete damage;
and 3.2, providing a corrected reinforced concrete constitutive model, and considering the yield stress of the steel bar based on a tensile experiment for the reinforced concrete cubic unit with a single shaft in tension, wherein the tensile stress sigma of the reinforced concrete cubic unittCalculated according to the following formula:
Figure FDA0003407805970000045
for a uniaxially stressed reinforced concrete cubic unit, the compressive stress σ thereofcCalculated according to the following formula:
Figure FDA0003407805970000046
Figure FDA0003407805970000047
where θ is 0.075 ρs/ds，ρsReinforcement ratio for reinforcing bars, dsIs the diameter of the steel bar, ftFor tensile peak stress,. epsilontTensile strain, epsilon, of reinforced concrete cubic unit stressed for a single axiscCompressive strain, f, of a single-axis stressed reinforced concrete cubic unitc'cTo constrain the peak compressive stress of the concrete,. epsilonccIs fc'cCorresponding compressive strain, EsecCore concrete elastic modulus;
step 3.3, combining concrete structure design specifications (GB50010-2010) and the allowance equivalence principle, and assuming that the tensile damage of the steel bars is not considered in the cracking process of the concrete, calculating the evolution parameters of the tensile damage of the reinforced concrete cubic unit under the single-shaft stress according to the following formula:
Figure FDA0003407805970000051
step 3.4, considering the constraint action of the transverse stirrups on the concrete and the reinforcement action of the reinforcing steel bars on the concrete units, the concrete is not damaged in the compression and crushing process, and the compression damage evolution parameters of the reinforced concrete cubic unit under the single-shaft stress are calculated according to the following formula:
Figure FDA0003407805970000052
5. the concrete constitutive model calculation method based on the steel bar three-dimensional reinforcement effect according to claim 4, wherein: the process of establishing the three-dimensional entity nonlinear finite element model in the step 4 is as follows:
step 4.1, establishing a three-dimensional nonlinear finite element model by using ABAQUS, simulating a reinforced concrete cubic unit stressed by a single shaft by using a three-dimensional eight-node linear reduction unit C3D8R, and simulating a prestressed steel strand by using a three-dimensional truss unit T3D2 when the structure is a prestressed system, wherein the material performance is based on actual test data and a double-fold model is adopted;
and 4.2, applying the corrected constitutive relation curve obtained based on the steps to an ABAQUS finite element software CDP model, and applying load or displacement constraint to the built reinforced concrete beam to calculate the structural plastic damage and the bearing capacity.
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