CN112858039A - Inverse analysis method for steel fiber concrete stress-crack width constitutive relation - Google Patents

Inverse analysis method for steel fiber concrete stress-crack width constitutive relation Download PDF

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CN112858039A
CN112858039A CN202110123269.9A CN202110123269A CN112858039A CN 112858039 A CN112858039 A CN 112858039A CN 202110123269 A CN202110123269 A CN 202110123269A CN 112858039 A CN112858039 A CN 112858039A
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reinforced concrete
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高丹盈
丁冲
庞育阳
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Zhengzhou University
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/20—Investigating strength properties of solid materials by application of mechanical stress by applying steady bending forces
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract

The invention belongs to the technical field of constitutive relation of building materials; in particular to a reverse analysis method of the steel fiber concrete stress-crack width constitutive relation, which comprises the following steps: selecting a steel fiber concrete component to be tested, carrying out a three-point loading bending test, and drawing a test curve of load and crack opening displacement of the steel fiber concrete component to be tested; obtaining the initial crack load of the steel fiber concrete member on the test curve to obtain the initial crack bending strength of the steel fiber concrete member to be tested; establishing a calculation model of a standardized corner, a standardized bending moment, an external load, crack opening displacement caused by elastic deformation, crack opening displacement caused by initial crack geometric deformation and crack opening total displacement of the steel fiber concrete member to be measured in the bending process according to related parameters; and obtaining a constitutive relation curve of the stress and the crack opening displacement of the steel fiber concrete member through inverse analysis and calculation. The invention can provide theoretical support for the structural design of the steel fiber concrete.

Description

Inverse analysis method for steel fiber concrete stress-crack width constitutive relation
Technical Field
The invention belongs to the technical field of constitutive relation of building materials; in particular to a reverse analysis method of the constitutive relation of the stress-crack width of the steel fiber concrete.
Background
Steel Fiber Reinforced Concrete (FRC) is a building material made by blending short steel fibers distributed disorderly into brittle and easily cracked concrete. Due to its excellent mechanical properties, steel fiber concrete has been widely used in the fields of civil engineering and the like. The steel fiber penetrating through the crack surface of the concrete has strong bridging effect, so that one of the most important characteristics of the steel fiber concrete is excellent post-crack performance. The stress-crack width constitutive relation reflects the function of the steel fiber after the concrete structure is cracked, and is an important parameter in the design of the steel fiber concrete structure, so that the method for obtaining the steel fiber concrete tensile stress-crack constitutive relation by using a proper testing method has important theoretical significance and practical value, and is very necessary to provide a reverse analysis method capable of solving the steel fiber concrete stress-crack constitutive relation.
Disclosure of Invention
The invention aims to provide an inverse analysis method for the stress-crack width constitutive relation of steel fiber concrete, which simplifies the calculation amount of the inverse analysis method, can compile a programmed flow of inverse analysis operation, and can provide theoretical support for the structural design of the steel fiber concrete, wherein the obtained bending stress-crack width constitutive relation of the steel fiber concrete member is closer to an objective condition.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a reverse analysis method of a steel fiber concrete stress-crack width constitutive relation, which comprises the following steps:
step 1, selecting a steel fiber concrete member to be tested, carrying out a three-point loading bending test, and drawing a test curve of load and crack opening displacement of the steel fiber concrete member to be tested;
step 2, obtaining the initial crack load of the steel fiber concrete member on the test curve according to the load of the steel fiber concrete member to be tested and the crack opening displacement test curve, and obtaining the initial crack bending strength of the steel fiber concrete member to be tested;
step 3, according to the width b, the height H, the crack width w and the initial crack bending strength f of the steel fiber concrete member to be detectedtHeight h of non-opening of midspan section, depth a of cut0A net span L, a total crack development height d, a relative crack development height alpha and a nonlinear hinge length s, and establishing a bending process of the steel fiber concrete member to be measuredNormalized rotation angle theta ofiStandardized bending moment mui(theta), external load Fana,iCrack opening displacement w caused by elastic deformationana,i,eCrack opening displacement w caused by initial crack geometric deformationana,i,gFracture opening total displacement CMODana,iThe computational model of (2);
the bending process of the steel fiber concrete member to be tested is divided into a pre-cracking stage, a virtual crack development stage and a real-virtual crack common development stage; in the pre-cracking stage, the normalized bending moment muiThe calculation formula of (θ) is as follows:
μi(θ) ═ θ, (0 < θ < 1) (equation 1);
in the virtual crack development stage, the normalized turning angle thetaiAnd a standardized bending moment muiThe calculation formula of (θ) is as follows:
Figure BDA0002922821380000021
Figure BDA0002922821380000022
the normalized rotation angle theta is in a real-virtual crack co-development stageiAnd a standardized bending moment muiThe calculation formula of (θ) is as follows:
Figure BDA0002922821380000023
Figure BDA0002922821380000024
the external load Fana,iThe calculation formula of (a) is as follows:
Figure BDA0002922821380000025
the crack opening displacement w caused by the elastic deformationana,i,eThe calculation formula of (a) is as follows:
Figure BDA0002922821380000031
crack opening displacement w caused by the initial crack geometric deformationana,i,gThe calculation formula of (a) is as follows:
Figure BDA0002922821380000032
the fracture opening total displacement CMODana,iThe calculation formula of (a) is as follows:
CMODana,i＝wi+wana,i,e+wana,i,g(formula 9) of the reaction mixture,
wherein n is the number of bus segments in the stress-crack constitutive relation curve of the steel fiber concrete member, i is the ith line segment in the stress-crack width constitutive relation curve of the steel fiber concrete member, and i is 1,2, …, n; a isiAnd biRespectively represents the slope and intercept of the ith line segment in the constitutive relation curve of the stress-crack width of the steel fiber concrete member,
Figure BDA0002922821380000033
withe crack width w corresponding to the tail end of the ith line segment in the constitutive relation curve of the steel fiber concrete stress-crack width componenti-1The crack width corresponding to the end of the i-1 line segment or the crack width corresponding to the starting point of the i line segment in the constitutive relation curve of the steel fiber concrete stress-crack width member is w when no crack appears0＝0；
Figure BDA0002922821380000034
a0＝H-h；
Figure BDA0002922821380000035
V1(x)＝0.197+17.816x-107.63x2+338.21x3-494.26x4+298.86x5；
Step 4, let i equal to 1, assume the crack width w1Then b is0＝b 11 is ═ 1; suppose a1According to the formula in step 3, obtaining the normalized rotation angle theta1And a standardized bending moment mu1(θ), and the external load F of the inverse analysis process when i is 1 is obtainedana,1Crack opening displacement w caused by elastic deformationana,1,eCrack opening displacement w caused by initial crack geometric deformationana,1,gFracture opening total displacement CMODana,1；
Step 5, reading w from the load and crack opening displacement test curve of the steel fiber concrete member to be tested1Test load of time Fexp,1Judging the test load Fexp,1External load F of inverse analysis processana,1Whether the error precision of (a) meets a set threshold value, if the error precision of (b) is less than the set threshold value, a1The value meets the requirement, if the value is larger than the set threshold value, a is adjusted1Taking values, and repeating the step 4;
step 6, repeating the steps 4 and 5 to obtain Fana,1,Fana,2,……,Fana,nAnd CMODana,1,CMODana,2,……,CMODana,nDrawing a load and crack opening displacement inverse analysis curve of the steel fiber concrete member;
step 7, according to a1,a2,……,an，b1,b2,……,bnAnd obtaining a constitutive relation curve of the stress of the steel fiber concrete member and the crack opening displacement.
Preferably, the initial crack bending strength f of the steel fiber concrete member to be testedtThe calculation formula of (a) is as follows:
Figure BDA0002922821380000041
wherein, FcrThe initial crack load of the steel fiber concrete member to be detected is measured; l is steel fiber concrete structure that awaits measuringA net span of the piece; b is the width of the steel fiber concrete member to be measured; h is the height of the non-opening of the cross section of the steel fiber concrete member to be measured.
Preferably, the constitutive relation model of the stress and crack opening displacement of the steel fiber concrete member is as follows:
σ＝ft(bi-aiw)，wi-1≤w≤wii is 1,2, … …, n (equation 11).
Preferably, the set threshold in step 5 is 3%.
Compared with the prior art, the invention has the beneficial effects that:
the invention simplifies the operation amount of the inverse analysis method based on the nonlinear hinge model and the expression of the analytical solution of the standardized corner and the standardized bending moment of the whole bending process of the steel fiber concrete member, can compile the programmed flow of inverse analysis operation, and the bending stress-crack width constitutive relation of the obtained steel fiber concrete member is closer to the objective condition, thereby providing theoretical support for the structural design of the steel fiber concrete member. The inverse analysis method can be popularized and applied to the relation between the multi-linear stress and the crack width, and is suitable for the flat steel fibers, the 3D, 4D and 5D end hook steel fibers and other types of fibers; the method is suitable for notched beams and non-notched beams; it is suitable for common concrete, fiber concrete, regenerated concrete, high performance concrete, self-compacting concrete, etc.
Drawings
FIG. 1 is a flow chart of the inverse analysis method of the steel fiber concrete stress-crack width constitutive relation.
Fig. 2 is a test curve and a back analysis curve of the load and crack opening displacement of the 4D steel fiber reinforced concrete beam in the first embodiment of the present invention.
Fig. 3 is a constitutive relation curve of the stress and crack opening displacement of the 4D steel fiber concrete in the first embodiment of the invention.
Fig. 4 is a test curve and a back analysis curve of the load and crack opening displacement of the 5D steel fiber reinforced concrete beam in the second embodiment of the present invention.
Fig. 5 is a constitutive relation curve of 5D steel fiber concrete stress and crack opening displacement in the second embodiment of the present invention.
Detailed Description
The following examples are intended to illustrate the invention, but are not intended to limit the scope of the invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art. The test methods in the following examples are conventional methods unless otherwise specified.
Example one
In the embodiment, the 4D steel fiber doped concrete beam is used for carrying out inverse analysis operation on the nonlinear stress-crack width constitutive relation. The steel fiber type was 4D steel fiber, and the volume content was 1.0% (representing 1 m)378.5kg of steel fiber is added into the concrete), and the test piece size of the steel fiber concrete beam is as follows: length x width x height 550mm x 150mm, i.e. b 150mm, height H150 mm, and the depth a of the cut in the middle of the test piece0The net span L is 500mm at 25mm, and the strength of the concrete is C60. The three-point loading flexural test device adopts a 500kN fatigue testing machine, the acquisition frequency is 5Hz, and a clamp-type extensometer is used for measuring the crack opening displacement (CMOD) of the steel fiber concrete flexural beam in the whole process. Displacement control is adopted, when the opening displacement of the crack mouth is less than 0.1mm, the loading rate is 0.05 mm/min; when the opening displacement of the crack mouth is more than 0.1mm, the loading rate is 0.2 mm/min. The relevant parameters are as follows: the length s of the nonlinear hinge is 75 mm; the height h of the non-opening of the midspan section is 125 mm; the elastic modulus E of the concrete is 38000 MPa.
It is worth noting that the corners of the steel fiber concrete members are calculated during the calculation
Figure BDA0002922821380000051
The conversion equation from the normalized rotation angle θ is as follows:
Figure BDA0002922821380000052
the conversion formula of the bending moment M and the standard bending moment mu (theta) borne by the steel fiber concrete member is as follows:
Figure BDA0002922821380000061
reference is made to the flow chart of the reverse analysis method of the present invention shown in fig. 1. The test curve of the load and crack opening displacement CMOD of the sample subjected to the three-point loading bending test is shown in FIG. 2. Reading the initial crack load F of the point with obvious turning of the slope in the initial stage from the load-CMOD curve graphcrThe initial crack bending strength f of the steel fiber concrete was calculated by the formula (10) under 12.5kNt＝4MPa。
Let i equal to 1 and set w1＝0.05mm，b0＝b1＝1，w 00. Assuming a small value a1Calculating the normalized rotation angle theta of the virtual crack development stage1(equation 2) normalized bending moment μ1(theta) (equation 3), external load Fana,1(equation 6) crack opening displacement w caused by elastic deformationana,1,e(equation 7) crack opening displacement w caused by initial crack geometryana,1,g(equation 8) and fracture propagation Total Displacement CMODana,1(equation 9). Reading w from the load-CMOD test curve1Test load F at 0.05mmexp,1And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased1Until the error precision meets the requirement. The result of the calculation a1＝2.83。
The error calculation formula is as follows:
Figure BDA0002922821380000062
let i equal 2, set w2＝0.1mm，a1＝2.83，b 11. Assuming a small value a2Calculating the normalized rotation angle theta of the virtual crack development stage2(equation 2) normalized bending moment μ2(theta) (equation 3), external load Fana,2(equation 6) crack opening displacement w caused by elastic deformationana,2,e(equation 7) crack opening displacement w caused by initial crack geometryana,2,g(equation 8) and fracture propagation Total Displacement CMODana,2(equation 9). Reading w from the load-CMOD experimental curve2Test load F when 0.1mmexp,2And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased2Until the error precision meets the requirement. The result of the calculation a2When b is 1.66, b is obtained2＝0.94。
Let i equal to 3, set w3When the thickness is 0.2mm, a can be obtained3＝-0.31，b3＝0.74。
Let i be 4,5, … …,32, and let wiThe corresponding a can be obtainediAnd biThe specific process is not shown.
Let i equal 33, set w33＝3.2mm，a1＝2.83，b1＝1，a2＝1.66，b2＝0.94，a3＝-0.31，b3＝0.74，……，a32＝0.10，b321.11, assume a smaller value a33Calculating the normalized rotation angle theta of the virtual crack development stage33(equation 2) normalized bending moment μ33(theta) (equation 3), external load Fana,33(equation 6) crack opening displacement w caused by elastic deformationana,33,e(equation 7) crack opening displacement w caused by initial crack geometryana,33,g(equation 8) and fracture propagation Total Displacement CMODana,33(equation 9). Reading w from the load-CMOD experimental curve33Test load F at 3.2mmexp,33And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased33Until the error precision meets the requirement. The result of the calculation a33When b is 0.10, b is obtained33＝1.11。
From the above inverse analysis operation procedure, F is obtainedana,1,Fana,2,……,Fana,nAnd CMODana,1,CMODana,2,……,CMODana,nDrawing a load and crack opening displacement inverse analysis curve of the steel fiber concrete beam, as shown in FIG. 2; by contrast, Fana-CMODanaAnd Fexp-CMODexpCurve finding, inverse analysisThe results are well matched with the test results.
According to the obtained a1＝2.83，b1＝1，a2＝1.66，b2＝0.94，a3＝-0.31，b3＝0.74，……，a32＝0.10，b32＝1.11，a33＝0.10，b331.11, obtaining an constitutive relation curve of the 4D steel fiber concrete stress and the crack opening displacement according to the constitutive relation model of the steel fiber concrete stress and the crack opening displacement (formula 11), as shown in fig. 3.
Example two
In the embodiment, the inverse analysis operation of the nonlinear stress-crack width constitutive relation is carried out on the 5D steel fiber doped concrete beam. The steel fiber type was 5D steel fiber, and the volume content was 1.0% (representing 1 m)378.5kg of steel fiber is added into the concrete), and the test piece size of the steel fiber concrete beam is as follows: length x width x height 550mm x 150mm, i.e. b 150mm, height H150 mm, and the depth a of the cut in the middle of the test piece0The net span L is 500mm at 25mm, and the strength of the concrete is C60. The three-point loading flexural beam test device adopts a 500kN fatigue test machine, the acquisition frequency is 5Hz, and a clamp type extensometer is used for measuring the crack opening displacement (CMOD) of the steel fiber concrete flexural beam in the whole process. Displacement control is adopted, when the opening displacement of the crack mouth is less than 0.1mm, the loading rate is 0.05 mm/min; when the opening displacement of the crack mouth is more than 0.1mm, the loading rate is 0.2 mm/min. The relevant parameters are as follows: the length s of the nonlinear hinge is 75 mm; the height h of the non-opening of the midspan section is 125 mm; the elastic modulus E of the concrete is 38000 MPa.
Reference is made to the flow chart of the reverse analysis method of the present invention shown in fig. 1. The test curve of the load and crack opening displacement CMOD of the sample subjected to the three-point loading bending test is shown in FIG. 4. Reading the initial crack load F of the point with obvious turning of the slope in the initial stage from the load-CMOD curve graphcrThe initial crack bending strength f of the steel fiber concrete was calculated by the formula (10) under 12.5kNt＝4MPa。
Let i equal to 1 and set w1＝0.05mm，b0＝b1＝1，w 00. Assuming a small value a1Calculating virtual fracturesNormalized angle of rotation theta of development stage1(equation 2) normalized bending moment μ1(theta) (equation 3), external load Fana,1(equation 6) crack opening displacement w caused by elastic deformationana,1,e(equation 7) crack opening displacement w caused by initial crack geometryana,1,g(equation 8) and fracture propagation Total Displacement CMODana,1(equation 9). Reading w from the load-CMOD test curve1Test load F at 0.05mmexp,1And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased1Until the error precision meets the requirement. The result of the calculation a1＝3.45。
Let i equal 2, set w2＝0.1mm，a1＝2.83，b 11. Assuming a small value a2Calculating the normalized rotation angle theta of the virtual crack development stage2(equation 2) normalized bending moment μ2(theta) (equation 3), external load Fana,2(equation 6) crack opening displacement w caused by elastic deformationana,2,e(equation 7) crack opening displacement w caused by initial crack geometryana,2,g(equation 8) and fracture propagation Total Displacement CMODana,2(equation 9). Reading w from the load-CMOD experimental curve2Test load F when 0.1mmexp,2And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased2Until the error precision meets the requirement. The result of the calculation a21.12, find b2＝0.88。
Let i equal to 3, set w3When the thickness is 0.2mm, a can be obtained3＝-0.77，b3＝0.69。
Let i be 4,5, … …,32, and let wiThen, a can be obtainediAnd biThe specific process is not shown.
Let i equal 33, set w33＝3.2mm，a1＝3.45，b1＝1，a2＝1.12，b2＝0.88，a3＝-0.77，b3＝0.69，……，a32＝0.096，b321.22, assume a smaller value a33Calculating the virtual crack growth orderNormalized angle of rotation theta of the segments33(equation 2) normalized bending moment μ33(theta) (equation 3), external load Fana,33(equation 6) crack opening displacement w caused by elastic deformationana,33,e(equation 7) crack opening displacement w caused by initial crack geometryana,33,g(equation 8) and fracture propagation Total Displacement CMODana,33(equation 9). Reading w from the load-CMOD experimental curve33Test load F at 3.2mmexp,33And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased33Until the error precision meets the requirement. The result of the calculation a33When b is 0.097, b is obtained33＝1.23。
From the above inverse analysis operation procedure, F is obtainedana,1,Fana,2,……,Fana,nAnd CMODana,1,CMODana,2,……,CMODana,nDrawing a load and crack opening displacement inverse analysis curve of the steel fiber concrete beam, as shown in FIG. 4; by contrast, Fana-CMODanaAnd Fexp-CMODexpThe curve shows that the inverse analysis result is well matched with the test result.
According to the obtained a1＝3.45，b1＝1，a2＝1.12，b2＝0.88，a3＝-0.77，b3＝0.69，……，a32＝0.096，b32＝1.22，a33＝0.097，b331.23, obtaining an constitutive relation curve of the stress and the crack opening displacement of the 5D steel fiber concrete according to the constitutive relation model of the stress and the crack opening displacement of the steel fiber concrete (formula 11), as shown in fig. 5.
It should be noted that, a boundary point between the common development stage of the virtual crack and the real-virtual crack is about 15mm, and the actual crack width in the bending process of the 4D steel fiber reinforced concrete beam in the first embodiment and the 5D steel fiber reinforced concrete beam in the second embodiment is not large, and cannot be developed to the common development stage of the real-virtual crack, so that both the two stages are in the virtual crack development stage.
It is worth noting that example one and example 2 are in a reverse analyzerCalculating a in the process of calculating the constitutive relation between the stress of the steel fiber concrete beam and the crack opening displacementiAnd biWhen i ≧ 2, assume wiWhen the inverse analysis method of the invention is popularized to the constitutive relation of stress and crack opening displacement of other steel fiber concrete members, the w can be adjusted according to the actual situation and the precision requirementiAnd carrying out assumed value taking.
The above-mentioned embodiments are merely preferred embodiments of the present invention, which are merely illustrative and not restrictive, and it should be understood that other embodiments may be easily made by those skilled in the art by replacing or changing the technical contents disclosed in the specification, and therefore, all changes and modifications that are made on the principle of the present invention should be included in the scope of the claims of the present invention.

Claims (4)

1.一种钢纤维混凝土应力-裂缝宽度本构关系的反分析方法，其特征在于，包括以下步骤：1. a kind of inverse analysis method of steel fiber reinforced concrete stress-crack width constitutive relation, is characterized in that, comprises the following steps: 步骤1、选取待测钢纤维混凝土构件，进行三点加载受弯试验，绘制待测钢纤维混凝土构件的荷载与裂缝张开位移试验曲线；Step 1. Select the steel fiber reinforced concrete member to be tested, carry out a three-point loading and bending test, and draw the load and crack opening displacement test curve of the steel fiber reinforced concrete member to be tested; 步骤2、根据待测钢纤维混凝土构件的荷载与裂缝张开位移试验曲线，获得该试验曲线上钢纤维混凝土构件的初裂荷载，得到待测钢纤维混凝土构件的初裂抗弯强度；Step 2, according to the test curve of the load and crack opening displacement of the steel fiber reinforced concrete member to be tested, obtain the initial crack load of the steel fiber reinforced concrete member on the test curve, and obtain the initial crack flexural strength of the steel fiber reinforced concrete member to be tested; 步骤3、根据待测钢纤维混凝土构件的宽度b、高度H、裂缝宽度w、初裂抗弯强度ft、跨中截面未开口高度h、切口深度a0、净跨距L、裂缝发展总高度d、裂缝发展相对高度α、非线性铰长度s，建立待测钢纤维混凝土构件受弯过程的标准化转角θi、标准化弯矩μi(θ)、外载荷Fana,i、弹性形变引起的裂缝张开位移wana,i,e、初始裂缝几何形变引起的裂缝张开位移wana,i,g、裂缝张开总位移CMODana,i的计算模型；Step 3. According to the width b, height H, crack width w, initial crack flexural strength ft, unopened height h of mid-span section, notch depth a 0 , net span L, total crack development Height d, relative height α of crack development, nonlinear hinge length s, establish standardized rotation angle θ i , standardized bending moment μ i (θ), external load F ana,i , elastic deformation caused by the bending process of the steel fiber reinforced concrete member to be tested The calculation model of the crack opening displacement w ana,i,e , the crack opening displacement w ana,i,g caused by the initial fracture geometric deformation, and the total crack opening displacement CMOD ana,i ; 所述待测钢纤维混凝土构件受弯过程分为开裂前阶段、虚拟裂缝发展阶段和真实-虚拟裂缝共同发展阶段；在开裂前阶段，所述标准化弯矩μi(θ)的计算公式如下：The bending process of the steel fiber reinforced concrete member to be tested is divided into a pre-cracking stage, a virtual crack development stage and a real-virtual crack joint development stage; in the pre-cracking stage, the calculation formula of the standardized bending moment μ i (θ) is as follows: μi(θ)＝θ，(0＜θ＜1)；μ i (θ)=θ, (0<θ<1); 在虚拟裂缝发展阶段，所述标准化转角θi和标准化弯矩μi(θ)的计算公式如下：In the virtual crack development stage, the calculation formulas of the normalized rotation angle θ i and the normalized bending moment μ i (θ) are as follows:
Figure FDA0002922821370000011
Figure FDA0002922821370000011
Figure FDA0002922821370000012
Figure FDA0002922821370000012
 在真实-虚拟裂缝共同发展阶段，所述标准化转角θi和标准化弯矩μi(θ)的计算公式如下：In the joint development stage of real-virtual cracks, the calculation formulas of the normalized rotation angle θ i and normalized bending moment μ i (θ) are as follows:
Figure FDA0002922821370000021
Figure FDA0002922821370000021
Figure FDA0002922821370000022
Figure FDA0002922821370000022
 所述外载荷Fana,i的计算公式如下：The calculation formula of the external load F ana,i is as follows:
Figure FDA0002922821370000023
Figure FDA0002922821370000023
 所述弹性形变引起的裂缝张开位移wana,i,e的计算公式如下：The calculation formula of the crack opening displacement w ana,i,e caused by the elastic deformation is as follows:
Figure FDA0002922821370000024
Figure FDA0002922821370000024
 所述初始裂缝几何形变引起的裂缝张开位移wana,i,g的计算公式如下：The calculation formula of the crack opening displacement w ana,i,g caused by the geometric deformation of the initial crack is as follows:
Figure FDA0002922821370000025
Figure FDA0002922821370000025
 所述裂缝张开总位移CMODana,i的计算公式如下：The calculation formula of the total crack opening displacement CMOD ana,i is as follows: CMODana,i＝wi+wana,i,e+wana,i,g，CMOD ana,i =w i +w ana,i,e +w ana,i,g , 其中，n为钢纤维混凝土构件应力-裂缝本构关系曲线中的总线段数，i为钢纤维混凝土构件应力-裂缝宽度本构关系曲线中的第i条线段，i＝1,2,…,n；ai和bi分别表示钢纤维混凝土构件应力-裂缝宽度本构关系曲线中第i条线段的斜率和截距，
Figure FDA0002922821370000026
wi为钢纤维混凝土应力-裂缝宽度构件本构关系曲线中第i条线段末端对应的裂缝宽度，wi-1为钢纤维混凝土应力-裂缝宽度构件本构关系曲线中第i-1条线段末端对应的裂缝宽度或第i条线段起始点对应的裂缝宽度，裂缝未出现时w0＝0；
Figure FDA0002922821370000031
a0＝H-h；
Figure FDA0002922821370000032
V1(x)＝0.197+17.816x-107.63x2+338.21x3-494.26x4+298.86x5；Among them, n is the number of bus segments in the stress-crack constitutive relationship curve of the steel fiber reinforced concrete member, i is the ith line segment in the stress-crack width constitutive relationship curve of the steel fiber reinforced concrete member, i=1,2,...,n ; a i and b i represent the slope and intercept of the i-th line segment in the stress-crack width constitutive relation curve of the steel fiber reinforced concrete member, respectively,
Figure FDA0002922821370000026
w i is the crack width corresponding to the end of the i-th line segment in the steel fiber reinforced concrete stress-crack width component constitutive relationship curve, w i-1 is the i-1 line segment in the steel fiber reinforced concrete stress-crack width component constitutive relationship curve The crack width corresponding to the end or the crack width corresponding to the starting point of the i-th line segment, w 0 =0 when the crack does not appear;
Figure FDA0002922821370000031
a 0 =Hh;
Figure FDA0002922821370000032
V 1 (x)=0.197+17.816x-107.63x 2 +338.21x 3 -494.26x 4 +298.86x 5 ; 步骤4、令i＝1，假设裂缝宽度w1，则b0＝b1＝1；假设一个a1的数值，依据步骤3中公式得到标准化转角θ1和标准化弯矩μ1(θ)，进而得到i＝1时反分析过程的外载荷Fana,1、弹性形变引起的裂缝张开位移wana,1,e、初始裂缝几何形变引起的裂缝张开位移wana,1,g、裂缝张开总位移CMODana,1；Step 4. Let i=1, assuming the crack width w 1 , then b 0 =b 1 =1; assuming a value of a 1 , according to the formula in step 3, the normalized rotation angle θ 1 and the normalized bending moment μ 1 (θ) are obtained, Then, when i=1, the external load F ana,1 , the crack opening displacement w ana,1,e caused by the elastic deformation, the crack opening displacement w ana,1,g caused by the initial crack geometric deformation, Open total displacement CMOD ana,1 ; 步骤5、从待测钢纤维混凝土构件的荷载与裂缝张开位移试验曲线中读取w1时的试验载荷Fexp,1，判断试验载荷Fexp,1与反分析过程的外载荷Fana,1的误差精度是否满足设定阈值，若小于设定阈值，则a1取值满足要求，若大于设定阈值，则调整a1取值，重复步骤4；Step 5. Read the test load F exp,1 at w 1 from the test curve of the load and crack opening displacement of the steel fiber reinforced concrete member to be tested, and determine the test load F exp,1 and the external load F ana of the reverse analysis process, Whether the error accuracy of 1 meets the set threshold, if it is less than the set threshold, the value of a 1 meets the requirements; if it is greater than the set threshold, adjust the value of a 1 , and repeat step 4; 步骤6、重复步骤4和5，得到Fana,1,Fana,2,……,Fana,n和CMODana,1,CMODana,2,……,CMODana,n，绘制钢纤维混凝土构件的荷载与裂缝张开位移反分析曲线；Step 6. Repeat steps 4 and 5 to get F ana,1 ,F ana,2 ,...,F ana,n and CMOD ana,1 ,CMOD ana,2 ,...,CMOD ana,n , draw SFRC Inverse analysis curve of component load and crack opening displacement; 步骤7、根据a1,a2,……,an，b1,b2,……,bn和钢纤维混凝土构件应力与裂缝张开位移本构关系模型，得出该钢纤维混凝土构件应力与裂缝张开位移的本构关系曲线。Step 7. According to a 1 , a 2 , ..., a n , b 1 , b 2 , ..., bn and the constitutive relationship model between the stress and crack opening displacement of the steel fiber reinforced concrete member, the steel fiber reinforced concrete member is obtained Constitutive relationship between stress and crack opening displacement. 2.根据权利要求1所述的反分析方法，其特征在于，所述待测钢纤维混凝土构件的初裂抗弯强度ft的计算公式如下：2. inverse analysis method according to claim 1, is characterized in that, the calculation formula of the initial crack flexural strength f t of described steel fiber reinforced concrete member to be measured is as follows:
Figure FDA0002922821370000033
Figure FDA0002922821370000033
 其中，Fcr为待测钢纤维混凝土构件的初裂荷载；L为待测钢纤维混凝土构件的净跨距；b为待测钢纤维混凝土构件的宽度；h为待测钢纤维混凝土构件的跨中截面未开口高度。Among them, F cr is the initial crack load of the steel fiber reinforced concrete member to be tested; L is the net span of the steel fiber reinforced concrete member to be tested; b is the width of the steel fiber reinforced concrete member to be tested; h is the span of the steel fiber reinforced concrete member to be tested. Middle section unopened height. 3.根据权利要求1所述的反分析方法，其特征在于，所述钢纤维混凝土构件应力与裂缝张开位移本构关系模型如下：3. inverse analysis method according to claim 1, is characterized in that, described steel fiber reinforced concrete member stress and crack opening displacement constitutive relation model is as follows: σ＝ft(bi-aiw)，wi-1≤w≤wi,i＝1，2，……,n。σ=f t (b i -a i w), w i-1 ≤ w ≤ w i , i=1, 2, ..., n. 4.根据权利要求1所述的反分析方法，其特征在于，步骤5中所述设定阈值为3％。4 . The inverse analysis method according to claim 1 , wherein the set threshold value in step 5 is 3%. 5 .
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