A method for constructing a conventional triaxial constitutive model of hybrid steel fiber self-compacting concrete

Abstract

The invention relates to concrete, and provides a method for constructing a conventional triaxial constitutive model of a hybrid steel fiber self-compacting concrete. The method obtains expressions of uniaxial peak stress and uniaxial peak strain on skeleton volume fraction and expressions of triaxial peak stress / uniaxial peak stress, triaxial peak strain / uniaxial peak strain on confining pressure / uniaxial peak stress through uniaxial compression test and conventional triaxial compression test, and uses ductility correction coefficient to correct constitutive curve determining factors in the existing Popovics triaxial constitutive model, and establishes a modified Popovics triaxial constitutive model suitable for hybrid steel fiber self-compacting concrete according to the ductility correction coefficient. The model takes into account the phenomenon of post-peak ductility fluctuation increase and decrease of the conventional triaxial stress-strain curve with the increase of confining pressure, and uses the skeleton volume fraction as a parameter. The model has the advantages of simple model, few parameters, and reliable calculation results, and can provide a reference for the design and application of hybrid steel fiber self-compacting concrete.

Description

Technical Field

[0001] The invention relates to the technical field of building materials, in particular to concrete, and in particular to a method for constructing a conventional triaxial constitutive model of hybrid steel fiber self-compacting concrete. Background Art

[0002] Shield tunnels mainly use prefabricated reinforced concrete segments, which are densely reinforced and bulky. Due to the self-leveling properties of the matrix and the bridging effect of the hybrid steel fibers, the application of hybrid steel fiber self-compacting concrete in shield segments can provide a new solution to problems such as poor segment concrete pouring quality and segment cracking and damage. It is worth noting that the large jack eccentricity during the construction stage and the squeezing effect of the stratum and adjacent segments during the service stage will cause the segments to be locally in a complex three-dimensional stress state, which is very likely to cause cracking, damage, and collapse of the segments. Therefore, in order to fit the working state of segment concrete in actual projects, it is particularly critical to explore the multi-axial constitutive behavior and constitutive model of hybrid steel fiber self-compacting concrete. Based on the multiaxial constitutive model, the mechanical indicators of concrete such as multiaxial peak stress, multiaxial peak strain and multiaxial toughness can be quantitatively analyzed, and the mechanical constitutive behavior of concrete before and after the peak under multiaxial load can be comprehensively described, providing a theoretical basis for the production and preparation of shield tunnel segments and the calculation of bearing capacity. In addition, combining the multiaxial constitutive model with the numerical finite element modeling method is also a powerful means to promote the application and development of new hybrid steel fiber self-compacting concrete segments. This method can reveal the macroscopic and microscopic mechanical properties of hybrid steel fiber self-compacting concrete shield segments under complex loads, providing theoretical guidance at the structural level for the engineering application of new concrete segments.

[0003] In summary, in view of the fact that the shield segments are basically in a complex stress state of compression, bending and shear during assembly and service, if the hybrid steel fiber self-compacting concrete is to be applied as a new type of matrix material for the shield segments, it is necessary to determine the conventional triaxial constitutive model of the hybrid steel fiber self-compacting concrete. The existing conventional triaxial constitutive models, such as the Binici model, the Attard model and the Montoya model, are only applicable to ordinary concrete. The inventors found that the conventional triaxial constitutive curve of the hybrid steel fiber self-compacting concrete has a fluctuating change in toughness (how fast the post-peak decline) with the increase of confining pressure, and the above-mentioned model has limitations in the definition of the residual stress-strain of the post-peak decline section of the conventional triaxial constitutive curve, and cannot consider the local ductility change of post-peak toughness with confining pressure, and cannot be flexibly applied to other types of concrete. In addition, the existing conventional triaxial constitutive model does not consider the key variable of the skeleton volume fraction. The skeleton (steel fiber + aggregate) is the material with the largest proportion in concrete. It not only directly determines the mechanical properties of concrete, but also affects the amount of cement, an expensive material, and thus determines the economic performance of concrete preparation. Therefore, it is necessary to incorporate the skeleton volume fraction as a key variable into the conventional triaxial constitutive model.

[0004] In summary, with the increasing application of hybrid steel fiber self-compacting concrete in large-scale building, tunnel and bridge construction, proposing a reasonable and accurate method for constructing a conventional triaxial constitutive model of hybrid steel fiber self-compacting concrete is a key technical problem that needs to be solved urgently. Summary of the invention

[0005] The purpose of the present invention is to provide a conventional triaxial constitutive model construction method for hybrid steel fiber self-compacting concrete, so as to solve the problem that there is no constitutive model suitable for hybrid steel fiber self-compacting concrete in the prior art, other existing constitutive models are not applicable, and the existing models cannot consider the volume fraction of concrete aggregate-steel fiber solid skeleton Impact issues.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for constructing a conventional triaxial constitutive model of hybrid steel fiber self-compacting concrete comprises the following steps:

[0008] S1. According to the total volume content of steel fiber and different skeleton volume fractions, several standard specimens of hybrid steel fiber self-compacting concrete were prepared, and uniaxial compression test (σ2=σ3=0) and conventional triaxial compression test with different confining pressures (σ2=σ3≠0) were carried out respectively. The stress-strain curves of uniaxial compression test and conventional triaxial compression test were obtained, and the corresponding peak stress and peak strain were determined; the peak stress includes the uniaxial peak stress f c , triaxial peak stress f cc, the peak strain includes the uniaxial peak strain ε c , triaxial peak strain ε cc ;

[0009] S2, uniaxial peak stress f obtained according to S1 c and uniaxial peak strain ε c , and the uniaxial peak stress f c About the skeleton volume fraction Functional expression of uniaxial peak strain ε c About the skeleton volume fraction Function expression of ;

[0010] S3, triaxial peak stress f obtained according to S1 cc , triaxial peak strain ε cc And the uniaxial peak stress f obtained by S2 c , uniaxial peak strain ε c The expression of triaxial peak stress / uniaxial peak stress f is obtained by nonlinear regression analysis. cc / f c Confining pressure / uniaxial peak stress σ3 / f c The function expression of triaxial peak strain / uniaxial peak strain ε is obtained by fitting. cc / ε c Confining pressure / uniaxial peak stress σ3 / f c Function expression of ;

[0011] S4. According to the changing characteristics of the conventional triaxial stress-strain curve, the ductility correction factor K is proposed. r The constitutive curve determining factor r in the existing Popovics triaxial constitutive model is modified, and the ductility correction factor K is obtained by regression analysis. r Confining pressure / uniaxial peak stress σ3 / f c Expression of

[0012] S5. According to the ductility correction factor K r The modified constitutive curve determining factor r is obtained * , according to the modified constitutive curve, the factor r is determined * And the triaxial peak stress / uniaxial peak stress f obtained by S3 cc / f c , triaxial peak strain / uniaxial peak strain ε cc / ε c , a modified Popovics triaxial constitutive model suitable for hybrid steel fiber self-compacting concrete is established.

[0013] It should be noted that in S1, the total volume content of steel fiber is 0-1.5%, preferably 1%. When the steel fiber content relative to the total volume of the skeleton is 1%, the skeleton is the most densely packed; the skeleton volume fraction ranges from 58% to 62%, and at least 3 different skeleton volume fractions are selected; the confining pressure is 0-30% of the standard compressive strength of concrete, and at least 5 different confining pressures are selected. A confining pressure of 0 indicates a uniaxial compression test.

[0014] It should be noted that in S2, the inventors found that the uniaxial peak stress f c , uniaxial peak strain ε c and skeleton volume fraction There is a good linear relationship between them; therefore, the uniaxial peak stress f c About the skeleton volume fraction Functional expression of uniaxial peak strain ε c About the skeleton volume fraction The functional expression of is fitted by linear regression analysis according to formula (2.1) and (2.2):

[0015]

[0016]

[0017] Where: f c is the peak stress of the uniaxial compression test; ε c is the peak strain of the uniaxial compression test; is the skeleton volume fraction; s0 and s1 are the uniaxial peak stress f c The fitting parameters are s2 and s3, and the uniaxial peak strain ε c The fitting parameters of .

[0018] It should be noted that in S3, the triaxial peak stress / uniaxial peak stress f cc / f c Confining pressure / uniaxial peak stress σ3 / f c The functional expression of is obtained by fitting according to formula (3.1) using nonlinear regression analysis:

[0019]

[0020] Where: f cc / f c is triaxial peak stress / uniaxial peak stress; σ3 / f c is the confining pressure / uniaxial peak stress; a0 and a1 are the triaxial peak stress / uniaxial peak stress f cc / f c The fitting parameters of formula (3.1) are power functions.

[0021] Among them, a0 and a1 are determined according to formula (3.2):

[0022]

[0023] Where: s4, s5 are the volume fractions of a0 with respect to the skeleton The fitting parameters of a1 are as follows; s6 and s7 are the skeleton volume fractions of a1 The fitting parameters of .

[0024] It should be noted that in S3, triaxial peak strain / uniaxial peak strain ε cc / ε c Confining pressure / uniaxial peak stress σ3 / f c The functional expression of is obtained by fitting according to formula (3.3) using nonlinear regression analysis:

[0025]

[0026] Where: ε cc / ε c is triaxial peak strain / uniaxial peak strain; b i (i=0,1,2,3) is the triaxial peak strain / uniaxial peak strain ε cc / ε c The fitting parameter; e is the natural logarithm; the function form of formula (3.3) is the GaussAmp function;

[0027] Among them, b i Determine according to formula (3.4):

[0028]

[0029] Where: m i 、n i for b i About the skeleton volume fraction The fitting parameters of .

[0030] It should be noted that in S4, the inventors found that the conventional triaxial stress-strain curve of the hybrid steel fiber self-compacting concrete under the action of gradually increasing confining pressure will show a post-peak ductility fluctuation increase and decrease phenomenon. Therefore, the constitutive curve determining factor r value in the existing Popovics triaxial constitutive model is corrected to take ductility into account, that is, the r value before and after the peak is multiplied by a ductility correction parameter K r , including the pre-peak ductility correction factor K r1 , post-peak ductility correction factor K r2 The inventors use a sine function to characterize K r1 , K r2 With σ3 / f c The fluctuation relationship between the increase and decrease ofr (including pre-peak ductility correction parameter K r1 , post-peak ductility correction parameter K r2 ) About confining pressure / uniaxial peak stress σ3 / f c The expression of is obtained by fitting according to formula (4.1) using nonlinear regression analysis:

[0031]

[0032] Where: K r is the ductility correction factor; K r1 K is the pre-peak ductility correction factor; r2 is the queen ductility correction coefficient; σ3 is the confining pressure of the conventional triaxial test; d j K r1 , K r2 The fitting parameters of K are j = 0, 1, 2, ..., 7, that is, d0, d1, d2, d3 are K r1 The fitting parameters of K are d4, d5, d6, and d7. r2 The fitting parameters of formula (4.1) are sinusoidal functions.

[0033] Among them, d j Determine according to formula (4.2):

[0034]

[0035] Where: k j , l j is d i About the skeleton volume fraction The fitting parameters of .

[0036] It should be noted that in S5, according to the ductility correction factor K r (including pre-peak ductility correction parameter K r1 , post-peak ductility correction parameter K r2 ), the modified constitutive curve determines the factor r * Determine according to formula (5.1) and (5.2):

[0037]

[0038]

[0039] Where: r * is the determining factor of the modified constitutive curve; r is the determining factor of the constitutive curve; E c is the uniaxial compression elastic modulus;

[0040] Among them, E c It is obtained by elastic modulus test or determined by formula (5.3):

[0041]

[0042] It should be noted that in S5, the factor r is determined according to the modified constitutive curve. * And S3 obtained f cc / f c , ε cc / ε c The modified Popovics triaxial constitutive model applicable to hybrid steel fiber self-compacting concrete is established according to formula (5.4):

[0043]

[0044] Where: σ is the triaxial stress under conventional triaxial compression state, ε is the triaxial strain under conventional triaxial compression state.

[0045] Compared with the prior art, the present invention has the following beneficial technical effects:

[0046] Based on the conventional triaxial constitutive behavior of hybrid steel fiber self-compacting concrete, there is a phenomenon of fluctuating increase and decrease of post-peak ductility with increasing confining pressure. In this paper, the constitutive curve determining factor r in the Popovics model is corrected by considering ductility. By establishing the pre-peak and post-peak ductility correction coefficients K r1 , K r2 And multiply it by the original r value to get the modified determining factor r considering ductility * . In addition, considering that the parameter of skeleton volume fraction not only determines the mechanical properties of concrete, but also affects the economic performance of concrete, for this reason, the present invention also incorporates the skeleton volume fraction into the conventional triaxial constitutive model, thereby establishing a new conventional triaxial constitutive model suitable for the new material of hybrid steel fiber self-compacting concrete that takes into account confining pressure, ductility fluctuation changes and skeleton volume fraction. The model is simple to use and requires fewer parameters. It only needs to determine the skeleton volume fraction and the uniaxial compression peak stress-strain value to calculate the constitutive curve under conventional triaxial compression conditions. The calculated results are close to the measured results, which can provide a reference for the design and analysis of hybrid steel fiber self-compacting concrete and has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is the stress-strain curve of the conventional triaxial compression test of the hybrid steel fiber self-compacting concrete sample; among them, Figure (a) is The test curve of The test curve of The test curve.

[0048] Figure 2 is the uniaxial peak stress f c , uniaxial peak strain ε cand skeleton volume fraction The fitting curve of

[0049] (a) is f c and The fitting curve of ε is shown in Figure (b). c and The fitting curve of .

[0050] Figure 3 is the triaxial peak stress / uniaxial peak stress f cc / f c , triaxial peak strain / uniaxial peak strain ε cc / ε c and confining pressure / uniaxial peak stress σ3 / f c The fitting curve of f cc / f c and σ3 / f c The fitting curve of ε is shown in Figure (b). cc / ε c and σ3 / f c The fitting curve of .

[0051] Figure 4 is the triaxial peak stress / uniaxial peak stress f cc / f c , triaxial peak strain / uniaxial peak strain ε cc / ε c The fitting parameters of the skeleton volume fraction The fitting curve of f cc / f c The fitting parameters a0 and a1 are about The fitting curve of ε is shown in Figure (b). cc / ε c Fitting parameter b i (i=0,1,2,3) About The fitting curve of .

[0052] Figure 5 is the area specific ductility T ar Curve showing the change of confining pressure in conventional triaxial test.

[0053] Figure 6 K r1 K is the pre-peak ductility correction factor; r2 is the queen ductility correction factor and the confining pressure / uniaxial peak stress σ3 / f c The fitting curve of The fitting curve when The fitting curve of time (c) is The fitting curve of .

[0054] Figure 7 K is the pre-peak ductility correction factor r1 And the post-peak ductility correction factor K r2 The fitting parameters of the skeleton volume fraction The fitting curve of K r1 The fitting parameters are about The fitting curve of K r2 The fitting parameters are about The fitting curve of .

[0055] Figure 8 It is a comparison chart of the conventional triaxial compression test results with a confining pressure of 14 MPa and the calculated values ​​of the conventional triaxial constitutive model; among them, Figure (a) is a comparison chart of specimens 1-14, Figure (b) is a comparison chart of specimens 2-14, and Figure (c) is a comparison chart of specimens 3-14.

[0056] Fig. 9 Comparison diagram of the calculated values ​​of different conventional triaxial constitutive models; Figure (a) is for specimens 1-14 ( σ3=14MPa) and Figure (b) is a comparison diagram of specimen 2-14 ( σ3=14MPa) and Figure (c) is a comparison diagram of specimens 3-14 ( σ3=14MPa) comparison chart. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention; it is obvious that the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0058] Embodiment 1;

[0059] See also Figure 1-Figure 7 ;

[0060] This embodiment is a method for constructing a conventional triaxial constitutive model of a hybrid steel fiber self-compacting concrete. Figure 1 This is a flow chart of a conventional triaxial constitutive model construction method, which includes the following steps:

[0061] 1) Set three different sets of skeleton volume fractions (defined as the ratio of skeleton volume to concrete volume) 0.60, 0.62, and set σ3 = 0, 2, ..., 12 MPa for a total of seven groups of confining pressure values, σ3 = 0 represents a uniaxial compression test, σ3 = 2, ..., 12 MPa represents six groups of conventional triaxial compression tests with different confining pressures, thereby obtaining the stress-strain curve of the conventional triaxial compression test of the hybrid steel fiber self-compacting concrete specimen as shown in Figure 1 , where Figure (a) is The test curve of The test curve of The test curve of Figure 1 The stress-strain curve of the uniaxial compression test is also included; the specimen names are as shown in Table 1;

[0062] Table 1 Nomenclature of uniaxial compression test and conventional triaxial test specimens

[0063]

[0064]

[0065] 2) According to S1, the uniaxial peak stress f c and uniaxial peak strain ε c , linear functions such as equations (2.1) and (2.2) are used to fit the uniaxial peak stress f c , uniaxial peak strain ε c About the skeleton volume fraction The function expressions of are as follows (2.3) and (2.4);

[0066]

[0067]

[0068] Figure 2 is the uniaxial peak stress f c , uniaxial peak strain ε c and skeleton volume fraction The fitting curve of f c and The fitting curve of ε is shown in Figure (b). c and The fitting curve of

[0069] 3) According to S1, the triaxial peak stress f cc and triaxial peak strain ε cc and the uniaxial peak stress f c , uniaxial peak strain ε c The expression of triaxial peak stress / uniaxial peak stress f is obtained by fitting the power function as shown in formula (3.1). cc / f cConfining pressure / uniaxial peak stress (σ3 / f c ) is expressed as formula (3.5), and the triaxial peak strain / uniaxial peak strain (ε cc / ε c ) about confining pressure / uniaxial peak stress (σ3 / f c ) is expressed as formula (3.6):

[0070]

[0071]

[0072] Figure 3 is the triaxial peak stress / uniaxial peak stress f cc / f c , triaxial peak strain / uniaxial peak strain ε cc / ε c and confining pressure / uniaxial peak stress σ3 / f c The fitting curve of f cc / f c and σ3 / f c The fitting curve of ε is shown in Figure (b). cc / ε c and σ3 / f c The fitting curve of .

[0073] According to formula (3.2), we can further obtain that when When , the expressions of fitting parameters a0 and a1 are as follows (6.1) and (6.2):

[0074]

[0075]

[0076] According to formula (3.4), we can further obtain that when When , the expressions of fitting parameters b0, b1, b2, b3 are as follows (6.3) to (6.6):

[0077]

[0078]

[0079]

[0080]

[0081] Figure 4 is the triaxial peak stress / uniaxial peak stress f cc / f c, triaxial peak strain / uniaxial peak strain ε cc / ε c The fitting parameters of the skeleton volume fraction The fitting curve of f cc / f c The fitting parameters a0 and a1 are about The fitting curve of ε is shown in Figure (b). cc / ε c Fitting parameter b i (i=0,1,2,3) About The fitting curve of .

[0082] 4) The inventor Figure 1 It was found that in conventional triaxial tests, there was a fluctuation-like increase and decrease in ductility between the stress-strain curves of specimens with different confining pressures. Figure 1 It is not intuitive enough, so the inventors further proposed a new parameter to characterize this phenomenon, namely, the area ratio ductility T ar , area specific ductility T ar It is defined as the ratio of the area enclosed by the curve and the coordinate axis at 80% of the stress after the peak of the stress-strain curve to the area enclosed at the peak stress. The relationship between the area ratio ductility Tar and the confining pressure is as follows: Figure 5 ,from Figure 5 The fluctuation increase and decrease phenomenon can be observed intuitively;

[0083] In addition, the inventors consulted existing literature and found that the constitutive curve determining factor r value is usually regarded as a constant in existing literature. However, in the model of the present invention, the r value is greatly affected by the confining pressure and the skeleton volume fraction and is the key variable in the entire constitutive model. Since the pre-peak and post-peak characteristics of the stress-strain curve are determined by the r value, the inventors propose a ductility correction factor K r The constitutive curve determining factor r in the existing Popovics triaxial constitutive model is modified.

[0084] According to the confining pressure / uniaxial peak stress σ3 / f c , for different skeleton volume fractions The corresponding pre-peak ductility correction coefficient K is obtained by fitting the samples according to formula (4.1) r1 , post-peak ductility correction factor K r2 As shown in formula (4.3) and (4.4):

[0085]

[0086]

[0087] Figure 7 K r1 K is the pre-peak ductility correction factor;r2 is the queen ductility correction factor and the confining pressure / uniaxial peak stress σ3 / f c The fitting curve of The fitting curve of The fitting curve of time (c) is The fitting curve of .

[0088] According to formula (4.2), we can further obtain that when When , the expressions of fitting parameters d0, d1, d2, d3 are as follows (6.7) to (6.10):

[0089]

[0090]

[0091]

[0092]

[0093] According to formula (4.2), we can further obtain that when When , the expressions of fitting parameters d4, d5, d6, and d7 are as follows (6.11) to (6.14):

[0094]

[0095]

[0096]

[0097]

[0098] Figure 7 K is the pre-peak ductility correction factor r1 The fitting parameters d0, d1, d2, d3 and the post-peak ductility correction coefficient K r2 The fitting parameters d4, d5, d6, and d7 are related to the skeleton volume fraction The fitting curve of K r1 The fitting parameters are about The fitting curve of K r2 The fitting parameters are about The fitting curve of .

[0099] Substituting equations (4.3) and (4.4) into equation (5.1), we can obtain the modified constitutive curve determining factor r * ; Uniaxial compression elastic modulus E c According to the uniaxial compression peak stress f c Determine according to formula (5.5):

[0100]

[0101] According to f cc / f c , ε cc / ε c The triaxial peak stress f can be obtained respectively cc , triaxial peak strain ε cc According to formula (5.5) and formula (5.2), the constitutive curve determining factor r is obtained. According to formula (5.1), the modified constitutive curve determining factor r is obtained. * , f cc , ε cc 、r * 、E c Substituting into equation (5.5) we can obtain the modified Popovics triaxial constitutive model.

[0102] Comparative Example 1;

[0103] See also Figure 8 ;

[0104] In this comparative example, three groups of samples were selected for triaxial compression test with confining pressure σ2=σ3=14MPa according to the same triaxial compression test method as in Example 1. The skeleton volume fractions of the three groups of samples were The triaxial compression test stress-strain curve is obtained as a verification test, and the triaxial peak stress f is obtained. cc , triaxial peak strain ε cc , elastic modulus, pre-peak ductility correction factor K r1 , post-peak ductility correction factor K r2 The comparison between the experimental calculation results and the model calculation values ​​is shown in Table 2-4:

[0105] Table 2 Comparison of triaxial constitutive parameters

[0106]

[0107] Note: Relative error is defined as the ratio of absolute error (test value - model value) to the test value.

[0108] Table 3 Comparison of triaxial constitutive parameters

[0109]

[0110] Table 4 Comparison of triaxial constitutive parameters

[0111]

[0112] Figure 8The stress-strain curves of the conventional triaxial compression test with a confining pressure of 14 MPa are compared with the values ​​calculated by the conventional triaxial constitutive model; Figure (a) shows the stress-strain curves of specimens 1-14. Comparison chart, Figure (b) is specimen 2-14 Comparison chart, Figure (c) is specimen 3-14 A comparison chart of Figure 8 It can be seen that the model calculated stress-strain curve is in good agreement with the conventional triaxial test stress-strain curve. The model in the present invention is obtained from the conventional triaxial constitutive test results under 0-12MPa confining pressure conditions, but from Tables 2-4 and Figure 8 It can be found that the conventional triaxial constitutive model has only a small error with the verification test result of 14 MPa, so it can be considered that the conventional triaxial constitutive model in the present invention has good applicability to hybrid steel fiber self-compacting concrete.

[0113] Furthermore, the present invention uses the statistical indicators of formulas (7.1)-(7.3), including: mean value M, mean absolute error AAE and standard deviation SD, to Figure 8 The experimental curves and model curves in are quantitatively analyzed, and the calculation results are shown in Table 5.

[0114]

[0115]

[0116]

[0117] Where: Exp i Represents the measured stress value of conventional triaxial test, Pre i Representative and Exp i Stress values ​​calculated by the conventional triaxial constitutive model at the same strain, where n represents the number of data points used for the calculation.

[0118] Table 5 Calculated values ​​of statistical indicators of specimens with confining pressure of 14 MPa

[0119] Average value M Mean Absolute Error (AAE) Standard Deviation SD 1-14 1.121 -0.083 0.112 2-14 0.903 0.126 0.111 3-14 0.909 0.126 0.074

[0120] Theoretically, the closer M is to 1, the closer AAE is to 0, and the closer SD is to 0, the better the calculated value fits the experimental value. In order to better evaluate the applicability of the new model to each specimen, 0.15 is used as the maximum acceptance range of the three indicators. In other words, 1±0.15 is used as the upper and lower limits of M, 0±0.15 is used as the upper and lower limits of AAE, and 0±0.15 is used as the upper and lower limits of SD. It can be seen that the constitutive model in the present invention can fit the measured value well and has good applicability.

[0121] Comparative Example 2;

[0122] See also Fig. 9 ;

[0123] Table 6-11 gives the comparison of triaxial peak stress and triaxial peak strain between the modified Popovics and other models. Other models include the original Popovics model, Liao model and Attard model. Three sets of conventional triaxial compression test data with different skeleton volume fractions and confining pressure of 14 MPa are used for comparison;

[0124] Table 6 Comparison of triaxial peak stress of specimens 1-14 between different models

[0125] Model of the present invention Popovics Model Liao Model Attard Model Test value 82.0 82.0 82.0 82.0 Model Value 85.2 108.0 239.9 116.2 Absolute error -3.2 -26.0 -157.8 -34.6 Relative error -0.03924 -0.31659 -1.924 -0.41648

[0126] Table 7 Comparison of triaxial peak stress of specimens 2-14 between different models

[0127]

[0128]

[0129] Table 8 Comparison of triaxial peak stress of specimens 3-14 between different models

[0130] Model of the present invention Popovics Model Liao Model Attard Model Test value 89.2 89.2 89.2 89.2 Model Value 84.6 110.0 241.9 120.8 Absolute error 4.6 -20.8 -152.7 -31.6 Relative error 0.05121 -0.23360 -1.71241 -0.35457

[0131] Table 9 Comparison of triaxial peak strains of specimens 1-14 between different models

[0132] Model of the present invention Popovics Model Liao Model Attard Model Test value 0.00616 0.00616 0.00616 0.00616 Model Value 0.00641 0.01095 0.01687 0.01726 Absolute error -0.00025 -0.00479 -0.01071 -0.01110 Relative error -0.04020 -0.77799 -1.74012 -1.80266

[0133] Table 10 Comparison of triaxial peak strains of specimens 2-14 between different models

[0134] Model of the present invention Popovics Model Liao Model Attard Model Test value 0.00663 0.00663 0.00663 0.00663 Model Value 0.00657 0.01121 0.01723 0.01763 Absolute error 0.00006 -0.00457 -0.01060 -0.01099 Relative error 0.01015 -0.68867 -1.59721 -1.65627

[0135] Table 11 Comparison of triaxial peak strains of specimens 3-14 between different models

[0136] Model of the present invention Popovics Model Liao Model Attard Model Test value 0.00727 0.00727 0.00727 0.00727 Model Value 0.00676 0.01148 0.01761 0.01801 Absolute error 0.00052 -0.00420 -0.01033 -0.01073 Relative error -0.07682 -0.36603 -0.58679 -0.59594

[0137] It can be seen from Tables 6-11 that for the theoretical calculation of conventional triaxial peak stress and triaxial peak strain of specimens with different skeleton volume fractions, the calculation results of different models are very different. Among them, the calculation relative error of the model provided by the present invention is basically less than ±0.12, while the calculation values ​​of other models are basically higher, and the relative errors are greater than ±0.25, and even exceed ±1.00. Obviously, the applicability of the model in the present invention to the new material of hybrid steel fiber self-compacting concrete is better than other models.

[0138] Fig. 9 Comparison diagram of the calculated values ​​of different conventional triaxial constitutive models; Figure (a) is for specimens 1-14 ( σ3=14MPa) specimens, and Figure (b) is a comparison of specimens 2-14 ( σ3=14MPa) and Figure (c) is a comparison diagram of specimens 3-14 ( σ3=14MPa) comparison chart. Fig. 9 It can be seen that for each 14MPa specimen, the conventional triaxial constitutive model provided by the present invention is in the best agreement with the test data, followed by the Popovics model and the Attard model, and the worst performance is the Liao model;

[0139] Tables 12-14 give the statistical index calculation results of the conventional triaxial constitutive curves of the modified Popovics model and other models. The statistical indexes also include the mean value M, the average absolute error AAE and the standard deviation SD. Fig. 9 The test curve and model curve in are quantitatively analyzed. Theoretically, the closer M is to 1, the closer AAE is to 0, and the closer SD is to 0, the better the calculated value fits the test value. Therefore, 0.15 is used as the maximum acceptance range of the three indicators, that is, 1±0.15 is used as the upper and lower limits of M, 0±0.15 is used as the upper and lower limits of AAE, and 0±0.15 is used as the upper and lower limits of SD. It can be seen that the constitutive model in the present invention can fit the measured value well and has good applicability, while the other three conventional triaxial constitutive models cannot be well applied to hybrid steel fiber self-compacting concrete, and all exceed the upper and lower limits of 0.15.

[0140] Table 12 Calculated values ​​of statistical indicators for specimens 1-14

[0141]

[0142] Table 13 Calculated values ​​of statistical indicators for specimens 2-14

[0143]

[0144] Table 14 Calculated values ​​of statistical indicators for specimen 3-14

[0145]

[0146] In summary, the model described in the present invention is simple to use and requires fewer parameters. It only needs to determine the skeleton volume fraction and the peak stress-strain value of uniaxial compression to calculate the constitutive curve under conventional triaxial compression conditions. The calculated results are close to the measured results, which can provide a theoretical reference for the design and analysis of hybrid steel fiber self-compacting concrete, and provide theoretical guidance for the engineering application of tunnel segments based on new hybrid steel fiber self-compacting concrete, and has important engineering application value.

[0147] It should be noted that although the triaxial peak stress / uniaxial peak stress f cc / fc , triaxial peak strain / uniaxial peak strain ε cc / ε c Confining pressure / uniaxial peak stress σ3 / f c Functional expression of the peak pre-ductility correction parameter K r1 , post-peak ductility correction parameter K r2 About f cc / f c The expression is used for hybrid steel fiber self-compacting concrete, but theoretically, for other types of concrete, f can also be determined according to formulas (3.1) and (3.2) cc / f c , ε cc / ε c , and determine K according to formula (4.1) r1 , K r2 Then the stress-strain curve is corrected to take ductility into account.

[0148] The above description is only used to illustrate the technical solution of the present invention and is not intended to limit it. Any modification or replacement of the technical solution made by other technicians in this professional field should be included in the scope of the claims of the present invention as long as it does not deviate from the connotation of the technical solution of the present invention.

Claims

1. A method for constructing a conventional triaxial constitutive model of hybrid steel fiber self-compacting concrete, characterized in that: The steps include: S1. According to the total volume content of steel fiber and different skeleton volume fractions, several standard specimens of hybrid steel fiber self-compacting concrete are prepared, and uniaxial compression tests and conventional triaxial compression tests with different confining pressures are respectively carried out to obtain stress-strain curves of the uniaxial compression test and the conventional triaxial compression test, and determine the corresponding peak stress and peak strain; S2, uniaxial peak stress f obtained according to S1 c and uniaxial peak strain ε c , and the uniaxial peak stress f c About the skeleton volume fraction Functional expression of uniaxial peak strain ε c About the skeleton volume fraction Function expression of ; S3, triaxial peak stress f obtained according to S1 cc , triaxial peak strain ε cc And the uniaxial peak stress f obtained by S2 c , uniaxial peak strain ε c The expression of triaxial peak stress / uniaxial peak stress f is obtained by nonlinear regression analysis. cc / f c Confining pressure / uniaxial peak stress σ3 / f c The function expression of triaxial peak strain / uniaxial peak strain ε is obtained by fitting. cc / ε c About σ3 / f c Function expression of ; S4. According to the changing characteristics of the conventional triaxial stress-strain curve, the ductility correction factor K is proposed. r The constitutive curve determining factor r in the existing Popovics triaxial constitutive model was modified, and the K r About σ3 / f c Expression of According to the fluctuation-type increase and decrease characteristics of the post-peak ductility of the conventional triaxial stress-strain curve, the ductility correction factor K is obtained by fitting according to formula (4.1) using the nonlinear regression analysis method. r Confining pressure / uniaxial peak stress σ3 / f c The expression is: Where: K r is the ductility correction factor; K r1 K is the pre-peak ductility correction factor; r2 is the post-peak ductility correction factor; σ3 / f c is the confining pressure / uniaxial peak stress; d j K r1 , K r2 The fitting parameters of , j = 0, 1, 2, ..., 7; Among them, d j Determine according to formula (4.2): Where: k j , l j is d i About the skeleton volume fraction The fitting parameters of S5, will be based on the ductility correction factor K r The corrected constitutive curve determining factor r * And the triaxial peak stress / uniaxial peak stress f obtained by S3 cc / f c , triaxial peak strain / uniaxial peak strain ε cc / ε c Substituting into the existing Popovics triaxial constitutive model, a conventional triaxial constitutive model suitable for hybrid steel fiber self-compacting concrete is obtained; According to the ductility correction factor K r , the factor r determining the modified constitutive curve * Determine according to formula (5.1) and (5.2): Where: r * E is the determining factor of the modified constitutive curve; c is the uniaxial compression elastic modulus; f cc is the triaxial peak stress, ε cc is the triaxial peak strain; Among them, E c It is obtained by elastic modulus test or determined by formula (5.3): The modified Popovics triaxial constitutive model applicable to hybrid steel fiber self-compacting concrete is established according to formula (5.4): Where: σ is the triaxial stress under conventional triaxial compression state, ε is the triaxial strain under conventional triaxial compression state.

2. The conventional triaxial constitutive model construction method of hybrid steel fiber self-compacting concrete according to claim 1, characterized in that: In S1, the total volume content of steel fiber is 0-1.5%; the skeleton volume fraction ranges from 58% to 62%, and at least 3 different skeleton volume fractions are selected; the confining pressure is 0-30% of the standard compressive strength of concrete, and at least 5 different confining pressures are selected.

3. The conventional triaxial constitutive model construction method of hybrid steel fiber self-compacting concrete according to claim 1, characterized in that: S2, the uniaxial peak stress f c About the skeleton volume fraction Functional expression of uniaxial peak strain ε c About the skeleton volume fraction The functional expression of is fitted by linear regression analysis according to formula (2.1) and (2.2): Where: f c is the peak stress of the uniaxial compression test; ε c is the peak strain of the uniaxial compression test; is the skeleton volume fraction; s0 and s1 are the uniaxial peak stress f c The fitting parameters are s2 and s3, and the uniaxial peak strain ε c The fitting parameters of .

4. The conventional triaxial constitutive model construction method of hybrid steel fiber self-compacting concrete according to claim 1, characterized in that: In S3, triaxial peak stress / uniaxial peak stress f cc / f c Confining pressure / uniaxial peak stress σ3 / f c The functional expression of is obtained by fitting according to formula (3.1) using nonlinear regression analysis: Where: f cc / f c is triaxial peak stress / uniaxial peak stress; σ3 / f c is the confining pressure / uniaxial peak stress; a0 and a1 are the triaxial peak stress / uniaxial peak stress f cc / f c The fitting parameters of Among them, a0 and a1 are determined according to formula (3.2): Where: s4, s5 are the volume fractions of a0 with respect to the skeleton The fitting parameters of a1 are as follows; s6 and s7 are the skeleton volume fractions of a1 The fitting parameters of .

5. The conventional triaxial constitutive model construction method of hybrid steel fiber self-compacting concrete according to claim 1, characterized in that: In S3, triaxial peak strain / uniaxial peak strain ε cc / ε c Confining pressure / uniaxial peak stress σ3 / f c The functional expression of is obtained by fitting according to formula (3.3) using nonlinear regression analysis: Where: ε cc / ε c is the triaxial peak strain / uniaxial peak strain; σ3 / f c is the confining pressure / uniaxial peak stress; b i is the triaxial peak strain / uniaxial peak strain ε cc / ε c The fitting parameters are as follows: i = 0, 1, 2, 3; e is the natural logarithm; Among them, b i Determine according to formula (3.4): Where: m i 、n i for b i About the skeleton volume fraction The fitting parameters of .

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