Prediction method and system for shrinkage and creep deformation of high-performance concrete of early-age loaded steel pipe

Abstract

The invention provides a method and system for predicting shrinkage and creep deformation of high-performance concrete of an early-age loaded steel pipe, and belongs to the field of concrete. The problem that self-constriction of steel pipe high-performance concrete is underestimated is solved The problem that the creep deformation prediction result of the steel pipe high-performance concrete is not accurate due to the fact that different influences of loading periods on the creep deformation of the component under different water-binder ratios are not considered is solved. The method comprises the following steps: carrying out shrinkage and creep tests of different loading ages on steel tube high-performance concrete with different concrete water-binder ratios to obtain shrinkage strain and creep strain experimental results; performing nonlinear regression analysis on shrinkage and creep test results of the steel tube high-performance concrete with different concrete water-binder ratios in different loading periods, introducing influence coefficients of the concrete water-binder ratios on shrinkage and creep, and establishing a high-performance concrete shrinkage and creep model; and adopting a step-by-step integral method to consider the shrinkage and creep deformation after the stress redistribution of the high-performance concrete of the steel pipe.

Description

Technical Field

[0001] The present invention relates to the technical field of concrete, and in particular, to a method and system for predicting the shrinkage and creep deformation of high-performance concrete filled in steel tubes under early-age loading. Background Art

[0002] High-performance concrete filled in steel tubes is a high-performance composite member formed by filling high-strength self-compacting concrete into a steel tube and adding high-quality expansive agents, which solves common problems in concrete-filled steel tubes such as non-dense pouring of concrete inside the tube and debonding between the steel tube and concrete during service, and has become the development direction of large concrete-filled steel tube structures. This type of new composite member inherits the advantages of high bearing capacity, high stiffness, good ductility, and high construction efficiency of steel tube high-strength concrete, and at the same time has performance advantages such as easy pumping and low shrinkage. Its competitiveness is particularly prominent in high-intensity earthquake areas and has been applied to many super high-rise buildings, long-span bridges, and high-rise structures in recent years.

[0003] In high-performance concrete filled in steel tubes, early-age loading of concrete is common. In a concrete-filled steel tube structure, the steel tube not only bears the load together with the concrete, but also serves as a formwork during concrete pouring, so that the concrete begins to bear the load once it forms strength. Also due to the urgency of the construction period, the core concrete in the project often begins to bear the subsequent load 3 to 7 days after pouring. The early-age creep of high-performance concrete filled in steel tubes can cause the long-term deformation of the member to reach 0.5 to 1.3 times the short-term deformation, and this deformation increment is 1.5 to 3 times the creep deformation under 28-day loading. Early-age loading not only significantly increases the creep deformation, but also the shrinkage deformation of high-performance concrete is relatively high. In order to further clarify the development of shrinkage and creep deformation of high-performance concrete filled in steel tubes under early-age loading and ensure the service life and structural safety of the project, it is urgent to consider the differences in the influence of loading age on the creep deformation of members under different water-binder ratios and propose a method for predicting the shrinkage and creep deformation of high-performance concrete filled in steel tubes under early-age loading.

[0004] The existing technologies mainly include: BS EN 1992 creep model, fib MC2010 creep model, ACI 209 creep model, B4 creep model, AFREM creep model, etc. The main defects of the existing technologies are as follows:

[0005] (1) Due to the confinement effect of the outer steel tube, the moisture exchange between the high-performance concrete and the outside air is blocked, and only autogenous shrinkage occurs in the confined concrete. The existing technologies basically underestimate the shrinkage of the confined concrete, especially the shrinkage of the confined low water-binder ratio concrete can be underestimated by 1.5 to 2.6 times. Therefore, a model for accurately predicting the shrinkage deformation of the confined concrete is needed.

[0006] (2) The existing technology only considers the influence of the loading age on the creep of concrete, and has not yet considered that the influence of the loading age on the creep deformation of components is different under different water-binder ratios. Ignoring this influence will lead to an underestimation of the creep deformation of concrete with a low water-binder ratio by 60% - 80%. Summary of the Invention

[0007] The technical problem to be solved by the present invention is:

[0008] To solve the problems that the autogenous shrinkage of high-performance concrete filled steel tubes is underestimated; the influence of the loading age on the creep deformation of components under different water-binder ratios is not considered, resulting in inaccurate prediction results of the creep deformation of high-performance concrete filled steel tubes.

[0009] The technical solution adopted by the present invention to solve the above technical problems:

[0010] The present invention provides a method for predicting the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading, including the following steps:

[0011] S100. Conduct shrinkage and creep tests on high-performance concrete filled steel tubes with different concrete water-binder ratios at different loading ages to obtain the experimental results of shrinkage strain and creep strain;

[0012] S200. Calculate the shrinkage deformation and creep deformation at the concrete level;

[0013] S300. At the level of composite components, use the step-by-step integration method to calculate the shrinkage deformation and creep deformation.

[0014] Further, in step S100, it includes: pouring N groups of high-performance concrete filled steel tube specimens and conducting shrinkage and creep tests; where N≥8, each group of specimens includes 2 parallel specimens; the concrete water-binder ratios and loading ages in the N groups of high-performance concrete filled steel tube specimens are different.

[0015] Further, the value range of the concrete water-binder ratio is 0.25 - 0.45, and the values of the loading age are 3 days, 7 days, 14 days, and 28 days.

[0016] Further, in step S200, calculating the shrinkage deformation at the high-performance concrete level includes performing non-linear regression analysis on the shrinkage strains of high-performance concrete filled steel tubes with different concrete water-binder ratios, and establishing a high-performance concrete shrinkage model by introducing the influence coefficient of the concrete water-binder ratio on shrinkage to obtain the shrinkage strains of high-performance concrete with different water-binder ratios;

[0017] The calculation formula for the shrinkage deformation is:

[0018]

[0019] In the formula, εsh is the shrinkage deformation of high-performance concrete; w is the water consumption of high-performance concrete; b is the mass of cement, silica fume, fly ash, slag powder and expansive agent in high-performance concrete; t is the age of high-performance concrete in days; α1, α2 and α3 are unknown parameters;

[0020] The specific method for obtaining the three constants α1, α2 and α3 is as follows: By using the least squares method, a non-linear regression analysis is performed on the test results. Considering the influence of the water-binder ratio of concrete on concrete shrinkage, the mathematical expressions for α1, α2 and α3 obtained by fitting are:

[0021] α1 = 6(2)

[0022] α2 = 21(3)

[0023] α3 = 18(4).

[0024] Furthermore, in step S200, the creep deformation of the high-performance concrete layer is calculated, including performing a non-linear regression analysis on the creep tests of high-strength concrete filled steel tubes with different loading ages and different water-binder ratios. Based on the different effects of the loading age on the creep of high-strength concrete filled steel tubes under different water-binder ratios, by introducing the influence coefficient of the water-binder ratio of concrete on creep, a creep model of high-performance concrete is established, and the creep strain of high-strength concrete filled steel tubes with different water-binder ratios at different loading ages is obtained;

[0025] The calculation formula for creep deformation is:

[0026] C(t, t0) = k(t0)·C(t, 28)(5)

[0027]

[0028] In the formula, C(t, t0) is the creep coefficient of high-performance concrete from the t0-th day after the specimen is cast until the t-th day under sustained load (the creep coefficient is the ratio of creep deformation to the stress of concrete at the initial stage of loading); C(t, 28) is the creep coefficient of high-performance concrete from the 28th day after the specimen is cast until the t-th day under sustained load; k(t0) is the loading age influence coefficient; t is the age of high-performance concrete; t0 is the loading age of high-performance concrete; β1, β2 and β3 are unknown parameters;

[0029] The specific method for obtaining the two constants β1 and β2 is:

[0030] Formula (6) satisfies boundary condition 1: when the loading age t0 = 28, k(t0) = 1; boundary condition 2: when the loading age t0 approaches infinity, k(t0) = 0.5; based on the above two conditions, the mathematical expressions for β1 and β2 are:

[0031] β1 = 0.5(7)

[0032] β2 = 0.5(β3 + 28)(8)

[0033] The specific method for obtaining the constant β3 is as follows: Based on the different effects of the loading age on the creep of high-performance concrete filled steel tubes under different water-binder ratios of concrete, a function of β3 with respect to the water-binder ratio of concrete is constructed as:

[0034]

[0035] where γ1 and γ2 are unknown parameters;

[0036] The specific method for obtaining the two constants γ1 and γ2 is as follows: Through the least squares method, a non-linear regression analysis is performed based on the test results, and the mathematical expressions for γ1 and γ2 obtained by fitting are:

[0037] γ1 = 15 (10)

[0038] γ2 = 2(11).

[0039] Furthermore, in step S300, it includes

[0040] Using the step-by-step integration method, considering the influence that the creep deformation develops rapidly in the early stage and slowly in the later stage, the time step is divided into M steps, and the division method is:

[0041]

[0042] where Δt k is the time step length between any time t k and the previous time t k-1 ; Δt i is the time step length between any time t i and the previous time t i-1 ; t end is the age of the high-performance concrete when the high-performance concrete filled steel tube stops bearing the load; k is the time step number; M is the number of time steps into which the time period from the start of sustained load on the t0th day to the tth day is divided;

[0043] Using the step-by-step integration method, considering the influence of stress redistribution between the high-performance concrete and the steel components in the high-performance concrete filled steel tube member under a constant load, the stress-strain relationship of the concrete is established according to the trapezoidal integration rule as:

[0044]

[0045] where t k-1 and t k are respectively the start time and the end time of the kth step; σ ckand σ cj are respectively the stresses of concrete at time t k and at time t j ; ε totk and ε shk are respectively the total deformation and total shrinkage of concrete at time t k ; M c1k and M c2kj are both creep influence coefficients;

[0046] J(t k , t j ) is the creep function of concrete from time tj when it starts to bear a constant load to time tk;

[0047] Considering that in a high-performance concrete-filled steel tube member under a constant load, the high-performance concrete and the steel component jointly bear the vertical load, and the deformations of the two parts are coordinated, the shrinkage deformation and creep deformation of the high-performance concrete-filled steel tube member are calculated according to the force equilibrium equation and the deformation coordination equation. Specifically,

[0048] Using the step-by-step integration method, the calculation method of creep deformation is as follows:

[0049]

[0050] ε ck = ε totk - ε shk (17)

[0051] In the formula, N L is the constant load borne by the high-performance concrete-filled steel tube; A c is the cross-sectional area of the concrete; E s is the elastic modulus of the steel tube; A s is the cross-sectional area of the steel tube; σ cj is the stress of concrete at time t j ; ε totk and ε ck are respectively the total deformation and creep deformation of concrete at time t k ; ε shk is the shrinkage deformation of concrete at time t k ;

[0052] The creep function J(t k , t j ) is calculated using formula (5), and the calculation method is as follows:

[0053]

[0054] In the formula, E c (t j ) is the elastic modulus of high-performance concrete at time t j ; Ec E(t0) is the elastic modulus of high-performance concrete at time t0; c E(28) is the elastic modulus of high-performance concrete on the 28th day after pouring; k C(t, tj) is the creep degree of high-performance concrete from the tjth day after pouring the specimen until the tth day after holding the load; k

[0055] The elastic modulus E of high-performance concrete at time t j is calculated using the elastic modulus calculation formula provided by BSEN1992. c (t j )

[0056] A prediction system for the shrinkage and creep deformation of high-strength concrete-filled steel tubular members under early-age loading. The system has program modules corresponding to the above steps and executes the steps in the prediction method for the shrinkage and creep deformation of high-strength concrete-filled steel tubular members under early-age loading when running.

[0057] A computer-readable storage medium stores a computer program configured to implement the steps of the prediction method for the shrinkage and creep deformation of high-strength concrete-filled steel tubular members under early-age loading when called by a processor.

[0058] Compared with the prior art, the beneficial effects of the present invention are:

[0059] (1) The present invention provides a method for determining the shrinkage deformation and creep deformation models of high-strength concrete-filled steel tubular members. According to the variation characteristics of the shrinkage and creep of high-strength concrete-filled steel tubular members, a shrinkage deformation model of high-performance concrete considering the influence of the water-binder ratio of concrete is established, and a shrinkage strain prediction model of high-performance concrete under different water-binder ratios is determined.

[0060] (2) The present invention considers the differences in the influence of the loading age on the creep deformation of high-strength concrete-filled steel tubular members under different water-binder ratios. By introducing the influence coefficient of the water-binder ratio of concrete on creep, a creep deformation prediction model of high-performance concrete with different water-binder ratios under early-age loading is determined.

[0061] (3) The present invention uses the step-by-step integration method to analyze the shrinkage deformation and creep deformation of high-performance concrete under variable stress conditions caused by the stress redistribution between the steel tube and the concrete during the load-holding process (i.e., the phenomenon that the stress borne by the steel tube increases with time and the stress borne by the concrete decreases with time).

[0062] (4) Tests show that the prediction results of the method for predicting the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading in the present invention are relatively consistent with the test results, demonstrating that the model established in the present invention has high accuracy. Description of the Drawings

[0063] Figure 1 It is a flow chart of a method for predicting the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading in an embodiment of the present invention;

[0064] Figure 2 It is a diagram of the experimental device for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading in an embodiment of the present invention;

[0065] Figure 3 It is a comparison diagram of the predicted results and the test measured results of the shrinkage deformation of high-performance concrete in an embodiment of the present invention;

[0066] Figure 4 It is a comparison diagram of the predicted results and the test measured results of the creep deformation of high-performance concrete filled steel tubes with a water-binder ratio of 0.32 under early-age loading in an embodiment of the present invention;

[0067] Figure 5 It is a comparison diagram of the predicted results and the test measured results of the creep deformation of high-performance concrete filled steel tubes with a water-binder ratio of 0.26 under early-age loading in an embodiment of the present invention.

[0068] Description of the Reference Numerals:

[0069] 1, nut; 2, hydraulic jack; 3, reaction top plate; 4, spherical hinge; 5, prestressing tendon; 6, sustained load creep specimen; 7, loading plate; 8, force sensor; 9, disc spring; 10, unloaded shrinkage specimen; 11, creep loading frame support. Detailed Embodiments

[0070] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention is provided with reference to the accompanying drawings.

[0071] Specific Embodiment 1: Combining Figure 1 and Figure 2 shown, the present invention provides a method for predicting the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading, including the following steps:

[0072] S100. Conduct shrinkage and creep tests on high-performance concrete filled steel tubes with different concrete water-binder ratios at different loading ages to obtain the experimental results of shrinkage strain and creep strain;

[0073] Using Figure 2The test is carried out on the shown experimental device. The experimental device includes a creep loading frame support 11 at the bottom. An unloaded shrinkage specimen 10 is provided on the creep loading frame support 11 and is connected to the bottom plate through a plurality of disc springs 9. A force sensor 8, a loading plate 7 and a loaded creep specimen 6 are successively arranged at the center above the bottom plate. The upper end of the loaded creep specimen 6 is connected to a reaction top plate 3 through a spherical hinge 4. A hydraulic jack 2 is arranged above the reaction top plate 3. The output end of the hydraulic jack 2 is connected to the center of the reaction top plate 3. At least two prestressed tendons 5 are arranged between the top end of the hydraulic jack 2 and the bottom plate. The prestressed tendons 5 are connected to the top end of the hydraulic jack 2 through nuts 1, and the prestressed tendons 5 penetrate through the reaction top plate 3;

[0074] N groups of steel tube high-performance concrete specimens are cast and shrinkage and creep tests are carried out; where N≥8, and each group of specimens includes 2 parallel specimens; the water-binder ratios and loading ages of the concrete in the N groups of steel tube high-performance concrete specimens are different; where the value range of the water-binder ratio of the concrete is 0.25 to 0.45, and the values of the loading age are 3 days, 7 days, 14 days and 28 days;

[0075] S200. Calculate the shrinkage deformation and creep deformation at the concrete level, including,

[0076] S210. Calculate the shrinkage deformation at the high-performance concrete level, including performing a non-linear regression analysis on the shrinkage strains of steel tube high-performance concrete with different concrete water-binder ratios, introducing the influence coefficient of the concrete water-binder ratio on shrinkage, establishing a high-performance concrete shrinkage model, and obtaining the shrinkage strains of high-performance concrete with different water-binder ratios;

[0077] The calculation formula for the shrinkage deformation is:

[0078]

[0079] In the formula, ε sh is the shrinkage deformation of high-performance concrete, ×10 -6 ; w is the water consumption of high-performance concrete, kg / m 3 ; b is the mass of cement, silica fume, fly ash, slag powder and expansive agent in high-performance concrete, kg / m 3 ; t is the age of high-performance concrete, days; α1, α2 and α3 are unknown parameters;

[0080] The specific method for obtaining the three constants α1, α2 and α3 is: through the least squares method, perform a non-linear regression analysis based on the test results, consider the influence of the concrete water-binder ratio on concrete shrinkage, and the mathematical expressions for fitting α1, α2 and α3 are:

[0081] α1 = 6(2)

[0082] α2 = 21(3)

[0083] α3 = 18(4)

[0084] S220. Calculate the creep deformation of the high-performance concrete layer, including performing non-linear regression analysis on the creep tests of high-strength concrete-filled steel tubes with different concrete water-binder ratios at different loading ages, and based on the different effects of loading ages on the creep of high-strength concrete-filled steel tubes with different concrete water-binder ratios, establish a creep model for high-performance concrete by introducing the influence coefficient of concrete water-binder ratio on creep, and obtain the creep strain of high-strength concrete-filled steel tubes with different concrete water-binder ratios at different loading ages;

[0085] The calculation formula for creep deformation is:

[0086] C(t, t0) = k(t0)·C(t, 28)(5)

[0087]

[0088] In the formula, C(t, t0) is the creep coefficient of high-performance concrete from the t0th day after the specimen is cast until the tth day under sustained load (the creep coefficient is the ratio of creep deformation to the stress of concrete at the initial stage of loading), ×10 -6 / MPa; C(t, 28) is the creep coefficient of high-performance concrete from the 28th day after the specimen is cast until the tth day under sustained load, ×10 -6 / MPa. The reason for taking the creep coefficient at 28-day loading as a reference is that 28 days is the most common loading age for high-strength concrete-filled steel tube structures; k(t0) is the loading age influence coefficient; t is the age of high-performance concrete, in days; t0 is the loading age of high-performance concrete, in days; β1, β2, and β3 are unknown parameters;

[0089] The specific method for obtaining the two constants β1 and β2 is as follows:

[0090] The formula (6) must satisfy boundary condition 1: when the loading age t0 = 28, k(t0) = 1; boundary condition 2: when the loading age t0 approaches infinity, k(t0) = 0.5; based on the above two conditions, the mathematical expressions for β1 and β2 are:

[0091] β1 = 0.5(7)

[0092] β2 = 0.5(β3 + 28)(8)

[0093] The specific method for obtaining the constant β3 is as follows: based on the different effects of loading ages on the creep of high-strength concrete-filled steel tubes with different concrete water-binder ratios, construct β3 as a function of concrete water-binder ratio as:

[0094]

[0095] where γ1 and γ2 are unknown parameters;

[0096] The specific method for obtaining the two constants γ1 and γ2 is as follows: Through the least squares method, perform a non-linear regression analysis based on the test results, and the mathematical expressions for γ1 and γ2 obtained by fitting are:

[0097] γ1 = 15(10)

[0098] γ2 = 2(11)

[0099] S300. At the level of the composite member, calculate the shrinkage deformation and creep deformation, including

[0100] Adopt the Step-by-Step Method, considering the influence that the creep deformation develops rapidly in the early stage and slowly in the later stage. Divide the time step into M steps, and the division method is:

[0101]

[0102] where Δt k is the time step length between any time t k and the previous time t k-1 ; Δt i is the time step length between any time t i and the previous time t i-1 ; t end is the age of the high-performance concrete when the high-strength concrete-filled steel tube stops bearing the load; k is the time step number; M is the number of time steps into which the time period from the start of load holding on the t0th day to the tth day is divided;

[0103] Adopt the Step-by-Step Method, considering the influence of stress redistribution between the high-performance concrete and the steel component in the high-strength concrete-filled steel tube member under a constant load. Establish the stress-strain relationship of the concrete according to the trapezoidal integration rule as:

[0104]

[0105]

[0106] where t k-1 and t k are the start time and end time of the kth step, in days; σ ck and σ cj are the stresses of the concrete at t k and t j respectively, in MPa; ε totk and ε shk are the strains of the concrete at tk Total deformation and total shrinkage of concrete at a certain time; M c1k and M c2kj are both creep influence coefficients; J(t k ,t j ) is the creep function of concrete from time tj when it starts to bear a constant load to time tk;

[0107] Considering that in a high-performance concrete-filled steel tubular member under a constant load, the high-performance concrete and the steel component jointly bear the vertical load, and the deformations of the two parts are coordinated, the shrinkage deformation and creep deformation of the high-performance concrete-filled steel tubular member are calculated according to the force equilibrium equation and the deformation coordination equation. Specifically,

[0108] Using the step-by-step integration method (Step-by-Step Method), the calculation method of creep deformation is:

[0109]

[0110] ε ck = ε totk - ε shk (17)

[0111] In the formula, N L is the constant load borne by the high-performance concrete-filled steel tube, N; A c is the cross-sectional area of the concrete, mm 2 ; E s is the elastic modulus of the steel tube, MPa; A s is the cross-sectional area of the steel tube, mm 2 ; σ cj is the stress of the concrete at time t j , MPa; ε totk and ε ck are the total deformation and creep deformation of the concrete at time t k , ×10 -6 ; ε shk is the shrinkage deformation of the concrete at time t k , ×10 -6 , calculated according to formula (1);

[0112] The creep function J(t k ,t j ) is calculated using formula (5), and the calculation method is:

[0113]

[0114] In the formula, E c (t j ) is the elastic modulus of the high-performance concrete at time t j , MPa; E cE(t0) is the elastic modulus of high-performance concrete at time t0, MPa; c E(28) is the elastic modulus of high-performance concrete on the 28th day after pouring, MPa; k C(t j , tj) is the creep coefficient of high-performance concrete from the t k th day after casting the specimen until the t -6 th day, ×10

[0115] / MPa, calculated according to formula (5); j The elastic modulus E c (t j ) of high-performance concrete at time t is calculated using the elastic modulus calculation formula provided by BSEN 1992.

[0116] Specific implementation plan II: The present invention provides a prediction system for the shrinkage and creep deformation of high-strength concrete filled steel tubes under early-age loading. The system has program modules corresponding to the above steps, and when running, it executes the steps in the prediction method for the shrinkage and creep deformation of high-strength concrete filled steel tubes under early-age loading.

[0117] The other combinations and connection relationships in this implementation plan are the same as those in specific implementation plan I.

[0118] Specific implementation plan III: The present invention provides a computer-readable storage medium storing a computer program configured to implement the steps of the prediction method for the shrinkage and creep deformation of high-strength concrete filled steel tubes under early-age loading when called by a processor.

[0119] The other combinations and connection relationships in this implementation plan are the same as those in specific implementation plan I.

[0120] Simulation experiment

[0121] The shrinkage strain development characteristics of concrete with different water-binder ratios were obtained from a 410-day shrinkage test of high-strength concrete filled steel tubes; the creep strain development characteristics of members with different water-binder ratios at different loading ages were obtained from a 325-day creep test of high-strength concrete filled steel tubes.

[0122] Conduct the shrinkage and creep tests on high-performance concrete filled steel tubes according to the test plan in Table 1. Use two high-performance concrete mix ratios with water-binder ratios of 0.26 and 0.32 to fabricate high-performance concrete filled steel tube specimens with dimensions of 140 mm (outer diameter) × 2.9 mm (wall thickness) × 400 mm (height). After curing for 24 hours, seal the top of the specimens with three layers of adhesive aluminum foil to ensure that the concrete cannot exchange moisture with the external environment. Remove the adhesive aluminum foil one day before the loading age, grind the concrete flush with the top of the steel tube, and cover with end plates. The loading ages are determined as the 3rd, 7th, 14th, 15th, and 32nd days after concrete pouring, and two parallel specimens (a, b) are set for each test parameter. Set the constant temperature and humidity environment to a relative humidity of 55% and a temperature of 17.5°C. In this embodiment, the loading age, water-binder ratio, average value of the compressive strength of concrete cylinders and elastic modulus at the loading age, outer diameter and wall thickness of the steel tube of the high-performance concrete filled steel tube are shown in Table 1; the loads borne are as shown in Table 1; the elastic modulus of the outer steel tube is 2.10×10 5 GPa, the yield strength is 327.3 MPa, the ultimate strength is 428.5 MPa, and the Poisson's ratio is 0.284. The shrinkage and creep tests are carried out in accordance with Figure 2 . Use a handheld DEMEC displacement gauge to measure the elastic deformation and creep deformation generated after the high-performance concrete filled steel tube bears the load, and use an embedded strain gauge to measure the shrinkage deformation of the high-performance concrete filled steel tube. Number description: Taking T3-w0.32-a as an example, T3 indicates that the loading age of the component is the 3rd day after concrete pouring; w0.32 indicates that the water-binder ratio of the high-performance concrete is 0.32; a indicates the number of parallel specimens with the same parameters; S-w0.32 indicates that the water-binder ratio of the component concrete is 0.32.

[0123] Table 1 Specimen parameters of high-performance concrete filled steel tube, properties of concrete and steel tube, shrinkage and creep test information

[0124]

[0125]

[0126] Using the prediction method for shrinkage and creep deformation of high-performance concrete filled steel tube under early-age loading in the present invention, calculate by taking the basic parameters of the high-performance concrete, outer steel tube, and creep test measured by the experiment. The calculation process is as follows:

[0127] (1) Determine the basic performance parameters of the shrinkage and creep tests of high-performance concrete filled steel tube: The loading age, water-binder ratio, average value of the compressive strength of concrete cylinders and elastic modulus at the loading age, outer diameter and wall thickness of the steel tube, and the load borne by the high-performance concrete filled steel tube are taken according to Table 1; the elastic modulus of the outer steel tube is 2.10×10 5GPa, the yield strength is 327.3 MPa, the ultimate strength is 428.5 MPa, and the Poisson's ratio is 0.284; the size of the component is 140 mm (outer diameter) × 2.9 mm (wall thickness) × 400 mm (height); the relative humidity of the environment is 55% and the temperature is 17.5 °C.

[0128] (2) Perform shrinkage and creep tests on high-performance concrete filled steel tubes, and the test results are as Figures 3 - 5 shown. It can be seen from Figure 3 that the shrinkage deformation of high-performance concrete filled steel tubes has tended to be stable at 410 days, and the lower the water-binder ratio, the greater the autogenous shrinkage; it can be seen from Figure 4 and Figure 5 that the creep degree (the creep degree is the ratio of the creep deformation to the stress of the concrete at the initial stage of loading) has tended to be stable at 325 days. The earlier the loading age, the greater the creep degree, and the lower the water-binder ratio, the more significant the influence of the early-age loading on creep. All the above influencing factors need to be considered in the shrinkage and creep prediction models proposed in the present invention.

[0129] (3) Based on the autogenous shrinkage model of the code BS EN 1992, considering the influence of the water-binder ratio of concrete, by introducing the influence coefficient of the water-binder ratio of concrete on shrinkage, the calculation formula for the shrinkage model of high-performance concrete considering the influence of the water-binder ratio is established:

[0130]

[0131] In the formula, ε sh is the shrinkage deformation of high-performance concrete, ×10 -6 ; w is the water consumption of high-performance concrete, kg / m 3 ; b is the mass of cement, silica fume, fly ash, slag powder and expansive agent in high-performance concrete, kg / m 3 ; t is the age in high-performance concrete, days;

[0132] α1, α2 and α3 are unknown parameters.

[0133] (4) Through the least squares method, perform non-linear regression analysis on the shrinkage test results, considering the influence of the water-binder ratio of concrete on concrete shrinkage, and the mathematical expressions of α1, α2 and α3 obtained by fitting are:

[0134] α1 = 6(20)

[0135] α2 = 21(21)

[0136] α3 = 18(22)

[0137] The comparison between the predicted results of the shrinkage deformation of high-performance concrete filled steel tubes calculated by this prediction method and the measured test results is as Figure 3 shown. FromFigure 3 It can be seen that the calculated values of the shrinkage model of high-performance concrete are in good agreement with the test results, and the prediction error at 240 days is only 5%. The results show that the results of the prediction method for the shrinkage and creep deformation of high-strength concrete filled steel tubes under early-age loading of the present invention can accurately reflect the development law of the shrinkage deformation of high-performance concrete with different water-binder ratios.

[0138] (5) In this paper, to consider the different effects of the loading age on the creep deformation of components under different water-binder ratios, by introducing the influence coefficient of the water-binder ratio of concrete on creep, a calculation formula for the shrinkage model of high-performance concrete considering the different effects of the loading age on the creep deformation of components under different water-binder ratios is established:

[0139] C(t,t0) = k(t0)·C(t,28)(23)

[0140]

[0141] In the formula, C(t,t0) is the creep coefficient of high-performance concrete from the t0th day after the specimen is cast until the tth day while maintaining the load (the creep coefficient is the ratio of the creep deformation to the stress of the concrete at the initial stage of loading), ×10 -6 / MPa; C(t,28) is the creep coefficient of high-performance concrete from the 28th day after the specimen is cast until the tth day while maintaining the load, ×10 -6 / MPa; k(t0) is the influence coefficient of the loading age; t is the age of high-performance concrete, in days; t0 is the loading age of high-performance concrete, in days; β1, β2 and β3 are unknown parameters.

[0142] (6) Considering that the formula (6) must satisfy boundary condition 1: when the loading age t0 = 28, k(t0) = 1; boundary condition 2: when the loading age t0 approaches infinity, k(t0) = 0.5; based on the above two conditions, the mathematical expressions for β1 and β2 are:

[0143] β1 = 0.5(25)

[0144] β2 = 0.5(β3 + 28)(26)

[0145] (7) Based on the different effects of the loading age on the creep of high-strength concrete filled steel tubes under different concrete water-binder ratios, a function of the concrete water-binder ratio is constructed as:

[0146]

[0147] In the formula, γ1 and γ2 are unknown parameters.

[0148] (8) By using the least squares method, perform a non-linear regression analysis on the creep test results, considering the influence of the water-binder ratio of concrete on concrete shrinkage. The mathematical expressions for γ1 and γ2 obtained by fitting are:

[0149] γ1 = 15(28)

[0150] γ2 = 2(29)

[0151] (9) Use programming software such as C++ and Matlab to implement the Step-by-Step Method. Considering the influence that the creep deformation develops rapidly in the early stage and slowly in the later stage, divide the time step into 100 steps. The division method is:

[0152]

[0153] where Δt k is the time step length between any time t k and the previous time t k-1 ; Δt i is the time step length between any time t i and the previous time t i-1 ; k is the time step serial number.

[0154] (10) Use programming software such as C++ and Matlab to implement the Step-by-Step Method. Considering the influence of stress redistribution between high-performance concrete and steel components when the high-strength concrete-filled steel tubular member is under a constant load, establish the stress-strain relationship of concrete according to the trapezoidal integration rule as:

[0155]

[0156] where t k-1 and t k are the start time and end time of the k-th step respectively, in days; σ ck and σ cj are the stresses of concrete at time t k and t j respectively, in MPa; ε totk and ε shk are the total deformation and shrinkage of concrete at time t k respectively; M c1k and M c2kj are the creep influence coefficients respectively; J(t k , t j ) is the creep function of concrete from the time tj when it starts to bear a constant load to the time tk.

[0157] (11) The calculation method for implementing creep deformation using programming software such as C++ and Matlab is:

[0158]

[0159] ε ck = ε totk -ε shk (35)

[0160] Wherein, N L is the constant load borne by the high-performance concrete-filled steel tube, N; A c is the cross-sectional area of the concrete, mm 2 ; E s is the elastic modulus of the steel tube, MPa; A s is the cross-sectional area of the steel tube, mm 2 ; σ cj is the stress of the concrete at time t j , MPa; ε totk and ε ck are the total deformation and creep deformation of the concrete at time t k , ×10 -6 ; ε shk is the shrinkage deformation of the concrete at time t k , ×10 -6 , calculated according to formula (1).

[0161] (12) The creep function J(t k , t j ) is calculated using formula (23), and the calculation method is as follows:

[0162]

[0163] Wherein, E c (t j ) is the elastic modulus of the high-performance concrete at time t j , MPa; E c (t0) is the elastic modulus of the high-performance concrete at time t0, MPa; E c (28) is the elastic modulus of the high-performance concrete on the 28th day after pouring; C(t k , tj) is the creep degree of the high-performance concrete from the t j th day after pouring the specimen until the t k th day, ×10 -6 / MPa, calculated according to formula (23).

[0164] (13) The elastic modulus E j of the high-performance concrete at time t c (t j ) is calculated using the elastic modulus calculation formula provided by BSEN1992.

[0165] The predicted results of the creep coefficient of high-performance concrete filled steel tubes (the creep coefficient is the ratio of creep deformation to the stress of concrete at the initial stage of loading) calculated by this prediction method are compared with the measured results of the test as follows Figure 4 and Figure 5 shown. It can be seen from Figure 4 and Figure 5 that the calculated values of the creep model of high-performance concrete filled steel tubes are in good agreement with the test results, and the prediction error at 325 days is only 6%. The results show that the results of the prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading of the present invention can accurately reflect the creep development law of high-performance concrete filled steel tubes with different water-binder ratios under early-age loading.

[0166] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art of the present invention can make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will all fall within the protection scope of the present invention.

Claims

1. A prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading, characterized in that It includes the following steps: S100. Conduct shrinkage and creep tests on high-performance concrete filled steel tubes with different concrete water-binder ratios at different loading ages to obtain the experimental results of shrinkage strain and creep strain. S200. Calculate the shrinkage deformation and creep deformation at the concrete level. S300. Calculate the shrinkage deformation and creep deformation at the composite member level by using the step-by-step integration method.

2. The prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading according to claim 1, characterized in that, In step S100, it includes: pouring N groups of high-performance concrete filled steel tube specimens and conducting shrinkage and creep tests; where N≥8, and each group of specimens includes 2 parallel specimens; the concrete water-binder ratios and loading ages of the N groups of high-performance concrete filled steel tube specimens are different.

3. The prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading according to claim 2, wherein: The value range of the concrete water-binder ratio is 0.25 - 0.45, and the values of the loading age are 3 days, 7 days, 14 days, and 28 days.

4. The prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading according to claim 1, characterized in that: In step S200, when calculating the shrinkage deformation at the high-performance concrete level, it includes conducting a non-linear regression analysis on the shrinkage strains of high-performance concrete filled steel tubes with different concrete water-binder ratios, and by introducing the influence coefficient of the concrete water-binder ratio on shrinkage, establishing a shrinkage model for high-performance concrete to obtain the shrinkage strains of high-performance concrete with different water-binder ratios. The calculation formula for the shrinkage deformation is: where ε sh is the shrinkage deformation of high-performance concrete; w is the water consumption of high-performance concrete; b is the mass of cement, silica fume, fly ash, slag powder and expansive agent in high-performance concrete; t is the age of the high-performance concrete, in days; α1, α2, and α3 are unknown parameters. The specific method for obtaining the three constants α1, α2, and α3 is: through the least squares method, conduct a non-linear regression analysis on the test results, considering the influence of the concrete water-binder ratio on concrete shrinkage, and the mathematical expressions for α1, α2, and α3 obtained by fitting are: α1＝6(2) α2＝21(3) α3＝18(4)。 5. The prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading according to claim 4, wherein: In step S200, when calculating the creep deformation at the high-performance concrete level, it includes conducting a non-linear regression analysis on the creep tests of high-performance concrete filled steel tubes with different concrete water-binder ratios at different loading ages. Based on the different influences of the loading age on the creep of high-performance concrete filled steel tubes under different concrete water-binder ratios, by introducing the influence coefficient of the concrete water-binder ratio on creep, establishing a creep model for high-performance concrete to obtain the creep strains of high-performance concrete filled steel tubes with different concrete water-binder ratios at different loading ages. The calculation formula for the creep deformation is: C(t,t0)=k(t0)·C(t,28)(5) In the formula, C(t,t0) is the creep coefficient of high-performance concrete from the t0th day after pouring the specimen to the tth day under sustained load (the creep coefficient is the ratio of the creep deformation to the stress of the concrete at the initial stage of loading); C(t,28) is the creep coefficient of high-performance concrete from the 28th day after pouring the specimen to the tth day under sustained load; k(t0) is the influence coefficient of the loading age. t is the age of the high-performance concrete; t0 is the loading age of the high-performance concrete; β1, β2, and β3 are unknown parameters. The specific method for obtaining the two constants β1 and β2 is: Formula (6) satisfies boundary condition 1: when the loading age t0 = 28, k(t0) = 1; boundary condition 2: when the loading age t0 approaches infinity, k(t0) = 0.5; based on the above two conditions, the mathematical expressions for β1 and β2 are: β1＝0.5(7) β2＝0.5(β3+28)(8) The specific method for obtaining the constant β3 is as follows: Based on the different effects of loading age on the creep of high-performance concrete filled steel tubes under different water-binder ratios of concrete, the function of β3 with respect to the water-binder ratio of concrete is constructed as: where γ1 and γ2 are unknown parameters; The specific method for obtaining the two constants γ1 and γ2 is as follows: Through the least squares method, based on the test results, a non-linear regression analysis is performed, and the mathematical expressions for γ1 and γ2 obtained by fitting are: γ1 = 15(10) γ2 = 2(11).

6. The prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading according to claim 5, characterized in that: In step S300, it includes Using the step-by-step integration method, considering the influence that the creep deformation develops rapidly in the early stage and slowly in the later stage, the time step is divided into M steps, and the division method is: where, Δt k is the time step length between any time t k and the previous time t k-1 ; Δt i is the time step length between any time t i and the previous time t i-1 ; t end is the age of the high-performance concrete when the high-strength concrete-filled steel tube stops bearing the load; k is the time step number; M is the number of time steps into which the time period from the start of load holding on the t0th day to the tth day is divided; Using the step-by-step integration method, considering the influence of stress redistribution between high-performance concrete and steel components in a high-performance concrete filled steel tube component under a constant load, the stress-strain relationship of concrete is established according to the trapezoidal integration rule as: where t k-1 and t k are the start time and end time of the k-th step respectively; σ ck and σ cj are the stresses of the concrete at times t k and t j respectively; ε totk and ε shk are respectively the total deformation and total shrinkage of concrete at time t; M k and M c1k are both creep influence coefficients; J(t c2kj , t k is the creep function of concrete from time t j when it starts to bear a constant load to time t j ; k ​ Considering that in a high-performance concrete filled steel tube component under a constant load, the high-performance concrete and the steel component jointly bear the vertical load, and the deformations of the two parts are coordinated, the shrinkage deformation and creep deformation of the high-performance concrete filled steel tube component are calculated according to the force balance equation and the deformation coordination equation, specifically including Using the step-by-step integration method, the calculation method of creep deformation is: ε ck = ε totk -ε shk (17) Where N L is the constant load borne by the high-performance concrete-filled steel tube; A c is the cross-sectional area of the concrete; E s is the elastic modulus of the steel tube; A s is the cross-sectional area of the steel tube; σ cj is the stress of the concrete at time t j ; ε totk and ε ck are the total deformation and creep deformation of concrete at time t k respectively; ε shk is the shrinkage deformation of concrete at time t k respectively. Creep function J(t k ,t j ) is calculated using formula (5), and the calculation method is as follows: Where, E c (t j ) is the elastic modulus of high-performance concrete at time t j ; E c (t0) is the elastic modulus of high-performance concrete at time t0; E c (28) is the elastic modulus of high-performance concrete on the 28th day after pouring; C(t k , t j ) is the creep degree of high-performance concrete from the t j th day after the specimen is poured until the t k th day after holding the load; The elastic modulus E of high-performance concrete at time t j is calculated using the elastic modulus calculation formula provided by BSEN1992. c (t j ) 7. Prediction system for shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading, characterized in that: This system has program modules corresponding to the steps of any one of the above claims 1-5, and when running, it executes the steps in the above prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the prediction method for the shrinkage and creep deformation of high-performance concrete filled steel tubes under early-age loading as described in any one of claims 1-5 when called by a processor.

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