Method and system for predicting shrinkage and creep deformation of high performance concrete filled steel tube under early age loading

Abstract

The application provides a method and system for predicting the shrinkage and creep deformation of early-age loaded steel pipe high-performance concrete, and belongs to the field of concrete. In order to solve the problems that the self-shrinkage of the steel pipe high-performance concrete is underestimated, the influence of loading age on the creep deformation of the component under different water-binder ratios is not considered, and the prediction result of the creep deformation of the steel pipe high-performance concrete is inaccurate, the application comprises the following steps: carrying out shrinkage and creep tests on the steel pipe high-performance concrete with different water-binder ratios under different loading ages, obtaining experimental results of shrinkage and creep strain, carrying out nonlinear regression analysis on the shrinkage and creep test results of the steel pipe high-performance concrete with different water-binder ratios under different loading ages, introducing the influence coefficient of the water-binder ratio of the concrete on the shrinkage and creep, establishing a high-performance concrete shrinkage and creep model, and adopting a step-by-step integration method to consider the shrinkage and creep deformation of the steel pipe high-performance concrete after stress redistribution.

Description

Technical Field

[0001] This invention relates to the field of concrete technology, and more specifically, to a method and system for predicting shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading. Background Technology

[0002] High-performance concrete in steel tubes (HPTCs) are high-performance composite components formed by filling high-strength self-compacting concrete into steel tubes and adding high-quality expansion agents. This technology solves common problems associated with HPTCs, such as insufficient compaction of the concrete inside the tube and debonding between the steel tube and concrete during service. It has become the development direction for large-scale HPTC structures. This new type of composite component inherits the advantages of high-strength HPTCs, such as high load-bearing capacity, high stiffness, good ductility, and efficient construction, while also possessing advantages such as easy pumping and low shrinkage. Its competitiveness is particularly prominent in high-intensity earthquake zones, and it has been applied in many super high-rise buildings, long-span bridges, and tall structures in recent years.

[0003] In high-performance concrete (HPC) steel-tube structures, early-age loading of concrete is a common occurrence. In HPC structures, the steel tube not only shares the load with the concrete but also serves as a formwork during concrete pouring, meaning the concrete begins to bear loads once it reaches strength. Furthermore, due to tight construction schedules, the core concrete often begins to bear subsequent loads 3–7 days after pouring. Early-age creep in HPC steel-tube structures can lead to long-term deformation of the member reaching 0.5–1.3 times the short-term deformation, and this deformation increment is 1.5–3 times that of creep deformation after 28 days of loading. Early-age loading not only significantly increases creep deformation but also results in higher shrinkage deformation of HPC. To further clarify the development of shrinkage and creep deformation in HPC steel-tube structures under early-age loading and to ensure the service life and structural safety of the project, it is crucial to consider the differences in the impact of loading age on creep deformation under different water-cement ratios and to propose a method for predicting shrinkage and creep deformation in HPC steel-tube structures under early-age loading.

[0004] Existing technologies mainly include: BS EN 1992 creep model, fib MC2010 creep model, ACI 209 creep model, B4 creep model, and AFREM creep model, etc. The main drawbacks of existing technologies are:

[0005] (1) Due to the sealing effect of the outer steel pipe, the high-performance concrete is prevented from exchanging moisture with the outside air, and the sealed concrete only undergoes autogenous shrinkage. Existing technology basically underestimates the shrinkage of sealed concrete, especially the shrinkage of sealed low water-cement ratio concrete, which can be underestimated by 1.5 to 2.6 times. Therefore, an accurate model for predicting the shrinkage deformation of sealed concrete is needed.

[0006] (2) Existing technology only considers the effect of loading age on concrete creep, and does not yet consider that the effect of loading age on creep deformation of components is different under different water-cement ratios. Failure to consider this effect will lead to an underestimation of creep deformation of low water-cement ratio concrete by 60% to 80%. Summary of the Invention

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

[0008] To address the issue that the autogenous shrinkage of high-performance concrete in steel tubes is underestimated, and the different effects of loading age on creep deformation of components under different water-cement ratios are not considered, which leads to inaccurate prediction results of creep deformation of high-performance concrete in steel tubes.

[0009] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0010] This invention provides a method for predicting the shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading, comprising the following steps:

[0011] S100. Shrinkage and creep tests were conducted on high-performance steel-tube concrete with different water-cement ratios at different loading ages to obtain the experimental results of shrinkage strain and creep strain.

[0012] S200, On the concrete layer, shrinkage deformation and creep deformation are calculated;

[0013] S300. At the level of composite components, the shrinkage deformation and creep deformation are calculated using the step-by-step integration method.

[0014] Further, step S100 includes: casting N groups of high-performance concrete specimens in steel tubes and conducting shrinkage and creep tests; wherein, N≥8, each group of specimens includes 2 parallel specimens; the water-cement ratio and loading age of the concrete in the N groups of high-performance concrete specimens in steel tubes are different.

[0015] Furthermore, the water-cement ratio of the concrete ranges from 0.25 to 0.45, and the loading age ranges from 3 days, 7 days, 14 days, and 28 days.

[0016] Further, in step S200, the shrinkage deformation of the high-performance concrete layer is calculated, including nonlinear regression analysis of the shrinkage strain of steel-tube high-performance concrete with different water-cement ratios. By introducing the influence coefficient of the water-cement ratio on shrinkage, a high-performance concrete shrinkage model is established to obtain the shrinkage strain of high-performance concrete with different water-cement ratios.

[0017] The formula for calculating shrinkage deformation is:

[0018]

[0019] In the formula, εsh α1 is the shrinkage deformation of high-performance concrete; w is the water content of high-performance concrete; b is the mass of cement, silica fume, fly ash, mineral powder and expansion agent of 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: Using the least squares method, a nonlinear regression analysis is performed on the experimental results, considering the influence of the concrete water-cement ratio on concrete shrinkage. The mathematical expressions for α1, α2, and α3 are then fitted as follows:

[0021] α1=6(2)

[0022] α2=21(3)

[0023] α3=18(4).

[0024] Further, in step S200, the creep deformation of the high-performance concrete layer is calculated, including nonlinear regression analysis of creep tests of steel-tube high-performance concrete at different loading ages with different concrete water-cement ratios. Based on the different effects of loading age on the creep of steel-tube high-performance concrete under different concrete water-cement ratios, a high-performance concrete creep model is established by introducing the influence coefficient of concrete water-cement ratio on creep, and the creep strain of steel-tube high-performance concrete at different loading ages with different concrete water-cement ratios is obtained.

[0025] The formula for calculating creep deformation is:

[0026] C(t,t0)=k(t0)·C(t,28)(5)

[0027]

[0028] In the formula, C(t,t0) is the creep degree of high-performance concrete from day t0 after the specimen is poured to day t after the load is applied (creep degree is the ratio of creep deformation to the stress of the concrete in the initial stage of loading); C(t,28) is the creep degree of high-performance concrete from day 28 after the specimen is poured to day t after the load is applied; 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 as follows:

[0030] Formula (6) satisfies boundary condition one: when the loading age t0 = 28, k(t0) = 1; boundary condition two: 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 loading age on the creep of high-performance steel-tube concrete under different concrete water-cement ratios, β3 is constructed as a function of the concrete water-cement ratio:

[0034]

[0035] In the formula, γ1 and γ2 are unknown parameters;

[0036] The specific method for obtaining the two constants γ1 and γ2 is as follows: Using the least squares method, based on the experimental results, a nonlinear regression analysis is performed to fit the mathematical expressions for γ1 and γ2 as follows:

[0037] γ1=15 (10)

[0038] γ2=2(11).

[0039] Further, in step S300, the following are included:

[0040] Using the step-by-step integration method, considering the rapid early-stage and slow-stage development of creep deformation, the time step is divided into M steps, and the division method is as follows:

[0041]

[0042] In the formula, Δt k It is any time t k Compared to the previous time t k-1 The length of the time step; Δt i It is any time t i Compared to the previous time t i-1 The length of the time step; t end is the age of the high-performance concrete when the steel-tube high-performance concrete stops bearing load; k is the time step number; M is the number of time steps divided into the period from the start of the load on day t0 to after day t.

[0043] Using the successive integration method, considering the stress redistribution effect between high-performance concrete and steel components under constant load, the stress-strain relationship of concrete is established according to the trapezoidal integration rule:

[0044]

[0045] In the formula, t k-1 With t k These are the start and end times of step k, respectively; σ ckand σ cj They are t k With t j The stress in concrete at any given moment; ε totk and ε shk They are t k The total deformation and total shrinkage of concrete at any given moment; M c1k and M c2kj All are creep influence coefficients;

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

[0047] Considering that a high-performance concrete (HPC) steel-tube member is subjected to a constant load, with the HPC and steel components sharing the vertical load and the two parts deforming in harmony, the shrinkage and creep deformations of the HPC steel-tube member are calculated according to the force balance equation and deformation compatibility equation. Specifically, this includes...

[0048] The creep deformation is calculated using the successive integration method as follows:

[0049]

[0050] ε ck =ε totk -ε shk (17)

[0051] In the formula, N L It is a constant load borne by high-performance concrete with steel pipes; A c It is the cross-sectional area of ​​the concrete; E s It is the elastic modulus of the steel pipe; A s It is the cross-sectional area of ​​the steel pipe; σ cj It is t j The stress in concrete at any given moment; ε totk and ε ck They are t k Total deformation and creep deformation of concrete at any given time; ε shk It is t k The shrinkage and deformation of concrete at all times;

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

[0053]

[0054] In the formula, E c (t j ) is high-performance concrete in t j The elastic modulus at time 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 ,tj) refers to the period from day tj after the specimen is poured until day t. k Creep of high-performance concrete in Tianhou;

[0055] High-performance concrete in t j Elastic modulus E at time t c (t j The calculation was performed using the elastic modulus calculation formula provided by BSEN1992.

[0056] A prediction system for shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete. The system has program modules corresponding to the above steps, and executes the steps in the prediction method for shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete during operation.

[0057] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement steps of a method for predicting shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete.

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

[0059] (1) This invention provides a method for determining the shrinkage and creep deformation models of high-performance concrete components with steel tubes. Based on the shrinkage and creep characteristics of high-performance concrete with steel tubes, a shrinkage deformation model of high-performance concrete considering the influence of water-cement ratio is established, and a shrinkage strain prediction model of high-performance concrete under different water-cement ratios is determined.

[0060] (2) This invention considers the difference in the influence of loading age on the creep deformation of high-performance concrete components with different water-cement ratios. By introducing the influence coefficient of concrete water-cement ratio on creep, a creep deformation prediction model for high-performance concrete with different water-cement ratios under early loading is determined.

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

[0062] (4) Experiments show that the prediction results of the method for predicting shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading of the present invention are relatively consistent with the experimental test results, proving that the model established by the present invention has high accuracy. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating a method for predicting shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading, as described in an embodiment of the present invention.

[0064] Figure 2 This is a diagram of the experimental setup for early-age loading of high-performance steel-tube concrete to study shrinkage and creep deformation in an embodiment of the present invention.

[0065] Figure 3 This is a comparison chart of the predicted shrinkage deformation results of high-performance concrete and the experimental measured results in the embodiments of the present invention;

[0066] Figure 4 This is a comparison chart of the predicted creep deformation results and the experimental measured results of high-performance steel-tube concrete with a water-cement ratio of 0.32 under early-age loading in this embodiment of the invention.

[0067] Figure 5 This is a comparison chart of the predicted creep deformation results and the experimental measured results of high-performance steel-tube concrete with a water-cement ratio of 0.26 under early-age loading in this embodiment of the invention.

[0068] Explanation of reference numerals in the attached figures:

[0069] 1. Nut; 2. Hydraulic jack; 3. Reaction plate; 4. Ball joint; 5. Prestressed tendon; 6. Loaded creep specimen; 7. Loading plate; 8. Force sensor; 9. Disc spring; 10. Unloaded shrinkage specimen; 11. Creep loading frame support. Detailed Implementation

[0070] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0071] Specific Implementation Plan 1: Combining Figure 1 and Figure 2 As shown, this invention provides a method for predicting the shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading, comprising the following steps:

[0072] S100. Shrinkage and creep tests were conducted on high-performance steel-tube concrete with different water-cement ratios at different loading ages to obtain experimental results of shrinkage strain and creep strain.

[0073] use Figure 2The experimental setup shown is used for testing. The setup includes a creep loading frame support 11 at the bottom, on which an unloaded shrinkage specimen 10 is placed. The specimen is connected to the base plate via multiple disc springs 9. At the center of the base plate, a force sensor 8, a loading plate 7, and a loaded creep specimen 6 are arranged in sequence. The upper end of the loaded creep specimen 6 is connected to the reaction plate 3 via a ball joint 4. A hydraulic jack 2 is placed above the reaction plate 3. The output end of the hydraulic jack 2 is connected to the center of the reaction plate 3. At least two prestressing tendons 5 are provided between the top of the hydraulic jack 2 and the base plate. The prestressing tendons 5 are connected to the top of the hydraulic jack 2 via nuts 1, and the prestressing tendons 5 penetrate the reaction plate 3.

[0074] N groups of high-performance concrete specimens with steel tubes were poured and shrinkage and creep tests were carried out; where N≥8, each group of specimens included 2 parallel specimens; the water-cement ratio and loading age of the concrete in the N groups of high-performance concrete specimens with steel tubes were different; the water-cement ratio ranged from 0.25 to 0.45, and the loading age ranged from 3 days, 7 days, 14 days and 28 days.

[0075] S200, at the concrete level, calculations are performed on shrinkage and creep deformation, including...

[0076] S210. Calculate the shrinkage deformation of high-performance concrete layers, including nonlinear regression analysis of the shrinkage strain of steel-tube high-performance concrete with different water-cement ratios. By introducing the influence coefficient of water-cement ratio on shrinkage, a high-performance concrete shrinkage model is established to obtain the shrinkage strain of high-performance concrete with different water-cement ratios.

[0077] The formula for calculating shrinkage deformation is:

[0078]

[0079] In the formula, ε sh It is the shrinkage deformation of high-performance concrete, ×10 -6 w represents the water content of high-performance concrete, in kg / m³. 3 b represents the mass of cement, silica fume, fly ash, mineral powder, and expansive agent in high-performance concrete, in kg / m³. 3 t is the age of high-performance concrete, in days; α1, α2, and α3 are unknown parameters.

[0080] The specific method for obtaining the three constants α1, α2, and α3 is as follows: Using the least squares method, based on the experimental results, a nonlinear regression analysis is performed, considering the influence of the concrete water-cement ratio on concrete shrinkage. The mathematical expressions for α1, α2, and α3 are then fitted as follows:

[0081] α1=6(2)

[0082] α2=21(3)

[0083] α3=18(4)

[0084] S220. Calculate the creep deformation of high-performance concrete layers, including nonlinear regression analysis of creep tests of high-performance steel-tube concrete with different concrete water-cement ratios at different loading ages. Based on the different effects of loading age on the creep of high-performance steel-tube concrete with different concrete water-cement ratios, a creep model of high-performance concrete is established by introducing the influence coefficient of concrete water-cement ratio on creep, and the creep strain of high-performance steel-tube concrete with different concrete water-cement ratios at different loading ages is obtained.

[0085] The formula for calculating creep deformation is:

[0086] C(t,t0)=k(t0)·C(t,28)(5)

[0087]

[0088] In the formula, C(t,t0) represents the creep of the high-performance concrete from day t0 after the specimen is poured until day t after the load is applied (creep is the ratio of creep deformation to the initial stress of the concrete under load), ×10 -6 / MPa; C(t,28) is the creep of high-performance concrete from day 28 after casting to day t after holding the load, ×10 -6 / MPa, the creep rate at 28 days of loading is used as a reference because 28 days is the most common loading age for steel-tube high-performance concrete 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] Formula (6) must satisfy boundary condition one: when the loading age t0 = 28, k(t0) = 1; boundary condition two: 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 obtained as follows:

[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 age on the creep of high-performance steel-tube concrete under different concrete water-cement ratios, β3 is constructed as a function of the concrete water-cement ratio:

[0094]

[0095] In the formula, γ1 and γ2 are unknown parameters;

[0096] The specific method for obtaining the two constants γ1 and γ2 is as follows: Using the least squares method, based on the experimental results, a nonlinear regression analysis is performed to fit the mathematical expressions for γ1 and γ2 as follows:

[0097] γ1=15(10)

[0098] γ2=2(11)

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

[0100] The step-by-step integration method is adopted, considering the influence of rapid early-stage creep deformation and slow late-stage creep deformation. The time step is divided into M steps, and the division method is as follows:

[0101]

[0102] In the formula, Δt k It is any time t k Compared to the previous time t k-1 The length of the time step; Δt i It is any time t i Compared to the previous time t i-1 The length of the time step; t end is the age of the high-performance concrete when the steel-tube high-performance concrete stops bearing load; k is the time step number; M is the number of time steps divided into the period from the start of the load on day t0 to after day t.

[0103] Using the step-by-step integration method, considering the stress redistribution between the high-performance concrete and the steel components in a steel-tube high-performance concrete member under constant load, the stress-strain relationship of the concrete is established according to the trapezoidal integration rule as follows:

[0104]

[0105]

[0106] In the formula, t k-1 With t k These are the start and end times of step k, respectively, in days; σ ck and σ cj They are t k With t j The stress in concrete at any given time, in MPa; ε totk and ε shk They are tk The total deformation and total shrinkage of concrete at any given moment; M c1k and M c2kj Both are creep influence coefficients; J(t) k ,t j ) is the creep function of concrete from time tj to time tk under constant load;

[0107] Considering that a high-performance concrete (HPC) steel-tube member is subjected to a constant load, with the HPC and steel components sharing the vertical load and the two parts deforming in harmony, the shrinkage and creep deformations of the HPC steel-tube member are calculated according to the force balance equation and deformation compatibility equation. Specifically, this includes...

[0108] The step-by-step integration method is used to calculate creep deformation as follows:

[0109]

[0110] ε ck =ε totk -ε shk (17)

[0111] In the formula, N L It is the constant load borne by the steel-tube high-performance concrete, N; A c It is the cross-sectional area of ​​the concrete, in mm. 2 E s A is the elastic modulus of the steel pipe, measured in MPa. s It is the cross-sectional area of ​​the steel pipe, in mm². 2 ;σ cj It is t j The stress in concrete at any given time, in MPa; ε totk and ε ck They are t k Total deformation and creep deformation of concrete at any time, ×10 -6 ;ε shk It is t k Shrinkage deformation of concrete at all times, ×10 -6 Calculate according to formula (1);

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

[0113]

[0114] In the formula, E c (t j ) is high-performance concrete in t j Elastic modulus at time t, MPa; E c(t0) is the elastic modulus of high-performance concrete at time t0, in MPa; E c (28) is the elastic modulus of high-performance concrete on the 28th day after pouring, in MPa; C(t) k ,tj) is the tth day after the specimen is poured. j The load begins to hold from day t until day t. k Creep of high-performance concrete, ×10 -6 / MPa, calculated according to formula (5);

[0115] High-performance concrete in t j Elastic modulus E at time t c (t j The calculation was performed using the elastic modulus calculation formula provided by BSEN 1992.

[0116] Specific Implementation Scheme 2: The present invention provides a prediction system for shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete. The system has a program module corresponding to the above steps, and executes the steps in the above-described prediction method for shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete when running.

[0117] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0118] Specific Implementation Scheme 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement, when called by a processor, a method for predicting shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading.

[0119] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0120] Simulation Experiment

[0121] Shrinkage test of high-performance concrete with steel tubes for 410 days was used to obtain the shrinkage strain development characteristics of concrete with different water-cement ratios; creep test of high-performance concrete with steel tubes for 325 days was used to obtain the creep strain development characteristics of components with different water-cement ratios at different loading ages.

[0122] Shrinkage and creep tests of high-performance concrete in steel tubes were conducted according to the test scheme in Table 1. Two high-performance concrete mix proportions with water-cement ratios of 0.26 and 0.32 were used. High-performance concrete specimens in steel tubes with dimensions of 140 mm (outer diameter) × 2.9 mm (wall thickness) × 400 mm (height) were prepared. After curing for 24 hours, the top of the specimens was sealed with three layers of adhesive aluminum foil to prevent moisture exchange between the concrete and the external environment. One day before the loading age, the adhesive aluminum foil was removed, the concrete was ground smooth until it was level with the top of the steel tube, and end plates were added. The loading ages were determined to be 3, 7, 14, 15, and 32 days after concrete pouring. Two parallel specimens (a and b) were prepared for each test parameter. The constant temperature and humidity environment was set at a relative humidity of 55% and a temperature of 17.5℃. In this embodiment, the loading age, water-cement ratio, average compressive strength and elastic modulus of the concrete cylinder at the loading age, outer diameter and wall thickness of the steel pipe high-performance concrete are shown in Table 1; the loads borne are shown in Table 1; the elastic modulus of the outer steel pipe is 2.10 × 10⁻⁶. 5 The strength is GPa, yield strength is 327.3 MPa, ultimate strength is 428.5 MPa, and Poisson's ratio is 0.284. Shrinkage and creep tests are conducted according to... Figure 2 The experiment used a handheld DEMEC displacement gauge to measure the elastic deformation and creep deformation of the high-performance concrete in the steel tube under load, and an embedded strain gauge to measure the shrinkage deformation of the high-performance concrete in the steel tube. Numbering explanation: For example, T3-w0.32-a, T3 indicates that the loading age of the component is the 3rd day after concrete pouring; w0.32 indicates that the water-cement 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-cement ratio of the component concrete is 0.32.

[0123] Table 1. Specimen parameters, concrete and steel pipe properties, shrinkage and creep test information for high-performance concrete with steel tubes.

[0124]

[0125]

[0126] The method for predicting shrinkage and creep deformation of high-performance concrete with steel tubes under early-age loading, as described in this invention, is used to calculate the deformation based on the basic parameters of high-performance concrete, the outer steel tube, and the creep test, as determined by experiments. The calculation process is as follows:

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

[0128] (2) Shrinkage and creep tests were conducted on high-performance concrete with steel tubes. The test results are as follows: Figures 3-5 As shown. By Figure 3 It can be seen that the shrinkage deformation of high-performance concrete with steel pipes tends to stabilize after 410 days, and the lower the water-cement ratio, the greater the autogenous shrinkage; from Figure 4 and Figure 5 It can be seen that the creep degree (creep degree is the ratio of creep deformation to the stress of concrete at the initial loading stage) tends to stabilize at 325 days. The earlier the loading age, the greater the creep degree, and the lower the water-cement ratio, the more significant the effect of early-age loading on creep. All of the above influencing factors need to be considered in the shrinkage and creep prediction model proposed in this invention.

[0129] (3) Based on the autogenous shrinkage model of standard BS EN 1992, this paper considers the influence of concrete water-cement ratio and establishes a calculation formula for a high-performance concrete shrinkage model that considers the influence of water-cement ratio by introducing the influence coefficient of concrete water-cement ratio on shrinkage:

[0130]

[0131] In the formula, ε sh It is the shrinkage deformation of high-performance concrete, ×10 -6 w represents the water content of high-performance concrete, in kg / m³. 3 b represents the mass of cement, silica fume, fly ash, mineral powder, and expansive agent in high-performance concrete, in kg / m³. 3 t represents the middle age of high-performance concrete, in days.

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

[0133] (4) Using the least squares method, a nonlinear regression analysis was performed on the shrinkage test results. Considering the influence of the concrete water-cement ratio on concrete shrinkage, the mathematical expressions for α1, α2, and α3 were obtained by fitting:

[0134] α1=6(20)

[0135] α2=21(21)

[0136] α3=18(22)

[0137] The predicted shrinkage deformation results of high-performance concrete with steel tubes calculated by this method are compared with the experimental results, for example... Figure 3 As shown, from Figure 3 As can be seen, the calculated values ​​of the high-performance concrete shrinkage model are in good agreement with the experimental results, with a prediction error of only 5% at 240 days. The results indicate that the prediction method for shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading can accurately reflect the shrinkage deformation development law of high-performance concrete with different water-cement ratios.

[0138] (5) To consider the different effects of loading age on creep deformation of components under different water-cement ratios, this paper introduces the influence coefficient of concrete water-cement ratio on creep and establishes a calculation formula for a high-performance concrete shrinkage model that considers the different effects of loading age on creep deformation of components under different water-cement ratios:

[0139] C(t,t0)=k(t0)·C(t,28)(23)

[0140]

[0141] In the formula, C(t,t0) represents the creep of the high-performance concrete from day t0 after the specimen is poured until day t after the load is applied (creep is the ratio of creep deformation to the initial stress of the concrete under load), ×10 -6 / MPa; C(t,28) is the creep of high-performance concrete from day 28 after casting to day t after holding the load, ×10 -6 / MPa; k(t0) is the loading age influence coefficient; t is the age of high-performance concrete, days; t0 is the loading age of high-performance concrete, days; β1, β2 and β3 are unknown parameters.

[0142] (6) Considering that formula (6) must satisfy boundary condition one: when the loading age t0 = 28, k(t0) = 1; boundary condition two: 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 obtained as follows:

[0143] β1=0.5(25)

[0144] β2=0.5(β3+28)(26)

[0145] (7) Based on the different effects of loading age on the creep of high-performance steel-tube concrete under different concrete water-cement ratios, a function of concrete water-cement ratio is constructed as follows:

[0146]

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

[0148] (8) Using the least squares method, a nonlinear regression analysis was performed on the creep test results. Considering the influence of the concrete water-cement ratio on concrete shrinkage, the mathematical expressions for γ1 and γ2 were obtained by fitting:

[0149] γ1=15(28)

[0150] γ2=2(29)

[0151] (9) Implement the step-by-step integration method using programming software such as C++ and Matlab. Considering the influence of rapid early-stage creep deformation and slow late-stage creep deformation, the time step is divided into 100 steps. The division method is as follows:

[0152]

[0153] In the formula, Δt k It is any time t k Compared to the previous time t k-1 The length of the time step; Δt i It is any time t i Compared to the previous time t i-1 The time step length; k is the time step number.

[0154] (10) Using programming software such as C++ and Matlab, the step-by-step integration method is implemented. Considering the influence of stress redistribution between high-performance concrete and steel components under constant load, the stress-strain relationship of concrete is established according to the trapezoidal integration rule as follows:

[0155]

[0156] In the formula, t k-1 With t k These are the start and end times of step k, respectively, in days; σ ck and σ cj They are t k With t j The stress in concrete at any given time, in MPa; ε totk and ε shk They are t k The total deformation and shrinkage of concrete at any given moment; M c1k and M c2kj These are the creep influence coefficients; J(t) k ,t j ) is the creep function of concrete from time tj when it is subjected to a constant load to time tk.

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

[0158]

[0159] ε ck =ε totk -ε shk (35)

[0160] In the formula, N L It is the constant load borne by the steel-tube high-performance concrete, N; A c It is the cross-sectional area of ​​the concrete, in mm. 2 E s A is the elastic modulus of the steel pipe, measured in MPa. s It is the cross-sectional area of ​​the steel pipe, in mm². 2 ;σ cj It is t j The stress in concrete at any given time, in MPa; ε totk and ε ck They are t k Total deformation and creep deformation of concrete at any time, ×10 -6 ;ε shk It is t k Shrinkage deformation of concrete at all times, ×10 -6 Calculate according to formula (1).

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

[0162]

[0163] In the formula, E c (t j ) is high-performance concrete in t j Elastic modulus at time t, MPa; E c (t0) is the elastic modulus of high-performance concrete at time t0, in MPa; E c (28) is the elastic modulus of high-performance concrete on the 28th day after pouring, in MPa; C(t) k ,tj) is the tth day after the specimen is poured. j The load begins to hold from day t until day t. k Creep of high-performance concrete, ×10 -6 / MPa, calculated according to formula (23).

[0164] (13) High-performance concrete at t j Elastic modulus E at time t c (t j The calculation was performed using the elastic modulus calculation formula provided by BSEN1992.

[0165] The predicted creep rate (creep rate is the ratio of creep deformation to the initial stress of the concrete) of high-performance concrete with steel tubes calculated by this method is compared with the experimental results as follows: Figure 4 and Figure 5 As shown, from Figure 4 and Figure 5 As can be seen, the calculated values ​​of the creep model for high-performance concrete in steel tubes are in good agreement with the experimental results, with a prediction error of only 6% at 325 days. The results indicate that the prediction method for shrinkage and creep deformation of high-performance concrete in steel tubes under early-age loading can accurately reflect the creep development law of high-performance concrete in steel tubes with different water-cement ratios under early-age loading.

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

Claims

1. A method of predicting the shrinkage and creep deformation of early-age loaded high-performance concrete filled steel tube, characterized in that, Includes the following steps: S100. Shrinkage and creep tests were conducted on high-performance steel-tube concrete with different water-cement ratios at different loading ages to obtain the experimental results of shrinkage strain and creep strain. S200, On the concrete layer, shrinkage deformation and creep deformation are calculated; Among them, the shrinkage deformation of high-performance concrete is calculated, including nonlinear regression analysis of the shrinkage strain of steel-tube high-performance concrete with different water-cement ratios. By introducing the influence coefficient of water-cement ratio on shrinkage, a high-performance concrete shrinkage model is established to obtain the shrinkage strain of high-performance concrete with different water-cement ratios. The formula for calculating shrinkage deformation is: （1） In the formula, is the shrinkage deformation of the high-performance concrete; w is the water content of the high-performance concrete; b is the sum of the mass of cement, silica fume, fly ash, mineral powder, and expansive agent of the high-performance concrete; is the age of the high-performance concrete, days; , and are unknown parameters; The three constants mentioned above are obtained. , and The specific method is as follows: Using the least squares method, a nonlinear regression analysis is performed on the experimental results, considering the influence of the concrete water-cement ratio on concrete shrinkage, and the results are fitted to obtain... , and The mathematical expression is: （2） （3） （4） S300. At the level of composite components, the shrinkage deformation and creep deformation are calculated using the step-by-step integration method.

2. The method for predicting shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete according to claim 1, characterized in that, Step S100 includes: casting N groups of high-performance concrete specimens in steel tubes and conducting shrinkage and creep tests; wherein, N≥8, each group of specimens includes 2 parallel specimens; the water-cement ratio and loading age of the concrete in the N groups of high-performance concrete specimens in steel tubes are different.

3. The method for predicting shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete according to claim 2, characterized in that: The water-cement ratio of concrete ranges from 0.25 to 0.45, and the loading age is 3 days, 7 days, 14 days, and 28 days.

4. The method for predicting shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete according to claim 1, characterized in that: In step S200, the creep deformation of the high-performance concrete layer is calculated, including nonlinear regression analysis of creep tests of steel-tube high-performance concrete at different loading ages with different concrete water-cement ratios. Based on the different effects of loading age on the creep of steel-tube high-performance concrete under different concrete water-cement ratios, a high-performance concrete creep model is established by introducing the influence coefficient of concrete water-cement ratio on creep, and the creep strain of steel-tube high-performance concrete at different loading ages with different concrete water-cement ratios is obtained. The formula for calculating creep deformation is: （5） （6） In the formula, From the day after the specimen was poured The day began to hold the load until the [number]th The creep of high-performance concrete after loading, wherein creep is the ratio of creep deformation to the stress of concrete at the initial loading stage; The load was maintained from the 28th day after the specimen was poured until the [date missing]. Creep of high-performance concrete in Tianhou; It is the loading age influence coefficient; It refers to the age of high-performance concrete; It refers to the loading age of high-performance concrete; , and It is an unknown parameter; The two constants mentioned above are obtained. and The specific method is as follows: Formula (6) satisfies boundary condition one: loading age hour, Boundary condition two: loading age When it approaches infinity, ; Based on the above two conditions, we obtain and The mathematical expression is: （7） （8） The constants are obtained. The specific method is as follows: based on the different effects of loading age on the creep of high-performance steel-tube concrete under different concrete water-cement ratios, a system is constructed. The function of the water-cement ratio in concrete is: （9） In the formula, and It is an unknown parameter; The two constants mentioned above are obtained. and The specific method is as follows: using the least squares method, nonlinear regression analysis is performed based on the experimental results to obtain the fit. and The mathematical expression is: （10） （11）。 5. The method for predicting shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete according to claim 4, characterized in that: Step S300 includes, Using the step-by-step integration method, considering the rapid early-stage and slow-stage development of creep deformation, the time step is divided into M steps, and the division method is as follows: （12） In the formula, It is any time t k Compared to the previous time t k-1 The length of the time step; It is any time t i Compared to the previous time t i-1 The length of the time step; It represents the age of the high-performance concrete when the steel-tube high-performance concrete ceases to bear load; k is the time step number. It is the first The day began to hold the load until the [number]th The number of time steps that the Empress's time period is divided into; Using the successive integration method, considering the stress redistribution effect between high-performance concrete and steel components under constant load, the stress-strain relationship of concrete is established according to the trapezoidal integration rule: （13） （14） （15） In the formula, t k-1 With t k These are the start and end times of step k, respectively; and They are t k With t j The stress of concrete at any given moment; and They are t k The total deformation and total shrinkage of concrete at any given moment; and All are creep influence coefficients; It is concrete from t j From time t onwards, the system will be subjected to a constant load until t k The creep function at time t; Considering that a high-performance concrete (HPC) steel-tube member is subjected to a constant load, with the HPC and steel components sharing the vertical load and the two parts deforming in harmony, the shrinkage and creep deformations of the HPC steel-tube member are calculated according to the force balance equation and deformation compatibility equation. Specifically, this includes... The creep deformation is calculated using the successive integration method as follows: （16） （17） In the formula, It is a constant load borne by high-performance concrete with steel pipes; It is the cross-sectional area of ​​the concrete; It is the elastic modulus of the steel pipe; It is the cross-sectional area of ​​the steel pipe; It is t j The stress of concrete at any given moment; and They are t k The total deformation and creep deformation of concrete at any given time; It is t k The shrinkage and deformation of concrete at all times; creep function The calculation is performed using formula (5), and the calculation method is as follows: （18） In the formula, High-performance concrete in The elastic modulus at time t; High-performance concrete in The elastic modulus at time t; It is the elastic modulus of high-performance concrete 28 days after pouring; From the day after the specimen was poured The day began to hold the load until the [number]th Creep of high-performance concrete in Tianhou; High-performance concrete in elastic modulus at time The calculation of the elastic modulus was performed using the formula provided by BS EN 1992.

6. A prediction system for shrinkage and creep deformation of high-performance steel-tube concrete under early-age loading, characterized in that: The system has a program module corresponding to the steps of any one of the claims 1-5 above, and executes the steps in the above-described method for predicting shrinkage and creep deformation of early-age loaded high-performance steel-tube concrete when it is run.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the method for predicting shrinkage and creep deformation of early-age loaded steel-tube high-performance concrete as described in any one of claims 1-5.

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