Four-element model for modulus and creep of concrete under action of long-period cyclic load

Abstract

The invention discloses a four-element model for modulus and creep of concrete under the action of long-period cyclic loading and a parameter determination method of the four-element model. The model simulates behaviors of concrete under the action of long-period cyclic load through four mechanical elements connected in series, and the four mechanical elements comprise an instantaneous elastic deformation element with rigidity increasing along with time, a recoverable creep viscoelastic element, an unrecoverable compression creep element and an unrecoverable tension creep element. According to the method, in order to overcome the difficulty that the available sample size of an application object is small, a step-by-step progressive mode is adopted, and classification and staged parameter calibration is carried out on the concrete modulus and a creep model of the application object.

Description

Technical Field

[0001] The invention relates to the field of engineering structure analysis, and specifically discloses a four-component model of concrete modulus and creep under long-period cyclic load and a method for determining parameters thereof. Background Art

[0002] Creep of concrete refers to the time-related deformation of concrete under long-term loads. It is usually manifested as strain increasing with time, but the increment gradually decreases and tends to be stable. Macroscopically, it is manifested as the aging deformation of the structure increasing year by year. The creep phenomenon has a profound impact on the stability and durability of large structures such as dams. Excessive creep may cause the deformation of the structure to exceed the design safety range, which in turn causes serious problems such as cracks and settlement. In many cases, creep is also a harmless deformation, and sometimes even helps to passivate local concentrated stresses. When more obvious aging deformation occurs in a project, it will be suspected whether it contains plastic deformation that may cause progressive failure and cause concern. Therefore, it is necessary to accurately separate different factors such as creep from aging deformation in order to accurately evaluate the safety of the structure.

[0003] Low-heat cement is often used in large-volume concrete such as dams, which has a low hydration rate. The strength and modulus of concrete will continue to grow after pouring, which will last for a considerable period of time from the construction period to the initial operation. In addition, the influence of the creep properties of concrete under long-term cyclic loads (main loads such as dam reservoir water and temperature show interannual quasi-periodic changes) on large structures such as dams, the constitutive relationship of concrete in the initial operation has complex time-varying nonlinear characteristics. The existing models only focus on the growth of strength or modulus with age, or are limited to creep models under continuous loads. There is no effective physical and mechanical model that can fully and accurately express the above constitutive relationship. A new "modulus growth + creep" model that can cover the growth of concrete modulus and is suitable for any loading and unloading process is urgently needed.

[0004] Concrete with different uses and types has very different modulus growth and creep characteristics, and even different test specimens under the same conditions have a certain degree of discreteness. To obtain these significantly different characteristics, it is necessary to rely on long-term and multi-sample experimental or measured data of specific application objects for parameter calibration. However, the long-term experimental or long-term measured data of a specific single object is expensive to obtain, resulting in a scarcity of data samples, making it difficult to calibrate the more than 10 parameters of the model proposed in the present invention based on this. For this reason, a phased calibration method is proposed, which screens and fully utilizes existing "modulus growth / creep" models and experimental results with similar backgrounds, and based on the calibration analysis of these large sample sets and multiple sample sets, gradually frames and narrows the parameter range, reduces the number of parameters by merging parameters, and then combines the experimental data of the specific application object and the measured data during the operation period, and finally calibrates the concrete modulus and creep model parameters of the specific object. Summary of the invention

[0005] The purpose of the present invention is to provide a four-component model of concrete modulus and creep under long-period cyclic loads and a method for determining its parameters. The model combines the characteristics of modulus growth, transient elasticity, viscoelasticity (recoverable creep), and irrecoverable creep, and can effectively describe the creep behavior of large concrete structures under complex loading and unloading conditions such as long-period loads.

[0006] To achieve the above object, the technical solution provided by the present invention includes the following contents:

[0007] The technical solution adopted by the present invention to solve the technical problem is as follows: a four-element model of concrete modulus and creep under long-term cyclic load and a method for determining its parameters. The model quantitatively and effectively expresses the complex change process of concrete modulus and creep by connecting in series an instantaneous elastic deformation element whose stiffness increases with time, a recoverable creep viscoelastic element, an irrecoverable compressive creep element, and an irrecoverable tensile creep element; the method adopts a step-by-step calibration analysis method from a large sample set with similar backgrounds, to multiple small sample sets of similar projects, and then to a small sample set of a specific object to overcome the difficulty of a small number of available samples of a specific object itself.

[0008] The four-element model of concrete modulus and creep under long-term cyclic loading is composed of an instantaneous elastic deformation element, a recoverable creep viscoelastic element, an irrecoverable compressive creep element and an irrecoverable tensile creep element connected in series to form an overall modulus and creep model.

[0009] The instantaneous elastic deformation element is composed of a spring whose stiffness increases with time; the recoverable creep viscoelastic element is composed of a spring whose stiffness can be increased and a damper in parallel; the irreversible compressive creep element is composed of a spring whose stiffness can be increased, a damper and a friction device in parallel; the irreversible tensile creep element is composed of a spring whose stiffness can be increased, a damper and a friction device in parallel.

[0010] The four-element model is as follows:

[0011] (1) The instantaneous elastic deformation element consists of a 0 # Spring composition;

[0012] 0 # The spring modulus growth model is:

[0013]

[0014] In the formula, E e is 0 # The instantaneous elastic modulus of the spring, t0 is the design age, E0 is 0# The instantaneous elastic modulus of the spring at the design age, c e is 0 # Undetermined parameters in the spring modulus growth model;

[0015] The instantaneous strain increment Δε of the instantaneous elastic deformation element e Calculated by the following formula:

[0016]

[0017] Δσ is the stress increment of the entire assembly consisting of four elements, and the stress increment of each element is Δσ;

[0018] (2) The recoverable creep viscoelastic element consists of a 1 # Spring and a 1 # The dampers are connected in parallel;

[0019] 1 # The spring modulus growth model is:

[0020]

[0021] Where E1 is 1 # The elastic modulus of the spring, t0 is the design age, E 1_0 is 1 # The elastic modulus of the spring at the design age, c1 is 1 # Undetermined parameters in the spring modulus growth model;

[0022] The stress σ of the recoverable creep viscoelastic element is changed from 1 # Spring and 1 # The relationship between the damper load, σ and the strain ε1 of this element is as follows:

[0023]

[0024] Iterate according to the time step. Within the time step, σ and ε1 are approximately regarded as unchanged. The strain rate is deduced from the above formula Then the strain increment of this element in this time step is obtained as:

[0025]

[0026] Where η1 is 1 # Damping parameters of the damper;

[0027] (3) The irreversible compressive creep element is composed of a 2# spring with increasing stiffness, a 2# damper and a friction device in parallel;

[0028] 2 # The spring modulus growth model is:

[0029]

[0030] Where E2 is 2 # The elastic modulus of the spring, t0 is the design age, E 2_0 For 2 # The elastic modulus of the spring at the design age, c2 is 2 # Undetermined parameters in the spring modulus growth model;

[0031] When the compressive strain increases, the stress σ of the irrecoverable compressive creep element changes from 2 # Spring and 2 # The relationship between the damper load, σ and the strain ε2 of this element is as follows:

[0032]

[0033] Iterate according to the time step. Within the time step, σ and ε2 are approximately regarded as unchanged. The strain rate is deduced from the above formula It is then obtained that when the compressive strain increases, the compressive strain increment of this element in this time step is:

[0034]

[0035] Where η2 is 2 # Damper damping parameters;

[0036] When the compressive strain tries to decrease, the friction device completely prevents the reduction of the compressive strain, so that the compressive strain of the element only increases and does not decrease, and the compressive strain cannot be restored;

[0037] (4) The irreversible tensile creep element consists of a 3 # Spring, one 3 # The damper and a friction device are connected in parallel;

[0038] 3 # The spring modulus growth model is:

[0039]

[0040] Where E3 is 3 # The elastic modulus of the spring, t0 is the design age, E 3_0 For 3 # The elastic modulus of the spring at the design age, c3 is 3 # Undetermined parameters in the spring modulus growth model;

[0041] When the tensile strain increases, the tensile stress σ of the irreversible tensile creep element changes from 3 # Spring and 3 # The relationship between the damper load, σ and the tensile strain ε3 of this element is as follows:

[0042]

[0043] Iterate according to the time step. Within the time step, σ and ε3 are approximately regarded as unchanged. The strain rate is deduced from the above formula It is then obtained that when the tensile strain increases, the tensile strain increment of this element in this time step is:

[0044]

[0045] Where η3 is 3 # Damper damping parameters;

[0046] When the tensile strain tries to decrease, the friction device completely prevents the tensile strain from decreasing, so that the tensile strain of the component only increases but does not decrease, and the tensile strain cannot be restored.

[0047] The calibration method of the related parameters of the four-element model is carried out in a classified and staged manner, specifically:

[0048] The parameters of instantaneous modulus and its growth have relatively reliable sample data, large sample size, and weak coupling with other factors. Such parameters are calibrated separately in advance.

[0049] The remaining parameters are calibrated in stages. First, a creep model with similar background and samples with rich creep experimental data are used for preliminary calibration to define the parameter range and examine whether the parameters can be condensed to reduce their number. For example, c e , c1, c2, c3 are reduced to 1-2 parameters, and η1, η2, η3 are reduced to 1-2; secondly, the short-term, long-term test and creep test data of the application object are combined to further calibrate and narrow the parameter range; finally, the measured data of the application object during operation are used to finally determine the concrete modulus and creep model parameters.

[0050] In the present invention, the four springs in the four elements adopt different initial stiffnesses; the stiffness growth model adopts the same form and different model parameters, and the same parameters (such as c e, c1, c2, c3) value rules, the same parameters are associated in a certain way to reduce the number of parameters; the three dampers in the four components can use different parameters, and can also be associated in a certain way. For specific application projects, the calibration of model parameters is carried out in three stages: In the first stage, existing experimental results and creep models with similar background conditions are selected, and large samples and multiple small samples with different characteristics are used to divide calibration samples and test samples. A preliminary parameter calibration analysis is carried out on this model, and a reasonable range of parameter values ​​is framed. The sensitivity of different parameters and the correlation between them are studied, and the parameters are connected and reduced accordingly to meet the needs of small sample calibration in the subsequent stage, and the simulation accuracy of the connected and reduced model is tested; In the second stage, the short-term and long-term experiments and creep experiment results of concrete specimens of specific application objects are used. According to the characteristics of rich short-term sample data and scarce long-term sample data, the parameters are classified and calibrated and analyzed, and the range of parameter values ​​is further framed and reduced, and the simulation effect of the model is tested; In the third stage, the measured data of large concrete structures such as dams are used to try to mine the available data samples, and finally the parameters of concrete modulus and creep model are calibrated to test the simulation effect and prediction ability of the model for the measured data.

[0051] The present invention introduces instantaneous elastic deformation elements whose stiffness increases with time, recoverable creep viscoelastic elements, irrecoverable compressive creep elements, and irrecoverable tensile creep elements, and takes into account the modulus growth, elasticity, viscoelasticity, and creep deformation of concrete under different time scales and arbitrary loading and unloading conditions. It overcomes the disadvantage of the existing model with relatively single functions, can effectively simulate the time-dependent deformation law of the structure under long-period loads, and predict its development and change trend.

[0052] The four-element model of the present invention can accurately reflect the modulus growth and creep behavior of concrete. The model has more model parameters and can also expand the one-dimensional model to the spatial stress state, making the model have good applicability and ensuring the simulation accuracy of the model for different engineering objects.

[0053] The present invention provides a calibration method for the parameters of each component, which can be effectively calibrated and tested through long-term experiments and long-term measured results with very limited specific application objects. With the help of data of similar backgrounds and similar engineering data, from large sample sets to multiple small sample sets, staged calibration analysis is carried out, and the number of parameters and the range of parameter values ​​are gradually merged and reduced, and finally the purpose of calibrating a multi-parameter complex model and achieving good simulation effect can be achieved with data of small sample sets of specific objects.

[0054] The present invention can provide a scientific basis for the time-dependent deformation analysis of large structures such as dams by accurately simulating the creep behavior of concrete, and better predict and evaluate the impact of time-dependent deformation on structural safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Schematic diagram of the four-element creep model of concrete under long-term cyclic loading.

[0056] Figure 2 The stress-strain variation diagram of the example concrete under annual cycle load.

[0057] Figure 3 This is a diagram showing the annual increase in strain and rope-shaped change of example concrete under annual cyclic load. DETAILED DESCRIPTION

[0058] The present invention will be further described in detail below through specific implementation methods. However, it should not be understood that the scope of the above subject matter of the present invention is limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

[0059] Example 1: A four-element model of concrete modulus and creep under long-term cyclic loading. The four-element model is composed of an instantaneous elastic deformation element, a recoverable creep viscoelastic element, an irrecoverable compressive creep element and an irrecoverable tensile creep element connected in series to form an overall modulus and creep model.

[0060] Each element describes the deformation characteristics of concrete under arbitrary loading and unloading conditions according to different physical mechanisms.

[0061] The calibration method of the four-element model and its related parameters is as follows:

[0062] (1) Instantaneous elastic deformation element

[0063] The instantaneous elastic deformation element adopts a spring model, which is 0 # Spring, elastic modulus is E e , the stiffness increases with time and is used to describe the elastic modulus of concrete under instantaneous load; E e The initial value of is determined by the instantaneous elastic modulus E0 at the design age, and the growth model is used to reflect the characteristics of concrete modulus increasing with age;

[0064] 0 # The spring modulus growth model is:

[0065]

[0066] In the formula, E e is 0 # The instantaneous elastic modulus of the spring, t0 is the design age, E0 is 0 # The instantaneous elastic modulus of the spring at the design age, c e is 0 # Undetermined parameters in the spring modulus growth model;

[0067] For large concrete projects, the instantaneous elastic modulus E0 at the design age is directly obtained based on experimental results, and then all parameters in this element model are inverted using instantaneous modulus measurements at more than one other age.

[0068] For a concrete project, according to multi-sample statistics, the instantaneous elastic modulus of concrete at the design age of 90 days is 30 GPa. The instantaneous modulus at the age of 365 days increases by 10%, so E0 = 30, t0 = 90, t = 365. Substituting into the growth model, we get:

[0069]

[0070] Find c e =0.071424;

[0071] The concrete modulus growth model of this project is:

[0072]

[0073] Since the sample data of instantaneous modulus is reliable, the sample size is large, and the coupling with other factors is weak, this type of parameter was calibrated separately in advance.

[0074] Since the four elements are connected in series, the stress increment of each element of the entire assembly composed of four elements is Δσ under the action of stress increment Δσ, and the instantaneous strain increment of the instantaneous elastic deformation element is Δε e Calculated by the following formula:

[0075]

[0076] The above formula is the strain correction formula of the instantaneous elastic deformation element under the stress increment Δσ when iterating according to the time step.

[0077] (2) Recoverable creep viscoelastic element

[0078] The recoverable creep viscoelastic element is composed of 1 # Spring and 1 # The dampers are connected in parallel, and their stiffness increases with time;

[0079] 1 # The spring modulus growth model is:

[0080]

[0081] Where E1 is 1 # The elastic modulus of the spring, t0 is the design age, E 1_0 is 1 # The elastic modulus of the spring at the design age, c1 is 1 # Undetermined parameters in the spring modulus growth model.

[0082] The stress σ of the recoverable creep viscoelastic element is shared by the spring and the damper. The relationship between σ and the strain ε1 of the element is as follows:

[0083]

[0084] Iterate according to the time step. Within the time step, σ and ε1 are approximately regarded as unchanged. The strain rate is deduced from the above formula Then the strain increment of this element in this time step is obtained as:

[0085]

[0086] Where η1 is 1 # From the perspective of parameter calibration, the damping parameters of the damper have a strong coupling relationship with the irreversible compressive creep element and will be combined with the next element for parameter calibration.

[0087] (3) Irrecoverable compressive creep components

[0088] Irrecoverable compressive creep element consists of 2 # Spring, 2 # The damper is connected in parallel with a one-way friction device, and the stiffness increases with time;

[0089] 2 # The spring modulus growth model is:

[0090]

[0091] Where E2 is 2 # The elastic modulus of the spring, t0 is the design age, E 2_0 For 2 # The elastic modulus of the spring at the design age, c2 is 2 # Undetermined parameters in the spring modulus growth model;

[0092] When the compressive strain increases, the one-way friction device does not work; when the compressive strain tries to decrease, the one-way friction device of the present element completely prevents the recovery of the compressive creep of the present element, making the compressive creep of the present element become irreversible creep.

[0093] When the compressive strain increases, the stress σ of the irrecoverable compressive creep element changes from 2 # Spring and 2 # The relationship between the damper load, σ and the strain ε2 of this element is as follows:

[0094]

[0095] Iterate according to the time step. Within the time step, σ and ε2 are approximately regarded as unchanged. The strain rate is deduced from the above formula It is then obtained that when the compressive strain increases, the compressive strain increment of this element in this time step is:

[0096]

[0097] Where η2 is 2 # Damper damping parameters;

[0098] When the compressive stress attempts to decrease, the compressive strain increment of this element is zero.

[0099] In the above-mentioned recoverable creep viscoelastic elements and irreversible compressive creep elements, the concrete design age t0 is a determined parameter for a specific application object, so the parameters to be determined are:

[0100] E 1_0 、E 2_0 There are 6 parameters in total: c1, c2, η1 and η2.

[0101] The above six parameters are determined through calibration analysis of large sample sets and multiple sample sets, thereby reducing the number of parameters and calibrating them in categories and stages. Specifically:

[0102] By collecting creep models and experimental data with similar backgrounds, and based on the analysis and comparison of calibration results, the similarities and differences of the spring parameters of several components in the model are analyzed, and the corresponding parameters are connected and reduced; according to the actual situation of the specific case, for example, c1=c2=c e , at this time, the stiffness growth pattern of the three springs is exactly the same, and two multiple parameters β1 and β2 are used to express the relationship between the three springs: E1(t)=β1E e (t), E2(t) = β2E e (t), the four parameters E 1_0 、E 2_0 , c1 and c2 are merged into two parameters β1 and β2, reducing the number of parameters.

[0103] Setting 0 # Spring, 1 # Spring, 2 # The spring stiffness growth pattern is exactly the same, using the calibrated c e , then c1=c2=c e =0.071424, and use the multiple parameters β1 and β2 to express the relationship between the three springs:

[0104] E 1_0 =β1E0;

[0105] E1(t)=β1E e (t);

[0106] E 2_0 =β2E0;

[0107] E2(t)=β2E e (t);

[0108] For specific application objects, the following concrete specimen creep test is carried out:

[0109] A compressive stress of 9 MPa was applied for one year from the design age. The compressive strains measured in the middle and end of the first year were 328×10 -6 and 365×10 -6 ; Then it is completely unloaded at the beginning of the second year, and after half a year and one year, that is, in the middle and end of the second year, the residual compressive strains are 113×10 -6 and 100×10 -6 Based on these four strain measurements, conventional inversion analysis software, such as parameter inversion algorithms based on least squares and optimization methods, or some open source matlab inversion analysis codes, are used to perform parameter inversion in this case. The multiple parameter β1≈β2≈2 and the damping parameter η1≈η2≈100 (GPa·year) can be calibrated.

[0110] The parameters of the concrete modulus creep model can also be calibrated using neural network methods and Gaussian regression models. The specific process of using neural network methods to calibrate mechanical component parameters includes multiple steps such as data collection and preprocessing, model design, training and optimization, evaluation and verification. The core of this method is to learn the laws of unknown parameters from experimental data or simulation data samples through neural network models, so as to achieve accurate simulation of sample characteristics by mechanical component performance; the specific process of using Gaussian regression models to calibrate mechanical component parameters includes data preparation, model establishment, training and optimization, prediction and evaluation. Gaussian regression is a non-parametric regression method based on Bayesian theory, which is suitable for solving regression problems with complex nonlinear relationships, especially for the prediction of small sample data. It describes the relationship between input and output by constructing a joint Gaussian distribution model, and can provide uncertainty estimates during prediction, which makes it have important application value in mechanical parameter calibration.

[0111] Through the above parameter calibration, the strain increment formula of the recoverable creep viscoelastic element in one iterative time step applicable to this embodiment is:

[0112]

[0113] The 365 in the formula is the unit conversion factor for converting "GPa·year" to "GPa·day".

[0114] For the irreversible compressive creep element applicable to this embodiment, when the compressive strain attempts to decrease, the compressive strain increment in an iterative time step is zero; when the compressive strain increases, the compressive strain increment formula in an iterative time step is:

[0115]

[0116] The above classification and phased calibration first defines the parameter range and reduces the number of parameters through the calibration analysis of large sample sets and multiple sample sets in the early stage, creating conditions for parameter calibration under the condition of small sample sets for specific objects. The above calibration is an ideal scenario, that is, assuming that the test specimens used in the experiment are very representative and the accuracy of the four strain measurements is high, then at least four samples can be used to calibrate the four parameters. Based on the above-mentioned sample representativeness and the discreteness of the experimental results, to calibrate the four parameters, more sample data should be collected as much as possible, and strain values ​​at more time points can be collected during the experiment. Concrete experiments usually have three specimens in a group, and the same experiment is performed. The mean of the three is taken as the adopted value. If there is a measured value that deviates greatly from the mean, it will be eliminated. In order to improve the diversity of samples, different load values ​​and loading and unloading time points can be set in the same group of specimens, and the specimen data with large deviations from the model can be eliminated during the calibration process.

[0117] If there are fewer samples available at this stage, it is necessary to use the calibration analysis of the large sample set in the previous stage to further reduce the number of parameters in this stage, such as setting β1=β2, η1=η2, or setting a certain proportional relationship to further reduce the 4 parameters to 2 parameters. At the same time, based on the reasonable range of parameter values ​​obtained from the calibration analysis in the previous stage, ensure that the calibration based on the small sample set in this stage will not have a large deviation.

[0118] Where conditions permit, the model parameters should be calibrated using the available data collected and the concrete test results of the specific application object, and then the model should be applied to large concrete structures in design or actual operation to predict the time-dependent deformation of the structure caused by creep and other effects, or to reveal the internal mechanism of time-dependent deformation of existing buildings. If the sample data relied on for the early calibration is poor or the number of samples is small, and the reliability of the obtained model parameters is not good, the field measured data of the specific application object can be used for inversion analysis to correct the model parameters.

[0119] (4) Irrecoverable tensile creep components

[0120] The irreversible tensile creep element is similar to the irreversible compressive creep element, except that the one-way friction device changes direction. When the tensile strain increases, the one-way friction device does not work; when the tensile strain tries to decrease, the one-way friction device of this element completely prevents the reduction of the tensile strain of this element, making the tensile creep of this element irreversible creep.

[0121] The irreversible tensile creep element consists of 3# Spring, 3 # The damper is connected in parallel with a one-way friction device, and the stiffness increases with time;

[0122] 3 # The spring modulus growth model is:

[0123]

[0124] Where E3 is 3 # The elastic modulus of the spring, t0 is the design age, E 3_0 For 3 # The elastic modulus of the spring at the design age, c3 is 3 # Undetermined parameters in the spring modulus growth model;

[0125] When the tensile strain increases, the one-way friction device does not work; when the tensile strain tries to decrease, the one-way friction device completely prevents the tensile strain of the component from decreasing.

[0126] When the tensile strain increases, the tensile stress σ of the irreversible tensile creep element changes from 3 # Spring and 3 # The relationship between the damper load, σ and the tensile strain ε3 of this element is as follows:

[0127]

[0128] Iterate according to the time step. Within the time step, σ and ε3 are approximately regarded as unchanged. The strain rate is deduced from the above formula , and then we can get that when the tensile strain increases, the tensile strain increment of this element in this time step is:

[0129]

[0130] Where η3 is 3 # Damper damping parameters.

[0131] When the tensile stress attempts to decrease, the tensile strain increment of the element is zero.

[0132] The tensile strength of concrete is much lower than its compressive strength, and the concrete in concrete structures is mainly subjected to compression. It is generally believed that when the tensile stress is less than the designed tensile strength, the deformation properties under tension are similar to those under compression at a low stress level. Therefore, the model parameters of the irreversible compressive creep element can be borrowed as the model parameters of this element. In the absence of available tensile creep calibration samples, the parameters of the compressive creep element can be directly borrowed, and E 3_0 =E 2_0 , c3=c2, β3=β2, η3=η2, thus the tensile strain increment formula of the irreversible tensile creep element in this embodiment in one iterative time step is obtained as follows:

[0133]

[0134] If the parameters of the compressive creep element are not directly borrowed, a "tension-unloading" creep experiment can be carried out to measure the strain value. After calibrating the parameters of the first three elements, the parameters of this element can be calibrated.

[0135] The creep test of concrete specimens under tension and unloading is as follows: a tensile stress of 1 MPa is applied for one year from the design age. In the middle and end of the first year, the tensile strains are assumed to be 37×10 -6 and 42×10 -6 ; Then, it is completely unloaded at the beginning of the second year. After another half year and one year, that is, in the middle and end of the second year, the residual tensile strain is assumed to be 13×10 -6 and 12×10 -6 Based on these four strain measurements and assuming the same modulus growth parameter as that of the transient elastic deformation element, E 3_0 , c3 are merged into a parameter β3. By using conventional inverse analysis software, the spring parameter β3≈2 and the damping parameter η3≈90 (GPa·year) of this element can be calibrated. Then, the strain increment formula of the irreversible tensile creep element in one iterative time step applicable to this embodiment is:

[0136]

[0137] According to the above-mentioned model with relevant parameters calibrated, the stress-strain variation of concrete under annual cyclic load (0-10MPa changes according to a sine function) is shown in the attached figure. The stress-strain variation curve shows a rope-like variation law with increasing deformation year by year, revealing the internal mechanism of the strange phenomenon of time-dependent deformation of some large-scale projects under long-term cyclic load.

Claims

1. A four-element model of concrete modulus and creep under long-term cyclic loading, characterized by The four-element model is composed of an instantaneous elastic deformation element, a recoverable creep viscoelastic element, an irrecoverable compressive creep element and an irrecoverable tensile creep element connected in series to form an overall modulus and creep model. The instantaneous elastic deformation element is composed of a spring whose stiffness increases with time; the recoverable creep viscoelastic element is composed of a spring whose stiffness can be increased and a damper in parallel; the irreversible compressive creep element is composed of a spring whose stiffness can be increased, a damper and a friction device in parallel; the irreversible tensile creep element is composed of a spring whose stiffness can be increased, a damper and a friction device in parallel.

2. The four-element model of concrete modulus and creep under long-term cyclic loading as claimed in claim 1, characterized in that The four-component model is as follows: (1) The instantaneous elastic deformation element consists of a 0 # Spring composition; 0 # The spring modulus growth model is: In the formula, E e is 0 # The instantaneous elastic modulus of the spring, t0 is the design age, E0 is 0 # The instantaneous elastic modulus of the spring at the design age, c e is 0 # Undetermined parameters in the spring modulus growth model; The instantaneous strain increment Δε of the instantaneous elastic deformation element e Calculated by the following formula: Δσ is the stress increment of the entire assembly consisting of four elements, and the stress increment of each element is Δσ; (2) The recoverable creep viscoelastic element consists of a 1 # Spring and a 1 # The dampers are connected in parallel; 1 # The spring modulus growth model is: Where E1 is 1 # The elastic modulus of the spring, t0 is the design age, E 1_0 is 1 # The elastic modulus of the spring at the design age, c1 is 1 # Undetermined parameters in the spring modulus growth model; The stress σ of the recoverable creep viscoelastic element is changed from 1 # Spring and 1 # The relationship between the damper load, σ and the strain ε1 of this element is as follows: Iterate according to the time step. Within the time step, σ and ε1 are approximately regarded as unchanged. The strain rate is deduced from the above formula Then the strain increment of this element in this time step is obtained as: Where η1 is 1 # Damping parameters of the damper; (3) The irreversible compressive creep element is composed of a 2# spring with increasing stiffness, a 2# damper and a one-way friction device in parallel; 2 # The spring modulus growth model is: Where E2 is 2 # The elastic modulus of the spring, t0 is the design age, E 2_0 For 2 # The elastic modulus of the spring at the design age, c2 is 2 # Undetermined parameters in the spring modulus growth model; When the compressive strain increases, the stress σ of the irrecoverable compressive creep element changes from 2 # Spring and 2 # The relationship between the damper load, σ and the strain ε2 of this element is as follows: Iterate according to the time step. Within the time step, σ and ε2 are approximately considered to remain unchanged. When the compressive strain increases, the compressive strain increment of this element within the time step is: Where η2 is 2 # Damper damping parameters; When the compressive strain tries to decrease, the friction device completely prevents the reduction of the compressive strain, so that the compressive strain of the element only increases and does not decrease, and the compressive strain cannot be restored; (4) The irreversible tensile creep element consists of a 3 # Spring, one 3 # The damper and a one-way friction device are connected in parallel; 3 # The spring modulus growth model is: Where E3 is 3 # The elastic modulus of the spring, t0 is the design age, E 3_0 For 3 # The elastic modulus of the spring at the design age, c3 is 3 # Undetermined parameters in the spring modulus growth model; When the tensile strain increases, the tensile stress σ of the irreversible tensile creep element changes from 3 # Spring and 3 # The relationship between the damper load, σ and the tensile strain ε3 of this element is as follows: Iterate according to the time step. Within the time step, σ and ε3 are approximately regarded as unchanged. The strain rate is deduced from the above formula It is then obtained that when the tensile strain increases, the tensile strain increment of this element in this time step is: Where η3 is 3 # Damper damping parameters; When the tensile strain tries to decrease, the friction device completely prevents the tensile strain from decreasing, so that the tensile strain of the component only increases but does not decrease, and the tensile strain cannot be restored.

3. The four-element model of concrete modulus and creep under long-term cyclic loading as claimed in claim 2, characterized in that The calibration method of the related parameters of the four-element model is carried out in a classified and staged manner, specifically: The parameters of instantaneous modulus and its growth have relatively reliable sample data, large sample size, and weak coupling with other factors. Such parameters are calibrated separately in advance. The remaining parameters are calibrated in stages. First, a creep model with similar background and samples with rich creep experimental data are used for preliminary calibration to define the parameter range and examine whether the parameters can be condensed to reduce their number. For example, c e , c1, c2, c3 are reduced to 1-2 parameters, and η1, η2, η3 are reduced to 1-2; secondly, the short-term, long-term test and creep test data of the application object are combined to further calibrate and narrow the parameter range; finally, the measured data of the application object during operation are used to finally determine the concrete modulus and creep model parameters.

Images