CN112485114B - Method for predicting ultra-slow creep of concrete - Google Patents

Method for predicting ultra-slow creep of concrete Download PDF

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CN112485114B
CN112485114B CN202011318659.3A CN202011318659A CN112485114B CN 112485114 B CN112485114 B CN 112485114B CN 202011318659 A CN202011318659 A CN 202011318659A CN 112485114 B CN112485114 B CN 112485114B
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梁英杰
管佩瑶
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Abstract

The invention discloses a method for predicting ultra-slow creep of concrete, which comprises the following steps: s1, selecting a certain concrete as a research object, and determining to perform a creep experiment on the concrete to obtain creep experiment data of the concrete; s2, constructing a local structure derivative Maxwell constitutive relation model by adopting a structural sticky kettle; s3, under the creep experiment condition of the concrete in the step S1, obtaining a creep equation of the concrete with parameters by the constitutive relation model in the step S2; s4, combining creep experimental data of the concrete, and obtaining parameters in a creep equation through data fitting; s5, substituting the parameters in the creep equation into the creep equation in the step S3 to obtain a complete concrete creep equation; and predicting the ultra-slow creep process of the concrete according to the concrete creep equation. The method improves the accuracy of the creep constitutive relation of the concrete, and can effectively predict and indirectly control the structural damage and destruction caused by the ultra-slow deformation of the concrete.

Description

Method for predicting ultra-slow creep of concrete
Technical Field
The invention relates to application of civil engineering materials, in particular to a method for predicting ultra-slow creep of concrete.
Background
Concrete is a typical viscoelastic material, which generally exhibits both elastic and viscous properties. Concrete creep refers to a mechanical phenomenon that strain of a material continuously increases with time under the condition that the stress is kept unchanged. As a composite material with multiple components and a complex structure, the creep property of concrete is always one of important indexes for evaluating the mechanical property of concrete building materials. Engineering practices show that the cracking and the instability of the concrete structure do not occur immediately after the pouring is finished, but are caused by the continuous adjustment and development of the stress and the strain of the concrete structure along with the change of time and the accumulation of the stress and the strain for a long time. When the damage to the concrete accumulates to a certain extent, it can lead to macroscopic damage and even catastrophic results.
The traditional constitutive models include Maxwell model, Kelvin model, Zener model, Burgers model and the like, and the models are composed of series connection or parallel connection of elastic elements and viscous elements. These models are integral derivative models, with viscous element stress being linearly related to strain rate. While integer-order derivative physico-mechanical models have enjoyed great success in classical mechanics, acoustics, thermal conduction, diffusion, electromagnetism, and even quantum mechanics, physicists and laborers have found an increasing number of "anomalous" phenomena that cannot be well explained by integer-order derivative models, such as the phenomenon of very slow creep of viscoelastic materials. To better explain this type of "anomalous" phenomenon, more spring elements and newton's sticky pots are usually added on the basis of the traditional model, so as to obtain a better fitting. However, such a processing method leads to more material parameters being introduced into the constitutive equation, and also leads to a complex form of constitutive relation.
Therefore, there is a need to propose a new method for describing the "abnormal" phenomena of very slow concrete creep.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a novel method for predicting the ultra-slow creep of concrete so as to better guide the application of viscoelastic materials such as concrete in actual life, production and construction.
The technical scheme is as follows: the invention discloses a method for predicting ultra-slow creep of concrete, which comprises the following steps:
s1, selecting a certain concrete as a research object, and determining to perform a creep experiment on the concrete to obtain creep experiment data of the concrete;
s2, constructing a local structure derivative Maxwell constitutive relation model by adopting a structural sticky kettle;
s3, under the creep experiment condition of the concrete in the step S1, obtaining a creep equation of the concrete with parameters by the constitutive relation model in the step S2;
s4, combining the creep experimental data of the concrete in the step S1, and obtaining parameters in a creep equation through data fitting;
s5, substituting the parameters obtained in the step S4 into the creep equation in the step S3 to obtain a complete concrete creep equation; and predicting the ultra-slow creep process of the concrete according to the concrete creep equation.
Further, the obtaining of creep test data of the concrete in step S1 includes: the value of the strain over time under the initial stress.
Further, the step S2 is to adopt a structure of sticking the kettle:
Figure BDA0002792115030000021
the corresponding local structural derivative Maxwell constitutive relation model is as follows:
Figure BDA0002792115030000022
where eta represents a viscosity coefficient, E represents an elastic coefficient, sigma represents stress, epsilon represents strain, alpha represents an order, and tau0Is a non-dimensionalization process for t.
Further, the creep test condition in step S3 refers to the initial stress σ0Under the condition of;
the resulting creep equation for the belt parameters is:
Figure BDA0002792115030000023
wherein σ0For the initial stress, η represents the viscosity coefficient, E represents the elastic coefficient, α represents the order, τ0Is a non-dimensionalization process for t.
Further, step S4 is specifically: describing the experimental data in the step S1 by using a creep equation corresponding to the constitutive relation model, and obtaining the most appropriate matching parameters in the creep equation by using an lsqcurvefit command in Matlab software, namely a least square method, wherein the parameters enable the mean square error between the creep equation and the creep experimental data to be minimum; the parameters include: expressing the elastic coefficient E, expressing the viscosity coefficient eta, and performing dimensionless processing on t0And order alpha.
Further, in step S5, the values of the parameters obtained in step S4 are substituted into the creep equation in step S3 to obtain a complete concrete creep equation, and the value of the concrete creep at any time is calculated according to the concrete creep equation to realize the long-term evolution process of the concrete creep.
Has the advantages that: with the intensive research on viscoelastic materials, more and more creep processes, the growth rate of which is generally slow, cannot be predicted by using the conventional integer order derivative model and fractal derivative model. The traditional integer order derivative model is suitable for describing the creep process of exponential growth, and the fractal derivative model is suitable for describing the creep process of extended exponential growth. The model which was first applied to the study of the very slow creep of viscoelastic materials is the traditional Lomnitz model, but the traditional Lomnitz model is only an empirical model, and a corresponding creep function cannot be obtained through analytical derivation. The method adopts a method of combining a local structural derivative and a Maxwell model to establish a model capable of predicting the ultra-slow creep of the concrete. The method can accurately predict the concrete ultra-slow creep phenomenon, and can effectively predict and indirectly control the structural damage and destruction caused by the deformation of the concrete.
Drawings
FIG. 1 is a flow chart of a method of predicting very slow creep in concrete according to the present invention;
FIG. 2 is a graph showing the effect of the model of the present invention and other models applied to the prediction of the concrete creep process.
Detailed Description
The following detailed description of the present invention will be provided in conjunction with the accompanying drawings and specific embodiments to facilitate a more thorough understanding of the present invention by those skilled in the art. It is to be understood that the present disclosure is only one representative embodiment. It will be apparent that the invention is not limited to any specific structure, function, device and method described herein, but may have other embodiments and the scope of the invention is not limited to the described embodiments.
The invention discloses a method for predicting ultra-slow creep of concrete. The method is suitable for the creep process of the viscoelastic material. In this embodiment, a high-strength self-compacting concrete is selected as a research object, and a specific method of analysis is explained in detail. It should be noted that the analysis steps of the present invention are not limited to high strength self-compacting concrete nor to this class of viscoelastic materials, and that other viscoelastic materials may be similarly subjected to very slow creep.
As shown in FIG. 1, the concrete ultra-slow creep prediction method comprises the following specific operation steps:
s1, selecting a certain concrete as a research object, determining a creep experiment to be carried out on the concrete, and obtaining creep experiment data of the concrete, namely a value of strain changing along with time under the action of initial stress.
S2, constructing a local structure derivative Maxwell constitutive relation model by adopting a structure viscosity kettle, wherein the structure viscosity kettle is as follows:
Figure BDA0002792115030000031
the corresponding local structural derivative Maxwell constitutive relation model is as follows:
Figure BDA0002792115030000041
where eta represents a viscosity coefficient, E represents an elastic coefficient, sigma represents stress, epsilon represents strain, alpha represents an order, and tau0Is a non-dimensionalization process for t.
S3, under the creep experiment condition of the concrete in the step S1, obtaining a creep equation of the concrete with parameters by the constitutive relation model in the step S2;
creep test conditions refer to the conditions at initial stress σ0Under the condition of;
the resulting creep equation for the belt parameters is:
Figure BDA0002792115030000042
wherein σ0For the initial stress, η represents the viscosity coefficient, E represents the elastic coefficient, α represents the order, τ0Is a pair ofAnd (5) carrying out dimensionless processing on t.
S4, combining the creep experimental data of the concrete in the step S1, and obtaining parameters in a creep equation through data fitting;
describing the experimental data in the step S1 by using a creep equation corresponding to the constitutive relation model, and obtaining the most appropriate matching parameters in the creep equation by using an lsqcurvefit command in Matlab software, namely a least square method, wherein the parameters enable the mean square error between the creep equation and the creep experimental data to be minimum; the parameters include: expressing the elastic coefficient E, expressing the viscosity coefficient eta, and performing dimensionless processing on t0And order alpha.
S5, substituting the parameters obtained in the step S4 into the creep equation in the step S3 to obtain a complete concrete creep equation; and calculating the concrete creep value at any moment according to the concrete creep equation, and realizing the long-term evolution process of the concrete creep.
Example (b):
(1) this embodiment adopts high strength self-compaction concrete to be experimental test piece to use plane hydraulic jack to exert creep load (unipolar) on the test piece. To keep the stress constant throughout the test, the laboratory technician attaches a jack to a bottle containing pressurized nitrogen (about 80%) and oil (about 20%) to offset the volume change due to sample specimen deformation. The load was applied at a rate of about 0.2MPa/s for this experiment. In the MTS testing machine, the concrete test piece is loaded with 30% of stress intensity ratio after 16h of age, namely the initial stress is 16.56MPa, and the stress intensity ratio is kept constant at least for 600 days. Under the initial condition, the creep test data of the concrete can be obtained by recording the strain amount of the test piece within 600 days by using a linear displacement transducer (LVDT). More detailed experimental equipment and procedures are disclosed in the literature (Maia L, Figueiras J. early-age skin definition of a high strength self-refining Materials,2012,34: 602-Materials 610.).
(2) The method adopts a structure to stick a kettle, constructs a local structure derivative Maxwell constitutive relation model, and the structure sticking kettle is as follows:
Figure BDA0002792115030000051
the corresponding local structural derivative Maxwell constitutive relation model is as follows:
Figure BDA0002792115030000052
where eta represents a viscosity coefficient, E represents an elastic coefficient, sigma represents stress, epsilon represents strain, alpha represents an order, and tau0Is a non-dimensionalization process for t.
(3) At initial stress σ0Under the action of 16.56MPa, a creep equation with parameters is obtained:
Figure BDA0002792115030000053
(4) the creep equation corresponding to the constitutive relation model provided by the invention is adopted to describe the experimental data in the step S1, and the most appropriate matching parameters in the creep equation are obtained by applying an lsqcurvefit (least square method) command in Matlab software, wherein the parameters enable the mean square error between the creep equation and the creep experimental data to be minimum. The parameters are specified in Table 1.
TABLE 1 local structural derivatives Maxwell constitutive relation model parameter values
Figure BDA0002792115030000054
(5) And (4) substituting the parameters obtained in the step (4) into the creep equation obtained in the step (3) to obtain a complete creep equation. And predicting the ultra-slow creep process of the concrete according to the creep equation of the concrete. Dividing ε (t) by the initial stress σ0The time-dependent creep compliance curve can be obtained. In this example, Matlab software was used to plot the J-t curve, see FIG. 2, to visually describe the increase in creep compliance. Meanwhile, in the embodiment, the local structural derivative Maxwell model, the traditional integer order derivative model and the fractal derivative model are usedType, Lomnitz empirical derivative models were compared. From the results, the Maxwell model of local structural derivatives has an advantage in predicting the concrete creep at a very slow speed.
The invention discloses a method for predicting ultra-slow creep of concrete. By introducing a structural function, the strain rate of the classic Newton clay pot is corrected, and the Maxwell constitutive relation of the ultra-slow creep of the concrete is obtained and used for predicting the ultra-slow creep of the concrete. The Maxwell constitutive relation comprises a local structural derivative, is few in parameters, good in fitting effect and small in calculation amount, and can describe the logarithmic dependence phenomenon of the creep process of the viscoelastic material on a time domain. Compared with the traditional integer order derivative model and the Hausdorff fractal derivative model, the model has a slower growth rate and can describe a very slow creep process. The order in the local structural derivative is related to the material itself, the smaller the order, the slower the creep rate. The method improves the accuracy of the creep constitutive relation of the concrete, and can effectively predict and indirectly control the structural damage and destruction caused by the ultra-slow deformation of the concrete.

Claims (4)

1. A method for predicting ultra-slow creep of concrete, comprising the steps of:
s1, selecting a certain concrete as a research object, and determining to perform a creep experiment on the concrete to obtain creep experiment data of the concrete;
s2, constructing a local structure derivative Maxwell constitutive relation model by adopting a structural sticky kettle;
the structure adopted for sticking the kettle is as follows:
Figure FDA0003159741630000011
the corresponding local structural derivative Maxwell constitutive relation model is as follows:
Figure FDA0003159741630000012
wherein eta represents a viscosity coefficientE represents the elastic coefficient, σ represents the stress, ε represents the strain, α represents the order, τ0Is a dimensionless treatment of t;
s3, under the creep experiment condition of the concrete in the step S1, obtaining a creep equation of the concrete with parameters by the constitutive relation model in the step S2;
creep test conditions refer to the conditions at initial stress σ0Under the condition of;
the resulting creep equation for the belt parameters is:
Figure FDA0003159741630000013
wherein σ0For the initial stress, η represents the viscosity coefficient, E represents the elastic coefficient, α represents the order, τ0Is a dimensionless treatment of t;
s4, combining the creep experimental data of the concrete in the step S1, and obtaining parameters in a creep equation through data fitting;
s5, substituting the parameters obtained in the step S4 into the creep equation in the step S3 to obtain a complete concrete creep equation; and predicting the ultra-slow creep process of the concrete according to the concrete creep equation.
2. The method of claim 1, wherein the step of obtaining creep test data of the concrete in step S1 comprises: the value of the strain over time under the initial stress.
3. The method for predicting very slow creep of concrete according to claim 1, wherein step S4 is specifically: describing the experimental data in the step S1 by using a creep equation corresponding to the constitutive relation model, and obtaining the most appropriate matching parameters in the creep equation by using an lsqcurvefit command in Matlab software, namely a least square method, wherein the parameters enable the mean square error between the creep equation and the creep experimental data to be minimum; the parameters include: representing elastic coefficient E, representing viscosity coefficient eta, dimensionless processing on tτ0And order alpha.
4. The method for predicting very slow creep of concrete according to claim 1, wherein the values of the parameters obtained in step S4 are substituted into the creep equation in step S3 in step S5 to obtain a complete concrete creep equation, and the values of the concrete creep at any time are calculated according to the concrete creep equation to realize the long-term evolution process of the predicted concrete creep.
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