Construction of asphalt mixture multi-damage fractional order creep constitutive model and method thereof

Abstract

The invention discloses an asphalt mixture multi-damage fractional order creep constitutive model construction method, and belongs to the technical field of road engineering, and the method specifically comprises the following steps: constructing a fractional order viscoelastic plastic constitutive model; solving an expression of the fractional order viscoelastic plastic constitutive model for the strain response and the accumulated strain under the action of the single intermittent semi-normal load; introducing a plurality of relative damage variables into the fractional order viscoelastic plastic constitutive model to construct an asphalt mixture multi-damage fractional order creep constitutive model; and solving the expression of the multi-damage fractional order creep constitutive model of the asphalt mixture on the strain response and accumulated strain under the action of the single intermittent semi-normal load. According to the method, the evolution process of different mechanical properties of the asphalt mixture can be reflected, the model parameters of the dynamic loading test are obtained through the parameter identification method, and accurate characterization of the strain response and the accumulated strain of the asphalt mixture is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of road engineering, and particularly relates to the construction of a multi-damage fractional-order creep constitutive model for asphalt mixture and its method. Background Art

[0002] As a complex multi-phase composite material, asphalt mixture is the main pavement material in road infrastructure construction and directly bears the action of traffic loads. The constitutive characteristics of asphalt mixture determine its complex mechanical properties. Constructing an accurate constitutive model for asphalt mixture is crucial for characterizing the mechanical behavior of asphalt pavement and revealing the evolution of its service performance. Compared with static creep tests, the repeated intermittent semi-sine load in dynamic loading tests can better simulate the real traffic load conditions of asphalt pavement. At the same time, with the development of intelligent sensing technology, the mechanical response data of asphalt pavement under traffic loads are gradually sufficient for more in-depth analysis. How to accurately express the strain response of asphalt mixture during the entire dynamic loading test through a constitutive model is a key issue for further studying its creep behavior.

[0003] The creep constitutive model of asphalt mixture is constructed based on its viscoelastic or viscoelastic-plastic mechanical properties. The viscoelastic constitutive model represented by the traditional Burgers model cannot characterize the accelerated creep stage of asphalt mixture. By introducing plastic elements to construct a viscoelastic-plastic constitutive model, the characterization of the three creep stages can be achieved. At the same time, in order to improve the expression effect of the constitutive model on the strain curve, basic elements based on fractional-order theory are introduced into the constitutive model. Meanwhile, in related research, many scholars use a damage variable to characterize the mechanical evolution process of asphalt mixture during creep and introduce damage theory into the constitutive model. However, as a complex viscoelastic-plastic material, the different mechanical properties of asphalt mixture have different evolution trends during creep, and a single damage variable is difficult to characterize the evolution of different mechanical properties of asphalt mixture.

[0004] At the present stage, the research on the dynamic creep behavior and damage constitutive model of asphalt mixture mainly focuses on the evolution and expression of cumulative strain. However, in the process of constructing and applying the creep constitutive model of asphalt mixture, the evolution process of different mechanical properties is not considered, and the characterization of the real-time strain response during the entire creep process is in a blank stage, and no relevant research reports are available. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for constructing a multi-damage fractional-order creep constitutive model of asphalt mixture, which can reflect the evolution process of different mechanical properties of asphalt mixture, and obtain the model parameters of dynamic loading tests through the parameter identification method of the present invention, so as to accurately characterize the strain response and cumulative strain of asphalt mixture, and overcome the deficiency that the existing technology is in a blank stage in characterizing the real-time strain response during the whole creep process.

[0006] To achieve the above purpose, the present invention provides the following technical solutions: In the first aspect, the present invention provides a method for constructing a multi-damage fractional-order creep constitutive model of asphalt mixture. The method for constructing the multi-damage fractional-order creep constitutive model of asphalt mixture and its derivation of the expressions of strain response and cumulative strain specifically includes: Construct a fractional-order viscoelastic-plastic constitutive model; Solve the expressions of strain response and cumulative strain of the fractional-order viscoelastic-plastic constitutive model under a single intermittent half-sine load; Introduce multiple relative damage variables into the fractional-order viscoelastic-plastic constitutive model to construct a multi-damage fractional-order creep constitutive model of asphalt mixture; Solve the expressions of strain response and cumulative strain of the multi-damage fractional-order creep constitutive model of asphalt mixture under a single intermittent half-sine load.

[0007] Further, the process of constructing the fractional-order viscoelastic-plastic constitutive model is specifically as follows: Connect a Hookean spring element, an Abel element, a Newton dashpot element, and a Bingham model in series to construct a fractional-order viscoelastic-plastic constitutive model; among them, the elastic strain of asphalt mixture is described by the Hookean spring element, the viscoelastic strain of asphalt mixture is described by the Abel element, the viscous strain of asphalt mixture is described by the Newton dashpot element, and the viscoplastic strain of asphalt mixture is described by the Bingham model; The constitutive relationship of the fractional-order viscoelastic-plastic constitutive model is: Equation (1); Among them, the subscript e represents elastic, v represents viscous, ve represents viscoelastic, vp represents viscoplastic, and n represents the number of loading times; is the elastic modulus of the Hookean spring element under the -th loading, is the viscosity coefficient of the Newton dashpot element under the -th loading, is the order of the Abel element under the -th loading ( ), The viscosity coefficient of the Abel element under the first loading, is the viscosity coefficient of the Bingham model under the th loading, is the yield stress,

[0008] Furthermore, since the elements are in series, the strain response expressions of each element under the intermittent haversine load are solved separately; the expression of the intermittent haversine load is: Equation (2); where is the stress value at the moment of each intermittent loading, is the peak stress, is the loading frequency, is the period time, is the time variable, The process of solving the expressions of the strain response and the cumulative strain of the fractional viscoelastic-plastic constitutive model under a single intermittent haversine load is specifically as follows: Substitute the stress expression during loading in Equation (2) into the constitutive relation of the Hookean spring element, perform Laplace transform and inverse transform on the constitutive relation of the Hookean spring element, and obtain the expression of the elastic strain response under the th loading; During unloading, the elastic strain described by the Hookean spring element is 0; Substitute the stress expression during loading in Equation (2) into the constitutive relation of the Newtonian dashpot element, perform Laplace transform and inverse transform, and obtain the expression of the viscous strain response under the th loading; During unloading, the viscous strain described by the Newtonian dashpot element remains at the strain value at the end of loading; Substitute the stress expression during loading in Equation (2) into the constitutive relation of the Abel element, perform Laplace transform and inverse transform, and obtain the expression of the viscoelastic strain response under a single haversine load; After the stress drops to the yield stress, the viscoplastic strain described by the Bingham model will remain unchanged; The elastic strain value, viscoelastic strain value, viscous strain value, and viscoplastic strain value during loading and unloading obtained according to the above expressions are respectively superimposed to obtain the expression of the strain response of the fractional viscoelastic-plastic constitutive model under the th intermittent half-sine load as: ; where is the strain value at the th moment during the th intermittent loading; The relationship for the fractional viscoelastic-plastic constitutive model to express the cumulative strain is: ; where is the cumulative strain after the th intermittent loading, is the viscoelastic strain at the end of the th intermittent loading, , is the viscous strain at the end of the th intermittent loading, is the viscoplastic strain at the end of the th intermittent loading.

[0009] Furthermore, in the fractional viscoelastic-plastic constitutive model, multiple relative damage variables are introduced to construct the multi-damage fractional creep constitutive model of asphalt mixture, specifically: In the dynamic loading test, the deformation mechanism and dominant mechanism of asphalt mixture are different in different creep stages. The evolution analysis of strain response confirms that different mechanical properties of asphalt mixture have different evolution processes. Therefore, introducing multiple damage indicators is an effective method to accurately describe the evolution processes of different mechanical properties. The definition of traditional damage variables is based on the undamaged state. However, when multiple damage states are introduced, it is difficult to accurately grasp the undamaged state of different mechanical properties; therefore, based on the definition of traditional damage variables and taking the reference damage state as the basis, the relative damage variable under the th loading is defined as: ; where is the relative damage variable under the th loading; is the effective bearing area under the th loading; the subscript represents the index in the reference damage state, that is: is the effective bearing area in the reference damage state; Therefore, the effective stress under the th loading is expressed as: ; where is the effective stress under the nth loading; is the effective stress in the reference damage state; Based on the fractional viscoelastic-plastic constitutive model, four relative damage variables, namely the elastic relative damage variable, the viscous relative damage variable, the viscoelastic relative damage variable, and the viscoplastic relative damage variable, are introduced to construct a multi-damage fractional creep constitutive model for asphalt mixtures; The constitutive relationship of the multi-damage fractional creep constitutive model for asphalt mixtures is: ; where is the elastic modulus of the Hookean spring element in the reference damage state, is the viscosity coefficient of the Newtonian dashpot element in the reference damage state, is the viscosity coefficient of the Abel element in the reference damage state, is the viscosity coefficient of the Bingham model in the reference damage state; is the elastic relative damage variable of the asphalt mixture during the th intermittent loading, is the viscous relative damage variable of the asphalt mixture during the th intermittent loading, is the viscoelastic relative damage variable of the asphalt mixture during the th intermittent loading, is the viscoplastic relative damage variable of the asphalt mixture during the th intermittent loading.

[0010] Furthermore, the strain response expression of the multi-damage fractional creep constitutive model of the asphalt mixture under the th loading is; ; The cumulative strain expression of the multi-damage fractional creep constitutive model of the asphalt mixture is: ; The relationship between the viscous relative damage variable and the cumulative strain is established through an exponential relationship, and its expression is: ; where is the cumulative strain, is the ultimate strain; The relationship between the viscoplastic relative damage variable and the ultimate strain is established through an exponential relationship, and its expression is: ; When the viscoelastic properties do not change during the loading process, i.e.: ; The cumulative strain expression of the multi-damage fractional creep constitutive model of asphalt mixture can be expressed as: .

[0011] In a second aspect, the present invention provides a method for identifying parameters of a multi-damage fractional creep constitutive model of asphalt mixture, comprising the following steps: Step 1: Keep the asphalt mixture specimen at the target temperature, conduct a dynamic loading test, apply stress using a repeated intermittent semi-sine load, and collect the strain response data throughout the dynamic loading test; Step 2: Take the measured strain value at the end of each loading as the cumulative strain data, and fit the cumulative strain data in the asphalt mixture loading test to obtain the non-recoverable viscoelastic strain , viscous strain , viscoplastic strain , viscous relative damage variable parameter and viscoplastic relative damage variable parameter ; Step 3: Based on the viscous strain and viscoplastic strain at the reference damage state obtained in Step 2, calculate the viscous coefficient of the Newton viscous pot element and the viscous coefficient of the Bingham model at the reference damage state; Step 4: Based on Step 3, use the viscous relative damage variable parameter and viscoplastic relative damage variable parameter obtained in Step 2 to calculate the viscous relative damage variable and viscoplastic relative damage variable under the -th loading, and further calculate the viscous coefficient of the Newton viscous pot element and the viscous coefficient of the Bingham model under the -th loading; Step 5: Based on Step 3, use the viscous relative damage variable parameter and viscoplastic relative damage variable parameter obtained in Step 2 to calculate the viscous strain and viscoplastic strain under the , the viscoelastic strain response during unloading is obtained, which is the viscoelastic strain recovery behavior described by the Abel element, and the fractional order and viscous coefficient of the Abel element under different stress conditions are obtained by fitting. and the viscous coefficient ; Step 6: Calculate the viscous strain, viscoelastic strain and viscoplastic strain at the peak stress moment under the th loading. Subtract the viscous strain, viscoelastic strain and viscoplastic strain at this moment from the strain value at the peak stress moment under each loading to obtain the maximum elastic strain of the asphalt mixture, and calculate the elastic modulus of the Hookean spring under the th loading.

[0012] Furthermore, in Step 2, the cumulative strain data is fitted by the expression of the cumulative strain of the multi-damage fractional order creep constitutive model, and the Solver function of Excel software is used for fitting by the least square method; where is the viscoelastic strain at the end of the intermittent loading under the reference damage state, the viscous strain at the end of the intermittent loading under the reference damage state, the viscoplastic strain at the end of the intermittent loading under the reference damage state; In Step 3, the viscous coefficient at the reference damage state is calculated by the expression of the viscous strain during loading.

[0013] Furthermore, in Step 4, and

[0014] are used to calculate the relative damage variable and the viscous coefficient under the nth loading; where is the cumulative strain;

[0015] Furthermore, in Step 5, the fractional order and the viscous coefficient of the Abel element under different stress conditions are obtained by fitting the expression of the viscoelastic strain during unloading.

[0016] Furthermore, in Step 6, the elastic modulus of the Hookean spring under the th loading is calculated by the expression of the elastic strain during loading.

[0017] Compared with the prior art, the present invention has the following beneficial technical effects: 1. The method of the present invention for constructing a multi-damage fractional-order creep constitutive model of asphalt mixture discloses a method for constructing a multi-damage fractional-order creep constitutive model of asphalt mixture and expressing strain response and cumulative strain. The physical meaning of the model components is clear, which is consistent with the mechanical performance of asphalt mixture under single loading and the evolution trend of different mechanical properties of asphalt mixture. And through the derivation of formulas, the expression relationship of the model for the strain response under single intermittent half-sine load is given.

[0018] Furthermore, the present invention first constructs a fractional-order viscoelastic-plastic constitutive model by introducing fractional-order basic elements in series; defines elastic relative damage variable, viscoelastic relative damage variable, viscous relative damage variable and viscoplastic relative damage variable, which reflects the evolution process of different mechanical properties of asphalt mixture, and proposes the relationship between viscous relative damage variable, viscoplastic relative damage variable of asphalt mixture and real-time cumulative strain, ultimate strain.

[0019] Furthermore, the present invention introduces the newly defined four relative damage variables into the fractional-order viscoelastic-plastic constitutive model, and finally constructs a multi-damage fractional-order creep constitutive model of asphalt mixture. The expressions of the multi-damage fractional-order creep constitutive model for the strain response and cumulative strain of asphalt mixture during the whole process of dynamic loading test are derived, and the strain response of asphalt mixture under single load is expressed with different model parameters.

[0020] Furthermore, the present invention provides a parameter identification method for the multi-damage fractional-order creep constitutive model of asphalt mixture. Through this method, the model parameters and relative damage variables during the whole process of the dynamic loading test of asphalt mixture can be obtained, and the real-time strain response and cumulative strain curves of asphalt mixture can be accurately described simultaneously.

[0021] Furthermore, through the multi-damage fractional-order creep constitutive model of asphalt mixture constructed by the present invention and the proposed model parameter identification method, the mechanical behavior and damage mechanism of asphalt mixture can be further explored in depth, and in the future, it can also provide a theoretical basis and application method for the analysis and application of intelligent perception data of asphalt pavement. Description of the Drawings

[0022] Figure 1 It is a schematic flow chart of the method for constructing a multi-damage fractional-order creep constitutive model of asphalt mixture and expressing strain response and cumulative strain in the embodiment of the present invention.

[0023] Figure 2 It is a schematic diagram of the multi-damage fractional-order creep constitutive model of asphalt mixture in the embodiment of the present invention.

[0024] Figure 3 It is a schematic flow chart of model parameter identification in the embodiment of the present invention.

[0025] Figure 4 Schematic diagram of the stress waveform in the dynamic loading test in the embodiment of the present invention.

[0026] Figure 5 Schematic diagram of the cumulative strain curve of asphalt mixture and the model expression result in the dynamic loading test in the embodiment of the present invention.

[0027] Figure 6 Schematic diagram of the strain response curve of asphalt mixture and the model expression result in different creep stages in the embodiment of the present invention.

[0028] Figure 7 Schematic diagram of the fitting effect of the model on the real-time strain response under single loading in the embodiment of the present invention. Detailed implementation manners

[0029] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0030] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order different from those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0031] Embodiment 1 First, as Figure 1 shown, a multi-damage fractional-order creep constitutive model for asphalt mixture was constructed, and its strain response and cumulative strain expressions were derived. The specific steps are as follows: Construct a fractional-order viscoelastic-plastic constitutive model: Construct a fractional viscoelastic - plastic constitutive model by connecting Hookean spring element, Abel element, Newton dashpot element and Bingham model in series. Among them, the elastic strain of asphalt mixture is described by the Hookean spring element, the viscoelastic strain is described by the Abel element, the viscous strain is described by the Newton dashpot element, and the viscoplastic strain is described by the Bingham model. The constitutive relation of the fractional viscoelastic - plastic constitutive model is: Equation (1); where the subscript e represents elasticity, v represents viscosity, ve represents viscoelasticity, vp represents viscoplasticity, and n represents the number of loading times; is the elastic modulus of the Hookean spring element under the -th loading; is the viscosity coefficient of the Newton dashpot element under the -th loading; is the order of the Abel element ( ) under the -th loading; is the viscosity coefficient of the Abel element under the -th loading; is the viscosity coefficient of the Bingham model under the -th loading; is the differential operator, representing the b - th derivative of a function.

[0032] Solve the expressions of strain response and cumulative strain of the fractional viscoelastic - plastic constitutive model under a single - interval half - sine load: The expression of the intermittent half - sine load is: Equation (2); where is the stress value at the time of each intermittent loading ; is the peak stress; is the loading frequency; is the period time; is the time variable; After substituting the stress expression of the load into the constitutive relation, the expressions of strain response and cumulative strain of the fractional viscoelastic - plastic constitutive model are obtained through Laplace transform and inverse transform. Specifically: Elastic strain response described by the Hookean spring element: Substitute the stress expression during loading in Equation (2) into the constitutive relation of the Hookean spring element, perform Laplace transform and inverse Laplace transform on the constitutive relation of the Hookean spring element, and obtain the expression for the elastic strain response under the th loading: Equation (3); where is the elastic strain value at time under the th intermittent loading; represents the inverse Laplace transform of the function; is the independent variable in the Laplace transform domain; is the elastic strain value under the th intermittent loading after Laplace transform; During unloading, the elastic strain described by the Hookean spring element is 0; Viscous strain response described by the Newton dashpot element: Substitute the stress expression during loading in Equation (2) into the constitutive relation of the Newton dashpot element, and then perform Laplace transform and inverse Laplace transform to obtain the expression for the viscous strain response under the th loading: Equation (4); where is the viscous strain value at time under the th intermittent loading; is the viscous strain value under the th intermittent loading after Laplace transform; During unloading, the viscous strain described by the Newton dashpot element remains at the strain value at the end of loading, which is ; Viscoelastic strain response described by the Abel element: Substitute the stress expression during loading in Equation (2) into the constitutive relation of the Abel element, and then perform Laplace transform and inverse Laplace transform to obtain the expression for the viscoelastic strain response under a single half-sine load: Equation (5); where is the viscoelastic strain value at time under the th intermittent loading; is the viscoelastic strain value under the th intermittent loading The value after Laplace transform; is the Gamma function, defined as ; is the two-parameter Mittag-Leffler function, defined as ; Substitute the stress expression during unloading in Equation (2) into the constitutive relation of the Abel element, and then perform Laplace transform and inverse transform to obtain the expression of the viscoelastic strain response during unloading: Equation (6); To reduce the computational difficulty and improve the generalization value of the model, necessary simplification and correction are carried out on the two-parameter Mittag-Leffler function in Expressions (5) and (6). During loading, in the Mittag-Leffler function is regarded as 1 for simplification, and during unloading, the Mittag-Leffler function is corrected to the natural exponential function to obtain the expression: Equation (7); The viscoplastic strain response described by the Bingham model: The Bingham model starts to take effect when the stress reaches the yield stress and remains unchanged after the stress decreases to the yield stress. Under the action of a single intermittent haversine load, the moment when the stress reaches the yield stress is denoted as . Then, within the time of , the real-time strain represented by Newton's viscous pot can be subtracted by the strain value at the moment of , which is the viscoplastic strain response during loading; therefore, the expression of the viscoplastic strain response during loading is: Equation (8); Among them, is the viscoplastic strain value at the moment of under the th intermittent loading; After the stress decreases to the yield stress, that is, when , the viscoplastic strain described by the Bingham model remains , that is: Equation (9); According to the above expressions, the elastic strain value, viscoelastic strain value, viscous strain value, and viscoplastic strain value during loading and unloading are obtained and superimposed respectively to obtain the expression of the strain response of the fractional viscoelastic-plastic constitutive model under the th intermittent haversine load as: Equation (10); Among them, is the strain value at the moment of the n-th intermittent loading; The expression of each strain response is achieved through different model parameters. The relationship formula for the fractional viscoelastic-plastic constitutive model to express the cumulative strain is: Equation (11); Among them, is the cumulative strain after the n-th intermittent loading, is the viscoelastic strain at the end of the n-th intermittent loading, , are the viscous strains at the end of the n-th intermittent loading, is the viscoplastic strain at the end of the n-th intermittent loading.

[0033] A multi-damage fractional creep constitutive model of asphalt mixture is constructed by introducing a variety of relative damage variables into the fractional viscoelastic-plastic constitutive model: In the dynamic loading test, the deformation mechanism and the dominant mechanism of asphalt mixture are different in different creep stages. The evolution analysis of the strain response confirms that different mechanical properties of asphalt mixture have different evolution processes. Therefore, introducing multiple damage indicators is an effective method to accurately describe the evolution processes of different mechanical properties. The definition of traditional damage variables is based on the undamaged state. However, when multiple damage states are introduced, it is difficult to accurately grasp the undamaged state of different mechanical properties; therefore, based on the definition of traditional damage variables and taking the reference damage state as the basis, the relative damage variable under the n-th loading is defined as: Equation (12); Among them, is the relative damage variable under the n-th loading; is the effective bearing area under the n-th loading; the subscript represents the index in the reference damage state, that is: is the effective bearing area in the reference damage state; Therefore, the effective stress under the n-th loading is expressed as: Equation (13); Among them, is the effective stress under the n-th loading; is the effective stress in the reference damage state; Then, the elastic relative damage variable is defined , the viscous relative damage variable , the viscoelastic relative damage variable and the viscoplastic relative damage variable are used to express the evolution process of different mechanical properties of asphalt mixtures during dynamic loading. The four relative damage variables are introduced into the fractional viscoelastic-plastic constitutive model to construct the multi-damage fractional creep constitutive model of asphalt mixtures (abbreviated as MD-FVEP model). The schematic diagram of the MD-FVEP model is shown in Figure 2 , and its constitutive relation is as follows: Equation (14); where is the elastic modulus of the Hookean spring element under the reference damage state, is the viscosity coefficient of the Newtonian dashpot element under the reference damage state, is the viscosity coefficient of the Abel element under the reference damage state, is the viscosity coefficient of the Bingham model under the reference damage state; is the elastic relative damage variable of the asphalt mixture during the th intermittent loading, is the viscous relative damage variable of the asphalt mixture during the th intermittent loading, is the viscoelastic relative damage variable of the asphalt mixture during the th intermittent loading, is the viscoplastic relative damage variable of the asphalt mixture during the th intermittent loading.

[0034] The specific process of solving the expressions of the strain response and cumulative strain of the multi-damage fractional creep constitutive model of asphalt mixtures under a single intermittent half-sine load is as follows: The strain response expression of the multi-damage fractional creep constitutive model of asphalt mixtures under the th loading is as follows; Equation (15); The cumulative strain expression of the multi-damage fractional creep constitutive model of asphalt mixtures is: Equation (16); The deformation mechanisms and dominant mechanisms of asphalt mixtures are different at different creep stages. Viscous strain is dominant in the initial creep stage, while viscoplastic strain is mainly manifested in the accelerated creep stage. During the creep process, the decrease, stabilization, and increase of the non-recoverable strain under a single loading can be regarded as a dynamic evolution process in which the viscous strain decreases and the viscoplastic strain increases. At the same time, taking the maximum damage state as the reference damage state, the relationships between the viscous relative damage variable, the viscoplastic relative damage variable and the cumulative strain, the ultimate strain are established respectively through an exponential relationship. Therefore, the expression of the viscous relative damage variable at the th loading time is: Equation (17); The th loading time of the viscoplastic relative damage variable expression is: Equation (18); Among them, is the cumulative strain; is the ultimate strain; At the same time, considering that the non-recoverable viscoelastic strain of the asphalt mixture under a single intermittent loading is at a relatively low level, it can be assumed that when the viscoelastic characteristics do not change during the loading process, that is, when, the cumulative strain expression of the multi-damage fractional creep constitutive model of the asphalt mixture is: Equation (19); Among them, is the viscoelastic strain at the end of the intermittent loading under the reference damage state, the viscous strain at the end of the intermittent loading under the reference damage state, the viscoplastic strain at the end of the intermittent loading under the reference damage state.

[0035] Example 2 The present invention provides a method for identifying parameters of a multi-damage fractional creep constitutive model of an asphalt mixture. Through the dynamic loading test of the asphalt mixture, the parameter identification of the MD-FVEP model is carried out according to the Figure 3 shown process. The specific steps are as follows: Step 1: Keep the asphalt mixture specimen at the target temperature, carry out a dynamic loading test, apply stress using a repeated intermittent half-sine load, and collect the strain response data throughout the dynamic loading test; the measured strain value at the end of each loading is used as the cumulative strain. Subtract the strain value at the initial moment of each loading from the strain response test data as the strain response data under a single loading. The ultimate strain can be set as the maximum strain condition for the termination of the dynamic loading test; Preferably, a gyratory compactor is used to form asphalt mixture specimens, and cylindrical specimens with a diameter of φ100mm and a height of 100mm are obtained after coring. The specimens are kept at a target temperature of 60°C for dynamic loading tests. The stress form is a repeated intermittent semi-sine load, and each cycle loading time is 1s, including a loading time of 0.1s and an unloading time of 0.9s. The stress waveform is as shown in Figure 4 . The stress peaks are set to 0.4MPa, 0.6MPa, 0.7MPa, 0.8MPa, and 1.0MPa respectively. The termination condition of the loading test is set to reach 10,000 loading times or the cumulative strain reaches 0.06. During the test, strain data is collected every 0.02s. The test strain value at the last moment of each loading is used as the cumulative strain. The strain response test data is subtracted by the strain value at the initial moment of each loading as the strain response data under the action of a single loading. The strain condition set for the test termination is 0.06. According to previous studies, the yield stress of asphalt mixture is in the range of 0.04 - 0.06MPa. In this embodiment, it is uniformly taken as 0.05MPa.

[0036] Step 2: Using the test strain value at the last moment of each loading as the cumulative strain data, the cumulative strain data in the asphalt mixture loading test is fitted to obtain the irrecoverable viscoelastic strain , viscous strain , viscoplastic strain , viscous relative damage variable parameter and viscoplastic relative damage variable parameter at the reference damage state; Preferably, in Step 2, the cumulative strain data is fitted through Equation (19) to obtain the irrecoverable viscoelastic strain , viscous strain , viscoplastic strain , viscous relative damage variable parameter and viscoplastic relative damage variable parameter at the reference damage state. And the application of Equation (19) involves the iteration of cumulative strain, so the Solver function of Excel software is used for fitting by the least squares method.

[0037] Specifically, the cumulative strain data in the asphalt mixture loading test is fitted through Equation (19) by using the Solver function of Excel software with the least squares method. The irrecoverable viscoelastic strain , viscous strain , viscoplastic strain , viscous relative damage variable parameter and viscoplastic relative damage variable parameter at the reference damage state under 5 stress conditions are obtained , as shown in Table 1; Table 1 MD-FVEP model parameters in the dynamic loading test of asphalt mixture

[0038] Step 3: Calculate the viscous coefficient of the Newton dashpot element and the viscous coefficient of the Bingham model at the reference damage state based on the viscous strain and viscoplastic strain at the reference damage state obtained in Step 2; Specifically, the viscous coefficients of the Newton dashpot element at the reference damage state under different stress conditions are calculated by Equation (4) to be: 8.3, 13.6, 13.5, 8.9, 7.4 respectively; the viscous coefficients of the Bingham model at the reference damage state under different stress conditions are calculated by Equation (9) to be: 99.6, 94.7, 70.2, 71.4, 54.4 respectively. ; Specifically, the viscous coefficients of the Newton dashpot element at the reference damage state under different stress conditions are calculated by Equation (4) to be: 8.3, 13.6, 13.5, 8.9, 7.4 respectively; the viscous coefficients of the Bingham model at the reference damage state under different stress conditions are calculated by Equation (9) to be: 99.6, 94.7, 70.2, 71.4, 54.4 respectively.

[0039] Step 4: Based on Step 3, use the viscous relative damage variable parameter and viscoplastic relative damage variable parameter obtained in Step 2, and calculate the viscous relative damage variable and viscoplastic relative damage variable under the i-th loading by Equations (17) and (18) respectively, and further calculate the viscous coefficient of the Newton dashpot element and the viscous coefficient of the Bingham model under the i-th loading; ; Step 5: Based on Step 3, use the viscous relative damage variable parameter and viscoplastic relative damage variable parameter obtained in Step 2, calculate the viscous strain and viscoplastic strain under the i-th loading, subtract the viscous strain and viscoplastic strain from the measured strain response data during unloading in the i-th loading cycle to obtain the viscoelastic strain response during unloading, which is the viscoelastic strain recovery behavior described by the Abel element, and fit the fractional order and viscous coefficient of the Abel element under different stress conditions; ; ; ; ; ; ; Step 5: Based on Step 3, use the viscous relative damage variable parameter and viscoplastic relative damage variable parameter obtained in Step 2, calculate the viscous strain and viscoplastic strain under the i-th loading, subtract the viscous strain and viscoplastic strain from the measured strain response data during unloading in the i-th loading cycle to obtain the viscoelastic strain response during unloading, which is the viscoelastic strain recovery behavior described by the Abel element, and fit the fractional order and viscous coefficient of the Abel element under different stress conditions; ; ; ; ; ; ; ; ; ; ; Specifically, the fractional orders of the Abel element under different stress conditions are obtained by fitting with Equation (7). They are respectively: 0.078, 0.120, 0.174, 0.203, and 0.326. The viscosity coefficients of the Abel element under different stress conditions are respectively: 546.6, 554.9, 458.4, 363.0, 314.2; Step 6: Calculate the viscous strain, viscoelastic strain, and viscoplastic strain at the peak stress moment during the nth loading. By subtracting the viscous strain, viscoelastic strain, and viscoplastic strain at this moment from the strain value at the peak stress moment during each loading, the maximum value of the elastic strain of the asphalt mixture is obtained. The elastic modulus of the Hookean spring during the nth loading is calculated using Equation (3). ; Step 7: After obtaining all the model parameters, the cumulative strain curve of the asphalt mixture in the dynamic loading test and the model expression results are as Figure 5 shown. The test curve and the model prediction curve are basically completely coincident. According to Table 1, the fitting correlation coefficients of the MD-FVEP model for the cumulative strain curve can all reach above 0.99. Therefore, the MD-FVEP model can accurately express the cumulative strain. Taking the loading condition of 60°C - 1.0 MPa as an example, the strain response curves of the asphalt mixture under single loading in the three creep stages and the expression results of the MD-FVEP model are as Figure 6 shown. Under 5 stress conditions, the asphalt mixture specimens experienced a total of 5494 intermittent half-sine loadings. The fitting correlation coefficients of the MD-FVEP model for the strain response under 5494 loadings are as Figure 7 shown. The average values under 5 stress conditions are all greater than 0.99, and are densely distributed above 0.98. The minimum value is still greater than 0.92 and the quantity is extremely small.

[0040] Therefore, the MD-FVEP model can accurately express the real-time strain response and cumulative strain curve of the asphalt mixture during the whole process of dynamic loading.

[0041] As described above, only the specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention fall within the protection scope of the present invention. The protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for constructing a multi-damage fractional creep constitutive model for asphalt mixture, characterized in that: include: Construct a fractional-order viscoelastic-plastic constitutive model; Solve the expression of strain response and cumulative strain of fractional-order viscoelastic-plastic constitutive model under single intermittent semi-haversine load; A multi-damage fractional creep constitutive model of asphalt mixture is constructed by introducing multiple relative damage variables into the fractional viscoelastic-plastic constitutive model. The expressions of strain response and accumulated strain of the multi-damage fractional creep constitutive model of asphalt mixture under single intermittent haversine load are solved.

2. The method for constructing a multi-damage fractional creep constitutive model for asphalt mixture according to claim 1, characterized in that: The specific process of constructing the fractional-order viscoelastic-plastic constitutive model is as follows: The Hookean spring element, Abel element, Newton viscosity pot element and Bingham model are connected in series to construct a fractional-order viscoelastic-plastic constitutive model; the constitutive relationship of the fractional-order viscoelastic-plastic constitutive model is: Formula (1); Among them, the subscript For elasticity, For viscosity, For viscoelasticity, Viscoplastic, is the number of loads; For the The elastic modulus of the Hookean spring element under secondary loading, For the The viscosity coefficient of the Newton viscosity element under the secondary loading, For the The order of the Abel element under the secondary loading ( )、 For the The viscosity coefficient of the Abel element under secondary loading, For the The viscosity coefficient of Bingham model under secondary loading, is the yield stress, is a differential operator, which means taking the b-order derivative of the function.

3. The method for constructing a multi-damage fractional creep constitutive model for asphalt mixture according to claim 2, characterized in that: The expression of the intermittent haversine load is: Formula (2); in, For each intermittent loading action The stress value at the moment; is the peak stress; is the loading frequency; is the cycle time; is a time variable; when is the stress expression during loading. is the stress expression during unloading; The specific process of solving the expression of strain response and cumulative strain of the fractional-order viscoelastic-plastic constitutive model under a single intermittent semi-haversine load is as follows: Substitute the stress expression during loading in equation (2) into the constitutive relation of the Hookean spring element, perform Laplace transformation and inverse transformation on the constitutive relation of the Hookean spring element, and obtain Expression for elastic strain response under secondary loading; During unloading, the elastic strain described by the Hookean spring element is 0; Substituting the stress expression during loading in equation (2) into the constitutive relation of the Newton viscosity element, Laplace transformation and inverse transformation are performed to obtain Expression for viscous strain response under secondary loading; During unloading, the viscous strain described by the Newton viscosity element remains at the strain value at the end of loading; After substituting the stress expression during loading in equation (2) into the constitutive relation of the Abel element, Laplace transformation and inverse transformation are performed to obtain the expression of the viscoelastic strain response under a single semi-haversine load; After substituting the stress expression during unloading in equation (2) into the constitutive relation of the Abel element, Laplace transformation and inverse transformation are performed to obtain the expression of the viscoelastic strain response during unloading; Under the action of single intermittent semi-haversine load, the Bingham model comes into play when the stress reaches the yield stress, and the expression of the viscoplastic strain response during loading is obtained; After the stress is reduced to the yield stress, the viscoplastic strain described by the Bingham model remains unchanged; The elastic strain values, viscoelastic strain values, viscous strain values ​​and viscoplastic strain values ​​during loading and unloading obtained by the above expressions are superimposed to obtain the fractional viscoelastic-plastic constitutive model for the first The expression of strain response under subintermittent haversine load is: ； in, For the Under intermittent loading The strain value at the moment; The relationship for expressing the cumulative strain of the fractional-order viscoelastic-plastic constitutive model is: ； in, For the The accumulated strain after the intermittent loading For the The viscoelastic strain at the end of the intermittent loading action, , for the The viscous strain at the end of the intermittent loading action, For the Viscoplastic strain at the end of the intermittent loading.

4. The method for constructing a multi-damage fractional creep constitutive model for asphalt mixture according to claim 3, characterized in that: In the fractional-order viscoelastic-plastic constitutive model, a variety of relative damage variables are introduced to construct a multi-damage fractional-order creep constitutive model of asphalt mixture. Specifically: According to the definition of traditional damage variables, based on the reference damage state, the first The relative damage variable under the secondary loading is: ； in, For the Relative damage variables under secondary loading; For the The effective bearing area under the secondary loading; Represents the index at the reference damage state, namely: is the effective bearing area in the reference damage state; Therefore, the The effective stress under the secondary loading is expressed as: ； Where, is the effective stress under the nth loading; is the effective stress at the reference damage state; On the basis of the fractional viscoelastic-plastic constitutive model, four relative damage variables, namely elastic relative damage variable, viscous relative damage variable, viscoelastic relative damage variable and viscoplastic relative damage variable, are introduced to construct a multi-damage fractional creep constitutive model for asphalt mixture. The constitutive relation of the multi-damage fractional-order creep constitutive model of asphalt mixture is: ； in, is the elastic modulus of the Hookean spring element in the reference damage state, is the viscosity coefficient of the Newton viscosity pot element under the reference damage state, is the viscosity coefficient of the Abel element under the reference damage state, is the viscosity coefficient of the Bingham model under the reference damage state; For the The relative elastic damage variable of asphalt mixture during intermittent loading, For the The relative damage variable of viscosity of asphalt mixture during intermittent loading, For the The relative damage variables of viscoelasticity of asphalt mixture under intermittent loading, For the Viscoplastic relative damage variable of asphalt mixture under intermittent loading.

5. The method for constructing a multi-damage fractional creep constitutive model for asphalt mixture according to claim 4, characterized in that: No. The strain response expression of the multi-damage fractional creep constitutive model of asphalt mixture under secondary loading is: ； The cumulative strain expression of the multi-damage fractional creep constitutive model of asphalt mixture is: ； The relationship between the viscous relative damage variable and the accumulated strain is established through an exponential relationship, and its expression is: ； in, is the accumulated strain, is the ultimate strain; The relationship between the limit strain of the viscoplastic relative damage variable is established through an exponential relationship, and its expression is: ； When the viscoelastic properties do not change during loading, that is: ； The cumulative strain expression of the multi-damage fractional creep constitutive model of asphalt mixture can be expressed as: 。 6. The parameter identification method for constructing a multi-damage fractional-order creep constitutive model for asphalt mixture according to any one of claims 1 to 5, characterized in that: The following steps are involved: Step 1: Keep the asphalt mixture specimens warm to the target temperature, conduct a dynamic loading test, apply stress using repeated intermittent semi-haversine loading, and collect strain response data throughout the dynamic loading test; Step 2: The test strain value at the last moment of each loading is used as the cumulative strain data, and the cumulative strain data in the asphalt mixture loading test is fitted to obtain the irreversible viscoelastic strain at the reference damage state. , viscous strain , viscoplastic strain , Viscous relative damage variable parameter and viscoplastic relative damage variable parameter ; Step 3: Viscous strain at the reference damage state obtained in step 2 Viscoplastic strain Based on the above, the viscosity coefficient of the Newton viscosity element under the reference damage state is calculated. Viscosity coefficient of Bingham model ; Step 4: Based on step 3, use the viscous relative damage variable parameter obtained in step 2 and viscoplastic relative damage variable parameter , calculate the Viscous relative damage variable under secondary loading Relative damage variable to viscoplasticity , further calculate the Viscosity coefficient of Newton viscosity element under secondary loading Viscosity coefficient of Bingham model ; Step 5: Based on step 3, use the viscosity relative damage variable parameter obtained in step 2 and viscoplastic relative damage variable parameter , calculate the Viscous strain under subintermittent haversine loading Viscoplastic strain , the viscoelastic strain response during unloading is obtained, which is the viscoelastic strain recovery behavior described by the Abel element. The fractional order of the Abel element under different stress conditions is obtained by fitting. and viscosity coefficient ; Step 6: Calculate the The viscous strain, viscoelastic strain and viscoplastic strain at the peak stress moment under the first loading are calculated. The maximum value of the elastic strain of the asphalt mixture is obtained by subtracting the viscous strain, viscoelastic strain and viscoplastic strain at the peak stress moment under each loading. Elastic modulus of Hookean spring under secondary loading .

7. The parameter identification method of the multi-damage fractional-order creep constitutive model of asphalt mixture according to claim 6 is characterized in that: The step 2 is to fit the cumulative strain data to the expression of the cumulative strain by using the multi-damage fractional creep constitutive model, and to fit it by the least squares method using the planning and solving function of the Excel software; wherein, is the viscoelastic strain at the end of intermittent loading in the reference damage state, Viscous strain at the end of intermittent loading under reference damage state, The viscoplastic strain at the end of intermittent loading in the reference damage state; Step 3 calculates the viscosity coefficient at the reference damage state through the expression of viscous strain during loading.

8. The parameter identification method of the multi-damage fractional-order creep constitutive model of asphalt mixture according to claim 6 is characterized in that: Step 4 is accomplished by and Calculate the relative damage variable and viscosity coefficient under the nth loading.

9. The parameter identification method of the multi-damage fractional-order creep constitutive model of asphalt mixture according to claim 6 is characterized in that: In step 5, the fractional order of the Abel element under different stress conditions is obtained by fitting the viscoelastic strain expression during unloading. and viscosity coefficient .

10. The parameter identification method of the multi-damage fractional-order creep constitutive model of asphalt mixture according to claim 6 is characterized in that: The step 6 calculates the elastic strain expression during loading. Elastic modulus of Hookean spring under secondary loading .

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