Asphalt cement fractional derivative burgers model and viscoelastic parameter analysis system

Abstract

The invention discloses an asphalt cement fractional derivative burgers model and a viscoelastic parameter analysis system. The Maxwell element is composed of a Maxwell element and a Kelvin element; in the creep relaxation data processing of an asphalt sample, a method of combining two parts of data of a creep stage and a relaxation stage is adopted to obtain six related indexes, namely a spring # imgabs0 #, a spring xi2, a fractional damper eta 1, a fractional damper eta 2, a fractional derivative alpha and a fractional derivative beta; through segmented element combination, the whole process of the material from elastic deformation to viscous damage is analyzed. The invention provides a brand new six-parameter fractional derivative Burgers model and constructs a corresponding calculation path so as to improve the data processing efficiency of a complex model. The data processing and analysis system constructed by the invention aims to quickly and accurately calculate the viscoelastic characteristics of the high-elasticity asphalt cement.

Description

Technical Field

[0001] The invention relates to the technical field of asphalt binder viscoelastic parameter analysis, in particular to an asphalt binder fractional derivative burgers model and a viscoelastic parameter analysis system. Background Art

[0002] In the creep and relaxation processes, the elastic and viscous components of asphalt binder always act together inside the material, and these two stages have the same mechanical characterization and physical meaning. However, most current studies usually only select a certain period of data in the creep stage or relaxation stage to fit the classic Burgers model, and use the fitting results to characterize the viscoelastic properties of asphalt binder. Please refer to Figure 1 This fitting idea regards the creep stage and the relaxation stage as independent processes, and models the viscoelastic characteristic parameters of the two stages separately. It is impossible to unify the fitting of the two stages, resulting in the viscoelastic characteristic parameters of asphalt being usually inconsistent in the two stages. This result is inconsistent with the actual situation. For the same asphalt material, its viscoelastic characteristic parameters should be consistent in the creep and relaxation stages, because the creep and relaxation stages are dominated by the same physical mechanism inside the material. In addition, the classic Burgers model is used to fit the model of asphalt with high elastic recovery rate, which often leads to poor fitting effect. The reason is that in the early stage of the relaxation stage, the strain of the asphalt material decreases rapidly, which manifests as rapid linear or nonlinear changes. The classic Burgers model is difficult to capture the complex mechanical behavior of this stage. At the end of the relaxation stage, the asphalt material exhibits a certain viscous deformation and cannot completely rebound to the initial state. This irreversible deformation causes the model to deviate when describing the stage where the strain tends to stabilize.

[0003] For the least nonlinear square method, the limitation of its fitting effect lies in the consideration of the balance between the rapid decline stage and the residual strain stage at the end. Specifically, during the model fitting process, if more attention is paid to the strain situation in the initial rapid decline stage, that is, the constraints of the model are set so that it can well capture the strain changes in the initial rapid decline stage, under the calculation formula of the classic Burgers model, its fitting degree will deviate greatly from the measured data at the end of the relaxation stage, resulting in poor overall fitting effect; on the contrary, during the model fitting process, if more attention is paid to the strain situation at the end of the relaxation stage, so that the model better fits the strain at the end of the relaxation stage, then the fitting effect of the rapid decline interval of the strain in the initial relaxation stage will be significantly reduced, as shown in the following example. Figure 2 In order to balance the fitting accuracy at the beginning and end stages, a compromise is usually automatically selected to make the overall determination coefficient This compromise reflects the limitations of the classic Burgers model in describing different mechanical behaviors, and also shows that the classic Burgers model is difficult to simultaneously meet the full-stage fitting requirements of complex strain behaviors.

[0004] Some literature mentions the use of the classic Burgers model to fit the creep loading curve of a single cycle of a repeated stress creep test (MSCR) test. Please refer to Figure 3 and Figure 4 In the calculation process, the residual strain measured at the tenth second of the relaxation stage is taken as the known viscous component and fixed to fit the other three model parameters. This method incorporates part of the data of the relaxation stage into the data fitting of the creep stage. However, the analysis of the classic Burgers model shows that the viscous deformation represented by the viscosity pot in its Kelvin element should be the residual deformation left after the asphalt binder completely stops relaxing and deforming after losing the external load, rather than the residual deformation corresponding to the relaxation deformation at a certain moment. However, in the MSCR test, only the residual strain at the tenth second of the relaxation stage is measured. It is still questionable to use it to represent the permanent residual strain. There are also corresponding studies pointing out that the permanent residual strain of asphalt should be smaller than the strain at the end of 10 seconds. To this end, we propose a Burgers model of asphalt binder with a graded derivative and a viscoelastic parameter analysis system. Summary of the invention

[0005] In view of the problems existing in the above-mentioned fitting method, the present invention constructs a graded derivative Burgers model of asphalt binder and a viscoelastic parameter analysis system, aiming to quickly and accurately calculate the viscoelastic properties of high-elastic asphalt binder.

[0006] To achieve the above object, the present invention provides the following technical solution: an asphalt binder graded derivative burgers model and a viscoelastic parameter analysis system, which performs viscoelastic parameter analysis on the asphalt binder by using the following steps: Step 1: Construct the burgers model using Maxwell elements and Kelvin elements; Step 2: In the creep relaxation data processing of asphalt samples, the method of combining the creep and relaxation phase data is adopted to obtain six related indices, namely, spring ,spring x 2. Fractional damper or 1. Fractional damper or 2. Differential derivatives α And the fractional derivatives β ; Step 3: Combine Maxwell elements and Kelvin elements in different sections; Step 4: Use the standard MSCR test to generate viscoelastic data points of asphalt binder and analyze the entire process from elastic deformation to viscous damage of the material.

[0007] Preferably, the system also includes the step of generating viscoelastic data points of asphalt binder using multiple cyclic MSCR tests, and then processing the multiple cyclic MSCR test data based on Python language for data processing and analysis under multiple cyclic tests.

[0008] Preferably, in the creep stage, the first spring in step 2 represents the critical point of linear viscoelasticity, after which the change in curvature during the creep phase initiates nonlinear viscoelasticity.

[0009] Preferably, in the final stage of the creep phenomenon, i.e., the viscous damage stage, the fractional damper Determined to characterize the residual viscous deformation of the asphalt material that is ultimately unable to relax.

[0010] Preferably, in the relaxation stage, the spring Characterizing its instantaneous elastic recovery, the Kelvin element consists of a fractional damper and Parallel configuration, used to characterize the delayed elastic capacity of the relaxation phase, fractional damper The value of the fractional derivative β is between 0 and 1.

[0011] Preferably, during the relaxation phase, the fractional damper in the Maxwell element The value of the fractional derivative α is between 0 and 1. When α is 0, the fractional damper It behaves like a spring. When the value of α is equal to 1, the fractional damper Become a Newton damper.

[0012] Preferably, the standard MSCR test method in step 4 is: a single test data is divided into thirty single cycles, of which ten are preloaded to eliminate experimental errors, ten are 0.1 kPa stress, and ten are 3.2 kPa stress. Each single cycle consists of 1 s of stress application and 9 s of autonomous relaxation. A data point is recorded every 0.1 s, including the microstrain value of the sample.

[0013] Preferably, the test method of using multiple cycles of MSCR test to generate viscoelastic data points of asphalt binder is: Since the test equipment will save the 1s stress and 9s relaxation in each single cycle separately, first connect the time axis and strain axis of a single cycle; assuming that the initial values ​​of the six parameters of this single cycle are set to their respective extreme values: x 1. x 2. or 1. or 2. α , β = 1, 1, 1, 1, 0.5, 0.5; use clip to write a 6-parameter derivative Burgers data model, perform mathematical fitting on the single-cycle data, and after model iteration, x 1. x 2. or 1. or 2. α , β， After the six parameters are adjusted to relatively reasonable values, they are fed back to the operation port. At the same time, the final recovery value of the sample after the time limit of the relaxation stage is released in a single cycle is calculated through equations 12-13 based on the six parameters fed back. On the basis of the single-cycle data processing flow, a data integration link is added to meet the processing needs of ten-cycle data under 0.1kpa and 3.2kpa stresses. The program will calculate each cycle in chronological order. Considering that it cannot be guaranteed that the fitting of each single cycle is successful, the calculation of the single cycle is embedded in the try function, which can clearly tell whether the single cycle is fitted successfully and point out when it fails. At the same time, in the overall calculation, it also avoids the impact of a single cycle error on the continued calculation of subsequent single cycles.

[0014] Preferably, the fractional damper or 1. Fractional damper or 2 is an Abel damper.

[0015] Preferably, the system integrates a visual interface for displaying parameter analysis results and comparisons of model predictions with experimental data.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a new six-parameter graded derivative Burgers model and its corresponding calculation path. All fitting parameters in the model are involved in the strain expression of the creep and relaxation stages of asphalt binders at the same time. Compared with the existing Buegers models, the model proposed by the present invention can more accurately capture the strain conditions at the end of creep and the beginning of relaxation, so that the viscoelastic parameters obtained by fitting calculation can more truly reflect the viscoelastic properties of asphalt binders. In order to improve the data processing efficiency of complex models, the present invention constructs a data processing and analysis system based on Python language. For cyclic loads used in some working scenarios (such as multiple stress creep tests of asphalt), the system can automatically perform cyclic fitting of data, and quickly and accurately calculate the viscoelastic properties of asphalt binder under each cyclic load, which is helpful to quickly analyze the decay law of the elastic properties of asphalt binder under cyclic loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a schematic diagram of the classic Burgers model; Figure 2 This is a schematic diagram of the Burgers model fitting that focuses on fitting the rapid decline stage and the final stable stage; Figure 3 This is a schematic diagram of the partial fitting of the creep stage data of the classic Burgers model; Figure 4 This is a schematic diagram of the partial fitting of the relaxation phase data of the classic Burgers model; Figure 5 Schematic diagram of the six-parameter derivative Burgers model of the present invention; Figure 6 This is a schematic diagram of the relationship between ten single cycle time and strain of a certain high elastic recovery asphalt 0.1kPa. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] The six-parameter fractional derivative Burgers model based on fractional differential theory proposed in the present invention has a constitutive model as follows: Figure 5 As shown in the figure, it is composed of Maxwell elements and Kelvin elements, and the two Newton dampers in the classic burgers model are replaced by Abel dampers.

[0020] In the creep relaxation data processing of asphalt samples, the method of combining the creep and relaxation stage data is adopted to obtain six related indexes, among which the creep stage contains all 6 performance indexes and the relaxation stage contains 5 performance indexes ( x 2. or 1. or 2. α , β ).

[0021] The model can reveal the whole process of material from elastic deformation to viscous damage through segmented component combination, such as Figure 6 As shown, in the creep stage, the first spring represents the critical point of linear viscoelasticity, after which the change in curvature in the creep phase triggers nonlinear viscoelasticity, and in the final stage of the creep phenomenon, the viscous damage phase, the fractional damper Determine, to characterize the residual viscous deformation of the asphalt material that cannot be relaxed. In the relaxation stage, the spring Characterizing its instantaneous elastic recovery, the Kelvin element is mainly composed of fractional dampers and Parallel configuration, used to characterize the delayed elastic capacity of the relaxation phase, fractional damper The addition of can well solve the problem that the classic Burgers model cannot well connect the strain curve after instantaneous elastic recovery. The value of its fractional derivative β is between 0 and 1. Fractional damper in Maxwell element The addition of can well fit the slope of the strain curve at the end of the creep stage. The value of the intermediate derivative α is also between 0 and 1. When α is 0, the fractional damper It behaves like a spring. When the value of α is equal to 1, the fractional damper It becomes a Newton damper. The existence of the fractional derivative α can partially supplement the delayed elastic recovery of the Kelvin element in terms of the entire relaxation stage of the asphalt, so as to better characterize the strain change law of the high elastic recovery asphalt in the delayed elastic recovery link.

[0022] The 6-parameter divided-order derivative Burgers model proposed in the present invention is actually a general form of the classic Burgers model and the FDBⅠ type Burgers model. As the two divided-order derivative parameters α and β are different, the results presented are also different, as summarized in Table 1.

[0023] Table 1: Different representations of the 6-parameter derivative Burgers model

[0024] Theoretically, the permanent deformation of asphalt means that after unloading, the internal colloidal structure of asphalt completely stops elastic contraction. The present invention proposes the concept of true residual strain in the relaxation stage (corresponding to the permanent deformation of asphalt). In this model, the residual strain with infinite recovery time obtained by fitting is characterized and recorded as , which is not mentioned in the existing burgers and its derivative models. Therefore, the calculation formula of the true elastic recovery rate of asphalt can be modified as follows: (1) Where: is the total strain of asphalt when loaded for 1 second; is the true residual strain; is creep stress, usually 0.1Kpa or 3.2Kpa; is the true elastic recovery rate, %.

[0025] According to Figure 6 The schematic diagram of the six-parameter derivative Burgers model shown in the figure first performs curve fitting on the deformation occurring in the creep phenomenon of asphalt materials. The specific calculation process is as follows: (2) Where: represents creep deformation; is the elastic property of the asphalt material, , is the viscosity property of the asphalt material; is the initial stress; is the gamma function; and is the fractional index; For time.

[0026] The deformation of the total system is: (3) The fractional differential equation is expressed as: (4) as well as (5) By taking the fractional order of equation (3) Derivative, we get the total deformation equation: (6) Then take equation (4) The derivative of equation (5) is The derivative is: (7) (8) Substituting the above equation into the total deformation equation (6), we obtain: (9) To express Eq. (11) as a function of the total deformation, we transform Eq. (3) The derivative is: (10) Solve , combined with equation (4), and substituted into equation (10), we get: (11) By eliminating the initial load And applying Laplace transform, the total relaxation function of asphalt binder can be obtained: (12) in and can reach a maximum value of 1, so . At this point, the summation term in the equation is eliminated, leaving only the initial deformation condition. Here, using the Maxwell model, combined with the modified Kelvin-Voigt model, we can get the equation for the relaxation stage: (13) in, Indicates relaxation deformation; is the elastic property of the asphalt material, is the viscosity property of the asphalt material; is the gamma function; is the fractional index; is the adjustment factor of the Maxwell element; is the adjustment factor of the Kelvin element; For time.

[0027] The above model and its calculation steps are for the creep and relaxation data of a single-cycle MSCR test. However, in the standard MSCR test, a single test data is divided into thirty single cycles, including ten preloads (0.1 kpa) to eliminate experimental errors, ten 0.1 kpa stresses, and ten 3.2 kpa stresses. Each single cycle consists of 1 s of stress application and 9 s of autonomous relaxation. A data point is recorded every 0.1 s, including the microstrain value of the sample.

[0028] In order to solve the data processing and analysis under multiple cycle tests, the present invention develops a Python data processing system for multiple cycle MSCR test data processing, and its construction method is as follows: Step 1: Construct the data processing flow of a single cycle: Since the test equipment will save the 1s stress and 9s relaxation in each single cycle separately, first connect the time axis and strain axis of a single cycle. Assume that the initial values ​​of the six parameters of this single cycle are set to their respective extreme values: x 1. x 2. or 1. or 2. α , β = 1, 1, 1, 1, 0.5, 0.5; use clip to write a 6-parameter derivative Burgers data model and perform mathematical fitting on the single-cycle data. After the model is iterated, x 1. x 2. or 1. or 2. α , βAfter the 6 parameters are adjusted to relatively reasonable values, they are fed back to the operation port. At the same time, the theoretical final recovery value of the sample after the time limit of the relaxation stage is released in a single cycle is calculated through equations 12-13 based on the 6 parameters fed back.

[0029] Step 2: Based on the single-cycle data processing flow, a data integration link is added to meet the processing needs of ten-cycle data under 0.1kpa and 3.2kpa stresses. The program will calculate each cycle in chronological order. Considering that it cannot be guaranteed that the fitting of each single cycle is successful, the calculation of the single cycle is embedded in the try function, which can clearly tell whether the single cycle is fitted successfully and point out the failure. At the same time, in the overall calculation, it also avoids the impact of a single cycle error on the continued calculation of subsequent single cycles.

[0030] The system can automatically process experimental data with different numbers of cycles, and at the same time, genetic parameters are added to the calculation of adjacent single cycles. Except for the first single cycle, the 6 parameters of the subsequent single cycles ( x 1, x 2, or 1, or 2, α , β ) The initial value will refer to the result of the previous single cycle. The use of result-oriented method greatly reduces the number of model iterations and improves calculation efficiency.

[0031] After clarifying the number of experimental cycles and test stress, the test results can be obtained with one click.

[0032] Example The six-parameter graded derivative Burgers model and its calculation method and the corresponding supporting data processing system proposed in the present invention are used to fit and analyze the MSCR test data of a high elastic recovery asphalt. The results are shown in the following table (Table 2).

[0033] Table 2: 6-parameter derivative fitting results of a high elastic recovery asphalt 0.1kpa

[0034] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0035] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A Burgers model of asphalt binder with different order derivatives and a viscoelastic parameter analysis system, characterized by: The following steps are used to analyze the viscoelastic parameters of asphalt binder: Step 1: Construct the burgers model using Maxwell elements and Kelvin elements; Step 2: In the creep relaxation data processing of asphalt samples, the method of combining the creep and relaxation phase data is adopted to obtain six related indices, namely, spring ,spring ξ 2. Fractional damper η 1. Fractional damper η 2. Differential derivatives α And the fractional derivatives β ; Step 3: Combine Maxwell elements and Kelvin elements in different sections; Step 4: Use the standard MSCR test to generate viscoelastic data points of asphalt binder and analyze the entire process from elastic deformation to viscous damage of the material.

2. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 1, characterized in that: It also includes the steps of generating viscoelastic data points of asphalt binder using multiple cyclic MSCR tests, and then processing the multiple cyclic MSCR test data based on Python language for data processing and analysis under multiple cyclic tests.

3. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 2, characterized in that: In the creep stage, the first spring in step 2 represents the critical point of linear viscoelasticity, after which the change in curvature during the creep phase initiates nonlinear viscoelasticity.

4. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 3, characterized in that: In the final stage of creep, the viscous damage stage, the fractional damper Determined to characterize the residual viscous deformation of the asphalt material that is ultimately unable to relax.

5. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 4, characterized in that: In the relaxation stage, the spring Characterizing its instantaneous elastic recovery, the Kelvin element consists of a fractional damper and Parallel configuration, used to characterize the delayed elastic capacity of the relaxation phase, fractional damper The value of the fractional derivative β is between 0 and 1.

6. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 5, characterized in that: During the relaxation phase, the fractional damper in the Maxwell element The value of the fractional derivative α is between 0 and 1. When α is 0, the fractional damper It behaves like a spring. When the value of α is equal to 1, the fractional damper Become a Newton damper.

7. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 1, characterized in that: The standard MSCR test method in step 4 is as follows: a single test data is divided into thirty single cycles, of which ten are preloaded to eliminate experimental errors, ten are 0.1 kPa stress, and ten are 3.2 kPa stress. Each single cycle consists of 1 s of stress application and 9 s of autonomous relaxation. A data point is recorded every 0.1 s, including the microstrain value of the sample.

8. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 2, characterized in that: The test method for generating viscoelastic data points of asphalt binder using multiple cycles of MSCR test is as follows: Since the test equipment will save the 1s stress and 9s relaxation in each single cycle separately, first connect the time axis and strain axis of a single cycle; assuming that the initial values ​​of the six parameters of this single cycle are set to their respective extreme values: ξ 1. ξ 2. η 1. η 2. α , β = 1, 1, 1, 1, 0.5, 0.5; use clip to write a 6-parameter derivative Burgers data model, perform mathematical fitting on the single-cycle data, and after model iteration, ξ 1. ξ 2. η 1. η 2. α , β， After the six parameters are adjusted to relatively reasonable values, they are fed back to the operation port. At the same time, the final recovery value of the sample after the time limit of the relaxation stage is released in a single cycle is calculated through equations 12-13 based on the six parameters fed back. On the basis of the single-cycle data processing flow, a data integration link is added to meet the processing needs of ten-cycle data under 0.1kpa and 3.2kpa stresses. The program will calculate each cycle in chronological order. Considering that it cannot be guaranteed that the fitting of each single cycle is successful, the calculation of the single cycle is embedded in the try function, which can clearly tell whether the single cycle is fitted successfully and point out when it fails. At the same time, in the overall calculation, it also avoids the impact of a single cycle error on the continued calculation of subsequent single cycles.

9. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 1, characterized in that: The fractional damper η 1. Fractional damper η 2 is an Abel damper.

10. The asphalt binder fractional derivative burgers model and viscoelastic parameter analysis system according to claim 1, characterized in that: The system integrates a visual interface to display parameter analysis results and the comparison between model predictions and experimental data.

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