A method for obtaining asphalt master curve considering measurement and modeling uncertainties

Abstract

The present invention provides a method for obtaining an asphalt master curve band that takes into account measurement and modeling uncertainties, and belongs to the field of characterization of asphalt rheological properties. The present invention considers the data differences existing in DSR measurement of asphalt rheology and the modeling differences caused by the type of asphalt rheological model and its fitting process in the process of asphalt master curve construction, thereby proposing a method for obtaining an asphalt master curve band. The asphalt master curve band acquisition method proposed by the present invention takes into account the uncertainties caused by DSR measurement and rheological models in the existing asphalt rheological characterization technology. At the same time, the asphalt master curve band width can quantitatively identify the sensitivity of asphalt to the rheological model, which is conducive to more accurate characterization of asphalt rheological properties.

Description

Technical Field

[0001] The invention belongs to the field of characterization of rheological properties of asphalt, and in particular relates to a method for obtaining a main curve band of asphalt taking into account measurement and modeling uncertainties. Background Art

[0002] The defects of asphalt pavement during service, such as high temperature rutting, fatigue cracking, potholes, and spalling, are closely related to the rheological properties of asphalt. Asphalt, as a typical viscoelastic material, has the property of changing with time and temperature. At present, the rheological properties of asphalt are usually characterized by the complex modulus and phase angle measured by the dynamic shear rheometer DSR. The complex modulus and phase angle of asphalt are only meaningful within a specific temperature and loading frequency range. Under a single temperature or load frequency, the complex modulus and phase angle of asphalt cannot reveal the viscoelastic properties of asphalt over a wide range of temperature and load frequencies.

[0003] Asphalt materials behave as viscoelastic materials, that is, the same physical properties can be obtained at high temperature and high load frequency or at low temperature and low load frequency. Therefore, the rheological properties of asphalt materials under different temperatures and load frequencies can be described by a master curve, which is the time-temperature conversion rule of asphalt materials. The time-temperature shift factor is used in the process of obtaining the master curve of asphalt, that is, the asphalt rheological data measured at different temperatures and load frequencies are formed into an overall continuous master curve through the shift factor. However, the change of the time-temperature shift factor depends on the selection of the rheological model that characterizes the viscoelastic properties of asphalt. At present, road scientific research workers have studied many models to describe the viscoelastic properties of asphalt materials, among which the main ones are the GS model and the CAM model. However, no matter how perfect the original data is, these models are obtained by mathematical fitting optimization of the master curve of asphalt, which leads to the change of the master curve that characterizes the viscoelastic properties of asphalt depending on the selection of the asphalt rheological model and the fitting optimization process of the model, resulting in the difference between the actual measured data and the predicted fitting data of the asphalt rheological properties. At the same time, when using DSR to measure the rheological properties of asphalt, the measurement uncertainty caused by the differences in laboratories or experimental operators is also unavoidable. To this end, the present invention proposes a method for obtaining a master curve band of asphalt, by taking the inevitable measurement errors and the uncertainty of the rheological model into consideration in the process of obtaining the master curve band of asphalt, so as to more accurately characterize the rheological properties of asphalt. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for obtaining an asphalt master curve band taking into account measurement and modeling uncertainties. By expanding the asphalt master curve to the asphalt master curve band, the dynamic shear rheometer DSR measurement error and modeling uncertainty existing in the existing asphalt rheological characterization technology are taken into account, thereby more accurately characterizing the rheological properties of asphalt.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] This proposal provides a method for constructing an asphalt master curve that takes into account measurement and modeling uncertainties, including the following steps:

[0007] S1. Use a dynamic shear rheometer DSR to perform a frequency sweep test on an asphalt sample according to a standard procedure. Based on at least 5 gradient temperatures selected within a preset measurement temperature selection range and each discrete load action frequency within a preset load action frequency range, obtain the asphalt rheological measurement data at each preset discrete load action frequency at each gradient temperature. Each set of asphalt rheological measurement data includes the asphalt complex modulus and phase angle.

[0008] S2. Select at least two coefficients of variation within a preset range of coefficients of variation, and expand the complex modulus and phase angle of asphalt in each set of asphalt rheological measurement data by the selected coefficients of variation, so that each set of asphalt rheological measurement data can obtain asphalt rheological expansion data corresponding to the coefficient of variation under the same temperature and load frequency range;

[0009] S3, selecting at least two asphalt rheological models for describing the rheological properties of asphalt, based on the groups of asphalt rheological measurement data obtained in step S1, using the time-temperature conversion rule, using the selected asphalt rheological models to construct asphalt complex modulus and phase angle master curves for the asphalt samples respectively, selecting the optimal asphalt rheological model according to the preset selection requirements, and obtaining the parameters of the master curve of the optimal asphalt rheological model;

[0010] S4, based on the asphalt rheological expansion data of each group obtained in step S2, using the time-temperature conversion rule, using the optimal asphalt rheological model to construct the asphalt complex modulus and phase angle expansion curves corresponding to each coefficient of variation, and obtaining the parameters of each optimal asphalt rheological model expansion curve;

[0011] S5. Select at least three different confidence intervals from the normal distribution of each parameter of the optimal asphalt rheological model master curve and each optimal asphalt rheological model extension curve to obtain the optimal asphalt rheological model parameter range corresponding to each parameter and the number of confidence intervals;

[0012] S6. Based on the optimal asphalt rheological model parameter range determined in step S5, at least 1000 sets of model parameters are selected through random functions to construct asphalt complex modulus and phase angle curves of at least 1000 asphalt samples respectively, which together with the optimal asphalt rheological model master curve and each optimal asphalt rheological model extension curve form the asphalt complex modulus and phase angle master curve band of the asphalt sample.

[0013] As a preferred technical solution, the asphalt rheology of the asphalt sample used for the DSR frequency sweep test in step S1 should be in the linear viscoelastic range.

[0014] As a preferred technical solution, the asphalt rheological model selected in step S3 includes GS and CAM models.

[0015] As a preferred technical solution, step S3 includes the following steps:

[0016] S301, select any one of the measurement temperatures in the preset measurement temperature range in step S1 as the reference temperature T ref ;

[0017] S302, determining the shift factor of different measurement temperatures corresponding to the reference temperature according to the WLF formula; determining the equivalent transformation of the complex modulus and phase angle measurement data of asphalt at different temperatures and load action frequencies;

[0018] S303. Use the selected asphalt rheological models to construct the asphalt complex modulus and phase angle master curves for the asphalt samples respectively, select the optimal asphalt rheological model according to the preset selection requirements, thereby obtaining the optimal asphalt rheological model master curve, and use the least squares method principle to generate the parameters of the optimal asphalt rheological model master curve.

[0019] As a preferred technical solution, step S4 includes the following steps:

[0020] S401, select any one of the measurement temperatures in the preset measurement temperature range in step S1 as the reference temperature T ref ;

[0021] S402, determining the shift factors of different measurement temperatures corresponding to the reference temperature according to the WLF formula; determining the equivalent transformation of the complex modulus and phase angle expansion data of asphalt at different temperatures and load action frequencies;

[0022] S403, using the optimal asphalt rheological model to construct the asphalt complex modulus and phase angle expansion curves corresponding to the respective coefficients of variation after expansion, and obtaining the parameters of each expansion curve.

[0023] As a preferred technical solution, the expression for calculating the shift factor by the WLF formula is as follows:

[0024]

[0025]

[0026] Where T represents the actual measured temperature, log(α T) represents the shift factor, C1 and C2 represent constants related to the properties of asphalt materials.

[0027] As a preferred technical solution, the equivalent transformation formula of the asphalt complex modulus and phase angle measurement data is as follows:

[0028] G * (T,α T f)=G * (T ref ,f);δ(T,α T f)=δ(T ref ,f)

[0029] Where T represents the actual measured temperature, G * represents the complex modulus, δ represents the phase angle, and f represents the load frequency.

[0030] As a preferred technical solution, the preset measurement temperature range in step S1 is 10°C to 80°C.

[0031] As a preferred technical solution, the preset range of the coefficient of variation in step S2 is 85% to 115%.

[0032] As a preferred technical solution, the confidence intervals of the normal distribution of the parameters of the optimal asphalt rheological model selected in step S5 include 68%, 95% and 99%.

[0033] Beneficial effects of the present invention:

[0034] (1) The method for obtaining the asphalt master curve band proposed in the present invention takes into account the uncertainty of the existing technology for characterizing the rheological properties of asphalt. It expands the asphalt rheological measurement data into multiple groups of asphalt rheological extended data through multiple coefficients of variation to characterize the data differences caused by the DSR measurement process. It describes the rheological properties of asphalt by using multiple asphalt rheological models such as GS and CAM, selects the optimal asphalt rheological model according to the preset selection requirements, and considers the different confidence levels of the normal distribution of the parameters of the optimal asphalt rheological model to characterize the asphalt rheological model and the modeling uncertainty caused by the fitting process.

[0035] (2) The present invention quantitatively describes the sensitivity of asphalt to different rheological models by obtaining an asphalt master curve band that takes into account different types of asphalt rheological models and the confidence of normal distributions of different model parameters.

[0036] (3) The method for obtaining the asphalt main curve band proposed in the present invention can help select a suitable asphalt rheological model to study the effects of asphalt aging or asphalt modification on the rheological properties of asphalt. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1Flow chart of the method of the present invention

[0038] Figure 2 Schematic diagram of data difference of DSR measurement in this embodiment

[0039] Figure 3 Schematic diagram of normal distribution of asphalt rheological model parameters in this embodiment

[0040] Figure 4 The main curve of the complex modulus of U70 asphalt in this embodiment is DETAILED DESCRIPTION

[0041] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0042] Example

[0043] like Figure 1 As shown, the present invention provides a method for obtaining an asphalt main curve band taking into account measurement and modeling uncertainties, and the implementation method thereof is as follows:

[0044] S1. Use a dynamic shear rheometer DSR to perform a frequency sweep test on an asphalt sample according to a standard procedure. Based on at least 5 gradient temperatures selected within a preset measurement temperature selection range and each discrete load action frequency within a preset load action frequency range, obtain the asphalt rheological measurement data at each preset discrete load action frequency at each gradient temperature. Each set of asphalt rheological measurement data includes the asphalt complex modulus and phase angle.

[0045] In this embodiment, DSR is used to perform frequency scanning on the prepared asphalt sample according to standard procedures, and the rheological property of the asphalt used for the DSR frequency scanning test should be in the linear viscoelastic range.

[0046] S2. Select at least two coefficients of variation within a preset range of coefficients of variation, and expand the complex modulus and phase angle of asphalt in each set of asphalt rheological measurement data by the selected coefficients of variation, so that each set of asphalt rheological measurement data can obtain asphalt rheological expansion data corresponding to the coefficient of variation under the same temperature and load frequency range;

[0047] In this embodiment, the asphalt complex modulus measurement data is expanded by selecting a total of 6 coefficients of variation, namely 85%, 90%, 95%, 105%, 110% and 115%, to obtain 6 sets of extended data under the same temperature and load frequency range, reflecting the data differences in the DSR measurement process.

[0048] S3, selecting at least two asphalt rheological models for describing the rheological properties of asphalt, based on the groups of asphalt rheological measurement data obtained in step S1, using the time-temperature conversion rule, using the selected asphalt rheological models to construct asphalt complex modulus and phase angle master curves for the asphalt samples, selecting the optimal asphalt rheological model according to the preset selection requirements, and obtaining the parameters of the optimal asphalt rheological model master curve, the implementation method is as follows:

[0049] S301, select any one of the measurement temperatures within the preset measurement temperature range in step S1 as the reference temperature T ref ;

[0050] S302, determining the shift factor of different measurement temperatures corresponding to the reference temperature according to the WLF formula; determining the equivalent transformation of the complex modulus and phase angle measurement data of asphalt at different temperatures and load action frequencies;

[0051] S303. Use the selected asphalt rheological models to construct the asphalt complex modulus and phase angle master curves for the asphalt samples respectively, select the optimal asphalt rheological model according to the preset selection requirements, thereby obtaining the optimal asphalt rheological model master curve, and use the least squares method principle to generate the parameters of the optimal asphalt rheological model master curve.

[0052] In this embodiment, the reference temperature T of the asphalt complex modulus and phase angle measurement data is first determined. ref , then through the WLF formula Determine the shift factor and then use the time-temperature conversion rule to calculate the G * (T,α T f)=G * (T ref ,f),δ(T,α T f)=δ(T ref ,f) Determine the equivalent transformation of the complex modulus and phase angle measurement data of asphalt at different temperatures and load frequencies, and select the GS and CAM asphalt rheological models to describe the asphalt rheological properties of the asphalt sample respectively. The expressions of the GS model and the CAM model are as follows:

[0053] The GS model expression is:

[0054]

[0055] The CAM model expression is:

[0056]

[0057] Among them, G * represents the complex modulus, f represents the load frequency, δ, α, β, λ and γ represent the GS model parameters; G g represents the glass transition modulus, ω c represents the crossover frequency, υ and ω represent the CAM model parameters. When the glass transition modulus G g When the pressure is 1Gpa, the CAM model expression is as follows:

[0058]

[0059] Finally, the optimal asphalt rheological model is selected, and the model parameters are obtained by using the least squares method in MATLAB to obtain the asphalt complex modulus and phase angle master curve.

[0060] S4, based on the rheological expansion data of each group of asphalt obtained in step S2, using the time-temperature conversion rule, using the optimal asphalt rheological model to construct the asphalt complex modulus and phase angle expansion curves corresponding to each coefficient of variation, and obtaining the parameters of each expansion curve, the implementation method is as follows:

[0061] S401, select any one of the measurement temperatures in the preset measurement temperature range in step S1 as the reference temperature T ref ;

[0062] S402, determining the shift factors of different measurement temperatures corresponding to the reference temperature according to the WLF formula; determining the equivalent transformation of the complex modulus and phase angle expansion data of asphalt at different temperatures and load action frequencies;

[0063] S403, using the optimal asphalt rheological model to construct the asphalt complex modulus and phase angle expansion curves corresponding to the respective coefficients of variation after expansion, and obtaining the parameters of the expansion curves of each optimal asphalt rheological model.

[0064] In this embodiment, the reference temperature T of the asphalt complex modulus and phase angle expansion data is first determined. ref , then through the WLF formula Determine the shift factor and then use the time-temperature conversion rule to calculate the G * (T,α T f)=G * (T ref ,f),δ(T,α T f)=δ(T ref,f) Determine the equivalent transformation of the complex modulus and phase angle expansion data of asphalt at different temperatures and load frequencies, and use the selected optimal asphalt rheological model to construct the expanded asphalt complex modulus and phase angle expansion curves corresponding to each coefficient of variation, and obtain the parameters of each expansion curve by using the least squares method principle in MATLAB, so as to obtain the expansion curves of each optimal asphalt rheological model.

[0065] S5. Select at least three different confidence intervals from the normal distribution of each parameter of the optimal asphalt rheological model master curve and each optimal asphalt rheological model extension curve to obtain the optimal asphalt rheological model parameter range corresponding to each parameter and the number of confidence intervals;

[0066] In this embodiment, the parameter distributions of the optimal asphalt rheological model master curve and each extended curve all satisfy the normal distribution, such as Figure 3 As shown, in this embodiment, the confidence interval of the normal distribution of the optimal asphalt rheological model parameters is set to three levels of 68.3%, 95.5% and 99.7% to consider the differences generated in the asphalt rheological model fitting process. At the same time, different confidence intervals of the model parameters can be used to indicate the sensitivity of asphalt to the rheological model.

[0067] S6. Based on the optimal asphalt rheological model parameter range determined in step S5, at least 1000 sets of model parameters are selected through random functions to construct asphalt complex modulus and phase angle curves of at least 1000 asphalt samples respectively, which together with the optimal asphalt rheological model master curve and each optimal asphalt rheological model extension curve form the asphalt complex modulus and phase angle master curve band of the asphalt sample.

[0068] In this embodiment, three parameter ranges of each optimal asphalt rheological model parameter are obtained through the three confidence intervals of 68.3%, 95.5% and 99.7% of the normal distribution of the optimal asphalt rheological model parameters. 1000 sets of parameters are selected within the corresponding range through a random function to obtain the asphalt complex modulus and phase angle curves of 1000 asphalt samples, which together with the optimal asphalt rheological model master curve obtained in step S3 and the optimal asphalt rheological model extension curves obtained in step S4 form the asphalt complex modulus and phase angle master curve band of the asphalt sample.

[0069] The present invention will be further described below:

[0070] Taking the domestic base asphalt with a needle penetration of 70 as an example, and recording it as U70, the above steps are carried out. First, the frequency scanning test of the prepared U70 asphalt is carried out using DSR according to the standard procedure, wherein the scanning frequency range is set to 0.1-10 Hz, the scanning temperature is set to 35°C-80°C (one interval every 5°C), and the asphalt complex modulus measurement data is taken for the asphalt complex modulus master curve band construction of this example; secondly, the obtained asphalt complex modulus measurement data is expanded using a total of 6 coefficients of variation of 85%, 90%, 95%, 105%, 110% and 115% to obtain 6 groups of expanded data under the same temperature and load frequency range; then, the GS rheological model is selected to describe the rheological properties of U70 asphalt, wherein the GS rheological model expression is: The confidence level of the model parameters is 95.5%; then, the reference temperature T for the measurement and expansion data of the complex modulus of U70 asphalt is determined. ref All are 55℃, and through the WLF formula Determine the shift factor; then, according to the time-temperature conversion rule, through G * (T,α T f)=G * (T ref ,f) Determine the equivalent transformation of the measurement and extension data of the complex modulus of U70 asphalt under different temperatures and load frequencies; then, select the GS rheological model to obtain the U70 asphalt complex modulus master curve and the asphalt complex modulus extension curve, and obtain the parameters of each curve by using the least squares principle in MATLAB, and finally obtain the value range of each parameter through the 95.5% confidence level of the normal distribution of each parameter. Randomly select 1000 groups of parameters within the value range of each parameter to obtain 1000 U70 asphalt complex modulus curves, which together with the previously obtained U70 asphalt complex modulus master curve and asphalt complex modulus extension curve constitute the U70 asphalt complex modulus master curve band. The U70 asphalt complex modulus master curve band established according to the above steps is as follows: Figure 4 As shown, in Figure 4 In the figure, the width of the main curve band reflects the sensitivity of U70 asphalt to the GS rheological model.

Claims

1. A method for obtaining an asphalt master curve band considering measurement and modeling uncertainties, for obtaining an asphalt complex modulus and phase angle master curve band of a prepared asphalt sample, characterized in that: The following steps are involved: S1. Use a dynamic shear rheometer DSR to perform a frequency sweep test on an asphalt sample according to a standard procedure. Based on at least 5 gradient temperatures selected within a preset measurement temperature selection range and each discrete load action frequency within a preset load action frequency range, obtain the asphalt rheological measurement data at each preset discrete load action frequency at each gradient temperature. Each set of asphalt rheological measurement data includes the asphalt complex modulus and phase angle. S2. Select at least two coefficients of variation within a preset range of coefficients of variation, and expand the complex modulus and phase angle of asphalt in each set of asphalt rheological measurement data by the selected coefficients of variation, so that each set of asphalt rheological measurement data can obtain asphalt rheological expansion data corresponding to the coefficient of variation under the same temperature and load frequency range; S3, selecting at least two asphalt rheological models for describing the rheological properties of asphalt, based on the groups of asphalt rheological measurement data obtained in step S1, using the time-temperature conversion rule, using the selected asphalt rheological models to construct asphalt complex modulus and phase angle master curves for the asphalt samples respectively, selecting the optimal asphalt rheological model according to the preset selection requirements, and obtaining the parameters of the master curve of the optimal asphalt rheological model; S4, based on the rheological expansion data of each group of asphalt obtained in step S2, using the time-temperature conversion rule, using the optimal asphalt rheological model to construct the asphalt complex modulus and phase angle expansion curves corresponding to each coefficient of variation, and obtain the parameters of each expansion curve; S5. Select at least three different confidence intervals from the normal distribution of each parameter of the optimal asphalt rheological model master curve and each optimal asphalt rheological model extension curve to obtain the optimal asphalt rheological model parameter range corresponding to each parameter and the number of confidence intervals; S6. Based on the optimal asphalt rheological model parameter range determined in step S5, at least 1000 sets of model parameters are selected through random functions to construct asphalt complex modulus and phase angle curves of at least 1000 asphalt samples respectively, which together with the optimal asphalt rheological model master curve and each optimal asphalt rheological model extension curve form the asphalt complex modulus and phase angle master curve band of the asphalt sample.

2. A method for obtaining an asphalt master curve considering measurement and modeling uncertainties according to claim 1, characterized in that: The asphalt rheology of the asphalt sample used for the dynamic shear rheometer DSR frequency sweep test in step S1 should be in the linear viscoelastic range.

3. A method for obtaining an asphalt master curve considering measurement and modeling uncertainties according to claim 1, characterized in that: The asphalt rheological models selected in step S3 include the GS model and the CAM model.

4. A method for obtaining an asphalt master curve considering measurement and modeling uncertainties according to claim 1, characterized in that: The step S3 comprises the following steps: S301, select any one of the measurement temperatures within the preset measurement temperature range in step S1 as the reference temperature T ref ; S302, determining the shift factor of different measurement temperatures corresponding to the reference temperature according to the WLF formula; determining the equivalent transformation of the complex modulus and phase angle measurement data of asphalt at different temperatures and load action frequencies; S303. Use the selected asphalt rheological models to construct the asphalt complex modulus and phase angle master curves for the asphalt samples respectively, select the optimal asphalt rheological model according to the preset selection requirements, thereby obtaining the optimal asphalt rheological model master curve, and use the least squares method principle to generate the parameters of the optimal asphalt rheological model master curve.

5. A method for obtaining an asphalt main curve zone considering measurement and modeling uncertainties according to claim 1, characterized in that: The step S4 comprises the following steps: S401, select any one of the measurement temperatures in the preset measurement temperature range in step S1 as the reference temperature T ref ; S402, determining the shift factors of different measurement temperatures corresponding to the reference temperature according to the WLF formula; determining the equivalent transformation of the complex modulus and phase angle expansion data of asphalt at different temperatures and load action frequencies; S403, using the optimal asphalt rheological model to construct the asphalt complex modulus and phase angle expansion curves corresponding to the respective coefficients of variation after expansion, and obtaining the parameters of each expansion curve.

6. A method for obtaining an asphalt main curve zone considering measurement and modeling uncertainties according to claim 4 or 5, characterized in that: The expression for calculating the shift factor by the WLF formula is as follows: Where T represents the actual measured temperature, α T represents the shift factor, and C1 and C2 represent constants related to the properties of asphalt materials.

7. A method for obtaining an asphalt main curve zone considering measurement and modeling uncertainties according to claim 4 or 5, characterized in that: The equivalent transformation formula of the asphalt complex modulus and phase angle measurement data is as follows: G * (T,a T ·f)=G * (T ref ,f);δ(T,α T ·f)=δ(T ref ,f) Where T represents the actual measured temperature, G * represents the complex modulus, δ represents the phase angle, and f represents the load frequency.

8. A method for obtaining an asphalt master curve considering measurement and modeling uncertainties according to claim 1, characterized in that: The preset measurement temperature range is 10°C to 80°C.

9. A method for obtaining an asphalt master curve considering measurement and modeling uncertainties according to claim 1, characterized in that: The preset coefficient of variation is selected in the range of 85% to 115%.

10. A method for obtaining an asphalt master curve considering measurement and modeling uncertainties according to claim 1, characterized in that: The confidence intervals of the normal distribution of the parameters of the optimal asphalt rheological model selected in step S5 include 68%, 95% and 99%.

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