A method for constructing a master curve of viscoelastic parameters of SBS modified asphalt

Abstract

This invention relates to the field of road engineering materials technology, and particularly to a method for constructing the master curve of viscoelastic parameters for SBS modified asphalt. Addressing the problems of existing models' inability to accurately characterize the asymmetric viscoelasticity of modified asphalt and the lack of rigorous mathematical foundations in traditional variable-order operators, this invention introduces the Scarpi variable-order fractional differential operator to establish a variable-order fractional viscoelastic model. This operator strictly follows the exponential law of the fundamental theorem of calculus. After deriving the expressions for dynamic shear modulus and phase angle, rheological tests are performed on SBS modified asphalt, and the data is smoothed. Combining the time-temperature equivalence principle, an optimization algorithm is used to jointly fit and solve the model parameters and construct the master curve. This invention can accurately characterize the complex asymmetric viscoelastic evolution of SBS modified asphalt without increasing model complexity, especially accurately matching the phase angle master curve with a special shape.

Description

Technical Field

[0001] This invention relates to the field of road engineering materials technology, and in particular to a method for constructing the master curve of viscoelastic parameters of SBS modified asphalt. Background Technology

[0002] SBS modified asphalt operates in complex environments, requiring it to withstand dynamic alternating loads. Its viscoelasticity exhibits temperature sensitivity and time dependence. A comprehensive analysis of its dynamic viscoelastic characteristics is the theoretical foundation for accurately evaluating the mechanical and road performance of asphalt. For dynamic loading, the time-temperature equivalence principle is typically used to construct master curves of viscoelastic parameters (i.e., dynamic modulus and phase angle) to characterize its rheological properties over a wide frequency range.

[0003] Fractional calculus has become the mainstream tool for modeling the viscoelasticity of asphalt. To characterize the complex viscoelastic response of materials, several classic fractional viscoelastic models have emerged, such as the Huet model, the Huet-Sayegh model, and the 2S2P1D model. However, existing constant-order fractional viscoelastic models rely on a fixed order to describe the relaxation behavior of materials, and the microstructural evolution they represent is uniform and symmetrical. Since SBS-modified asphalt is a multiphase blend system composed of matrix asphalt and a three-dimensional elastic network of SBS, its relaxation mechanisms differ at high and low frequencies. This leads to asymmetric viscoelasticity and complex phase angle master curves, specifically manifested in concave Black plots, bimodal or long plateau-type complex phase angle master curves. Constant-order fractional viscoelastic models struggle to distinguish the differentiated relaxation characteristics of SBS-modified asphalt at both ends of the frequency domain, resulting in poor fitting accuracy and insufficient adaptability of its phase angle master curves.

[0004] Variable-order fractional calculus, an extension of constant-order fractional calculus, allows the order to be a function of either the independent or dependent variable, enabling the realization of non-stationary memory effects in materials. Introducing variable-order fractional differential operators into viscoelastic constitutive models allows the order to vary with frequency or time. This promises to provide a precise description of the asymmetric viscoelasticity of SBS-modified asphalt at the physical mechanism level without increasing model complexity.

[0005] While variable-order fractional differential operators offer a promising tool for describing the asymmetric viscoelasticity of materials, most existing theories lack a rigorous mathematical framework. Traditional methods for defining variable-order fractional calculus often employ a heuristic shortcut: directly replacing the constant order with a function of time in the time-domain integral kernel. This approach results in variable-order fractional differential operators that do not satisfy the exponential law of the fundamental theorem of calculus.

[0006] Therefore, there is an urgent need in this field for a variable-order fractional-order viscoelastic model with a rigorous mathematical foundation that can accurately characterize the complex phase angle evolution of SBS modified asphalt, and thereby accurately construct the master curve of viscoelastic parameters. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method for constructing the master curve of viscoelastic parameters of SBS modified asphalt, which solves the technical problems that existing models cannot accurately characterize the asymmetric viscoelasticity of modified asphalt and that traditional variable-order operators lack a rigorous mathematical foundation.

[0008] To address the shortcomings of existing constant-order fractional-order viscoelastic models, such as difficulty in distinguishing the differentiated relaxation characteristics of SBS modified asphalt at both ends of the frequency domain, poor accuracy of fitting the principal phase angle curve, and the lack of a rigorous mathematical framework and exponential law in traditional variable-order fractional operators, this invention provides a method for constructing the principal curve of viscoelastic parameters for SBS modified asphalt. This method includes the following steps: S1. Introduce the Scarpi variable-order fractional differential operator to construct a variable-order fractional viscoelastic model that includes a variable-order fractional damper element connected in parallel with an elastic element, and then the whole is connected in series with another elastic element. S2. Based on the linear viscoelastic theory and the definition of the Scarpi variable-order fractional differential operator, derive the dynamic mechanical performance indices of the variable-order fractional viscoelastic model under dynamic loading, including dynamic shear modulus and phase angle. S3. Frequency scanning tests were conducted on SBS modified asphalt at different temperatures to obtain test data including dynamic shear modulus and phase angle. S4. Draw a Black diagram based on the test data, and remove data points that deviate to obtain smoothed rheological test data; S5. Combining the time-temperature equivalence principle, the rheological test data and the dynamic mechanical performance index are globally combined and calculated using an optimization algorithm, and the dynamic shear modulus master curve and phase angle master curve are constructed.

[0009] Furthermore, the order function of the variable-order fractional-order damper element For time The expression for a changing exponential function is: .

[0010] in, For the initial order, For the final order, limited ; It is the rate constant; The differential constitutive equations for the variable-order fractional-order viscoelastic model are as follows: .

[0011] in, The elastic modulus of the series-connected elastic elements; The elastic modulus of the parallel elastic elements; These are the parameters of the variable-order fractional-order damper element; For a variable-order fractional-order viscoelastic model, the stress is... For the Scarpi variable-order fractional differential operator; Strain is the strain of a variable-order fractional-order viscoelastic model.

[0012] Furthermore, the dynamic shear modulus and phase angle are used to characterize the overall stiffness and viscous loss of SBS modified asphalt under dynamic loading, respectively. The dynamic shear modulus and phase angle The expressions are as follows: .

[0013] .

[0014] in, Storage modulus of SBS modified bitumen; The loss modulus of SBS modified asphalt; , These are the magnitude function and the phase angle function, respectively. The elastic modulus of the series-connected elastic elements; The elastic modulus of the parallel elastic elements; These are the parameters of a variable-order fractional-order damper element.

[0015] Furthermore, frequency scanning tests were conducted at different temperatures using a dynamic shear rheometer. The test temperatures were 10℃, 20℃, 30℃, 40℃, 50℃, 60℃ and 70℃, and the test frequency range was from 0.628 rad / s to 62.8 rad / s.

[0016] Furthermore, before conducting the frequency scanning test, the linear viscoelastic region of the SBS modified asphalt is determined by the amplitude scanning test, and the strain boundary conditions of the frequency scanning test are all controlled within the linear viscoelastic region.

[0017] Furthermore, the linear viscoelastic region of SBS-modified asphalt was determined to include: Based on the temperature, the asphalt samples were divided into two intervals, and strain scanning tests were performed on the asphalt samples under the most unfavorable conditions. The test details are as follows: The most unfavorable conditions for medium and low temperature (10℃~30℃) are 10℃ and 10Hz. Use 8mm parallel plates with a gap size of 2mm. The most unfavorable conditions for high temperature 40℃~70℃ are 40℃ and 10Hz, using 25mm parallel plates with a gap size of 1mm; The strain at which the dynamic shear modulus drops to 95% is the boundary of the linear viscoelastic region.

[0018] Furthermore, the removal of data points that deviate refers to removing data points where isotherms do not coincide and exhibit regular parallel bifurcation, in order to simplify SBS modified asphalt into a simple thermorheological material.

[0019] Furthermore, in step S5, the time-temperature equivalence principle adopts the WLF formula, and the optimization algorithm adopts the least squares method.

[0020] Furthermore, a global joint fitting method is adopted to combine the WLF formula with the expressions for dynamic shear modulus and phase angle; Using 40℃ as a reference temperature, the least squares method was used to fit a variable-order fractional-order viscoelastic model and rheological test data to construct the master curve of dynamic shear modulus and the master curve of phase angle.

[0021] The present invention also provides a system for constructing the master curve of viscoelastic parameters of SBS modified asphalt, for performing the method for constructing the master curve of viscoelastic parameters of SBS modified asphalt.

[0022] By employing the above technical solution, the present invention provides a method for constructing the master curve of viscoelastic parameters of SBS modified asphalt, which has at least the following beneficial effects: 1. This invention uses the Scarpi variable-order fractional differential operator with a rigorous mathematical foundation to establish a variable-order fractional viscoelastic model, which can accurately characterize the complex asymmetric viscoelastic evolution of SBS modified asphalt without increasing the complexity of the model, especially accurately matching the phase angle master curve with a special shape.

[0023] 2. This invention establishes a variable-order fractional-order damper element by introducing the Scarpi variable-order fractional-order differential operator. This operator not only retains the complex variable-order memory characteristics, but also strictly follows the exponential law of the fundamental theorem of calculus, solving the inherent deficiencies of traditional heuristic variable-order operators in mathematical theory, and providing a rigorous mathematical framework for the characterization of complex rheological properties.

[0024] 3. This invention, through a continuously variable order function, can accurately capture the non-stationary memory effect caused by the non-uniform evolution of the material's microstructure. Compared to the traditional 2S2P1D model, which relies on a fixed order to control the high and low frequency regions separately, the method of this invention can improve the fitting variance of the complex phase angle master curve of SBS modified asphalt with "bimodal" or "long plateau" characteristics, and accurately characterize the asymmetric viscoelasticity of multiphase blend systems in a wide frequency range. Attached Figure Description

[0025] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the method for constructing the master curve of viscoelastic parameters of SBS modified asphalt in Example 1; Figure 2 This is a schematic diagram of the mechanical components of the variable-order fractional-order viscoelastic model in Example 1; Figure 3 The image shows the Black graph of the SBS-modified asphalt in Example 1. Figure 4 A new Black diagram of SBS-modified asphalt in Example 1; Figure 5 The figure shows the fitting results of the variable-order fractional-order viscoelastic model in Example 1; Figure 6 This is a graph showing the fitting results of the 2S2P1D model in Example 1; Figure 7 Black image of aged SBS modified asphalt in Example 2; Figure 8 The image shows a new Black diagram of the aged SBS modified asphalt in Example 2.

[0026] Figure 9 The figure shows the fitting results of the variable-order fractional-order viscoelastic model in Example 2; Figure 10 The figure shows the fitting result of the 2S2P1D model in Example 2. Detailed Implementation

[0027] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding and implementation of how the present application uses technical means to solve technical problems and achieve technical effects.

[0028] Example 1: This embodiment proposes a method for constructing the master curve of viscoelastic parameters of SBS modified asphalt. It employs the Scarpi variable-order fractional-order differential operator, which has a rigorous mathematical foundation, to establish a variable-order fractional-order viscoelastic model. This method can accurately characterize the complex asymmetric viscoelastic evolution of SBS modified asphalt without increasing model complexity, especially accurately matching the phase angle master curve with a special shape. For example... Figure 1 As shown, the method includes the following steps: S1. Introduce the Scarpi variable-order fractional differential operator to construct a variable-order fractional damper element that is connected in parallel with an elastic element and then connected in series with another elastic element.

[0029] This embodiment extends the classic fractional-order damper to a damper whose order varies with time. A variable-order fractional-order damper element. Its constitutive relation is as follows: .

[0030] in, These are the parameters of the variable-order fractional-order damper element; For the stress of the variable-order fractional-order damper element; For the Scarpi variable-order fractional differential operator, the superscript is... This represents a variable-order fractional operator defined by Scarpi. It is a differential operator. For time A variable-order function; The strain is for the variable-order fractional-order damper element.

[0031] For functions of varying order We choose an exponential function that conforms to the actual physical evolution laws. This exponential function is a solution to the classical relaxation equation, meaning that the change in order follows the physical relaxation mechanism. Its expression is: .

[0032] in, For the initial order, For the final order, limited , is the rate constant.

[0033] like Figure 2 As shown, a variable-order fractional-order damper element is connected in parallel with the first elastic element to form a whole, and then connected in series with the second elastic element to establish a variable-order fractional-order viscoelastic model. The time-domain differential constitutive equation of the variable-order fractional-order viscoelastic model is as follows: .

[0034] in, The elastic modulus of the series-connected elastic elements; The elastic modulus of the parallel elastic elements; These are the parameters of the variable-order fractional-order damper element; For a variable-order fractional-order viscoelastic model, the stress is... For the Scarpi variable-order fractional differential operator; Strain is the strain of a variable-order fractional-order viscoelastic model.

[0035] S2. Based on linear viscoelastic theory and the definition of the Scarpi variable-order fractional-order differential operator, the dynamic mechanical performance indices of the variable-order fractional-order viscoelastic model under dynamic loading, including dynamic shear modulus and phase angle, are derived. The dynamic shear modulus and phase angle are used to characterize the overall stiffness and viscous loss of SBS modified asphalt under dynamic loading, respectively.

[0036] To obtain the analytical solution of the dynamic mechanical response of a variable-order fractional viscoelastic model in the frequency domain, this invention performs a Laplace transform on the differential constitutive equation based on linear viscoelastic theory and the definition of the Scarpi variable-order fractional differential operator. Subsequently, by setting the complex frequency variable in the Laplace transform... By mapping the differential constitutive equation from the time domain to the frequency domain, the expression for the complex modulus is derived: .

[0037] in, The imaginary unit, i.e. ; Angular frequency; This represents the frequency-dependent equivalent order (or equivalent exponential function) term derived from the Scarpi variable-order fractional operator in the frequency / Laplace domain.

[0038] For ease of calculation, use The properties of logarithmic functions are used to handle exponential terms, and the magnitude function is defined. and phase angle function Finally, the complex modulus in the form of combining the real and imaginary parts is derived. The expression is: .

[0039] Then, by separating the real and imaginary parts, dynamic mechanical performance indicators for characterizing the elastic energy storage capacity, viscous dissipation capacity, overall stiffness, and viscous loss degree of SBS modified asphalt were derived, corresponding to the energy storage modulus, respectively. Loss modulus Dynamic shear modulus With phase angle The expressions are as follows: .

[0040] .

[0041] .

[0042] .

[0043] in: .

[0044] .

[0045] In the formula, Storage modulus of SBS modified bitumen; The loss modulus of SBS modified asphalt.

[0046] This invention starts with the classical fractional damper, introduces a variable-order function that evolves exponentially with time, constructs a variable-order fractional viscoelastic model including a variable-order fractional damper element and a dual-elastic element, and then uses the Laplace transform of the Scarpi variable-order fractional differential operator to realize the complex modulus in the frequency domain. The derivation of the energy storage modulus, loss modulus, dynamic shear modulus and phase angle and other dynamic mechanical performance indicators were further decomposed.

[0047] In this embodiment, the dynamic shear modulus and phase angle comprehensively reflect the dissipation effect of the variable-order fractional-order damper element and the energy storage effect of the two elastic elements in the entire variable-order fractional-order viscoelastic model. They are used to characterize the overall stiffness of SBS modified asphalt under dynamic loading and the ratio of viscous loss to elastic energy storage (the degree of viscous loss), respectively, and are jointly determined by the two elastic elements and the variable-order fractional-order damper element in the variable-order fractional-order viscoelastic model.

[0048] S3. Perform frequency scanning tests on SBS modified asphalt at different temperatures to obtain test data including dynamic shear modulus and phase angle.

[0049] In this embodiment, an SBS modified asphalt was selected, and frequency scanning tests were performed at different temperatures using a dynamic shear rheometer. The test temperatures were 10℃, 20℃, 30℃, 40℃, 50℃, 60℃, and 70℃, and the test frequency range was from 0.628 rad / s to 62.8 rad / s.

[0050] Before conducting frequency scanning tests, amplitude scanning tests are needed to determine the linear viscoelastic region (LVER) of the SBS modified asphalt. The strain boundary conditions for subsequent frequency scanning tests are all within this LVER. For the frequency scanning tests, two temperature ranges are used, with strain scanning tests performed on the asphalt samples under the most unfavorable conditions. The test details are as follows: For the medium-low temperature range (10℃–30℃), the most unfavorable conditions are 10℃ and 10Hz, using an 8mm parallel plate with a 2mm gap. For the high temperature range (40℃–70℃), the most unfavorable conditions are 40℃ and 10Hz, using a 25mm parallel plate with a 1mm gap. The strain at which the dynamic shear modulus drops to 95% is the boundary of the LVER. Based on the test results, the LVER strains for the medium-low and high temperatures of the SBS modified asphalt are selected as 0.2% and 0.5%, respectively. Then, frequency scanning tests are performed based on the LVER, with the parallel plate and gap dimensions consistent with the amplitude scanning tests.

[0051] S4. Draw a Black diagram based on the test data, and remove data points that deviate to obtain smoothed rheological test data.

[0052] In this embodiment, the test data is plotted as follows: Figure 3 The Black plot is shown. Analysis revealed that the Black plot curve of SBS modified asphalt exhibits a plateau region and a complex shape with a leftward indentation in the middle section, characterizing its unique asymmetric viscoelastic response.

[0053] In this embodiment, removing data points that deviate from the expected path means removing data points where isotherms do not coincide and exhibit regular parallel bifurcation, thus simplifying the SBS-modified asphalt into a thermorheologically simple material. Due to polymer modification or limitations of the testing equipment, bifurcation occurs in the Black plot curves. To facilitate subsequent model calculations, these deviating data points are removed to create a smoother Black plot curve. The new Black plot curve is as follows: Figure 4 As shown.

[0054] S5. Combining the time-temperature equivalence principle, the rheological test data and the dynamic mechanical performance index are globally combined and calculated using an optimization algorithm, and the dynamic shear modulus master curve and phase angle master curve are constructed.

[0055] In this embodiment, the time-temperature equivalence principle adopts the WLF formula, and the optimization algorithm is the least squares method. A global joint fitting method is used to combine the WLF formula with the expressions for dynamic shear modulus and phase angle derived in step S2. Using 40℃ as a reference temperature, the least squares method is used to fit the variable-order fractional-order viscoelastic model and rheological test data. The fitting results are as follows: Figure 5 As shown, the fitting variance R of dynamic shear modulus and phase angle is... 2The values ​​are 0.9980 and 0.9355 respectively.

[0056] In this embodiment, the following formula is used as the optimization objective function: .

[0057] in, , These are the test and calculated values ​​of the dynamic shear modulus, respectively. , These are the measured and calculated values ​​of the phase angle, respectively. This refers to the total number of all data points involved in the fitting calculation.

[0058] Simultaneously, the 2S2P1D model was used to construct the master curves of dynamic shear modulus and phase angle based on the test results, further exploring the effectiveness of the variable-order fractional-order viscoelastic model. The fitting results are as follows: Figure 6 As shown, the fitting variance R of dynamic shear modulus and phase angle is... 2 The values ​​are 0.9974 and 0.9169, respectively. The expression for the 2S2P1D model is: .

[0059] In the formula, It is the static modulus; It is the glass modulus; It is a dimensionless constant; For the dimensionless constants related to the sticky pot; Relaxation time; , Let be the exponential parameters of the two parabolic elements.

[0060] According to the fitting results, the variable-order fractional-order viscoelastic model is better at describing the dynamic viscoelastic response of multiphase blends such as SBS modified asphalt, and it has more advantages in describing the phase angle master curve with bimodal or long plateau regions, with higher accuracy.

[0061] To describe viscoelasticity with significant variations across a wide frequency range, traditional constant-order models often rely on increasing the number of springs and fractional-order dampers to improve the fitting effect, leading to model complexity. This invention, however, leverages the powerful applicability of variable-order fractional calculus to non-stationary memory effects, using only a single variable-order fractional-order damper combined with an elastic element to meet the requirements for representing complex rheological master curves. The variable-order fractional-order viscoelastic model of this invention has a simple structure and fewer fitting parameters, reducing the computational complexity of global joint fitting.

[0062] Example 2: Based on Example 1, this example constructs the master curve for SBS modified asphalt that has undergone short-term aging.

[0063] First, the original SBS modified asphalt was treated using a rotating thin film oven test (RTFOT) to simulate the short-term aging process of asphalt, resulting in a short-term aged SBS modified asphalt binder. Subsequently, the same steps S1 to S5 as in Example 1 were performed. In step S3, the linear viscoelastic region (LVER) was determined by amplitude scanning, and frequency scanning tests were conducted at temperatures ranging from 10°C to 70°C. In step S4, the Black diagram of the short-term aged asphalt was plotted as follows. Figure 7 As shown, after removing biased data points and smoothing the data, the new Black plot is as follows. Figure 8 As shown. Finally, in step S5, using 40℃ as the reference temperature, a global joint fitting calculation is performed using the least squares method to obtain the model parameters under this aging state, and the corresponding dynamic shear modulus principal curve and phase angle principal curve are constructed. The fitting results are as follows. Figure 9 As shown, the fitting variance R of dynamic shear modulus and phase angle is... 2 The values ​​are 0.9618 and 0.9212, respectively. Similarly, the 2S2P1D model was used for fitting calculations to further explore the effectiveness of the variable-order fractional-order viscoelastic model. The fitting results are as follows: Figure 10 As shown, the fitting variance R of dynamic shear modulus and phase angle is... 2 The values ​​are 0.9910 and 0.9063, respectively.

[0064] The results show that even if the aging process causes degradation of the SBS three-dimensional elastic network, the variable-order fractional-order viscoelastic model of this invention can still accurately capture its viscoelastic evolution through its continuously changing order, and the fitting variance R of the phase angle principal curve is [not specified]. 2 It is superior to the traditional 2S2P1D model.

[0065] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0066] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0067] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for constructing the master curve of viscoelastic parameters of SBS modified asphalt, characterized in that, The method includes the following steps: S1. Introduce the Scarpi variable-order fractional differential operator to construct a variable-order fractional viscoelastic model that includes a variable-order fractional damper element connected in parallel with an elastic element, and then the whole is connected in series with another elastic element. S2. Based on the linear viscoelastic theory and the definition of the Scarpi variable-order fractional differential operator, derive the dynamic mechanical performance indices of the variable-order fractional viscoelastic model under dynamic loading, including dynamic shear modulus and phase angle. S3. Frequency scanning tests were conducted on SBS modified asphalt at different temperatures to obtain test data including dynamic shear modulus and phase angle. S4. Draw a Black diagram based on the test data, and remove data points that deviate to obtain smoothed rheological test data; S5. Combining the time-temperature equivalence principle, the rheological test data and the dynamic mechanical performance index are globally combined and calculated using an optimization algorithm, and the dynamic shear modulus master curve and phase angle master curve are constructed.

2. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 1, characterized in that, The order function of the variable-order fractional-order damper element For time The expression for a changing exponential function is: ； in, For the initial order, For the final order, limited ; It is the rate constant; The differential constitutive equations for the variable-order fractional-order viscoelastic model are as follows: ； in, The elastic modulus of the series-connected elastic elements; The elastic modulus of the parallel elastic elements; These are the parameters of the variable-order fractional-order damper element; For a variable-order fractional-order viscoelastic model, the stress is... For the Scarpi variable-order fractional differential operator; Strain is the strain of a variable-order fractional-order viscoelastic model.

3. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 1, characterized in that, The dynamic shear modulus and phase angle are used to characterize the overall stiffness and viscous loss of SBS modified asphalt under dynamic loading, respectively. The dynamic shear modulus and phase angle The expressions are as follows: ； ； in, Storage modulus of SBS modified bitumen; The loss modulus of SBS modified asphalt; , These are the magnitude function and the phase angle function, respectively. The elastic modulus of the series-connected elastic elements; The elastic modulus of the parallel elastic elements; These are the parameters of a variable-order fractional-order damper element.

4. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 1, characterized in that, Frequency scanning tests were conducted using a dynamic shear rheometer at different temperatures: 10℃, 20℃, 30℃, 40℃, 50℃, 60℃, and 70℃. The frequency range was from 0.628 rad / s to 62.8 rad / s.

5. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 4, characterized in that, Before conducting frequency scanning tests, the linear viscoelastic region of SBS modified asphalt is determined by amplitude scanning tests, and the strain boundary conditions of the frequency scanning tests are all controlled within the linear viscoelastic region.

6. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 5, characterized in that, Determining the linear viscoelastic region of SBS-modified bitumen includes: Based on the temperature, the asphalt samples were divided into two intervals, and strain scanning tests were performed on the asphalt samples under the most unfavorable conditions. The test details are as follows: The most unfavorable conditions for medium and low temperature (10℃~30℃) are 10℃ and 10Hz. Use 8mm parallel plates with a gap size of 2mm. The most unfavorable conditions for high temperature 40℃~70℃ are 40℃ and 10Hz, using 25mm parallel plates with a gap size of 1mm; The strain at which the dynamic shear modulus drops to 95% is the boundary of the linear viscoelastic region.

7. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 1, characterized in that, The removal of data points that deviate from the target data points refers to removing data points where isotherms do not coincide and exhibit regular parallel bifurcation, in order to simplify SBS modified bitumen into a simple thermorheological material.

8. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 1, characterized in that, In step S5, the time-temperature equivalence principle adopts the WLF formula, and the optimization algorithm adopts the least squares method.

9. The method for constructing the master curve of viscoelastic parameters of SBS modified asphalt according to claim 8, characterized in that, A global joint fitting method is adopted to combine the WLF formula with the expressions for dynamic shear modulus and phase angle; Using 40℃ as a reference temperature, the least squares method was used to fit a variable-order fractional-order viscoelastic model and rheological test data to construct the master curve of dynamic shear modulus and the master curve of phase angle.

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