A sa model-based main curve description method for plasticizer modified asphalt

Abstract

A plasticizer single modified asphalt master curve description method based on SA model belongs to the field of road engineering, and the specific scheme comprises the following steps: first, the viscoelastic characteristic parameter curve of modified asphalt obtained through test; second, the horizontal displacement is carried out on the curve obtained through test to obtain the viscoelastic characteristic parameter master curve in combination with the time-temperature equivalence principle; third, based on the planning solution function of Excel, the existing model is used to describe the complex modulus master curve, and the complex modulus description value is obtained; fourth, according to the shape of the storage modulus and phase angle master curve, based on the mathematical principle, the storage modulus and phase angle master curve equation (SA model) of modified asphalt is constructed; fifth, in combination with the complex modulus description value, based on the planning solution function of Excel, the SA model is used to describe the storage modulus and phase angle master curve of modified asphalt on the principle of minimum error.

Description

Technical Field

[0001] This invention belongs to the field of road engineering, specifically relating to a method for describing the master curve of plasticizer-modified asphalt based on the SA model. Background Technology

[0002] Rheological performance testing is an important means of evaluating asphalt performance. Researchers mainly rely on dynamic shear rheometers (DSR) to test the rheological properties of asphalt. Based on the time-temperature superposition principle (TTSP), they broaden the frequency (temperature) range to generate master curves of viscoelastic characteristic parameters. Further, modeling methods are introduced to quantify the complex mechanical behavior of asphalt and predict its viscoelastic properties outside the experimental frequency (temperature) range. Ideally, the linear viscoelastic (LVE) model of asphalt should be able to fully characterize its rheological behavior, generating smooth and continuous master curves to cover the full frequency (temperature) domain response. Existing pure asphalt models are mainly divided into mechanical models and mathematical models. The 2S2P1D model in mechanical models and the CAM model in mathematical models are widely used. However, when applying the 2S2P1D model and the CAM model to describe some viscoelastic characteristic parameters of asphalt, researchers have found that the master curves of complex modulus and loss modulus describe them well, while the master curves of storage modulus and phase angle do not describe them ideally in the low-frequency (high-temperature) region, making it difficult to accurately reflect the complex viscoelastic changes of asphalt in the low-frequency (high-temperature) region. Meanwhile, the storage modulus reflects changes in the elastic components of asphalt, and the phase angle reflects the proportion of the viscoelastic components, further limiting in-depth research on asphalt. Therefore, it is necessary to accurately describe the low-frequency region (high-temperature region) of the master curves for asphalt storage modulus and phase angle to comprehensively describe the rheological properties of asphalt. Summary of the Invention

[0003] To address the aforementioned shortcomings in the prior art, this invention provides a method for describing the master curve of plasticizer-modified asphalt based on the SA model, thereby solving the problem that the prior art cannot effectively construct the master curve of modified asphalt.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: A method for describing the master curve of plasticizer-modified asphalt based on the SA model includes the following steps: Step 1: Using linear range load, frequency scanning tests were conducted on asphalt at at least three equidistant temperatures within the range of 10℃ to 80℃. The test results of viscoelastic parameter curves under medium and high temperature conditions were obtained, with frequency as the abscissa and complex modulus, storage modulus, loss modulus and phase angle as the ordinate. Step 2: Based on the time-temperature equivalence principle, the complex modulus, storage modulus and phase angle viscoelastic parameter curves at multiple temperatures are horizontally shifted to establish main curves with complex modulus, storage modulus and phase angle as the vertical axis and frequency as the horizontal axis. Step 3: Based on the measured data of the complex modulus of modified asphalt, and based on the principle of minimizing error, the Solver function of Excel is used to accurately describe the master curve of the complex modulus using the existing model, and the descriptive value of the complex modulus is obtained.

[0005] Step 4: Based on the storage modulus and the principal phase angle curve, construct the equations for the modified asphalt storage modulus and the principal phase angle curve (SA model) according to mathematical principles. Step 5: Based on the measured data of the storage modulus and phase angle of modified asphalt, and based on the principle of minimizing error, the SA model is used with the Solver function of Excel to accurately describe the principal curves of storage modulus and phase angle simultaneously. The same set of parameter values ​​for the equations of the principal curves of storage modulus and phase angle are obtained, thus completing the description of the principal curves of storage modulus and phase angle of modified asphalt.

[0006] The beneficial effects of this invention are: As a method for describing the master curve of plasticizer-modified asphalt based on the SA model, the storage modulus equation and phase angle equation in this invention are more consistent with the measured data of storage modulus and phase angle of modified asphalt compared with other model equations. This is of great significance for further research on the changes in the elastic components of asphalt and the proportion of viscoelastic components, quantifying the complex mechanical behavior of modified asphalt, and predicting the rheological properties of modified asphalt outside the test frequency (temperature) range.

[0007] Furthermore, in step four, the established master curve equation for the storage modulus of modified asphalt is:

[0008] in, G ′(ω) represents the storage modulus of modified asphalt. G For the complex modulus description value of other models, ω Angular frequency, a , m For end shape parameters, c , q For front-end shape parameters, b For mid-range shape parameters, n These are the overall shape parameters.

[0009] The beneficial effects of the above-mentioned further scheme are as follows: the master curve equation of the storage modulus of modified asphalt describes the curve trend of the master curve of the storage modulus of modified asphalt over a wide frequency (temperature) range, making up for the shortcomings of other models in accurately describing the low frequency (high temperature) region of the storage modulus master curve of modified asphalt.

[0010] Furthermore, in step four, the established principal curve equation for the phase angle of the modified asphalt is:

[0011] in, α For the phase angle of modified asphalt, ω Angular frequency, a , m For end shape parameters, c , q For front-end shape parameters, b For mid-range shape parameters, n These are the overall shape parameters.

[0012] The beneficial effects of the above-mentioned further scheme are as follows: the phase angle principal curve equation of modified asphalt describes the curve trend of the phase angle principal curve of modified asphalt over a wide frequency (temperature) range, making up for the shortcomings of other models in accurately describing the low-frequency (high-temperature) and mid-frequency regions of the phase angle principal curve of modified asphalt.

[0013] Furthermore, in step three, the error is:

[0014] Wherein, the Goal function is the objective function. n The number of data points G m * This is the measured value of the complex modulus. G p * This is a description value for the complex modulus.

[0015] The beneficial effects of the above-mentioned further scheme are as follows: This objective function combines the dimensionless minimum absolute error (MNE) and the average normalized error (MLE) to balance the characteristics of predicting values ​​that are too high or too low. Furthermore, it uses logarithmic values ​​to accurately reflect the error changes of the principal curves of complex modulus and storage modulus in logarithmic coordinates.

[0016] Furthermore, in step five, the error is:

[0017] Wherein, the Goal function is the objective function. n The number of data points G m ′ represents the measured value of storage modulus. G p ′ represents the storage modulus description value. δ m This is the phase angle measurement value. δ p This is a phase angle description value.

[0018] The beneficial effects of the above-mentioned further scheme are as follows: This objective function combines the characteristics of both dimensionless minimum absolute error (MNE) and average normalized error (MLE) in balancing the predicted values ​​for both overestimation and underestimation. It can accurately reflect the error changes of the storage modulus principal curve and phase angle principal curve in logarithmic coordinates.

[0019] Preferably, in step one, frequency scanning tests are conducted on asphalt at 10℃, 20℃, 30℃, 40℃, 50℃, and 60℃ using linear range loads.

[0020] Preferably, in step three, the existing model used is the 2S2P1D model.

[0021] Furthermore, in step one, the linear range load refers to a linear relationship between the load applied to the material and the deformation of the material, where any value is taken within this load range.

[0022] Specifically, the linear range refers to the range within which there is a linear relationship between the stress or strain applied to the material and the deformation of the material. In other words, the stress and strain of the material are directly proportional, conforming to Hooke's Law. Within this linear range, the shear modulus of the material is a constant and does not change with variations in stress or strain.

[0023] The linear range load refers to a load where the stress or strain value and the material deformation exhibit a linear relationship, and the value taken is any value within this linear range. The linear range is defined by whether a linear relationship exists between the stress or strain applied to the material and the material deformation.

[0024] The linear range load is different for each type of asphalt (different modified asphalt, asphalt with different modifier dosages, asphalt with different aging degrees). Attached Figure Description

[0025] Figure 1 This is a flowchart of a method for describing the master curve of plasticizer-modified asphalt based on the SA model; Figure 2 A diagram illustrating the abbreviation for asphalt; Figure 3 This is a comparison chart describing the master curves of the storage modulus of unaged 2% DOA modified asphalt established by different modeling methods; Figure 4 This is a comparison chart describing the principal phase angle curves of unaged 2% DOA modified asphalt established by different modeling methods; Detailed Implementation

[0026] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. Example

[0027] A method for describing the master curve of plasticizer-modified asphalt based on the SA model includes the following steps: Step 1: Using a DSR dynamic shear rheometer, frequency scanning tests were conducted on modified asphalt at 10℃, 20℃, and 30℃ based on an 8mm parallel plate and at 40℃, 50℃, and 60℃ based on a 25mm parallel plate under a linear range load of 200Pa. The test results of complex modulus, storage modulus, loss modulus, and phase angle viscoelastic parameter curves under multiple temperature conditions were obtained. Step 2: Using the WLF formula based on the temperature equivalence principle of asphalt, the curves of complex modulus, storage modulus and phase angle viscoelastic parameters at different temperatures are horizontally shifted to establish a wide frequency (temperature) range master curve with complex modulus, storage modulus and phase angle as the vertical axis and frequency as the horizontal axis. Step 3: Based on the master curve of the complex modulus of modified asphalt, and based on the principle of minimizing error, use the solver function of EXCEL to accurately describe the master curve of the complex modulus using the existing model, and obtain the description value of the complex modulus.

[0028] The objective function for the complex modulus error in step three is:

[0029] Wherein, the Goal function is the objective function. n The number of data points G m * This is the measured value of the complex modulus. G p * This is a description value for the complex modulus.

[0030] Step 4: Based on the storage modulus and the principal phase angle curve, construct the equations for the modified asphalt storage modulus and the principal phase angle curve (SA model) according to mathematical principles. The principal curve equation for the storage modulus established in step four is as follows:

[0031] in, G ′(ω) represents the storage modulus of modified asphalt. G For the complex modulus description value of other models, ω Angular frequency, a , m For end shape parameters, c , q For front-end shape parameters, b For mid-range shape parameters, n These are the overall shape parameters.

[0032] The equation for the principal phase angle curve established in step four is:

[0033] in, α For the phase angle of modified asphalt, ω Angular frequency, a , m For end shape parameters, c , q For front-end shape parameters, b For mid-range shape parameters, n These are the overall shape parameters.

[0034] Step 5: Based on the modified asphalt storage modulus and phase angle master curve, and based on the principle of minimizing error, use the solver function of EXCEL to accurately describe the storage modulus and phase angle master curve simultaneously using the SA model, obtain the same set of parameter values ​​for the equations of the storage modulus and phase angle master curve, and complete the description of the modified asphalt storage modulus master curve and phase angle master curve.

[0035] The objective function for the error in step five is:

[0036] Wherein, the Goal function is the objective function. n The number of data points G m ′ represents the measured value of storage modulus. G p ′ represents the storage modulus description value. δ m This is the phase angle measurement value. δ p This is a phase angle description value.

[0037] In this embodiment, the comparison results of the principal curves of the modified asphalt storage modulus and the principal curves of the phase angle established by the SA model and the CAM model methods are as follows: Figure 3 and Figure 4As shown, the CAM model's storage modulus master curve exhibits significant deviations in the low-frequency region (high-temperature region), and its phase angle master curve performs poorly in describing the transition segment between the low-frequency (high-temperature) and mid-frequency regions. However, the SA model compensates for the shortcomings of the CAM model, accurately reflecting the changes in the ratio of elastic and viscoelastic components in modified asphalt, thus laying the foundation for further in-depth research on modified asphalt.

[0038] In frigid regions, numerous asphalt pavements require asphalt with excellent low-temperature cracking resistance. Plasticizers are commonly used as modifiers to improve the low-temperature performance of asphalt. However, while improving the low-temperature performance of asphalt, its high-temperature performance decreases due to the addition of plasticizers. This results in a significant difference between the low-frequency (high-temperature) and high-frequency (low-temperature) regions of the storage modulus master curve in the vertical direction. The phase angle master curve in the low-frequency (high-temperature) region is very close to 90° (the larger the phase angle, the more viscous the asphalt tends towards a viscous state, with an upper limit of 90°). Commonly used CAM models cannot accurately capture this asymptotic behavior and struggle to describe the modified asphalt master curve, which resembles the shape of a base asphalt curve. However, the SA model provides excellent descriptive performance and can accurately describe the rheological properties of asphalt at high temperatures.

[0039] This invention establishes a model for unaged 2% DOA modified asphalt based on the SA model, and its storage modulus principal curve and phase angle principal curve are shown below. Figure 3 and Figure 4 As shown, the modified asphalt exhibits a significant difference in amplitude between the low-frequency (high-temperature) and high-frequency (low-temperature) regions of the storage modulus master curve, while the phase angle master curve approaches 90° in the low-frequency (high-temperature) region. Nevertheless, compared to the CAM model, the SA model can still accurately describe the shapes of the storage modulus master curve and the phase angle master curve.

[0040] In summary, this invention establishes the principal curve equations for the storage modulus and phase angle of modified asphalt based on a self-developed SA model. Compared with existing asphalt rheological models, this model equation provides a more accurate description of the low-frequency region (high-temperature region) of the principal curves for the storage modulus and phase angle, thereby enabling a precise understanding of the rheological properties of modified asphalt.

[0041] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this 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 this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0042] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for describing the master curve of plasticizer-modified asphalt based on the SA model, characterized in that: Includes the following steps: Step 1: Using linear range load, frequency scanning tests were conducted on asphalt at at least three equidistant temperatures within the range of 10℃ to 80℃. The test results of viscoelastic parameter curves under medium and high temperature conditions were obtained, with frequency as the abscissa and complex modulus, storage modulus, loss modulus and phase angle as the ordinate. Step 2: Based on the time-temperature equivalence principle, the complex modulus, storage modulus and phase angle viscoelastic parameter curves at different temperatures are horizontally shifted to establish a wide frequency (temperature) range master curve with complex modulus, storage modulus and phase angle as the vertical axis and frequency as the horizontal axis. Step 3: Based on the measured data of the complex modulus of modified asphalt, and based on the principle of minimizing error, the Solver function of Excel is used to accurately describe the master curve of the complex modulus using the existing model, and the descriptive value of the complex modulus is obtained. Step 4: Based on the storage modulus and the principal phase angle curve, construct the equations for the modified asphalt storage modulus and the principal phase angle curve (SA model) according to mathematical principles. Step 5: Based on the measured data of the storage modulus and phase angle of modified asphalt, and based on the principle of minimizing error, the SA model is used with the Solver function of Excel to accurately describe the principal curves of storage modulus and phase angle simultaneously. The same set of parameter values ​​for the equations of the principal curves of storage modulus and phase angle are obtained, thus completing the description of the principal curves of storage modulus and phase angle of modified asphalt.

2. The method for describing the master curve of plasticizer-modified asphalt based on the SA model according to claim 1, characterized in that: In step four, the established master curve equation for the storage modulus of modified asphalt is:

3. Among them, G ′(ω) represents the storage modulus of modified asphalt. G For the complex modulus description value of other models, ω Angular frequency, a , m For end shape parameters, c , q For front-end shape parameters, b For mid-range shape parameters, n These are the overall shape parameters.

4. The method for describing the master curve of plasticizer-modified asphalt based on the SA model according to claim 1, characterized in that: In step four, the established principal curve equation for the phase angle of the modified asphalt is:

5. Among them, α For the phase angle of modified asphalt, ω Angular frequency, a , m For end shape parameters, c , q For front-end shape parameters, b For mid-range shape parameters, n These are the overall shape parameters.

6. The method for describing the master curve of plasticizer-modified asphalt based on the SA model according to claim 1, characterized in that: In step three, the error is: Wherein, the Goal function is the objective function. n The number of data points, when describing the principal curve of the complex modulus, G m * This is the measured value of the complex modulus. G p * This is a description value for the complex modulus.

7. The method for describing the master curve of plasticizer-modified asphalt based on the SA model according to claim 1, characterized in that: In step five, the error is:

8. Among them, The goal function is the objective function. n The number of data points G m ′ represents the measured value of storage modulus. G p ′ represents the storage modulus description value. δ m This is the measured value of the phase angle. δ p This is a phase angle description value.

9. The method for describing the master curve of plasticizer-modified asphalt based on the SA model according to claim 1, characterized in that: In step one, the linear range load refers to a linear relationship between the load applied to the material and the deformation of the material, where any value is taken within this load range.

10. The method for describing the master curve of plasticizer-modified asphalt based on the SA model according to claim 1, characterized in that: In step one, frequency scanning tests were conducted on asphalt at 10℃, 20℃, 30℃, 40℃, 50℃, and 60℃ using linear range loads.

11. The method for describing the master curve of plasticizer-modified asphalt based on the SA model according to claim 1, characterized in that: In step three, the existing model is the 2S2P1D model.

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