Method for drawing asphalt viscoelastic parameter main curve based on generalized SPD model

Abstract

The invention discloses a method for drawing an asphalt viscoelastic parameter main curve based on a generalized SPD model. The method comprises the following steps: preparing an asphalt test piece; performing a frequency scanning test, and measuring dynamic shear moduli and phase angles at a plurality of temperatures and frequencies; drawing a black space diagram by taking the dynamic shear modulus as a horizontal axis and the phase angle as a longitudinal axis, and removing data points obviously deviating from the curve; constructing a generalized SPD model as an asphalt complex shear modulus main curve model; selecting a proper shift factor equation; performing regression analysis on test data, and solving an optimal solution of model parameters; and drawing an asphalt dynamic shear modulus main curve and a phase angle main curve at the reference temperature. Compared with a traditional main curve model, the generalized SPD model provided by the invention can accurately fit phase angle main curves of different types of asphalt, so that the application range is wider.

Description

Technical Field

[0001] The invention relates to the technical field of road engineering, and in particular to a method for drawing a master curve of asphalt viscoelastic parameters based on a generalized SPD model. Background Art

[0002] Asphalt pavement is the main paving form of highways and urban roads in my country. As an important component of asphalt mixture, asphalt plays a key role in cementing aggregates and fillers in asphalt mixture. Related studies have shown that the rheological properties of asphalt have a direct impact on the road performance of asphalt pavement, so it is of great significance to accurately evaluate the rheological properties of asphalt. Asphalt is a typical viscoelastic material, and its viscoelastic properties are affected by temperature and loading frequency. When asphalt is subjected to a small stress or strain level, it behaves as a linear viscoelastic material. At present, the main method for studying the linear viscoelastic properties of asphalt is the master curve method. This method is based on the time-temperature equivalence principle. By translating the mechanical response at different temperatures and loading frequencies to the reference temperature, the master curve of the asphalt viscoelastic parameters is drawn, thereby characterizing the viscoelastic properties of asphalt in a wider temperature and frequency range.

[0003] The core of the master curve method is the master curve model. The master curve models widely used at present can be divided into two categories, namely mathematical models and mechanical models. The mathematical model is proposed based on the shape of the dynamic shear modulus master curve. Commonly used mathematical models include CA model, CAM model, Sigmoidal model, etc. The mechanical model is based on a combination of mechanical elements such as springs, viscoelastic elements, parabolic creep elements, etc. Commonly used mechanical models include Huet model, Huet-Sayegh model, 2S2P1D model, etc. Compared with mathematical models, each mechanical element in the mechanical model has a clear physical meaning. Therefore, more and more scholars recommend the use of mechanical models to draw the master curve of asphalt viscoelastic parameters.

[0004] However, although the existing master curve model can accurately fit the dynamic shear modulus master curve of different types of asphalt, it cannot accurately fit the phase angle master curve of different types of asphalt, especially the phase angle master curve of polymer modified asphalt. This is because the shape of the dynamic shear modulus master curve is independent of the asphalt type and always shows a simple S-shaped curve, while the shape of the phase angle master curve is closely related to the asphalt type. Existing studies have found that the shape of the asphalt phase angle master curve can be divided into the following four types: (1) Type I: reverse S-shaped curve; (2) Type II: the curve increases with decreasing frequency at low frequencies, remains basically unchanged at medium frequencies, and decreases with increasing frequency at high frequencies; (3) Type III: the curve decreases with decreasing frequency at low frequencies, has a peak or remains basically unchanged at medium frequencies, and decreases with increasing frequency at high frequencies; (4) Type IV: the trend of the curve is similar to that of Type II, but decreases with decreasing frequency at very low frequencies.

[0005] When drawing the master curve of the phase angle of modified asphalt, the existing master curve model has some defects in applicability and fitting accuracy, so it is necessary to further explore and study new master curve models. Summary of the invention

[0006] Based on the technical problems existing in the background technology, the present invention proposes a method for drawing the master curve of asphalt viscoelastic parameters based on the generalized SPD model, which can not only accurately characterize the dynamic shear modulus master curve of different types of asphalt, but also accurately characterize the phase angle master curve of different types of asphalt. Therefore, the scope of application is wider, and the fitting accuracy of the generalized SPD model of the present invention is higher.

[0007] The present invention proposes a method for drawing a master curve of asphalt viscoelastic parameters based on a generalized SPD model, and the method steps are as follows:

[0008] S1: Prepare cylindrical asphalt specimens using the silicone mold method, and demould the asphalt specimens after they are cooled;

[0009] S2: A dynamic shear rheometer is used to perform a frequency sweep test on the demolded asphalt specimen to measure the dynamic shear modulus and phase angle of the asphalt specimen at multiple temperatures and frequencies;

[0010] S3: for the dynamic shear modulus and phase angle test data obtained in step S2, a black space graph is drawn with the dynamic shear modulus as the horizontal axis and the phase angle as the vertical axis, and it is checked whether the data points in the graph are located on a unique continuous and smooth curve; if data points that are obviously deviated from the curve are observed, they are removed;

[0011] S4: using the generalized SPD model to draw the master curve of asphalt viscoelastic parameters for the dynamic shear modulus and phase angle test data processed in step S3;

[0012] The generalized SPD model is shown in formula (1):

[0013]

[0014] Where ω is the angular frequency; G * (ω) is the complex shear modulus; G e is the equilibrium modulus; G j 、a j , b j 、c j , k j and h j are the parameters of the generalized SPD model, where j is the jth 1S2P1D model; i is the imaginary unit.

[0015] Preferably, the parallel plate fixture used in the frequency sweep test in step S1 needs to be selected according to the temperature range of the test, and can be a 4 mm parallel plate, an 8 mm parallel plate or a 25 mm parallel plate.

[0016] Preferably, the steps of step S2 are as follows:

[0017] S21: Select the appropriate frequency sweep test temperature range and frequency range according to the research purpose;

[0018] S22: Use a dynamic shear rheometer to perform a strain amplitude sweep test on the asphalt specimen, and determine the strain amplitude used in the frequency sweep test based on the test results;

[0019] S23: After determining the temperature range, frequency range and strain amplitude of the frequency sweep test through the above steps, a dynamic shear rheometer is used to perform a frequency sweep test on the asphalt specimen to measure the dynamic shear modulus and phase angle of the asphalt specimen at multiple temperatures and frequencies.

[0020] Preferably, after the strain amplitude scanning test in step S2 is completed, the change of the dynamic shear modulus with the strain amplitude is observed, and the strain amplitude range of the asphalt specimen when it is in the linear viscoelastic stage is determined based on the current modulus decreasing by 10% compared to the initial modulus, and a strain amplitude is selected as the strain amplitude used in the subsequent frequency scanning test.

[0021] Preferably, when drawing the black space diagram in step S3, the horizontal axis takes logarithmic coordinates and the vertical axis takes linear coordinates.

[0022] Preferably, the steps of step S4 are as follows:

[0023] S41: Based on the 2S2P1D model, a generalized SPD model is constructed as the master curve model of the complex shear modulus of asphalt by using a series-parallel combination of springs, parabolic creep elements and viscosity pots;

[0024] S42: separating the real part and the imaginary part of the generalized SPD model, the real part of the generalized SPD model is used as the master curve model of the asphalt storage modulus, and the imaginary part of the generalized SPD model is used as the master curve model of the asphalt loss modulus;

[0025] S43: According to the relationship between the dynamic shear modulus, phase angle, storage modulus and loss modulus, a master curve model of the dynamic shear modulus of asphalt and a master curve model of the phase angle are constructed;

[0026] S44: Select an appropriate shift factor equation;

[0027] S45: Setting reference temperature;

[0028] S46: Assign reasonable initial values ​​to the parameters in the generalized SPD model and the shift factor equation, and use the Excel planning solver function to perform regression analysis on the dynamic shear modulus and phase angle data measured by the frequency sweep test and the dynamic shear modulus and phase angle data fitted by the generalized SPD model to solve the optimal solution for the model parameters;

[0029] S47: Substitute the optimal solutions of the model parameters into the dynamic shear modulus master curve model and the phase angle master curve model respectively, and draw the dynamic shear modulus master curve and the phase angle master curve of the asphalt at the reference temperature in a double logarithmic coordinate system.

[0030] Preferably, when setting the shift factor equation in step S4, the shift factor equation is the WLF equation or the Arrhenius equation; or the free translation method is used, the shift factor at the reference temperature is set to 1, and the shift factors at other temperatures are regarded as unknown parameters.

[0031] Beneficial technical effects of the present invention:

[0032] Based on the 2S2P1D model, the present invention uses a series-parallel combination of springs, parabolic creep elements and viscoelastic pots to construct a generalized SPD model as the master curve model of the complex shear modulus of asphalt, which can not only accurately characterize the dynamic shear modulus master curve of different types of asphalt, but also accurately characterize the phase angle master curve of different types of asphalt. Compared with the existing master curve model, the generalized SPD model proposed in the present invention satisfies the Kramers-Kronig relationship, and thus strictly follows the linear viscoelastic theory, and has higher fitting accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the generalized SPD model proposed in the present invention.

[0034] Figure 2 It is the black space diagram drawn in Example 1 proposed by the present invention.

[0035] Figure 3 It is the dynamic shear modulus master curve drawn in Example 1 proposed by the present invention.

[0036] Figure 4 It is the phase angle master curve drawn in Example 1 proposed by the present invention.

[0037] Figure 5 It is the dynamic shear modulus master curve drawn in Example 2 proposed by the present invention.

[0038] Figure 6 It is the phase angle master curve drawn in Example 2 proposed by the present invention.

[0039] Figure 7It is the dynamic shear modulus master curve drawn in Example 3 proposed by the present invention.

[0040] Figure 8 It is the phase angle master curve drawn in Example 3 proposed by the present invention.

[0041] Fig. 9 It is the dynamic shear modulus master curve drawn in Example 4 proposed by the present invention.

[0042] Fig.10 It is the phase angle master curve drawn in Example 4 proposed by the present invention. DETAILED DESCRIPTION

[0043] The present invention will be further explained below in conjunction with specific embodiments.

[0044] Example 1

[0045] This embodiment discloses a method for drawing a master curve of asphalt viscoelastic parameters based on a generalized SPD model, including the following steps. The schematic diagram of the generalized SPD model is shown in FIG. Figure 1 As shown:

[0046] S1: Taking a base asphalt with a performance grade of PG 64-10 as an example, in this embodiment, the base asphalt is subjected to a rotary film oven heating aging test and a pressure aging container accelerated asphalt aging test. After the aging test, a silicone mold method is used to prepare cylindrical asphalt specimens with diameters of 8 mm and 25 mm, and the asphalt specimens are demolded after cooling;

[0047] S2: A dynamic shear rheometer is used to perform a frequency sweep test on the demolded asphalt specimen to measure the dynamic shear modulus and phase angle of the asphalt specimen at multiple temperatures and frequencies:

[0048] S21: Set the temperature range of the frequency sweep test to 10 to 70°C and the frequency range to 0.1 to 10 rad / s;

[0049] S22: Use a dynamic shear rheometer to perform a strain amplitude sweep test on the asphalt specimen. The test temperature is the lowest temperature in the temperature range used in the frequency sweep test, i.e., 10°C. The test frequency is the highest frequency in the frequency range used in the frequency sweep test, i.e., 10 rad / s. The strain amplitude range is set to 0.01% to 10%. After the strain amplitude sweep test, observe the change of the dynamic shear modulus with the strain amplitude. Determine the strain amplitude range when the asphalt specimen is in the linear viscoelastic stage based on the 10% decrease in the current modulus compared to the initial modulus, and select a strain amplitude as the strain amplitude used in the subsequent frequency sweep test. In this embodiment, the strain amplitude selected is 0.1%;

[0050] S23: After determining the temperature range, frequency range and strain amplitude of the frequency sweep test through the above steps, a dynamic shear rheometer is used to conduct a frequency sweep test on the asphalt specimen to measure the dynamic shear modulus and phase angle of the asphalt specimen at multiple temperatures and frequencies. In this embodiment, a frequency sweep test with a temperature range of 10 to 40°C is first conducted, using 8mm parallel plates and setting the parallel plate spacing to 2mm; then a frequency sweep test with a temperature range of 40 to 70°C is conducted, using 25mm parallel plates and setting the parallel plate spacing to 1mm. Before conducting the frequency sweep test at each temperature, the asphalt specimen needs to be subjected to a 10 to 15 minutes of insulation treatment to ensure that the temperature of the specimen reaches temperature equilibrium with the test temperature;

[0051] S3: For the dynamic shear modulus and phase angle test data obtained in step S2, a black space graph is drawn with the dynamic shear modulus as the horizontal axis and the phase angle as the vertical axis, and the data points in the graph are checked to see whether they are located on a unique continuous and smooth curve; if data points are observed to be significantly deviated from the curve, they are removed. The black space graph drawn in this embodiment is as follows: Figure 2 As shown;

[0052] S4: For the dynamic shear modulus and phase angle test data processed in step S3, the generalized SPD model is used to draw the master curve of asphalt viscoelastic parameters. The process is as follows:

[0053] S41: Based on the 2S2P1D model, the 1S2P1D model is first constructed by combining the spring, parabolic creep element and sticky pot in series, and then the spring element and several 1S2P1D models are combined in parallel to construct a generalized SPD model as the master curve model of the complex shear modulus of asphalt. Its expression is shown in formula (1);

[0054]

[0055] Where ω is the angular frequency; G * (ω) is the complex shear modulus; G e is the equilibrium modulus; G j 、a j 、b j 、c j , k j and h j are the parameters of the generalized SPD model, where j is the jth 1S2P1D model; i is the imaginary unit;

[0056] S42: separating the real part and the imaginary part of the generalized SPD model, the real part of the generalized SPD model is used as the master curve model of the asphalt storage modulus, as shown in formula (2), and the imaginary part of the generalized SPD model is used as the master curve model of the asphalt loss modulus, as shown in formula (3);

[0057]

[0058]

[0059] Where G'(ω) is the storage modulus; G"(ω) is the loss modulus; A(ω) and B(ω) are intermediate variables, and their expressions are shown in formula (4) and formula (5) respectively:

[0060]

[0061] S43: According to the relationship between the dynamic shear modulus, the phase angle, the storage modulus, and the loss modulus, as shown in formula (6) and formula (7), a master curve model of the dynamic shear modulus of asphalt and a master curve model of the phase angle are constructed;

[0062]

[0063] In the formula, |G * (ω)| is the dynamic shear modulus; δ(ω) is the phase angle;

[0064] S44: This embodiment adopts a free translation method to determine the shift factor at each test temperature, that is, the shift factor at the reference temperature is set to 1, and the shift factors at other temperatures are regarded as unknown parameters;

[0065] S45: In this embodiment, the reference temperature is set to 40°C;

[0066] S46: In this embodiment, the parameter n in the generalized SPD model is set to 2; reasonable initial values ​​are assigned to the parameters in the generalized SPD model and the shift factor equation, and the dynamic shear modulus and phase angle data measured by the frequency sweep test and the dynamic shear modulus and phase angle data fitted by the generalized SPD model are regressed using the Excel planning solver function. The objective function is shown in formula (8), and the optimal solution of the model parameters is solved;

[0067]

[0068] Where N is the total number of data points; |G * (ω)| m,k and δ(ω) m,k are the kth dynamic shear modulus measurement value and phase angle measurement value, respectively, |G * (ω)| f,k and δ(ω) f,k are the kth dynamic shear modulus fitting value and phase angle fitting value respectively;

[0069] S47: Substitute the optimal solutions of the model parameters into the dynamic shear modulus master curve model and the phase angle master curve model respectively, and draw the dynamic shear modulus master curve and the phase angle master curve of the asphalt at the reference temperature in a double logarithmic coordinate system.

[0070] The dynamic shear modulus master curve and phase angle master curve drawn in this embodiment are as follows: Figure 3 and Figure 4 shown.

[0071] Example 2

[0072] This embodiment takes an SBS modified asphalt with a performance grade of PG 70-22 as an example. Compared with Example 1, the shape of the main curve of the phase angle of the SBS modified asphalt in this embodiment is different.

[0073] After the cylindrical asphalt specimens with diameters of 8 mm and 25 mm were prepared by the silicone mold method, the asphalt specimens were first subjected to a strain amplitude sweep test using a dynamic shear rheometer. The test temperature of the strain amplitude sweep test was 10°C, the test frequency was 10 rad / s, and the strain amplitude range was 0.01% to 10%. According to the test results of the strain amplitude sweep test, 0.1% was selected as the strain amplitude used in the subsequent frequency sweep test. Then, a frequency sweep test was performed on the asphalt specimen using a dynamic shear rheometer. The temperature range of the frequency sweep test was 10 to 70°C, the frequency range was 0.1 to 10 rad / s, and the strain amplitude was 0.1%. The dynamic shear modulus and phase angle of the asphalt specimens at multiple temperatures and frequencies were measured. Finally, the generalized SPD model was used to draw the dynamic shear modulus and phase angle master curves of the SBS modified asphalt at a reference temperature of 40°C. The specific drawing method is the same as in Example 1.

[0074] The dynamic shear modulus master curve and phase angle master curve drawn in this embodiment are as follows: Figure 5 and Figure 6 shown.

[0075] Example 3

[0076] This embodiment takes an SBS modified asphalt with a performance grade of PG 76-22 as an example. Compared with Embodiment 1 and Embodiment 2, the shape of the main curve of the phase angle of the SBS modified asphalt in this embodiment is different, and the SBS modified asphalt is not subjected to an aging test.

[0077] After the cylindrical asphalt specimens with diameters of 8 mm and 25 mm were prepared by the silicone mold method, the dynamic shear rheometer was first used to perform a strain amplitude sweep test on the asphalt specimens. The test temperature of the strain amplitude sweep test was 10°C, the test frequency was 10 Hz, and the strain amplitude range was 0.01% to 10%. According to the test results of the strain amplitude sweep test, 0.5% was selected as the strain amplitude used in the subsequent frequency sweep test. Then, the dynamic shear rheometer was used to perform a frequency sweep test on the asphalt specimens. The temperature range of the frequency sweep test was 10 to 70°C, the frequency range was 0.1 to 10 Hz, and the strain amplitude was 0.5%. The dynamic shear modulus and phase angle of the asphalt specimens at multiple temperatures and frequencies were measured. Finally, the generalized SPD model was used to draw the dynamic shear modulus and phase angle master curves of the SBS modified asphalt at a reference temperature of 40°C. The specific drawing method is the same as in Example 1.

[0078] The dynamic shear modulus master curve and phase angle master curve drawn in this embodiment are as follows: Figure 7 and Figure 8 shown.

[0079] Example 4

[0080] This embodiment takes a rubber modified asphalt with a performance grade of PG 82-28 as an example. Compared with Embodiment 1, Embodiment 2 and Embodiment 3, the shape of the main curve of the phase angle of the rubber modified asphalt in this embodiment is different.

[0081] After the cylindrical asphalt specimens with diameters of 8 mm and 25 mm were prepared by the silicone mold method, the asphalt specimens were first subjected to a strain amplitude sweep test using a dynamic shear rheometer. The test temperature of the strain amplitude sweep test was 10°C, the test frequency was 10 rad / s, and the strain amplitude range was 0.01% to 10%. According to the test results of the strain amplitude sweep test, 0.1% was selected as the strain amplitude used in the subsequent frequency sweep test. Then, a frequency sweep test was performed on the asphalt specimen using a dynamic shear rheometer. The temperature range of the frequency sweep test was 10 to 70°C, the frequency range was 0.1 to 10 rad / s, and the strain amplitude was 0.1%. The dynamic shear modulus and phase angle of the asphalt specimens at multiple temperatures and frequencies were measured. Finally, the generalized SPD model was used to draw the dynamic shear modulus and phase angle master curves of the rubber-modified asphalt at a reference temperature of 40°C. The specific drawing method is the same as in Example 1.

[0082] The dynamic shear modulus master curve and phase angle master curve drawn in this embodiment are as follows: Fig. 9 and Fig.10 shown.

Claims

1. A method for drawing a master curve of asphalt viscoelastic parameters based on a generalized SPD model, characterized in that: The steps are as follows: S1: Prepare cylindrical asphalt specimens using the silicone mold method and demould the asphalt specimens after they are cooled; S2: A frequency sweep test was performed on the demoulding asphalt specimen using a dynamic shear rheometer to measure the dynamic shear modulus and phase angle of the asphalt specimen at multiple temperatures and frequencies; S3: for the dynamic shear modulus and phase angle test data obtained in step S2, a black space graph is drawn with the dynamic shear modulus as the horizontal axis and the phase angle as the vertical axis, and it is checked whether the data points in the graph are located on a unique continuous and smooth curve; if data points that are obviously deviated from the curve are observed, they are removed; S4: using the generalized SPD model to draw the master curve of asphalt viscoelastic parameters for the dynamic shear modulus and phase angle test data processed in step S3; The generalized SPD model is shown in formula (1): Where ω is the angular frequency; G * (ω) is the complex shear modulus; G e is the equilibrium modulus; G j 、a j , b j 、c j , k j and h j are the parameters of the generalized SPD model, where j is the jth 1S2P1D model; i is the imaginary unit.

2. The method for drawing the master curve of asphalt viscoelastic parameters based on the generalized SPD model according to claim 1 is characterized in that: The parallel plate fixture used in the frequency sweep test in step S1 needs to be selected according to the temperature range of the test, which can be a 4 mm parallel plate, an 8 mm parallel plate or a 25 mm parallel plate.

3. The method for drawing the master curve of asphalt viscoelastic parameters based on the generalized SPD model according to claim 1 is characterized in that: The steps of step S2 are as follows: S21: Select the appropriate frequency sweep test temperature range and frequency range according to the research purpose; S22: Use a dynamic shear rheometer to perform a strain amplitude sweep test on the asphalt specimen, and determine the strain amplitude used in the frequency sweep test based on the test results; S23: After determining the temperature range, frequency range and strain amplitude of the frequency sweep test through the above steps, a dynamic shear rheometer is used to perform a frequency sweep test on the asphalt specimen to measure the dynamic shear modulus and phase angle of the asphalt specimen at multiple temperatures and frequencies.

4. The method for drawing the master curve of asphalt viscoelastic parameters based on the generalized SPD model according to claim 3 is characterized in that: After the strain amplitude scanning test in step S2 is completed, the change of dynamic shear modulus with strain amplitude is observed, and the strain amplitude range of the asphalt specimen when it is in the linear viscoelastic stage is determined based on the current modulus decreasing by 10% compared with the initial modulus, and a strain amplitude is selected as the strain amplitude used in the subsequent frequency scanning test.

5. The method for drawing the master curve of asphalt viscoelastic parameters based on the generalized SPD model according to claim 1 is characterized in that: When drawing the black space diagram in step S3, the horizontal axis takes logarithmic coordinates and the vertical axis takes linear coordinates.

6. The method for drawing a master curve of asphalt viscoelastic parameters based on a generalized SPD model according to claim 1, characterized in that: The steps of step S4 are as follows: S41: Based on the 2S2P1D model, a generalized SPD model is constructed as the master curve model of the complex shear modulus of asphalt by using a series-parallel combination of springs, parabolic creep elements and viscosity pots; S42: separating the real part and the imaginary part of the generalized SPD model, the real part of the generalized SPD model is used as the master curve model of the asphalt storage modulus, and the imaginary part of the generalized SPD model is used as the master curve model of the asphalt loss modulus; S43: According to the relationship between the dynamic shear modulus, phase angle, storage modulus and loss modulus, a master curve model of the dynamic shear modulus of asphalt and a master curve model of the phase angle are constructed; S44: Select an appropriate shift factor equation; S45: Setting reference temperature; S46: Assign reasonable initial values ​​to the parameters in the generalized SPD model and the shift factor equation, and use the Excel planning solver function to perform regression analysis on the dynamic shear modulus and phase angle data measured by the frequency sweep test and the dynamic shear modulus and phase angle data fitted by the generalized SPD model to solve the optimal solution for the model parameters; S47: Substitute the optimal solutions of the model parameters into the dynamic shear modulus master curve model and the phase angle master curve model respectively, and draw the dynamic shear modulus master curve and the phase angle master curve of asphalt at the reference temperature in a double logarithmic coordinate system.

7. The method for drawing a master curve of asphalt viscoelastic parameters based on a generalized SPD model according to claim 6, characterized in that: When setting the shift factor equation in step S4, the shift factor equation is the WLF equation or the Arrhenius equation; or the free translation method is used, the shift factor at the reference temperature is set to 1, and the shift factors at other temperatures are regarded as unknown parameters.

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