Evaluation method for high temperature rutting resistance of asphalt mixture based on delay time spectrum

Abstract

The application discloses a kind of based on delay time spectrum's asphalt mixture high temperature anti-rutting performance evaluation method, it is related to the technical field of asphalt mixture performance evaluation.The method comprises: obtaining complex modulus data, complex compliance data under different temperature and loading frequency;Complex modulus data, complex compliance data are fitted jointly using complex modulus master curve model, time-temperature displacement equation, complex compliance master curve model, determine model parameters and calculate the dynamic modulus under temperature 50 DEG C, loading frequency 1Hz;Model parameters are substituted into continuous delay time spectrum model, and delay spectrum rutting index is extracted continuous delay spectrum characteristic parameter and combined with dynamic modulus calculation.This application solves the current difficulty to the asphalt mixture rutting performance is fast, effective evaluation of the limitation problem, from the angle of time scale distribution comprehensively represents the viscoelasticity delay response characteristics of asphalt mixture, clear in calculation process, physical meaning is clear, with strong engineering applicability.

Description

Technical Field

[0001] This invention relates to the field of asphalt mixture performance evaluation technology, specifically to a method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delayed time spectrum. Background Technology

[0002] Rutting is one of the most significant high-temperature distresses affecting asphalt pavements. It manifests as longitudinal grooves in the wheel track, reducing driving comfort and pavement service performance, and can also cause hydroplaning in rainy weather, posing safety hazards. Rutting development is influenced by the complex interactions of various factors, including asphalt mixture design, pavement structure configuration, climate conditions, and traffic loads. Material selection and mixture design are key factors leading to early rutting failure. Therefore, accurately and reliably evaluating the high-temperature rutting resistance of asphalt mixtures is a fundamental prerequisite for effectively controlling rutting and optimizing pavement durability.

[0003] Currently, methods for evaluating the rutting resistance of asphalt mixtures mainly fall into two categories: one is simulated rutting test methods, such as the Hamburg rutting test and the asphalt pavement analyzer test; the other is evaluation methods based on mechanical principles, such as flow time tests, flow value tests, dynamic modulus tests, and repeated load permanent deformation tests. Dynamic modulus (|E) * Due to its extreme sensitivity to temperature, loading frequency, aging degree, and mixture volume parameters, and its excellent repeatability, the dynamic modulus |E| has become the benchmark indicator in current performance evaluation. However, existing research has shown that relying solely on the dynamic modulus |E|... * |or its derived indicators|E * | / sin(δ) cannot fully and effectively predict rutting performance and is difficult to comprehensively characterize the viscoelastic response characteristics of asphalt mixtures from the perspective of time-scale distribution.

[0004] Chinese invention patent application CN 118942596 A discloses a method for determining the rutting resistance of asphalt mixtures. This method obtains the dynamic mechanical property parameters, shear property parameters, and external factor parameters of the asphalt mixture to be tested, wherein the dynamic mechanical property parameters include the rutting factor |E|. * The external factor parameters, including the number of load applications and road surface temperature, are input into a deformation prediction model based on a nonlinear regression function. The model outputs the estimated rutting depth to characterize rutting resistance. This method comprehensively considers the influence of dynamic mechanical properties, shear strength, and external factors on rutting deformation; however, its evaluation system is complex and still relies on the rutting factor |E|. * The single modulus-derived index | / sinφ only reflects the ratio of stiffness to viscoelasticity of the mixture under specific frequency and temperature conditions. It fails to comprehensively characterize the delayed response characteristics of asphalt mixtures from the perspective of time-scale distribution and has limited ability to distinguish the differences in high-temperature rutting resistance among different mixtures.

[0005] In summary, existing methods for evaluating the high-temperature rutting resistance of asphalt mixtures are mostly based on a single dynamic modulus index or its derived parameters, which fails to comprehensively reflect the viscoelastic delayed response characteristics of asphalt mixtures at different time scales. Therefore, there is an urgent need for a high-temperature rutting resistance evaluation method that can comprehensively characterize the viscoelastic delayed response characteristics of asphalt mixtures from the perspective of time scale distribution. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, the present invention aims to provide a method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delayed time spectra. This method overcomes the limitations of existing technologies that rely on a single dynamic modulus index or its derived parameters for rapid and effective evaluation of the rutting performance of asphalt mixtures. The invention extracts characteristic parameters with clear physical meaning from continuous delayed time spectra and constructs comprehensive evaluation indicators. This allows for better assessment and prediction of the rutting resistance of various asphalt mixtures, providing crucial support for laboratory screening of asphalt mixtures during the design phase, improving road service performance, and reducing subsequent maintenance costs.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delayed time spectra includes the following steps: 1) Conduct dynamic modulus tests on the asphalt mixture to be evaluated, obtain complex modulus data at different temperatures and loading frequencies, and calculate complex compliance data at different temperatures and loading frequencies based on the principle of linear viscoelasticity. 2) The complex modulus data and complex compliance data are jointly fitted using the complex modulus principal curve model, the time-temperature displacement equation, and the complex compliance principal curve model to determine the parameters of each model; and the dynamic modulus under the condition of 50℃ and 1Hz loading frequency is calculated based on the complex modulus principal curve model after determining the model parameters. 3) Substitute the parameters into the continuous delay time spectrum model to obtain the function of the continuous delay time spectrum model, and obtain the peak position and full width at half maximum (FWHM) of the delay spectrum peak based on the function of the continuous delay time spectrum model. 4) Construct a rutting index using the peak position, full width at half maximum (FWHM), and dynamic modulus at 50°C and 1Hz loading frequency of the rutting index. A higher rutting index indicates better high-temperature rutting resistance of the asphalt mixture. The formula for calculating the rutting index is as follows: ; Where: SERI is the rutting index of the delay spectrum; FWHM is the full width at half maximum (FWHM); ρ peakThe delay time, in seconds, is the time delay at which the peak of the delayed spectrum occurs. The value is the dynamic modulus (in MPa) under the experimental conditions of 50℃ and 1Hz.

[0008] Furthermore, the complex modulus includes storage modulus and loss modulus; the complex modulus principal curve model includes storage modulus principal curve model and loss modulus principal curve model; the storage modulus principal curve model adopts the generalized Sigmoidal model, and the loss modulus principal curve model is determined based on the approximate Kramers-Kronig relationship, or both the storage modulus principal curve model and the loss modulus principal curve model adopt the HN model; the time-temperature displacement equation adopts the WLF equation. In this invention, the calculation of the indices does not depend on a specific principal curve model and time-temperature displacement equation; both the generalized Sigmoidal model and the HN model can achieve the purpose of this invention, and the models have a wide range of applicability.

[0009] Furthermore, the complex compliance includes storage compliance D' and loss compliance D''; the complex compliance principal curve model is calculated from the complex modulus principal curve model based on the principle of linear viscoelasticity. By directly converting the complex modulus into complex compliance based on the principle of linear viscoelasticity, the fitting process simultaneously constrains information in both the stiffness and compliance domains, improving the uniqueness and stability of the model parameters.

[0010] Furthermore, in step 2), the target error equation used for the joint fitting simultaneously includes the relative errors of four components: storage modulus, loss modulus, storage compliance, and loss compliance. Using four-component joint fitting can simultaneously consider the fitting accuracy in both the stiffness and compliance domains, avoiding parameter deviations caused by single-domain fitting, and ensuring the accuracy of the obtained model parameters in the delay time spectrum calculation.

[0011] Further, in step 2), when the storage modulus principal curve model adopts the generalized Sigmund model, and the loss modulus principal curve model is determined based on the approximate Kramers-Kronig relationship, the continuous delay time spectrum model is derived based on the relationship between the continuous delay time spectrum and the storage compliance; when both the storage modulus principal curve model and the loss modulus principal curve model adopt the HN model, the continuous delay time spectrum model is derived based on the relationship between the continuous delay time spectrum and the complex modulus.

[0012] Furthermore, the storage modulus principal curve model adopts the generalized Sigmund model, and when the loss modulus principal curve model is determined based on the approximate Kramers-Kronig relationship, the formula for the continuous delay time spectrum model is as follows: ; in:

[0013] And: A = ln10 δ B=ln10 δ+α -A; C=β-γlg2π; D=γ / ln10; In the formula: L GS (ρ) represents the continuous delay time spectrum based on the GS model, MPa -1 ρ is the delay time, in seconds; 10 δ Minimum storage modulus, MPa; 10 δ+α Let be the maximum value of the storage modulus, in MPa; β, γ, and λ are the shape parameters of the master curve model of the storage modulus, dimensionless. An analytical expression is established based on rigorous mathematical relationships, eliminating the need for data inversion in the calculation of the delay time spectrum, avoiding data instability during the inversion process, and ensuring the reliability and consistency of the calculation results.

[0014] Furthermore, when both the storage modulus principal curve model and the loss modulus principal curve model adopt the HN model, the formula for the continuous delay time spectrum model is as follows: ; in: ; ; Among them, L HN (ρ) represents the continuous delay time spectrum based on the HN model, MPa -1 E e Minimum storage modulus, MPa; E g The maximum value of the storage modulus is MPa; , , The storage modulus master curve shape parameter is dimensionless; ρ is the delay time, in seconds.

[0015] Further, in step 3), the method for obtaining the peak position and full width at half maximum (FWHM) of the delay spectrum peak based on the function of the continuous delay time spectrum model includes: Within a preset logarithmic delay time range, the function of the continuous delay time spectrum model is discretely calculated at fixed intervals to obtain continuous delay time spectrum data under multiple logarithmic delay times. Determine the maximum value in the continuous time-delay spectrum data, and take this maximum value as the delay spectrum peak value L. peak , will be related to the delayed spectral peak L peak The corresponding logarithmic delay time is denoted as the peak position lg(ρ) peak ); According to the peak value of the delay spectrum L peak Determine the half-peak height level L half =Lpeak / 2; The continuous delay time spectrum is calculated as the half-peak height level L. half The logarithmic delay time is denoted as lg(ρ) 左 ), lg(ρ 右 ), where lg(ρ) 左 )≤lg(ρ 右 Based on the continuous delay time spectrum being a half-peak height level L... half The logarithmic delay time is used to calculate the full width at half maximum (FWHM) = lg(ρ 右 ) - lg(ρ 左 The above-mentioned method for extracting continuous delay spectrum feature parameters has a high degree of standardization in its operation process, does not rely on subjective judgment, and ensures the objectivity and repeatability of the evaluation results.

[0016] Furthermore, in step 3), the preset logarithmic delay time range is -15 to 15; the fixed interval for discrete calculation is 0.005.

[0017] Furthermore, the dynamic modulus test is conducted at at least three temperatures and at least three frequencies. Minimum requirements for temperature and frequency combinations are set to ensure that the test data covers a sufficiently wide timescale range, providing adequate data support for master curve fitting and the calculation of the time delay spectrum.

[0018] Furthermore, the method for evaluating the high-temperature rutting resistance of asphalt mixtures also includes obtaining the delayed spectral rutting index of various asphalt mixtures to be evaluated through steps 1) to 4), ranking and comparing the asphalt mixtures to be evaluated based on the delayed spectral rutting index, and the higher the delayed spectral rutting index, the better the high-temperature rutting resistance of the asphalt mixture.

[0019] This invention also provides a system for evaluating the high-temperature rutting resistance of asphalt mixtures based on a time delay spectrum, used to implement the above-mentioned method for evaluating the high-temperature rutting resistance of asphalt mixtures based on a time delay spectrum, comprising: The data storage module is used to store the complex modulus data of the asphalt mixture to be evaluated under different temperatures and loading frequencies obtained from dynamic modulus tests at different temperatures and loading frequencies. The complex compliance data calculation module is used to calculate and obtain complex compliance data at different temperatures and loading frequencies based on complex modulus data and the principle of linear viscoelasticity. The data fitting module is used to jointly fit complex modulus data and complex compliance data using the complex modulus principal curve model, the time-temperature displacement equation, and the complex compliance principal curve model to determine the parameters of each model. The feature parameter extraction module is used to substitute the parameters into the continuous delay time spectrum model to obtain the function of the continuous delay time spectrum model, and to obtain the peak position and full width at half maximum (FWHM) of the delay spectrum peak based on the function of the continuous delay time spectrum model. The dynamic modulus calculation module is used to calculate the dynamic modulus under the condition of 50℃ and 1Hz loading frequency based on the complex modulus master curve model after the model parameters are determined. The delay spectrum rutting index calculation module is used to calculate the delay spectrum rutting index using the peak position of the delay spectrum peak, the full width at half maximum (FWHM), and the dynamic modulus under the conditions of a temperature of 50°C and a loading frequency of 1Hz.

[0020] Furthermore, the high-temperature rutting resistance evaluation system for asphalt mixtures also includes: The ranking and comparison module uses the delayed rutting index of various different asphalt mixtures to be evaluated to rank and compare the asphalt mixtures to be evaluated based on the delayed rutting index.

[0021] The present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the above-mentioned method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delay time spectrum is implemented.

[0022] Compared with the prior art, the present invention has the following beneficial effects: This invention presents a method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delayed time spectra. It overcomes the limitations of existing technologies that rely on a single dynamic modulus index or its derived parameters to evaluate the high-temperature rutting resistance of asphalt mixtures. The method establishes an evaluation method based on characteristic parameters of continuous delayed time spectra, which comprehensively characterizes the viscoelastic delayed response characteristics of asphalt mixtures from the perspective of time scale distribution. It can fully reflect the changes of asphalt mixtures at different time scales and significantly improve the ability to distinguish and rank the differences in high-temperature rutting resistance of different types of mixtures.

[0023] This invention extracts three characteristic parameters from the delayed time spectrum: peak value, peak position, and full width at half maximum (FWHM). The peak value is used to determine the FWHM level and then calculate the FWHM. The peak position, FWHM, and dynamic modulus at 50℃ and 1Hz are combined to construct a delayed rutting index, which achieves a comprehensive evaluation of the three dimensions of dominant delayed time, response distribution range, and viscoelastic response intensity. The constructed delayed rutting index has a significant negative monotonic correlation with the permanent strain of asphalt mixture, verifying the effective characterization ability of this index for high-temperature rutting resistance.

[0024] This invention establishes a complete analytical solution path from the complex modulus master curve model to the complex compliance and then to the continuous delay time spectrum. It adopts the generalized Sigmund model or the HN model, which can make full use of conventional dynamic modulus test data without conducting additional permanent deformation tests. The calculation process is clear, the physical meaning is clear, the model has a wide range of applications, and it has strong engineering applicability. It can provide an efficient and reliable technical means for laboratory screening of asphalt mixtures in the design stage. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the characteristic parameters of the continuous delay time spectrum curve in Embodiment 1 of the present invention; Figure 2 This is a Cole-Cole curve of asphalt mixture I in Example 1 of the present invention; Figure 3 This is a Cole-Cole curve of asphalt mixture II in Example 1 of the present invention; Figure 4 This is a time delay spectrum curve of asphalt mixture I in Example 1 of the present invention; Figure 5 This is a time delay spectrum curve of asphalt mixture II in Example 1 of the present invention; Figure 6 This is a time delay spectrum curve of asphalt mixture I in Example 2 of the present invention; Figure 7 This is a time delay spectrum curve of asphalt mixture II in Example 2 of the present invention; In the figure, the delay intensity refers to the continuous delay time spectrum. Detailed Implementation

[0026] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0027] Example 1

[0028] In this embodiment, the storage modulus principal curve model adopts the generalized Sigmund model, and the loss modulus principal curve model is determined based on the approximate Kramers-Kronig relationship.

[0029] The derivation process of the formulas for each model in this embodiment is as follows: 1. Select the principal curve model of the complex modulus Complex modulus includes storage modulus E' and loss modulus E''; the generalized logistic sigmoidal model (GS model) shown in equation (1) is used as the master curve model of storage modulus, the function determined by equation (2) based on the approximate Kramers-Kronig relationship is used as the master curve model of loss modulus, and the WLF equation (3) is used as the time-temperature displacement equation.

[0030] (1) (2) (3) In the formula: E' GS (f r ) to set the reduced frequency f r The storage modulus, calculated based on the GS model, is in MPa; E'' GS (f r ) to set the reduced frequency f r Loss modulus based on GS model, MPa; 10 δ Minimum storage modulus, MPa; 10 δ+α β is the maximum value of the storage modulus, MPa; β, γ, and λ are the shape parameters of the principal curve model of the storage modulus, dimensionless; f r To reduce the frequency, f r =f×a T,GS f is the loading frequency, Hz; f is the loading frequency, Hz; a T,GS The time-temperature equivalence factor based on the GS model is dimensionless; T is the experimental temperature, in °C. r C1 is the reference temperature (°C); C2 is the model parameter of the time-temperature-displacement equation (°C).

[0031] 2. Determine the principal curve model for complex compliance. Based on the principle of linear viscoelasticity, the complex compliance principal curve model is calculated from the complex modulus principal curve model, including the storage compliance D' and the loss compliance D'', as shown in equations (4) and (5) respectively: (4) (5) In the formula: D' GS (f r ) to set the reduced frequency f r Storage compliance based on the GS model, MPa -1 ;D'' GS (f r ) to set the reduced frequency f rLoss compliance based on the GS model, MPa -1 .

[0032] 3. Determine the continuous delay time spectrum model Based on the physical relationship between the continuous delay time spectrum L(ρ) and the storage compliance D', as shown in Equation (6), the expression of the continuous delay time spectrum model is theoretically derived, as shown in Equation (7).

[0033] (6) (7) in: (8) And: A = ln10 δ B=ln10 δ+α -A; C=β-γlg2π; D=γ / ln10.

[0034] In the formula, i is the imaginary unit; Im represents taking the imaginary part of the complex number; L GS (ρ) represents the continuous delay time spectrum based on the GS model, MPa -1 ρ is the delay time, in seconds.

[0035] Based on the above model, the evaluation method of this invention evaluates the high-temperature rutting resistance of asphalt mixtures by determining the parameters of the continuous delay time spectrum model and establishing evaluation indicators for the high-temperature rutting resistance of asphalt mixtures. Specifically: The present invention provides a method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delayed time spectra, comprising the following steps: 1) Dynamic modulus tests were conducted on the asphalt mixture specimens to be evaluated using a dynamic mechanical testing apparatus. The tests were carried out at different temperatures and loading frequencies to obtain the storage modulus E' and loss modulus E'' at each temperature and loading frequency. The temperatures could be -10℃, 5℃, 20℃, 40℃, and 54℃; the loading frequencies could be 0.1 Hz, 0.5 Hz, 1 Hz, 5 Hz, 10 Hz, and 25 Hz. Then, a Cole-Cole curve was plotted with the storage modulus E'' as the abscissa and the loss modulus E'' as the ordinate. The data in the graph were checked to see if they lay on a unique, continuous, and smooth curve. If data points were observed to deviate significantly from the curve, they could be discarded based on existing experience.

[0036] Based on the linear viscoelastic theory formulas shown in equations (9) and (10), the storage compliance and loss compliance at different temperatures and loading frequencies are calculated from the storage modulus and loss modulus data.

[0037] (9) (10) 2) Select a reference temperature and formulate reasonable initial values ​​for the model parameters. Use the master curve model shown in equations (1) to (5) and the WLF equation to jointly fit the obtained storage modulus data, loss modulus data, storage compliance data and loss compliance data to determine the parameters of each model. The target error equation of the fitting simultaneously includes the relative errors of the four components of storage modulus, loss modulus, storage compliance and loss compliance, as shown in equation (11). The reference temperature can be selected as 50℃, which is used to calculate the time-temperature equivalence factor. 50℃ is the conventional test temperature for rutting resistance performance. And calculate the dynamic modulus under the condition of 50℃ and loading frequency of 1Hz by using the complex modulus master curve model after the parameters are determined. It is used to characterize the viscoelastic response strength of asphalt mixtures.

[0038] (11) In the formula: N is the number of measurement data points; E' m,i E'' represents the storage modulus obtained from the i-th experiment, in MPa; m,i D' represents the loss modulus obtained from the i-th experiment, in MPa; m,i The storage compliance obtained from the i-th trial is in MPa. -1 ;D'' m,i Let MPa be the loss compliance obtained from the i-th test. -1 ;E' GS,i E'' is the storage modulus calculated using equation (1) in MPa; GS,i The loss modulus calculated using equation (2) for the i-th time is given in MPa; D' GS,i For the i-th storage compliance calculated using equation (4), MPa -1 ;D'' GS,i For the i-th loss compliance calculated using equation (5), MPa -1 .

[0039] 3) Substitute the determined model parameters into the continuous delay time spectrum model shown in equation (7) to obtain the function of the continuous delay time spectrum model; based on the obtained function of the continuous delay time spectrum model, extract the characteristic parameters of the continuous delay spectrum in the logarithmic delay time domain, and then combine the dynamic modulus under the conditions of 50℃ temperature and 1Hz loading frequency to establish the evaluation index of the high temperature rutting resistance of asphalt mixture. The characteristic parameters of the continuous delay spectrum include the peak value of the delay spectrum, the peak position, and the full width at half maximum (FWHM).

[0040] The extraction method includes: within a preset logarithmic delay time range, performing discrete calculations on the function of the continuous delay time spectrum model at fixed intervals to obtain continuous delay time spectrum data under multiple logarithmic delay times; wherein, the logarithmic delay time range is -15 to 15, and the calculation interval of the logarithmic delay time lg(ρ) can optionally be set to ∆lg(ρ) as 0.005. Determine the maximum value in the continuous time-delay spectrum data, and take this maximum value as the delay spectrum peak value L. peak (MPa) -1 ), will be related to the delayed spectral peak L peak The corresponding logarithmic delay time is denoted as the peak position lg(ρ) peak );ρ peak The delay time, in seconds, is the time at which the peak value occurs. According to the peak value of the delay spectrum L peak Determine the half-peak height level L half =L peak / 2; Calculate the continuous delay time spectrum as the half-peak height level L half The logarithmic delay time is denoted as lg(ρ) 左 ), lg(ρ 右 ), where lg(ρ) 左 )≤lg(ρ 右 Based on the continuous delay time spectrum as a half-peak high-level L half The logarithmic delay time is used to calculate the full width at half maximum (FWHM) = lg(ρ 右 ) - lg(ρ 左 ).

[0041] This method allows for intuitive observation by plotting continuous delay time spectrum curves, such as... Figure 1 As shown, the specific determination process is as follows: a. Based on the function of the continuous delay time spectrum model, plot the continuous delay time spectrum curve; b. Within the preset logarithmic delay time range, the continuous delay time spectrum curve is discretized at fixed intervals; c. Determine the maximum value of the continuous delay time spectrum function L(ρ) from the discretely calculated continuous delay time spectrum data, and denote this maximum value as the delay spectrum peak value L. peak This can characterize the viscoelastic response intensity of asphalt mixtures near the dominant delay time; simultaneously, it will be compared with the peak value L of the delay spectrum. peak The corresponding logarithmic delay time is denoted as the peak position lg(ρ). peak ), that is: L peak =max[L(ρ)]; d. Based on the peak value L of the delay spectrum peak Determine the half-peak height level L halfThe half-peak height level is L half =L peak / 2; e. Determine the horizontal distance L between the continuous delay time spectrum curve and the half-peak height on the left and right sides of the peak position, respectively. half The intersection point. For cases where the discrete calculation point does not completely coincide with the half-peak height level, an interpolation method is used to determine the corresponding intersection point position, and the logarithmic delay time corresponding to the left intersection point is denoted as lg(ρ). 左 Let lg(ρ) denote the logarithmic delay time corresponding to the intersection point on the right. 右 );ρ 左 To the left of the peak position and horizontally at half-peak height L half The delay time at the intersection point, s; ρ 右 To the right of the peak position and the horizontal level of the half-peak height L half The delay time at the intersection point, in seconds; f. Calculate the full width at half maximum (FWHM) of the continuous delay spectrum curve in the logarithmic delay time domain based on the logarithmic delay times corresponding to the left and right intersection points. The formula is: FWHM = lg(ρ 右 ) - lg(ρ 左 ).

[0042] 4) The high-temperature rutting resistance performance evaluation index of asphalt mixtures, namely the retardation spectrum rutting index SERI, is constructed using the characteristic parameters of the continuous retardation spectrum and the dynamic modulus under the conditions of 50℃ and loading frequency of 1Hz, as shown in Equation (12). The larger the SERI value, the better the high-temperature stability of the asphalt mixture, that is, the better the high-temperature rutting resistance performance.

[0043] (12) Among them, the peak position of the delayed spectrum peak is lg(ρ) peak The full width at half maximum (FWHM) is used to characterize the time scale corresponding to the dominant delay process; the full width at half maximum (FWHM) is used to characterize the range of delay time distribution and the dispersion of the viscoelastic response of the asphalt mixture. FWHM + lg(ρ) peak It is used to comprehensively characterize the distribution range of the delay spectrum and the time scale corresponding to the dominant delay process; The dynamic modulus, expressed in MPa, is measured at 50°C and 1 Hz under experimental conditions. It is used to characterize the viscoelastic response strength of asphalt mixtures. By combining the above continuous delayed spectrum characteristic parameters, a delayed spectrum rutting index can be obtained for comparing, ranking, or classifying the high-temperature deformation sensitivities of different asphalt mixtures.

[0044] 5) Obtain the delayed rutting index (SERI) of various asphalt mixtures to be evaluated through steps 1) to 4). Sort and compare the asphalt mixtures according to the SERI. The higher the SERI, the better the high temperature rutting resistance of the asphalt mixture.

[0045] The following section further illustrates the invention by calculating the Retarded Spectrum Rutting Index (SERI) of asphalt mixture I and asphalt mixture II obtained by mixing base asphalt and SBS modified asphalt with aggregates, respectively, using the method of this invention. The aggregate used is basalt.

[0046] The gradation of the asphalt mixture is shown in Table 1, and the type and amount of asphalt in the asphalt mixture are shown in Table 2.

[0047] Table 1: Asphalt Mixture Gradation

[0048] Table 2: Asphalt Types and Dosage

[0049] In step 1), the test temperatures were -10℃, 5℃, 20℃, 40℃ and 54℃, respectively; the loading frequencies were 0.1Hz, 0.5 Hz, 1 Hz, 5 Hz, 10 Hz and 25 Hz, respectively; the complex modulus data obtained from the test are shown in Table 3.

[0050] Table 3: Complex Modulus Data

[0051] Plot the Cole-Cole curve with storage modulus on the x-axis and loss modulus on the y-axis. The results are as follows: Figure 2 and Figure 3 As shown, check whether the data in the graph lies on a unique, continuous, and smooth curve; according to experience, if data points that deviate significantly from the curve are observed, they should be removed.

[0052] In step 2), the reference temperature for the WLF equation was 50℃, and the parameter results obtained after joint fitting are shown in Table 4.

[0053] Table 4: GS Model Parameter Fitting Results

[0054] In step 3), using the above parameter data, the continuous delay time spectrum model functions for asphalt mixture I and asphalt mixture II are obtained respectively, and the continuous delay time spectrum curves are plotted respectively, as follows. Figure 4 and Figure 5As shown in Table 5, the calculation interval ∆lg(ρ) of the logarithmic delay time lg(ρ) was set to 0.005 within the range of -15 to 15 logarithmic delay time. Continuous delay time spectrum data under multiple logarithmic delay times were obtained, and the continuous delay spectrum characteristic parameters and SERI were calculated based on this data.

[0055] Table 5: SERI results based on the GS model

[0056] As shown in Table 5, the SERI of asphalt mixture I and asphalt mixture II prepared from base asphalt and SBS modified asphalt are 7.671 and 9.757, respectively. It can be seen that the high-temperature rutting resistance of SBS modified asphalt is significantly better than that of base asphalt, which is consistent with the current conventional understanding of base asphalt and SBS modified asphalt.

[0057] To further verify the characterization ability of the delayed spectral rutting index (SERI) on the high-temperature rutting resistance of asphalt mixtures, 11 different types of asphalt mixtures were selected as evaluation objects. The SERI of each asphalt mixture was calculated according to the aforementioned method, and the calculation results were compared with the permanent strain ε obtained from the corresponding permanent deformation test. p The comparison results are shown in Table 6. Table 6 includes the parameters of the complex modulus master curve model for the 11 types of asphalt mixtures, and the permanent strain ε. p (με) data are from the literature: Ling, M., Lee, SI, Ji, J., Fuentes, L., & Walubita, LF (2023). Assessing permanent deformation potential of asphalt mixtures based on viscoelastic characteristics. International Journal of Pavement Engineering, 24(1). Based on the parameters of the complex modulus master curve model provided in the literature, the delayed spectral rutting index (SERI) of each asphalt mixture can be calculated according to the scheme of this invention. The mixture type numbering follows the above literature.

[0058] Table 6: Evaluation results of the delayed spectral rutting index based on the GS model on the high-temperature rutting resistance of asphalt mixtures

[0059] Spearman rank correlation analysis was used to evaluate the relationship between the delayed spectral rutting index SERI and the permanent strain ε. pThe results show a monotonic correlation between the delayed spectral rutting index SERI and the permanent strain ε. p The Spearman rank correlation coefficient between them was -0.9000, and the two-sided significance test result was: p<0.001. Therefore, it can be concluded that the delayed spectral rutting index SERI is related to the permanent strain ε. p There is a significant negative monotonic correlation between them. As the delayed spectral rutting index (SERI) increases, the permanent strain of the asphalt mixture in the permanent deformation test generally decreases. The smaller the permanent strain, the stronger the asphalt mixture's resistance to high-temperature permanent deformation. Therefore, a larger SERI corresponds to better high-temperature rutting resistance.

[0060] The above results show that the rutting index of the delay spectrum can comprehensively reflect the peak intensity, dominant delay time and delay time distribution range of the continuous delay spectrum, and can be used for comparison, ranking and preliminary screening of the high temperature rutting resistance of different asphalt mixtures.

[0061] Example 2

[0062] The difference between this embodiment and Embodiment 1 is that both the storage modulus principal curve model and the loss modulus principal curve model adopt the Havriliak-Negami (HN) model, and the continuous delay time spectrum model is derived based on the relationship between the continuous delay time spectrum and the complex modulus.

[0063] The derivation process of the formulas for each model in this embodiment is as follows: 1. Select the principal curve model of the complex modulus The HN models shown in equations (13) to (15) represent the complex moduli ( Master curve model, storage modulus ( The master curve model and loss modulus ( The main curve model uses the WLF equation shown in equation (16) as the time-temperature displacement equation.

[0064] (13) (14) (15) (16) in: (17) In the formula: E* HN (f r ) to set the reduced frequency f r The complex modulus, MPa, is calculated based on the HN model; E' HN (fr ) to set the reduced frequency f r The storage modulus, calculated based on the HN model, is in MPa; E'' HN (f r ) to set the reduced frequency f r The loss modulus based on the HN model, in MPa; The minimum storage modulus is MPa; The maximum value of the storage modulus is MPa; , , The storage modulus master curve shape parameters are dimensionless; To reduce frequency, = , Hz; The loading frequency is Hz; i refers to an imaginary number. The time-temperature equivalence factor based on the HN model is dimensionless. The test temperature is in °C. Reference temperature, °C; These are model parameters, dimensionless; Here are the model parameters, in °C.

[0065] 2. Determine the principal curve model for complex compliance. Based on the principle of linear viscoelasticity, a complex compliance principal curve model is calculated from the complex modulus principal curve model, including the storage compliance. and loss compliance As shown in equations (18) and (19) respectively: (18) (19) and: (20) Among them, D' HN (f r ) to set the reduced frequency f r Storage compliance based on the HN model, MPa -1 ;D'' HN (f r ) to set the reduced frequency f r Loss compliance based on the HN model, MPa -1 .

[0066] 3. Determine the continuous delay time spectrum model Based on the physical relationship between the continuous delay time spectrum L(ρ) and the complex modulus E*, as shown in Equation (21), the expression of the continuous delay time spectrum model is theoretically derived, as shown in Equation (22).

[0067] (twenty one) (twenty two) in: (twenty three) (twenty four) In the formula, L HN (ρ) represents the continuous delay time spectrum based on the HN model, MPa -1 .

[0068] The rutting index (SERI) of the delayed spectral tracing indices was calculated for asphalt mixture I and asphalt mixture II in Example 1 using the method described in this embodiment. The parameter fitting results are shown in Table 7, and the continuous delayed spectral characteristic parameters and SERI results are shown in Table 8. Continuous delayed time spectrum curves were plotted based on the continuous delayed time spectrum model function, as follows: Figure 6 and Figure 7 As shown.

[0069] Table 7: HN model parameter fitting results

[0070] Table 8: SERI Results Based on the HN Model

[0071] As shown in Table 8, the SERI of asphalt mixture I and asphalt mixture II prepared from base asphalt and SBS modified asphalt are 7.238 and 8.167, respectively. It can be seen that the high-temperature rutting resistance of SBS modified asphalt is significantly better than that of base asphalt, which is consistent with the current conventional understanding of base asphalt and SBS modified asphalt.

[0072] The delayed spectral rutting index (SERI) of 11 different types of asphalt mixtures in Example 1 was calculated using the method of this embodiment, and the calculation results were compared with the permanent strain ε obtained from the corresponding permanent deformation tests. p The results of the comparison are shown in Table 9. The HN model parameters were obtained by back-calculating the storage modulus and loss modulus of each mixture under the same temperature and frequency combination as in Example 1, based on the generalized Sigmoidal model parameters provided in the literature. The data were then refitted according to equations (13) to (15), and the delay spectrum rutting index SERI was calculated based on the HN model parameters.

[0073] Table 9: Evaluation results of the delayed spectral rutting index based on the HN model on the high-temperature rutting resistance of asphalt mixtures

[0074] Table 9 shows that the Spearman rank correlation analysis method was used to evaluate the delayed spectral rutting index (SERI) and permanent strain. The monotonic correlation between the delayed spectral rutting index SERI and the permanent strain is shown in the calculation results. The Spearman rank correlation coefficient between them was -0.9091, and the two-sided significance test result was: p<0.001. Therefore, it can be concluded that the delayed spectral rutting index SERI is related to the permanent strain. There is a significant negative monotonic correlation between them. As the delayed spectral rutting index (SERI) increases, the permanent strain of the asphalt mixture in the permanent deformation test generally decreases. The smaller the permanent strain, the stronger the asphalt mixture's resistance to high-temperature permanent deformation. Therefore, a larger SERI corresponds to better high-temperature rutting resistance.

[0075] Example 3

[0076] A system for evaluating the high-temperature rutting resistance of asphalt mixtures based on a time delay spectrum, used to implement the aforementioned method for evaluating the high-temperature rutting resistance of asphalt mixtures based on a time delay spectrum, comprising: The data storage module is used to store the complex modulus data of the asphalt mixture to be evaluated under different temperatures and loading frequencies obtained from dynamic modulus tests at different temperatures and loading frequencies. The complex compliance data calculation module is used to calculate and obtain complex compliance data at different temperatures and loading frequencies based on complex modulus data and the principle of linear viscoelasticity. The data fitting module is used to jointly fit complex modulus data and complex compliance data using the complex modulus principal curve model, the time-temperature displacement equation, and the complex compliance principal curve model to determine the parameters of each model. The feature parameter extraction module is used to substitute the parameters into the continuous delay time spectrum model to obtain the function of the continuous delay time spectrum model, and to obtain the peak position and full width at half maximum (FWHM) of the delay spectrum peak based on the function of the continuous delay time spectrum model. The dynamic modulus calculation module is used to calculate the dynamic modulus under the condition of 50℃ and 1Hz loading frequency based on the complex modulus master curve model after the model parameters are determined. The delay spectrum rutting index calculation module is used to calculate the delay spectrum rutting index using the peak position of the delay spectrum peak, the full width at half maximum (FWHM), and the dynamic modulus under the conditions of a temperature of 50°C and a loading frequency of 1Hz. The ranking and comparison module uses the delayed rutting index of various different asphalt mixtures to be evaluated to rank and compare the asphalt mixtures to be evaluated based on the delayed rutting index.

[0077] Example 4

[0078] An electronic device includes a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the above-mentioned method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delay time spectrum is implemented.

[0079] This invention establishes a solution method for the continuous delayed time spectrum of asphalt mixtures based on the generalized Sigmoidal model. It expands the application of the generalized Sigmoidal model from dynamic modulus master curve fitting to complex compliance and delayed time spectrum analysis, enabling it to characterize the viscoelastic response features of asphalt mixtures from the perspective of time-scale distribution. Furthermore, this invention not only relies on the generalized Sigmoidal model but can also use the HN model to construct a delayed time spectrum model and evaluate the high-temperature rutting resistance of asphalt mixtures, demonstrating a wide range of model applicability. Simultaneously, this invention extracts the delayed spectral peak value, peak position, and full width at half maximum (FWHM) from the delayed time spectrum and constructs a delayed spectral rutting index, achieving a comprehensive evaluation of viscoelastic response intensity, dominant delayed time, and response distribution range. The constructed delayed spectral rutting index has a good correlation with the permanent strain of asphalt mixtures and can be used for comparing, ranking, and screening the high-temperature rutting resistance of different asphalt mixtures. This method can fully utilize dynamic modulus test data, reduce the need for additional permanent deformation tests, and has advantages such as a clear calculation process, clear physical meaning, wide model applicability, and strong engineering applicability.

[0080] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for evaluating the high-temperature rutting resistance of asphalt mixtures based on delayed time spectrum, characterized in that, Includes the following steps: 1) Conduct dynamic modulus tests on the asphalt mixture to be evaluated, obtain complex modulus data at different temperatures and loading frequencies, and calculate complex compliance data at different temperatures and loading frequencies based on the principle of linear viscoelasticity. 2) The complex modulus data and complex compliance data are jointly fitted using the complex modulus principal curve model, the time-temperature displacement equation, and the complex compliance principal curve model to determine the parameters of each model; and the dynamic modulus under the condition of 50℃ and 1Hz loading frequency is calculated based on the complex modulus principal curve model after determining the model parameters. 3) Substitute the parameters into the continuous delay time spectrum model to obtain the function of the continuous delay time spectrum model, and obtain the peak position and full width at half maximum (FWHM) of the delay spectrum peak based on the function of the continuous delay time spectrum model. 4) Construct a rutting index using the peak position, full width at half maximum (FWHM), and dynamic modulus at 50°C and 1Hz loading frequency of the rutting index. A higher rutting index indicates better high-temperature rutting resistance of the asphalt mixture. The formula for calculating the rutting index is as follows: ； Where: SERI is the rutting index of the delay spectrum; FWHM is the full width at half maximum (FWHM); ρ peak The delay time, in seconds, is the time delay at which the peak of the delayed spectrum occurs. The value is the dynamic modulus (in MPa) under the experimental conditions of 50℃ and 1Hz.

2. The method for evaluating the high-temperature rutting resistance of asphalt mixtures according to claim 1, characterized in that, The complex modulus includes storage modulus and loss modulus; the complex modulus principal curve model includes storage modulus principal curve model and loss modulus principal curve model; the storage modulus principal curve model adopts the generalized Sigmund model, and the loss modulus principal curve model is determined based on the approximate Kramers-Kronig relationship, or both the storage modulus principal curve model and the loss modulus principal curve model adopt the HN model; the time-temperature displacement equation adopts the WLF equation.

3. The method for evaluating the high-temperature rutting resistance of asphalt mixtures according to claim 2, characterized in that, The complex compliance includes storage compliance D' and loss compliance D''; the complex compliance principal curve model is calculated from the complex modulus principal curve model based on the principle of linear viscoelasticity.

4. The method for evaluating the high-temperature rutting resistance of asphalt mixtures according to claim 3, characterized in that, In step 2), the target error equation used for the joint fitting simultaneously includes the relative errors of four components: storage modulus, loss modulus, storage compliance, and loss compliance.

5. The method for evaluating the high-temperature rutting resistance of asphalt mixtures according to claim 3, characterized in that, In step 2), the storage modulus principal curve model adopts the generalized Sigmund model. When the loss modulus principal curve model is determined based on the approximate Kramers-Kronig relationship, the continuous delay time spectrum model is derived based on the relationship between the continuous delay time spectrum and the storage compliance. When both the storage modulus principal curve model and the loss modulus principal curve model adopt the HN model, the continuous delay time spectrum model is derived based on the relationship between the continuous delay time spectrum and the complex modulus.

6. The method for evaluating the high-temperature rutting resistance of asphalt mixtures according to claim 1, characterized in that, In step 3), the method for obtaining the peak position and full width at half maximum (FWHM) of the delay spectrum peak based on the function of the continuous delay time spectrum model includes: Within a preset logarithmic delay time range, the function of the continuous delay time spectrum model is discretely calculated at fixed intervals to obtain continuous delay time spectrum data under multiple logarithmic delay times. Determine the maximum value in the continuous time-delay spectrum data, and take this maximum value as the delay spectrum peak value L. peak , will be related to the delayed spectral peak L peak The corresponding logarithmic delay time is denoted as the peak position lg(ρ) peak ); According to the peak value of the delay spectrum L peak Determine the half-peak height level L half =L peak / 2; The continuous delay time spectrum is calculated as the half-peak height level L. half The logarithmic delay time is denoted as lg(ρ) 左 ), lg(ρ 右 ), where lg(ρ) 左 )≤lg(ρ 右 Based on the continuous delay time spectrum being a half-peak height level L... half The logarithmic delay time is used to calculate the full width at half maximum (FWHM) = lg(ρ 右 ) - lg(ρ 左 ).

7. The method for evaluating the high-temperature rutting resistance of asphalt mixtures according to claim 6, characterized in that, In step 3), the preset logarithmic delay time range is -15 to 15; the fixed interval for discrete calculation is 0.

005.

8. The method for evaluating the high-temperature rutting resistance of asphalt mixtures according to any one of claims 1 to 7, characterized in that, The method for evaluating the high-temperature rutting resistance of asphalt mixtures also includes obtaining the delayed spectral rutting index of various asphalt mixtures to be evaluated through steps 1) to 4), and ranking and comparing the asphalt mixtures to be evaluated based on the delayed spectral rutting index. The higher the delayed spectral rutting index, the better the high-temperature rutting resistance of the asphalt mixture.

9. A system for evaluating the high-temperature rutting resistance of asphalt mixtures based on a delayed time spectrum, used to implement the method for evaluating the high-temperature rutting resistance of asphalt mixtures based on a delayed time spectrum as described in any one of claims 1 to 8, characterized in that, include: The data storage module is used to store the complex modulus data of the asphalt mixture to be evaluated under different temperatures and loading frequencies obtained from dynamic modulus tests at different temperatures and loading frequencies. The complex compliance data calculation module is used to calculate and obtain complex compliance data at different temperatures and loading frequencies based on complex modulus data and the principle of linear viscoelasticity. The data fitting module is used to jointly fit complex modulus data and complex compliance data using the complex modulus principal curve model, the time-temperature displacement equation, and the complex compliance principal curve model to determine the parameters of each model. The feature parameter extraction module is used to substitute the parameters into the continuous delay time spectrum model to obtain the function of the continuous delay time spectrum model, and to obtain the peak position and full width at half maximum (FWHM) of the delay spectrum peak based on the function of the continuous delay time spectrum model. The dynamic modulus calculation module is used to calculate the dynamic modulus under the condition of 50℃ and 1Hz loading frequency based on the complex modulus master curve model after the model parameters are determined. The delay spectrum rutting index calculation module is used to calculate the delay spectrum rutting index using the peak position of the delay spectrum peak, the full width at half maximum (FWHM), and the dynamic modulus under the conditions of a temperature of 50°C and a loading frequency of 1Hz.

10. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the method for evaluating the high-temperature rutting resistance of asphalt mixtures based on the time delay spectrum as described in any one of claims 1 to 8.

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