Dynamic Modulus Of Asphalt Mixtures Research Articles

A testing theory for simultaneously determining asphalt mixture’s dynamic modulus in compression and tension by use of IDT test

The compressive and tensile moduli of asphalt mixtures are not equal. As a result, in order to obtain reasonable response calculation results, asphalt pavement mechanical analysis should first determine the compressive and tensile moduli of asphalt mixtures separately. Then, it should assign an appropriate modulus to the FEM element based on the stress state of the element. However, conventional uniaxial compression modulus testing protocol is typically unable to determine the actual asphalt pavement's coring specimen due to the limitation that general dynamic modulus testing protocol requires a larger size of specimen and conventional coring specimen from field usually cannot meet the requirement in regard to specimen size. In this case, the dynamic modulus of the asphalt mixture can only be ascertained using the IDT test method.Nevertheless, the current IDT test protocol is unable to distinguish between the compressive and tensile moduli of asphalt mixtures, and the testing results are usually different from those obtained by using the conventional uniaxial compression or tension method. This is because the current IDT test method for determining the dynamic modulus of asphalt mixtures generally treats asphalt mixtures as a kind of ideal elastic material and considers its compressive modulus is equal to its tensile modulus.Consequently, this paper presents a new theory, based on Ambartsumyan's bi-modulus constitutive relation theory, that can use the IDT test method to simultaneously determine the dynamic modulus of an asphalt mixture in both compression and tension. This theory assumes that the stress-strain relationship of asphalt mixture complies with the bi-modulus constitutive relation, and obtains the vertical deformation or horizontal deformation of the IDT specimen by solving a definite integral for the displacement of a small segment on the vertical or horizontal axis, which utilizes the results of the mathematical analysis of the stress distribution of the IDT specimen under distributed strip load. Then, the specimen's dynamic modulus in compression and tension can be obtained via back-calculating method, if the specimen's vertical and horizontal displacement are measured by a physical test in the lab. Obviously, this theory addresses the limitation of the conventional IDT method that cannot reflect the distinction of compressive modulus with tensile modulus, and can be better utilized to simultaneously determine compressive and tensile modulus of cored specimen from field. The verification test also demonstrates, the dynamic modulus determined by this theory are in line with the results of the conventional uniaxial test and is highly practicable.

The discussion of dynamic modulus of asphalt mixtures under biaxial stresses

Asphalt pavement in service is subjected to a complicated state of stress, especially in the uphill or starting and braking sections. The normal stress and the shear stress load it together. Only uniaxial vertical load was taken into account in the testing of dynamic modulus when a pavement was designed at present. In this paper, the dynamic response tests were carried out by applying the dynamic normal and shear loads to cylindrical specimens of asphalt mixtures. The dynamic modulus under vertical loading and vertical-horizontal loading were compared to analyze the effect of the combination loading. The result indicated vertical dynamic modulus under biaxial loading was significantly lower than vertical loading, as opposed to dynamic shear modulus. It could be concluded that the properties of asphalt mixture from biaxial stresses state should be paid more attention in the design of pavement, especially in the intersection and uphill sections.

Effect of Ceramic Waste Powder on Rutting and Dynamic Modulus of Asphalt Mixture

Abstract: Aggregates, asphalt binder, and mineral filler are blended in appropriate proportions to guarantee the desired characteristics of asphalt. Besides from aggregates and bitumen, the role of filler material in HMA is critical since it affects the mechanical characteristics and serviceability particularly when subjected to wheel load. The current research investigated the effect of Ceramic Waste Powder (CWP) used as filler in terms of rutting, and dynamic modulus of asphalt mixtures when used in different proportions 20%, 40%, 60%, 80% and 100% by weight of Marshall Specimen, and the results were compared to conventional mixture employing stone dust as a filler. The performance testing revealed that the rut resistance increases with the increase in CWP content from 40 % to 60 % in asphalt mixtures and showed 21 %, and 58 % decrease in rut depth value to that of conventional asphalt mixture at 55 ℃ respectively. While dynamic modulus increases as the frequency of the applied load increases from 0.1 Hz to 25 Hz and it decreases when the temperature of the dynamic modulus test increases from 4.4 °C to 54 °C. Higher values of Dynamic Modulus are observed at 21.1°C and 37.8 °C temperature for all frequencies. Therefore, using CWP as filler in asphalt not only increases the mechanical properties of HMA but also be a suitable approach towards reducing ceramic waste pollution.

Boosting Hot Mix Asphalt Dynamic Modulus Prediction Using Statistical and Machine Learning Regression Modeling Techniques

The prediction of asphalt mixture dynamic modulus (E*) was investigated based on 1128 E* measurements, using three regression and thirteen machine learning models. Asphalt binder properties and mixture volumetrics were characterized using the same feeding features in the NCHRP 1-37A Witczak model. However, three aggregate gradation characterization approaches were involved in both modelling techniques: the NCHRP 1-37A gradation parameters, Weibull distribution factors, and Bailey method parameters. This study evaluated the performance of these models based on various performance indicators, using both statistical and machine learning regression modeling techniques. K-fold cross-validation and learning curve analysis were conducted to assess the models’ generalization capabilities. The conclusions of this study demonstrate the superiority of the ML models, particularly the Catboost ensemble learning regression (CbR). Hyperparameter optimization and residual analysis were performed to fine-tune and confirm the heteroscedasticity of the CbR model. The Bailey-based CbR model showed the highest coefficient of determination (R2) of 0.998 and the lowest root mean square error (RMSE) of 220 MPa. Moreover, SHAP values interpreted the CbR model and showed the relative importance of its feeding features. Based on the findings of this study, the CbR model is suggested to accurately predict E* for a variety of asphalt mixtures. This information can be used to improve pavement design and construction, leading to more durable and long-lasting pavements.

Evaluation of the microscale structure and performance of asphalt mixtures under different design methods

Asphalt mixture design methods have an important influence on both the microscale structure formed and the corresponding properties. This research compared the performance of asphalt mixtures with the Balanced design method, Marshall design method, and Superpave design method. CT scans were performed on the mixture specimens under different design methods to analyze the mixtures' void distribution law and skeleton structure stability. Then, the water stability of asphalt mixtures with different skeleton structures was evaluated by the water immersion Marshall test and freeze–thaw splitting test, and the effects of temperature and loading frequency on the dynamic modulus of asphalt mixtures under different skeleton structures were assessed by uniaxial compression dynamic modulus test. Finally, based on the time–temperature equivalence principle and Sigmoid model, the master curves of the dynamic modulus of asphalt mixtures under different design methods were constructed. The results showed that the number of coarse aggregate contact points and the average coordination number of asphalt mixtures were relatively larger under the Balanced design method, and the residual strength ratio of asphalt mixture under the Marshall design method was 1.4% larger than that of the Balanced design method, and the residual strength ratio of specimens under Superpave design method was 6.1% larger than that of the Balanced design method. At the same time, based on the differences in the air void of the specimens under different design methods and the different skeleton structures, the dynamic modulus laws under the action of different frequencies were obtained, and the mechanism of the influence of the skeleton structure on the dynamic modulus of the mixture was revealed. This research has important implications for the durability improvement of asphalt mixtures.

Experimental Study on the Dynamic Modulus of an Asphalt Roadbed Grouting Mixture under the Influence of Complex and Multiple Factors

After long-term service, the ground will experience settlement and the stability of the roadbed will be lost. In order to effectively reinforce the roadbed, an asphalt roadbed grouting mixture has been applied to the filling of the roadbed. The rotary compaction method was used to prepare different gradation types of lime composite-modified oil sludge pyrolysis residue asphalt, mixtures Sup13, Sup19, and Sup25. This article takes the dynamic modulus of an asphalt roadbed grouting mixture as the mechanical index, and the uniaxial compression dynamic modulus test is carried out on three kinds of rotary compaction asphalt mixtures, Sup13, Sup19, and Sup25. The dynamic modulus master curves of different gradation composite-modified oil sludge pyrolysis residue asphalt mixtures are fitted to study the dynamic modulus of asphalt mixtures under different nominal maximum particle sizes, loading frequencies, and temperatures. The results show that (1) The dynamic modulus of different gradation composite-modified oil sludge pyrolysis residue asphalt mixtures increases with the decrease in temperature and the increase in frequency; (2) when other conditions are the same, the compound-modified asphalt mixture’s dynamic modulus decreases significantly under low-frequency and high-temperature conditions; (3) in the range of 4.4–37.8 °C and medium loading frequency, the dynamic modulus of the compound-modified asphalt mixture is more affected by temperature and loading frequency; (4) in the low-temperature and high-frequency range, the compound-modified asphalt mixture with a larger nominal maximum particle size has a higher dynamic modulus, and the asphalt mixture with better stability of skeleton structure has a higher dynamic modulus. The research results of this article will provide scientific guidance for the study of the mechanical properties of asphalt roadbed grouting mixtures.

Implementation of ensemble Artificial Neural Network and MEMS wireless sensors for In-Situ asphalt mixture dynamic modulus prediction

Dynamic modulus is an essential mechanical property for pavement structural condition assessment yet obtaining the in-situ dynamic modulus of asphalt mixture efficiently and accurately has never been easy. With the development of sensing technology, a type of Micro-Electromechanical Sensor (MEMS), SmartRock, has been applied in pavement monitoring because of its convenience and high efficiency; but interpreting the collected data as useful engineering information becomes a new challenge. This paper aims to present a data processing algorithm for sensing data in pavement engineering and develop a dynamic modulus predictive model based on the ensemble artificial neural network (ANN) model using SmartRock sensing data. Five asphalt mixtures were tested by the uniaxial dynamic modulus test, and one of the 5 mixes was also used in the third-scale model mobile load simulator (MMLS3) test. SmartRock sensors were installed in the specimens to collect the mechanical response during the tests. The empirical mode decomposition (EMD) method was used for data preprocessing. Dynamic modulus test data, in combination with a small portion of early-stage MMLS3 sensing data, were used as the training dataset, while the remaining MMLS3 data were used as the testing dataset. The results show that the ensemble ANN model is feasible and robust in predicting the dynamic modulus of the asphalt mixture in the MMLS3 test. The parametric analysis shows that the ensemble ANN model has reliable stability. Future studies are recommended to expand the database with more material variety and loading conditions for model verification.

Comparative study of indirect tensile test and uniaxial compression test on asphalt mixtures: Dynamic modulus and stress-strain state

Dynamic modulus is an essential parameter for the performance characterisation of asphalt materials for performance prediction and pavement design. The Indirect Tensile (IDT) test and the Uniaxial Compression (UC) test are both well-known experiments performed in the laboratory to characterise the dynamic modulus of asphalt mixtures over a range of temperatures and loading frequencies. A considerable amount of research has investigated the difference between two test modes, while few studies analysed the fundamental difference in stress–strain distributions for the two test setups. This work aims at comparing the effect of the two test methods on dynamic modulus of asphalt mixtures, as well as stress–strain state. For these purposes, two types of mixtures commonly employed to build road surface layers, namely Asphalt Concrete (AC) and Stone Mastic Asphalt (SMA), were created and tested. The specimens were prepared with a gyratory compactor. The master curves of dynamic modulus and the stress–strain states obtained from the two testing procedures were compared. The dynamic modulus and phase angle results are almost identical for medium frequency and temperature, whereas the results exhibit significant discrepancies for lower and higher frequency values. AC 11 and SMA 11 mixtures show differences in comparison between the two tests. Moreover, the strains measured by the IDT test are variable and the strains obtained from the UC test stabilise around 40 με. Similarly, both tests have poor strain control at 40 °C. The values of normalised stresses measured by the IDT test are approximately 3.26 and 2.34 times greater than the ones measured by the UC test for AC 11 and SMA 11 mixtures, respectively. In general, the results of the mechanical characterisation of the asphalt mixtures conducted using both tests are similar. The IDT test has the advantage of sample size for sample preparation methods in both laboratory and field, and the UC test has a better deformation control at low and medium temperatures.

Influence of material factors on the determination of dynamic moduli and associated prediction models for different types of asphalt mixtures

In a Mechanistic-Empirical (ME) pavement design system, the dynamic modulus is used to characterise asphalt mixtures, which are affected by many factors including environmental conditions and material properties. This study examined twenty types of asphalt mixtures containing nine types of bituminous binders that are commonly used for construction of road pavements in Norway. The objective of the study was to investigate the relationship between material factors and dynamic modulus. The dynamic moduli of asphalt mixtures were experimentally determined employing cyclic indirect tensile tests and were modelled with master curves implementing the sigmoidal function. The rheological properties of bitumen were characterised using a dynamic shear rheometer. The viscosity was simulated using a temperature-based log-linear relationship and the complex modulus was obtained based on the modified Huet-Sayegh model. The grey relational analysis revealed the correlation existing between the material factors and the dynamic modulus. A prediction model was established using a Multiple Linear Regression (MLR). The results indicate that the dynamic modulus of asphalt mixtures is greatly affected by the following parameters ranked in order of decreasing significance: viscosity and complex modulus of the binder, void filled with bitumen, air void content, bitumen penetration and softening point. Based on the MLR model, the correlation between the dynamic modulus and the bitumen viscosity and complex modulus fit well with Coefficient of Determination (R2) ≥ 0.901. The determination of the sigmoidal function parameters to predict the dynamic modulus had good reliability with R2 ≥ 0.973. This study contributes to the development of an accurate and convenient method to predict the dynamic moduli of asphalt mixtures based on the material factors for a ME pavement design system.

Evaluation and calibration of dynamic modulus prediction models of asphalt mixtures for hot climates: Qatar as a case study

The dynamic modulus (|E*|) of asphalt mixtures is one of the most important inputs in Mechanistic-Empirical (ME) pavement analysis and design. Several models have been developed to predict the dynamic modulus based on mixture volumetrics and material properties. This study aimed to calibrate and validate two commonly used models (i.e., Hirsch model and Alkhateeb model) for predicting the dynamic modulus of asphalt mixtures in Qatar. Based on the study outcomes, the Hirsch model was found to have a high prediction performance of asphalt mixture moduli before calibration with a coefficient of determination (R2) of 87.2 % between predicted and measured values. This R2 value improved slightly after calibration to 89.2 %, Alkhateeb model, on the other hand, had a coefficient of determination of 70.8 % before calibration, which also improved to 89.2 % after calibration. The moduli predicted by the Hirsch model before and after calibration were employed in this study to perform a mechanistic-empirical analysis of the performance of various typical pavement sections in Qatar. According to the findings, the percentage change in the predicted fatigue damage due to the use of the calibrated Hirsch model reached more than 50 % with an average value of 17.33 %, while the percent change in rutting reached 14 % with an average value of 3.65 %. These results highlight the importance of using locally calibrated models for the dynamic modulus in order to improve performance predictions.

Study of in situ dynamic modulus prediction of asphalt mixture utilizing Ground penetrating radar technology

• The small-scale specimen’s applicability in dynamic modulus test was investigated. • Empirical and ANN dynamic modulus prediction models were proposed using GPR data. • The proposed models provided acceptable results at the confidence level of 95%. It is widely known that the asphalt mixture dynamic modulus is the key mechanical property that affects the quality and service life of asphalt pavement greatly. Ground penetrating radar (GPR) technology is a prospective method commonly used in determining the material information of asphalt pavement. Its utilization is supported by studying the relationship between the characterizations of GPR waveform and the parameters representing the condition of asphalt pavement. However, it is rarely applied in dynamic modulus prediction of asphalt mixture. To fill this gap, this study focuses on developing the corresponding dynamic modulus predictive method on the basis of GPR data. First, the applicability of the ϕ 38 mm × h 110 mm small-scale specimen covering wide range of air void content in the uniaxial compression test was analyzed. Then, the empirical and artificial neural network (ANN) dynamic modulus prediction models were developed by taking into account the dielectric constant of asphalt mixture. Last, the two proposed models were validated based on four asphalt mixture lanes in the field. It was found that the test errors of small-scale specimens were smaller than 15 %, and the statistical difference of dynamic moduli and phase angles measured from the full-size and small-scale specimens is insignificant at the 95 % confidence level meaning the size influence can be ignored. According to the verification experiment, the proposed empirical model and ANN model could yield acceptable results with the average prediction error of 19.3 % and 24.8 %, respectively. It is recommended that the two proposed predictive models coupled with GPR data could be used as an alternative to the currently available methods in estimating the dynamic modulus of asphalt mixture in situ.

Dynamic modulus prediction model and analysis of factors influencing asphalt mixtures using gray relational analysis methods

In the design of asphalt pavement, the dynamic modulus of the asphalt mixture is an indispensable parameter used for checking the fatigue cracking and permanent deformation of the mixture. However, there are many parameters affecting the dynamic modulus. Designers often do not know how to choose among them, and obtaining the parameters required in the traditional prediction model usually require sophisticated instruments, which is not conducive to their development and use by road designers. In this study, the method of gray correlation analysis was used to screen out the important and easy-to-obtain material parameters of an asphalt mixture, and then the multiple linear regression equation was used to establish a prediction model suitable for obtaining the dynamic modulus of asphalt mixtures in Jilin province. Tested against the estimated data, the fitting result is good. This research demonstrates that gray relational theory and multiple linear regression analysis can be applied in the establishment of a dynamic modulus model.

Improving flexible pavement performance through suitable aggregate gradation

The objective of this study was to improve the performance of flexible pavement through suitable aggregate gradation. Thus, initially, the dynamic modulus of asphalt mixtures |E*| for different aggregate gradations were predicted, and suitable aggregate gradation was determined. Then the performance of three different pavement structures for two aggregate gradations (Mid and Suitable), using AASHTOWare Pavement ME Design 2.5. 5, were evaluated for local conditions of Izmir, Turkey. The analysis result revealed that using suitable values compared to middle values increased the |E*| and improved the rutting and fatigue resistance of all pavement structures for any traffic levels. The output of this study can be used as a guide for hot mixed asphalt mix design and pavement design based on Mechanistic-Empirical Pavement Design Guide as well.

Different approach for the determination of dynamic modulus of asphalt mixtures in Turkey

Different approach for the determination of dynamic modulus of asphalt mixtures in Turkey

Predicting the dynamic modulus of asphalt mixture using hybridized artificial neural network and grey wolf optimizer

ABSTRACT The dynamic modulus () of asphalt mixture, which is one of the fundamental parameters in asphalt industry, is used to characterise the performance of asphalt mixtures at a wide range of temperatures and loading conditions. Direct laboratory-based measurement of is time-consuming and requires trained operators and expensive equipment. In this paper, a modelling framework based on the artificial neural network (ANN) algorithm is proposed for the estimation of the of asphalt mixtures. The architecture of the ANN algorithm significantly influences its prediction accuracy. To determine the optimised architecture of the ANN algorithm and to identify the effective variables, grey wolf optimizer (GWO) was used. A large dataset containing experimental results from different laboratories was used to develop the predictive models. The dataset included information on aggregate gradation and characteristics, volumetric properties, binder properties, test conditions, and reclaimed asphalt pavement (RAP) content. The results show that a hybrid ANN and GWO can successfully provide a framework for the estimation of with the Pearson correlation coefficient (Pearson’s R) above 0.98. A graphical user interface (GUI) was also developed as a user-friendly environment that can be easily used by the pavement engineers for predicting the values.

Accurately predicting dynamic modulus of asphalt mixtures in low-temperature regions using hybrid artificial intelligence model

The applicability of the widely used Witczak model was evaluated for the first time regarding the asphalt mixtures produced in the East part of China. 16 asphalt mixtures by 2 binders and 8 aggregate gradations were designed and the dynamic modulus testing was performed under various loading temperatures and frequencies. The results obtained are similar to previous studies from different countries (areas): the dynamic modulus of the asphalt mixture in the low-temperature region is overestimated. So then, a hybrid artificial intelligence algorithm to replace the traditional Witcazak model is implemented in this paper to correct the overestimation, using the same input parameters in the Witczak model. A modified beetle antennae search (BAS) algorithm was proposed in this study to improve the searching efficiency in the random forest (RF) model. The calculation process showed fast convergence and higher efficiency. The comparative results between the predicted and actual dynamic modulus showed higher prediction accuracy at all the temperature and frequency ranges, overcoming the weaknesses of the traditional Witczak model. The variable importance results showed that G* and phase angle of the binders have the greatest impact on the dynamic modulus. Volumetric properties also show certain influence ability, but the change of the variable controlling aggregate gradation has a weak influence on the dynamic modulus.

Effects of using different dynamic moduli on predicted asphalt pavement responses in mechanistic pavement design

In this study, dynamic moduli of asphalt mixtures under uniaxial compression (UC), indirect tension (IDT) and four-point bending (4PB) loading modes were tested and incorporated in the MEPDG procedure to predict the pavement responses. The field responses from a full-scale asphalt pavement were used to evaluate the prediction accuracies of three types of moduli. It was found that the current MEPDG procedure using UC modulus underestimates the strain responses of the pavement. Alternatively, the use of 4PB modulus in the MEPDG generates accurate strain predictions at the intermediate temperatures, but not at high temperatures. The combined use of UC modulus and the adjusted loading frequency, also generates accurate strain predictions at the intermediate temperatures. At high temperatures, the combined use of the 4PB modulus and was found to generate the most accurate prediction results. Accurate prediction of asphalt pavement responses is apparently dependent on the proper selection of modulus type and loading frequency.

Establishing prediction master curve of dynamic modulus of asphalt mixture considering randomness of aggregate morphology

The objective of this paper is to study the influence of aggregate morphology on dynamic modulus of asphalt mixture and establish a method to predict dynamic modulus of asphalt mixture at different temperatures and loading frequencies based on aggregate morphology and asphalt mortar material parameters. The Digital image processing (DIP) method is used to obtain statistical laws of the fractal dimension D and aspect ratio lw of aggregate section profiles, and the midpoint displacement method is used to generate virtual random aggregate sections. Based on the 2P2S1D constitutive model using the WLF time temperature equivalence, master curves of dynamic modulus of asphalt mortar at different reference temperatures are obtained and converted into the Prony series. Interface Transition Zones (ITZs) between asphalt mortars and aggregates are modeled by the Coulomb friction model, and dynamic moduli of asphalt mixture calculated by this model are in the range of calculation results by the tie model and the frictionless model. A total of 100 virtual specimens including random aggregates, asphalt mortars, ITZs and air voids are generated. Under different temperature and frequency combinations, extensive virtual tests of dynamic modulus of asphalt mixture are carried out on the virtual specimens. Based on the virtual test data of dynamic modulus, prediction master curves of dynamic modulus of asphalt mixture are obtained. The results show that aggregate morphology has a significant effect on dynamic moduli of asphalt mixture, and this effect has a clear correlation with the distribution laws of aggregate morphology indexes. By comparing with the test data of different literature, the probabilistic prediction method of dynamic modulus of asphalt mixture established in this paper is feasible.

Correlation analysis between asphalt binder/asphalt mastic properties and dynamic modulus of asphalt mixture

The dynamic modulus |E*| of hot-mix asphalt (HMA) mixture can reflect its temperature and frequency dependent behaviors, and it has been utilized to characterize the viscoelastic behavior of HMA mixtures. The objective of this study is to investigate the correlations between asphalt binder/asphalt mastic properties and dynamic modulus of asphalt mixture. The influence of various asphalt and aggregate parameters on the dynamic modulus master curve of asphalt mixture was investigated firstly. The applicability of asphalt binder-based |E*| prediction models (B−|E*| models) and asphalt mastic-based |E*| prediction models (M−|E*| models) was analyzed afterwards. Moreover, the correlations between the asphalt binder/mastic G* and the mixture |E*| were established. The results show that the |E*| master curve of asphalt mixture is significant affected by the type of binder and the ratio of filler to binder, but is slightly affected by the type of gradation, aggregate and filler. Among the B−|E*| models, the improved Hirsch model prediction results are most consistent to the measured value, followed by Witczak 1-40D model. Whereas, the predicted |E*| values of M−|E*| models are lower than the measured value. Both B−|E*| models and M−|E*| models perform well under the conditions of dense gradation and appropriate filler-to-binder ratio. Additionally, there is a good correlation between the asphalt/mastic G* and the mixture |E*| in logarithmic coordinates.

Study on dynamic modulus of asphalt mixture in cold regionunder rotary accelerated loading

In order to study the evolution law of mechanical properties of asphalt pavement mixture in cold regions under long-term load, the rotary accelerated loading equipment was used to carry out a total of 500,000 accelerated loading tests on the full-scale pavement, and the dynamic modulus test of the mixture before and after wheel load was carried out respectively. The master curve of dynamic modulus and dynamic modulus ratio (dynamic modulus value after wheel load / dynamic modulus value before wheel load) of the mixture at -20ºC were established to predict the long-term mechanical response of the mixture at low temperature. The results show that: low-frequency (or high temperature) has a more significant effect on the viscoelastic properties of the asphalt mixture. In the conversion frequency range of 1.6×10–3~1.6×102 Hz, the dynamic modulus ratio decreases with the increase of frequency, and the maximum ratio is 0.62 when the frequency is 1.6×10–3 Hz, which indicates that the high frequency (low temperature) has little effect on the performance of asphalt mixture. This study can be used as a theoretical reference for the structural design and performance optimization of asphalt pavement in cold regions.