https://orcid.org/0000-0001-7746-3554
Figures
Abstract
Rutting tests were conducted to investigate the deformation resistance of asphalt mixtures under varying temperature and wheel load conditions. The significant effect of temperature and load on the deformation resistance of the asphalt mixture was investigated using ANOVA. Multiple deformation resistance indicators, including complex stability index (CSI), densification coefficient (D), shear index(1/E), and characteristic parameters (A, C, and A/C), were proposed based on the rutting deformation growth equation, and the correlation model between rutting deformation and each indicator was established. The validity and reliability of the deformation resistance indicators were verified and evaluated. The results demonstrated that both the dynamic stability and rutting deformation of the asphalt mixture are more sensitive to temperature than load at the 0.05 significance level. The correlation between the proposed indicators and rutting deformation were significantly stronger than that between dynamic stability and rutting deformation. Additionally, indicators A and A/C exhibit high level of correlation when predicting permanent rutting deformation. The proposed deformation resistance indicators can accurately predict the permanent rutting deformation in laboratory rutting tests, which can provide reference for studying long-time rutting deformation in laboratory rutting tests.
Citation: Liu L, Sun Z (2026) Laboratory study on the deformation resistance indicators of asphalt mixture based on the rutting deformation growth model. PLoS One 21(2): e0340720. https://doi.org/10.1371/journal.pone.0340720
Editor: Dajiang Geng, China Construction Fourth Engineering Division Corp. Ltd, CHINA
Received: November 17, 2025; Accepted: December 25, 2025; Published: February 12, 2026
Copyright: © 2026 Liu, Sun. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the paper and its Supporting Information files.
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
With the rapid development of economy and society over the past three decades, the road traffic volume has increased dramatically, leading to higher demands for pavement performance, particularly in terms of capacity and durability. Asphalt pavements, owing to its advantages such as good crack resistance, convenient construction, and cost-effectiveness, has become the predominant choice for expressways worldwide. In China, more than 90% of pavement used asphalt layers as the surface course. The typical forms of damage for asphalt pavements are rutting and cracking. Rutting refers to the longitudinal surface depression that occurs on the wheel paths of road due to shear and compressive stresses under repetitive traffic loading [1]. Rutting deformation is one of the most critical early diseases of asphalt pavement, which not only reduces the smoothness of the pavement and increases driving risks, but also affects the road performance and service life seriously [2]. However, as rutting is still a major disease for asphalt pavement, it is necessary to evaluate the rutting resistance of the materials used in each structural layer of asphalt pavement, to improve the safety and comfortability of the pavement.
Extensive research has been conducted to evaluate the rutting resistance of asphalt mixtures by different test methods were utilized to estimate the rutting performance of asphalt pavement [3–9]. And most of the previous research focused on the evaluation and improvement of the rutting resistance [10–13]. Some researchers developed rutting prediction models by employing several machine learning techniques such as Artificial Neural Network, regression tree, support vector machine, ensembles, Gaussian process regression, and Deep learning techniques [14–18]. However, these studies did not address the deformation resistance indicator. The Chinese specification of JTG F40-2004 [19] recommends dynamic stability (DS), which is determined by wheel tracking tests, as the indicator for evaluating the rutting deformation of asphalt mixture. Du and Dai examined the effects of both the DS index and the complex stability index (CSI) on the stiffness modulus of asphalt mixture, which demonstrating that the CSI serves as a more effective indicator of rutting deformation [20].
These indicators that characterize rutting performance can be broadly divided into two categories namely, direct rutting indicators and indirect rutting indicators. The direct rutting indicators can be obtained through laboratory tests, such as the rutting test, while the indirect rutting indicators require either repeated loading tests or further analysis of test data. Despite these efforts, most existing indicators fall short in predicting long-term rutting performance, especially under varying environmental and loading conditions.
Variations of material properties are the main factors that affect the rutting resistance of asphalt mixtures [21,22], while environmental factors, mainly temperature, and vehicle load have a significant effect on material properties [23]. Therefore, temperature and vehicle load are the main factors affecting rutting resistance. The accumulation of permanent deformation under repeated load is a function of temperature, vehicle load and velocity [24–27]. Higher temperature, heavy load and lower velocity result in greater permanent deformation. The laboratory rutting test is loaded at a uniform speed (42 times/min), so the effect of loading speed on deformation is not considered in laboratory test.
As one of the most important factors, temperature has greatly influenced on the performance of asphalt pavements [28]. This is because that the viscosity of asphalt decreases with the temperature increases, especially when the temperature exceeds the softening point of asphalt, which resulting in a reduction in the deformation resistance of the mixture [29]. In addition, the degree of aging and fatigue properties of pavement materials are also affected by temperature, which affects the deterioration of rutting. Previously study shows that temperature of asphalt pavement can exceed 60 °C when the air temperature reaches more than 40 °C [30]. When there is continuous high temperature weather, rutting damage will occur on asphalt pavement, and the rutting deformation develops rapidly. Pouranian et al investigated the influence of temperature and stress level on the rutting performance of modified stone matrix asphalt (SMA), and revealed that the stress sensitivity of rutting performance decreases with temperature increase [31]. Souza, F. V. et al used numerical simulations to study the combined effect of temperature and loading on the mechanical response of asphalt pavements, and the results showed that temperature and thermo-viscoelasticity must be considered in asphalt pavements design [32]. Wasage, T. L. J. et al investigated the rutting behaviors of different paving mixtures used the rutting test, and the results showed that the rutting deformation deepens with the increase of test temperature [33].
Vehicle load is another important factor that causes rutting deformation. Along with the increase of traffic volume, the proportion of overloaded vehicles and heavy-duty vehicles has increased, and the tire load of these vehicles is higher than the standard axle load (0.7MPa), or even more than 1.0 MPa, resulting in rapid deformation of the road surface [25,34,35]. Furthermore, the stress distribution and deformation pattern of pavement materials are influenced by vehicle load, which affects the deterioration degree of rutting.
Although researchers have put forward several indicators of rutting deformation resistance for asphalt mixture especially at the mixture proportion design. These indicators can reflect the performance of asphalt mixtures with conditions of different temperatures and loads, which providing a foundation for engineering design and material selection. However, most of these indicators reflect short-term rutting deformation, and current research lacks indicators for long-term rutting deformation. This paper aims to establish indicators for long-term rutting deformation through laboratory testing.
The surface structure of asphalt pavements is typically divided into the upper layer, middle layer, and lower layer. Different asphalt mixtures are used for each layer based on their functional requirements, and AC-13, AC-20, and ATB-30 are commonly employed for the surface layers of pavements. Therefore, in this paper, the AC-13, AC-20 and ATB-30 were taken as research objects to investigate deformation resistance indicators. Firstly, the relationship between deformation resistance of asphalt mixture and temperature and load were studied. Secondly, deformation resistance indicators are proposed based on rutting tests conducted under different temperatures and loads. Thirdly, the applicability of deformation resistance indicators was investigated and their effectiveness and reliability were compared. These indicators can be used to predict long-term rutting deformation. Investigating the objective law between rutting deformation and temperature and load can better understand the mechanical characteristics and deformation law of pavement structure, and provide a basis for pavement structure optimization design and construction. It can also provide reference for road maintenance and management, which is conducive to improving the performance of the road and extending the service life.
2. Materials and test methods
2.1. Materials
2.1.1. Asphalt.
In this study, the 70# heavy traffic road petroleum asphalt was used, which is manufactured in Shangqiu, Henan province, China. Table 1 presents the general specifications of asphalt. The test methods can refer to Chinese specification of JTG 3410−2025 [36]. All the indexes comply with Chinese specification of JTG F40-2004 [19].
2.1.2. Aggregate.
The coarse and fine aggregate used in this study was crushed limestone gravel sourced from Shangqiu, Henan province, China. The main technical indicators of aggregate are tabulated in Table 2. All the test method can refer to Chinese specification of JTG E42-2005 [37].
2.1.3. Mineral filler.
In the tests of this paper, the mineral filler was crushed limestone which sourced from Shangqiu, Henan province, China. The main technical indicators of mineral filler are shown in Table 3.
2.2. Aggregate gradation
Three aggregate gradations were used in this study, which are the asphalt mixture with a nominal maximum particle size of 13.2 mm (AC-13), 19 mm (AC-20), and 31.5 mm (ATB-30). The aggregate gradations are present in Table 4 and Fig 1, which simultaneously provides the upper limit and lower limit for all the asphalt mixtures.
2.3. Rutting test method
2.3.1. Rutting test condition.
Asphalt mixture is typical viscoelastic materials, and its deformation resistance is affected by temperature and load significantly. To evaluate the effects of temperature and vehicle load on deformation resistance of asphalt mixture, the index of deformation resistance, mainly dynamic stability and rutting deformation, were tested under different conditions of temperature and vehicle load. According to the climate characteristics and temperature of the pavement structure, the test temperatures (T) are set as 20oC, 30oC, 40oC, 50oC, 60oC, and 70oC in this study. This temperature region encompasses the entire process of asphalt pavement transitioning from elastic-dominated state to viscoelastic-dominated state, and this range covers pavement conditions from normal temperatures to extreme heat in China. Based on the actual stress exerted by wheels on the road surface and fully considering the high proportion of heavy-duty vehicles in China’s transportation, the test loads (P) were set as 0.5 MPa, 0.7 MPa, 0.9 MPa, and 1.1 MPa, respectively.
2.3.2. Preparation of rutting plate specimen.
The rutting plate specimens of AC-13, AC-20 and ATB-30 were formed in laboratory used the rutting specimen molding machine (shown in Fig 2), and the gradations used in these tests are shown in Fig 1. In the tests, AC-13, AC-20 and ATB-30 were used with target voids of 4.0%, 4.2%, and 4.4%respectively. Marshall test method was utilized to determine the optimum asphalt-aggregate ratio for AC-13, AC-20, and ATB-30 which were 4.8%, 4.2%, and 3.6% respectively. The rutting plate specimens, 300 mm wide by 300 mm long by 50 mm thick, were prepared for AC-13 and AC-20, and 300 mm wide by 300 mm long by 80 mm thick for ATB-30, which reference to T0703-2011 of the Chinese specification of JTG 3410−2025 [36]. In the rutting tests, the mixing temperature of the asphalt mixture was 140oC to 160oC and the compaction temperature was 120oC to 150oC. Before formal compaction of the rutting specimen, its density should be measured after pressure test. After the specimens are molded, the rolling direction is marked with chalk, and the specimens are cooled naturally at room temperature for at least 12 hours before it is demolded. In the rutting test, three parallel specimens were performed in each test, and the average value of the three test results was taken as the test results. The variation coefficient of the test results was controlled within 20%.
2.3.3. Rutting test.
The rutting test is carried out with reference to T0719-2025 of the Chinese specification of JTG 3410−2025 [36], and the loading rate is 42 times/min. The wheel rutting tester and rutting test were shown in Fig 3. The dynamic stability calculated using Eq. (1).
Where DS is the dynamic stability, times/mm; t1 and t2 are the loading times, which is 1890 times and 2520 times, respectively; d1 and d2 are the rutting deformation at t1 and t2, mm; C1 is the coefficient of the specimen width, for a standard specimen with a width of 300 mm, its value is 1.0.
3. Results and discussion
3.1. Results of rutting tests
Table 5 shows the test results of dynamic stability (DS) and rutting deformation at load time of 2520 (RD2520) and 12600 (RD12600) for AC-13, AC-20 and ATB-30 with variable temperature and loads. It could be noted that RD2520, RD12600 and DS were temperature and load sensitive.
To illustrate the progression of rutting deformation, plots the variation of rutting depth (RD) with loading cycles under a load of 0.7 MPa. To characterize the effect of temperature and load on the rutting deformation visually, Fig 7 illustrates the 3D surface plot of RD12600 of the mixtures versus temperature (T) and load (P).
From Fig 7, the rutting deformation development at different temperatures for each load are very comparable with the increase of loading cycles. The test results are consistent with research results of Zhou et al., which indicate that rutting deformation all tend to increase with increases in load and temperature [38]. It is found that the rutting growth rate of AC-13 is higher than that of AC-20 and ATB-30 during the initial stage of loading and reaches the steady state earlier. This is because the size of the coarse aggregate of AC-13 is smaller compared to AC-20 and ATB-30, and the skeleton formed by the coarse aggregate is poor, which resulting in weak rutting resistance, and the fine aggregate and asphalt can be pressed into the void easily under load. Correspondingly, the coarse aggregate of ATB-30 forms a skeleton with high strength, which makes it difficult for the coarse aggregate to be displaced due to the friction and bonding force under the load, and the skeleton damage degree is low, which makes it difficult for the fine aggregate to enter the void.
Fig 7 shows that the 3D surface plot of AC-13 is above of AC-20 and ATB-30, which indicating that the RD of ATB-30 is smaller than that of AC-13 and AC-20 under the same temperature and loading conditions. In other words, the high temperature performance of ATB-30 is better than that of AC-13 and AC-20. Take AC-13 as example, the rutting deformation under high temperature and heavy loads is about 15 times higher than that under low temperature and light loads (15.3 mm for 70°C and 1.1MPa, 1.01 mm for 20°C and 0.5MPa). Therefore, heavy load and high temperature have a significant effect on rutting deformation.
3.2. Coupling effect of temperature and load
The sensitivity of temperature and wheel load to the dynamic stability and rutting deformation at 0.05 level of significance was investigated by analysis of variance (ANOVA). The results of ANOVA are presented in Table 6. In Table 6, SS represent sum of squares and MS is mean sum of squares.
From Table 6, it can be seen that the F-value corresponding to temperature is greater than that corresponding to load for the three asphalt mixtures, that is, the sensitivity of the dynamic stability and rutting deformation to temperature is higher than that to load. The P-value corresponding to temperature and load are less than 0.05 for the three asphalt mixtures, illustrating that the dynamic stability and rutting deformation is more sensitive to temperature than load at 0.05 significance level.
3.3. Correlation analysis of RD2520 and RD12600
The correlation of RD2520 and RD12600 for the three asphalt mixture is shown in Fig 8.
Fig 8 shows that RD2520 and RD12600 are highly linearly correlated, and the correlation coefficient (R2) exceed 0.98. Therefore, the RD2520 can be used to predict RD12600.
3.4. Rutting deformation growth pattern
The whole process of rutting deformation development could be divided into three phases. The primary phase of rutting deformation is densification of the mixture, in which the strain rate decreases swiftly with the increase of loading cycles. The secondary phase is shear flow of the mixture, in which the strain rate is nearly constant. The tertiary phase is shear failure of the mixture, in which the strain rate increases dramatically with the increase of loading cycles [39,40]. However, taking into account the equipment and efficiency of the rutting test, it is difficult to reach the tertiary phase in laboratory test. And even with five hours of rutting tests, the rutting deformation still cannot reach the tertiary phase. Therefore, the growth pattern of rutting deformation in the first two phases were mainly investigated in the laboratory test.
Gladkikh et al. presented a two phases analytical model which describes the primary and secondary phases of rutting deformation [41]. Fig 9 shows the two phases of rutting deformation, the primary phases can be descried by exponential function, and the second phases can be described by linear function. The model can be described by Eq. (2).
As shown in Eq. (2), it can be easily deduced that the limit of the first term is equal to a constant value, as shown in Eq. (3). The constant value D was defined as densification coefficient.
The parameter E in the second term of Eq. (2) is the slope of the line, which is defined as the rate of plastic flow, and the index ‘1/E’ was labelled as shear index.
The rutting deformation development also can be simulated by another model, which is shown by Eq. (4) [42].
To eliminate the variability of parameter values while fitting rutting curves, B. Javilla etc. fixed the parameter B as 50000 empirically through experimental research [43]. The modified model is shown by Eq. (5).
Parameter A and C can be determined by means of nonlinear regression, the index ‘A/C’ was labelled as characteristic parameters of rutting deformation.
3.5 Deformation resistance indicators
The deformation resistance indicators of AC-13, AC-20 and ATB-30 can be determined by means of nonlinear regression. Actually, the densification coefficient (D) and shear index (1/E) can be determined by Eq. (2), and A and C can be determined by Eq. (5), all the parameters are shown in Table 4.
3.5.1. Dynamic stability and complex stability index.
The dynamic stability is an effective indicator to evaluate high temperature performance of asphalt mixture. Base on the dynamic stability, Du and Dai proposed complex stability index (CSI) to evaluate the rutting performance of asphalt mixture, and the results showed that CSI was a better indicator of asphalt mixture[20]. The CSI was determined by Eq. (6). And the results of CSI were shown in Table 4.
The correlations of RD2520 with DS and CSI, are shown in Figs 10 and 11. It could be seen that RD2520 exhibits a nonlinear relationship with both DS and CSI, and the correlation coefficient between CSI and RD2520 is higher than that between DS and RD2520. This was in agreement with the study by Du and Dai, where the authors pointed out that the index CSI was more effective than index DS in evaluating the deformation resistance of asphalt mixture.
To validate the effectiveness of index CSI in characterizing the long-term deformation of rutting, the index CSI which were obtained by RD2520 were used to establish the relationships with RD12600. The relationship curve between RD12600 and CSI was plotted, as shown in Fig 12. As evident from Fig 12, RD12600 and CSI exhibit a nonlinear correlation with a high correlation coefficient of 0.95, which was significantly stronger than the correlation coefficient RD2520 and CSI. This demonstrates that index CSI can characterize long-term rutting deformation effectively. Therefore, CSI could be considered as an efficient indicator to evaluate rutting performance of asphalt mixture.
3.5.2. Densification coefficient and shear index.
According to the data in Table 4, plot the relationship curves between RD2520 and D, as well as between RD2520 and 1/E, as shown in Figs 13 and 14. As shown in Figs 13 and 14, the parameters (D and 1/E) were significantly correlated with RD2520. The index 1/E had a stronger correlation coefficient of 0.98 than index D. This was reasonable because rutting is attributed primarily to the shear flow characteristics of asphalt mixture other than initial densification.
With a view to verifying the effectiveness of index D and 1/E in characterizing long-term rutting deformation, the index D and 1/E which were obtained by RD2520 were used to establish the relationships with RD12600. The relationship curve between RD12600 with D and 1/E were plotted, as shown in Figs 15 and 16. As evident from Figs 15 and 16, both RD12600 and D, RD12600 and 1/E exhibit high correlation coefficient. This indicates that index D and 1/E can effectively characterize long-term deformation of rutting. Therefore, both D and 1/E could be considered as efficient indicators to evaluate rutting performance of asphalt mixture.
Characteristic parameters of rutting deformation.
The index A and C was determined based on the Eq. (5) by means of non-linear regression, and the index A/C was labelled as characteristic parameters of rutting deformation. Figs 17 and 18 shows the correlation of RD2520 with A and A/C. From Figs 17 and 18, the RD2520 is linearly and positively correlated with both A and A/C, and the index A/C was more reliable rutting indicator than index A. Compare to the index DS and CSI, the index A/C had the strongest correlation coefficient.
To verify the effectiveness of index A and A/C in characterizing long-term rutting deformation, the index A and A/C which were obtained by RD2520 were used to establish the relationships with RD12600. Figs 19 and 20 shows the correlation of RD12600 with A and A/C, and the correlation coefficients are as high as 0.99, which indicted that A and A/C could be used for predicting the long-term deformation of rutting for asphalt mixtures. Therefore, A and A/C could be considered as efficient indicators to evaluate rutting performance of asphalt mixtures.
3.5.4. Comparison of rutting performance indicators.
Figs 21 and 22 shows the comparison of correlation coefficients between various indicators and rutting deformation (RD2520 and RD12600). The correlation coefficients with RD12600 for all indicators except indicator of D were exceed 0.90, which indicating that these indicators can characterize the deformation resistance of asphalt mixtures effectively. Furthermore, the relationship between the indicators and RD12600 also can be used to predict the long-term deformation of rutting in laboratory test. Since the index A and A/C were both exhibit high correlation with rutting deformation, then it is sufficient to select the index A/C for practical application.
3.6. Validation of indicators
In order to provide further verification of the reliability and effectiveness of the proposed indicators of deformation resistance, the rutting specimens were prepared in laboratory with the gradations which were shown in Fig 1. Multiple rutting tests were conducted under the same test temperature and loading conditions. The test results were shown in Table 7.
The test data from Table 7 were plotted on the relationship curves between each indicator and RD2520 which were established previously. The results are presented in Figs 23–27. As is shown in Figs 23–27, all the test data are distributed near the respective curves, which demonstrates that these indicators are effective in characterizing rutting deformation.
4. Conclusion and outlook
The deformation resistance of AC-13, AC-20 and ATB-30 asphalt mixtures with variable temperature and loads were investigated in this study, and the rutting performance indicators were proposed based on the rutting test results and rutting deformation growth pattern, then the following conclusions are derived.
- (1). The deformation resistance of AC-13, AC-20 and ATB-30 asphalt mixtures were all affected by temperature and load significantly, and the deformation resistance is more sensitive to temperature than load at 0.05 significance level.
- (2). All the rutting performance indicators proposed in this study, namely CSI, D, 1/E, and A/C were significantly correlation with rutting deformation.
- (3). The proposed deformation resistance indicators can accurately predict the permanent rutting deformation in laboratory rutting tests.
This study proposes the deformation resistance indicators for conventional asphalt mixtures. However, with the application of new materials such as high modulus asphalt, rubber modified asphalt, warm mix additives, and fibers, as well as novel structural layers like large-sized permeable and high-elasticity layers, taking into account the influence of multiple factors, such as humidity and aging effect, it is necessary to systematically validate and adjust the sensitivity of the proposed indicators to these new materials. Multiple materials will be employed to validate the reliability of these indicators and establish corresponding standards based on engineering practice in future research. Furthermore, the engineering applications of these indicators will also be incorporated into future research.
Supporting information
S1 File. Date.
This file includes all the test data of the asphalt and asphalt mixtures.
https://doi.org/10.1371/journal.pone.0340720.s001
(DOCX)
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