https://orcid.org/0009-0007-4256-6749
Figures
Abstract
The relationship between the micro technical indexes and the macro road performance of high modulus asphalt (HMA) is helpful for understanding its mechanism and performance, and promoting its application. To explore the relationship, two kinds of high modulus asphalt (HMA), LLDPE/SBS composite modified asphalt and rubber/PPA composite modified asphalt were prepared according to the HMA requirements. Secondly, Molecular models of two kinds of HMA were established through molecular dynamics (MD) simulations, and the high temperature parameters of LLDPE/SBS composite modified asphalt were obtained with the two methods, namely the micro molecular dynamics simulation and high temperature rheological test, respectively. Then, through correlation analysis and regression calculation, the estimation formula was established between the results of molecular dynamics simulation and high temperature rheological test. Finally, in order to evaluate and verify the rationality of the estimation formula, the two methods were carried out on the other HMA (rubber/PPA composite modified asphalt). The results show that the shear modulus obtained by molecular dynamics simulation has a good correlation with the high temperature rheological properties. The estimation formula based on molecular dynamics simulation can be used to estimate the high temperature shear modulus of high modulus asphalt, and the relative error is less than 7%, which means that the formula can be used to effectively predict the high temperature performance of high modulus asphalt.
Citation: Wang J, Zhang Z, Tian Z (2025) Correlation analysis between micro and macro indicators of high modulus modified asphalt for asphalt pavement. PLoS ONE 20(1): e0313820. https://doi.org/10.1371/journal.pone.0313820
Editor: Mayank Sukhija, Oregon State University, UNITED STATES OF AMERICA
Received: August 22, 2024; Accepted: October 31, 2024; Published: January 2, 2025
Copyright: © 2025 Wang et al. 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: The data are all contained within the manuscript.
Funding: This research was funded by Department of Education of Shaanxi Province (21JK0527) awarded to JW, the National Natural Science Foundation of China (51008031) awarded to ZZ and Natural Science Foundation of Shaanxi Province of China (2024JC-YBQN-0429) awarded to JW.
Competing interests: The authors confirm that there is no conflict of interests.
1 Introduction
Due to its good performance characteristics, high modulus asphalt can be used in heavy-load traffic sections and roads with severe rut deformation. Moreover, using high modulus asphalt concrete as pavement base is an important technical requirement for the structural design of long-life pavement. Road experts have done a lot of research and application on high modulus asphalt, and exploration from a micro perspective has also been carried out [1–6]. The current research on the micro layer of high modulus asphalt is mostly limited to qualitative analysis of its modification mechanism through image experiments such as infrared spectrum and scanning electron microscope, and it is difficult to conduct in-depth analysis of the intrinsic mechanism and performance of high modulus asphalt materials. In recent years, molecular dynamics simulation has been gradually used in the field of material performance prediction. Molecular dynamics simulation can be used to analyze the macro performance of polymer modified asphalt under the limited experimental conditions through iterative calculations of the constituent elements, molecular structure, and intermolecular interaction forces of materials. In the study of molecular dynamics of high modulus asphalt, Ding et al. [7] analyzed the effect of SBS on the aggregation behavior of asphalt molecules using radial distribution functions. The results show that the influence level of SBS on the performance of asphalt depends on the length of alkane side chain of asphaltene. Sun et al. [8] calculated the density and glass transition temperature of SBS modified asphalt through molecular dynamics simulation, and The self-healing properties and healing mechanism of SBS modified asphalt were studied by the simulation results of diffusion coefficient and activation energy of asphalt. Feng et al. [9] studied the molecular aggregation state of SBS and asphalt at the molecular level by molecular dynamics simulation. At present, the quantitative analysis of high modulus asphalt performance using molecular dynamics simulation methods are limited, and the relationship between micro technical indexes and the macro road performance of high modulus asphalt seldom investigated. Therefore, it is difficult to predict the performance of high modulus modified asphalt under some extreme test conditions.
If the relationship between the micro technical indexes and the macro road performance of high modulus asphalt can be established, and the performance of high modulus asphalt can be measured from the perspective of molecular dynamics, then the performance of high modulus asphalt can be evaluated under limited experimental conditions. For the purpose, the study is conduced as follows, first, two kinds of high modulus modified asphalt, LLDPE/SBS composite modified asphalt and rubber/PPA composite modified asphalt were prepared according to the technical requirement. The modulus simulation calculation results and high temperature rheological property test results of LLDPE/SBS composite modified asphalt were obtained by micro molecular dynamics simulation method and actual measurement method. Then, the correlation between simulation results and test results were established and analyzed, the appropriate parameters of molecular dynamics simulation were obtained, and the estimation formula between the results of molecular dynamics simulation and high temperature rheological properties was established. Finally, the simulation results and the rheological performance test results of rubber/PPA composite modified asphalt was selected to evaluate and verify the rationality of the estimation formula. Establishing the relationship between microscopic indicators and macroscopic road performance is of great significance for predicting the macroscopic performance of high modulus modified asphalt in the future.
2 Materials and preparations
2.1 Materials
2.1.1 Base asphalt.
SK70 base asphalt used in this study was obtained from Xiamen City, Fujian Province, China. The technical indexes of the base asphalt are listed in Table 1.
2.1.2 PE modifier.
PE modifier used in this study was LLDPE-DFD7042, produced by United Petroleum and Chemical Co., Ltd (Fujian Province, China), which has a good effect on improving the high temperature performance of asphalt. The technical indexes are shown in Table 2.
2.1.3 SBS modifier.
SBS modifier used in this study was Li Changrong 3411 (Star SBS), obtained from Guangzhou City, Guangdong Province, China. The technical indexes are shown in Table 3.
2.1.4 Rubber modifier.
The rubber used in this study comes from the high-grade tire rubber particles with more than 90% natural rubber content produced by Qiangcan rubber and plastic products Co., Ltd (Shanghai City, China). The technical indexes are shown in Table 4.
2.1.5 PPA modifier.
PPA modifier used in this study was No. 80104518, produced by Sinopharm Chemical Reagent Co., Ltd (Shanghai City, China). The technical indexes are shown in Table 5.
2.2 Preparation of high modulus asphalts
According to the previous research results of the research group, the preparation process of LLDPE/SBS composite modified asphalt and Rubber/PPA composite modified asphalt was determined as follows.
2.2.1 LLDPE/SBS composite modified asphalt.
22.5g LLDPE and 22.5g SBS were added to 500 g heated SK70 base asphalt (175 ± 5°C) and swelled for 30 min. Then the mix was sheared at 180°C for 50 min in a high-shear mixer at 4000 rpm/min and developed for 1 hour in an oven at 160°C to ensure the performance of final product.
2.2.2 Rubber/PPA composite modified asphalt.
A different method was used to prepare the rubber/PPA modified asphalt specimen. Firstly, 100g rubber powder was added to 500 g heated SK70 base asphalt (175 ± 5°C) and sheared for 40 min at 170°C in a high-shear mixer at 5000 rpm/min. Next 10g PPA was added to the blend and sheared for 20 min under the same shear conditions. Finally, the blend was developed for 30 min in an oven at 160°C to ensure the performance of final product.
3 Test methods
To explore the relationship between the micro technical indexes and the macro road performance of high modulus asphalt, rheological property test and molecular dynamics simulation of high modulus asphalts were performed. Rheological property testing was performed using a dynamic shear rheometer (Physical MCR101, manufactured by Antonpaar, Austria). Molecular dynamics simulations of asphalt were conducted using Materials Studio (MS) on the high-performance computing platform of Chang’an University.
3.1 Rheological property test
According to the test results of rheological properties of high modulus asphalt at the early stage of the research group [10], the shear modulus G*, rutting factor G*/sinδ and unrecoverable creep compliance (Jnr) with good regularity were selected as the rheological properties indexes of correlation analysis in this study. The performance indexes are shown in Table 6.
The complex shear modulus G* and phase angle δ are the indexes used to characterize the high temperature performance of SHRP system. According to AASHTO MP1a-04 specification, G*/sinδ was not thought a good parameter to reflect the rutting resistance in many researches because that it did not take into account of recovery capacity of the modified asphalt. As G*/sinδ cannot effectively evaluate the high temperature performance of modified asphalt [11, 12], the repeated creep recovery test (MSCR) was adopted in NCHRP 9–10 which was proposed by the National Highway Cooperation Research Program of American. The repeated creep recovery test (MSCR) can judge the resistance to permanent deformation of asphalt, which is usually used to determine the elastic response of asphalt binder under shear creep and recovery at two stress levers. The unrecoverable creep compliance (Jnr) is used as the main performance indicators, and the creep behavior can be used to investigate the rutting susceptibility of asphalt concrete [13–15]. The high modulus modified asphalt was subjected to Dynamic Shear Rheometer (DSR) tests at 60°C and 76°C.
3.2 Establishment of asphalt molecular model
The component content and element composition of asphalt of asphalt was tested according to the specifications (JTG E20-2011) and specifications (GB T11132-2008), The separation of the four components was carried out using solvent filtration method and chromatographic column separation method according to the specifications, as shown in Fig 1. The separated four components are shown in Fig 2.
(A) Solvent filtration method; (B) Chromatographic column separation method.
(A) Asphaltene;(B) Saturates;(C) Aromatics;(D) Resin.
Then, the representative molecular of each component was selected to establish the asphalt molecular model based on existing research results [16–20], as shown in Figs 3–6.
(A) Asphaltene 1;(B) Asphaltene 2; (C) Asphaltene 3.
(A) Resin 1;(B) Resin 2; (C) Resin 3; (D) Resin 4; (E) Resin 5.
(A) Saturates 1; (B) Saturates 2.
(A)Aromatics 1; (B) Aromatics 2.
Finally, the relative mass fractions of the main elements in the model were compared with the measured values in the elemental analysis test to verify the rationality of the four-component asphalt model, and based on the preliminary calculation results of the research group, the asphalt molecular model was assembled using the amorphous Amorphous Cell Calculate interface in MS. Firstly, the selected molecular structures of the four components of asphalt were randomly placed into a unit cell with a size of 39.7Å×39.7Å×39.7Å. Then, asphalt molecules were assembled at the interface of the amorphous “Amorphous Cell Calculate”, the task option was set to “Construction” in the interface parameter setting. Considering the computing power and accuracy of the server, “Quality” was set to “Fine”. In order to avoid large deviations in simulation results caused by the entanglement of molecular chains in the unit cell during the simulation process, the initial density of the simulation system was generally set to a smaller value. In this paper, the density was set to 0.8g/cm3. The electrostatic force and van der Waals interaction force were set to Ewald and Atom Baselaw, respectively. D. Calculate the force field using COMPASS force field, and establish a model after setting the parameters.
3.3 Molecular dynamics simulation
Firstly, combined with the results of asphalt molecular model, the molecular models of high modulus asphalt with different amounts of modifiers were assembled by Amorphous Cell Calculate interface in MS. Considering the computing power and precision of the server, Simulation quality is set to fine. In order to simulate the real state of material molecular movement as possible, Andersen and Berendsen methods [21, 22] were adopted for temperature and pressure control under periodic boundary conditions and Compass force fields, and The electrostatic and van der Waals forces were set to Ewald and Atom Based, respectively. After the parameters were set, the molecular model of the composite modified asphalt can be established. Then, the simulation system was subjected to 2000 steps of Geometry optimization by using the comprehensive method, and 100ps molecular dynamics simulation of the molecular system after the Geometry optimization was carried out under the NVT ensemble. That is, the model system in the state of energy stability was obtained. Finally, the physical modulus of high modulus asphalt molecular model in stable configuration was simulated at 333.15K (60°C) and 349.15K (76°C), respectively.
The Constant Strain method in the Forcite module was used to solve the physical modulus of the modified asphalt blend. After the dynamic superposition operation, the stiffness matrix and the flexibility matrix of the modified asphalt at 60°C and 76°C were obtained, as shown in Eq 1.
(1)
Where λ and u are lame constants; cij is stiffness constant.
Then the Young’s modulus (E), bulk modulus (K) and shear modulus (G) of high modulus asphalt were calculated by Formula (2)–(4) according to the stiffness matrix and flexibility matrix. The calculation formulas are as follows.
(2)
(3)
(4)
Where sij is flexibility constant.
3.4 Correlation analysis and verification of micro index and macro index
According to the test results of rheological properties and the results of molecular dynamics simulation of LLDPE/SBS composite modified asphalt, the correlation between macro performance indexes and micro indexes was analyzed. Then through correlation analysis and regression calculation, the appropriate parameters of molecular dynamics simulation were obtained, and the estimation formula between the results of molecular dynamics simulation and high temperature rheological properties was established. Finally, the estimation formula was verified by combining the high temperature rheological test results and molecular dynamics simulation results of rubber/PPA composite modified asphalt.
4 Results and discussion
4.1 Test results of rheological properties
Six kinds of LLDPE/SBS composite modified asphalts with a total content (LLDPE: SBS in LLDPE/SBS composite modified asphalt is 1:1) of modifiers of 6%, 7%, 8%, 9%, 10%, and 11% were selected for rheological performance testing. The test results are shown in Table 7.
It can be seen from Table 7 that the rutting factor and shear modulus of the composite modified asphalt increase with the increase of the total content of LLDPE and star SBS, and the unrecoverable creep compliance decreases, which indicates that the high temperature performance of the composite modified asphalt increases with the increase of the modifier. When the total content of the modifier reaches 9%, the high temperature performance of LLDPE/SBS composite modified asphalt meets the requirements of high modulus asphalt.
4.2 Assembly of asphalt molecular model
The results of the four-component separation test of SK70 asphalt are shown in Table 8.
According to the test results of asphalt components in Table 8 and the test results of asphalt chemical components in earlier stage of this paper [23], the molecular structure of each component of asphalt were selected combined with the existing research results and the trial results of the atoms number allowed in the simulation system, as shown in Table 9.
The content of each component of the asphalt was calculated according to the molecular composition of the asphalt molecular model in Table 9, and compared with the measured values, the comparison results are shown in Table 10.
Table 10 shows that compared with the measured value, the four-component content of the asphalt model system obtained through trial calculation is slightly higher, but the proportion of wax content in the asphalt meets the specification requirements, so the impact of error on the asphalt performance can also be ignored.
In order to verify the rationality of the asphalt model structure, the relative mass fraction of each element in the asphalt model system is calculated and compared with the measured value of the relative mass fraction of elements in the element analysis test. The comparison results are shown in Table 11.
It can be seen from Table 11 that the relative error between the relative mass fraction of each element in the four-component model established by the assembly method and the measured results in the element analysis test is less than 10%, and the effect of this error range on the molecular dynamics simulation of asphalt can be ignored.
According to the composition of asphalt in Table 9, the asphalt molecular model was assembled through the Amorphous Cell Calculate interface in MS, as shown in Fig 7.
4.3 Simulation results of physical modulus
Combined with the four component asphalt molecular model, taking the modified asphalt with the minimum content (the total content is 6%) in Table 7 as an example, the blending system model of LLDPE/SBS composite modified asphalt is as shown in Fig 8.
The initially constructed blend system model is in a high-energy state, which is easy to cause the discreteness and distortion of the molecular dynamics simulation results. The Geometry optimization of the high-energy unsteady simulation system was carried out by the comprehensive method, and the result is shown in Fig 9.
Fig 9 shows that with the increase of the optimization step, the total potential energy of the simulation system gradually decreases and tends to be gentle after the Geometry optimization process. In order to further improve the simulation accuracy and make the simulation system approach the actual structure of the material to the largest extent, the molecular dynamics simulation of the molecular model after the Geometry optimization was carried out. The molecular dynamics simulation result is shown in Fig 10.
According to the judgment standard for stable state of molecular dynamics simulation system [23], when the energy-time curve tends to be stable and the fluctuation presents regular changes, it can be determined that the system reaches the energy stable state, that is it reaches the termination condition of dynamics calculation before the simulation analysis of molecular dynamics performance. The total energy of the system is the sum of the total potential energy and the total kinetic energy of the system. From Fig 10, it can be seen that the change rule of the total potential energy and the total kinetic energy of the system is basically the same as the change rule of the total energy through molecular dynamics simulation. After 10ps molecular dynamics calculation, the total kinetic energy, the total potential energy, the total energy and the non-bonding energy of the system tend to be stable. That is to say, the simulation system has reached an energy stable state, and the structure system is in a stable state after 10ps molecular dynamics simulation, which can be further used in molecular dynamics simulation calculation and analysis.
The physical modulus of LLDPE/SBS composite modified asphalt stabilized system after molecular dynamics simulation was simulated by the mechanical properties command of the Force module in MS, and the simulation was carried out at 60°C and 76°C respectively. The results of simulation are shown in Tables 12–15.
By the same way, the model establishment and molecular dynamics calculation of LLDPE/SBS composite modified asphalt with different content of modifier were carried out. The stiffness matrix and flexibility matrix of high modulus composite modified asphalt with different content of modifier at 60°C and 76°C were obtained. Then, the physical modulus molecular dynamics simulation results of LLDPE/SBS composite modified asphalt at two temperatures were calculated by Formula (2)–(4), as shown in Table 16.
From the molecular dynamics simulation results in Table 16, it can be seen that the simulation results of modulus are quite different from the data measured in the laboratory, but with the increase of the total content of modifier, the molecular dynamics simulation results of shear modulus, bulk modulus and Young’s modulus of LLDPE/SBS composite modified asphalt increase, which is consistent with the change trend of the test results measured in Table 7. This shows that for the physical modulus, there is a certain correlation between the simulation results and the measured data in laboratory of LLDPE/SBS composite modified asphalt.
4.4 Correlation analysis and verification results of micro and macro indexes
According to the rheological performance test results and physical modulus molecular dynamics simulation results of the LLDPE/SBS composite modified asphalt in Tables 7 and 16, the correlation analysis between the macro and micro indexes was obtained. The linear fitting results of the modulus simulation results and the rheological performance test results of the LLDPE/SBS composite modified asphalt at different modifier content and temperature are shown in Figs 11 and 12.
(A) Young’s modulus-rheological property index; (B) Bulk modulus-rheological property index; (C) Shear modulus-rheological property index.
(A) Young’s modulus-rheological property index; (B) Bulk modulus-rheological property index; (C) Shear modulus-rheological property index.
Figs 11 and 12 show that the correlation between micro and macro indexes of LLDPE/SBS composite modified asphalt is relatively high. And the correlation coefficient statistical results of micro and macro indexes are shown in Table 17.
The correlation coefficient of linear fitting is above 0.9, which indicates that the correlation between the two indexes is good. Table 17 shows among the three modulus, only the correlation coefficient of shear modulus between the molecular dynamics simulation results and the rheological property test results is above 0.9, which not only shows that the modified asphalt can be effectively simulated and evaluated by molecular dynamics simulation, but also shows that the shear modulus is a high temperature index with a good correlation between molecular dynamics simulation results and rheological test results. Thus the estimation formulas between molecular dynamics simulation indexes and high temperature rheological performance indexes were established according to the linear fitting results of micro and macro indexes of High modulus asphalt, the estimation formula is shown in Formula (5)–(8).
(5)
(6)
(7)
(8)
Where xG is the result of molecular dynamics simulation calculation of shear modulus, MPa; y is the result of rheological property test, Pa.
To further verify the accuracy of the estimation formulas, the other modified asphalt, the rubber/PPA high modulus asphalt was subjected to molecular dynamics simulation of shear modulus and rheological properties test. Herein the Rubber asphalt (20% rubber) was modified by PPA with a content of 1%, 1.5%, 2%, 2.5%, and 3% respectively. Molecular models of rubber/PPA high modulus asphalt with different modifier content were established, and the shear modulus of different molecular models was simulated by the Constant Strain method in the Forcite module. The simulation results are shown in Table 18.
It can be seen from Table 18, with the increase of PPA content, the results of molecular dynamics simulation results of shear modulus of rubber/PPA high modulus asphalt gradually increase, while with the increase of simulation temperature, the shear modulus shows the opposite trend, has the same trend as laboratory test results.
According to the estimation formula of Formula (5)–(8), combined with the molecular dynamics simulation results of the shear modulus in Table 18, the estimated value of rheological properties of rubber/PPA composite modified asphalt with different PPA content is shown in Table 19.
In order to verify the accuracy of the estimation formulas of micro and macro indexes, the rheological properties were tested, and the test results are shown in Table 20.
The estimation value of rheological property in Table 19 was compared with the measured value in Table 20, and the relative error between the estimation value and the measured value is shown in Table 21.
Table 21 shows that the relative error between the measured value and the estimation value of high temperature parameters were obtained from the estimation formulas of micro and macro indexes of the high modulus asphalt is less than 7%, and the relative error of most of the indexes is less than 3%. It can be seen that the high temperature parameters obtained by molecular dynamics simulation can predict the high temperature performance of high modulus modified asphalt to a certain extent.
5 Conclusions
The molecular dynamics simulation results of modulus are different from the data measured in the laboratory, but the molecular dynamics simulation results of shear modulus, bulk modulus and Young’s modulus of high modulus asphalt are consistent with the change trend of the test results. This shows that, for LLDPE/SBS composite modified asphalt, there is a certain correlation between the simulation results of the physical modulus and the measured data in laboratory.
The estimation formulas of macro and micro indexes of the high modulus modified asphalt were established according to the correlation analysis between the rheological performance test results and physical modulus molecular dynamics simulation result. And among the three modulus, only the correlation coefficient of shear modulus is above 0.9, which shows that the shear modulus is a high temperature index, showing a good correlation between molecular dynamics simulation results and rheological test results.
For the high modulus asphalt, the relative error between the measured value and the estimation value of high temperature parameters were obtained from the estimation formulas of micro and macro indexes is less than 7%, and the relative error of most of the indexes is less than 3%, which show that the high temperature parameters obtained by molecular dynamics simulation can predict the high temperature performance of high modulus modified asphalt under the limited experimental conditions.
Molecular dynamics is an important simulation characterization method and is very helpful for simulating and predicting various properties of asphalt. The research results of this paper can effectively predict the high-temperature performance of high modulus asphalt, which has important reference value for improving the design level of high modulus modified asphalt and its mixtures, and have important theoretical guidance significance for the promotion and application of polymer modified asphalt. However, there are still some differences between the model established in the paper and the model of high modulus asphalt. In the future, the model will be further optimized to study the modification mechanism and mechanical properties of high modulus asphalt.
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