Analysis of Optimal RAP Content Based on Discrete Element Method

Methods of recycling a large amount of waste asphalt mixture generated in pavement maintenance and decreasing the waste of existing resources are one of the problems that will be solved in the future. In this study, the mechanical parameters of asphalt mixture containing dierent amounts of RAP were analyzed by discrete element method (DEM), and the reasonable RAP content was discussed in combination with uniaxial compression test results. And it is considered that the contact between dierent particles will produce the failure of stress transfer between particles with dierent modulus, and the contact denition between RAP particles and virgin aggregate particles is added tomake the discrete elementmodel more in line with the actual situation. e results indicated that the trend of discrete element analysis was consistent with that of the uniaxial penetration test, but there were dierences in the specic values. Uniaxial compression test results showed that the optimum RAP content of the recycled asphalt mixture was 30%. e optimal RAP content analysis result from the DEM simulation was smaller than the laboratory test result, and the theoretical optimal RAP content was 28%. e results of this study provide a reference for the mixture design of recycled asphalt mixture.


Introduction
With the substantial increase of tra c volume, some old pavements could not bear the surging tra c volume and produced many pavement surface diseases, such as ruts, pits, cracks, and dislocation [1][2][3]. ese diseases severely a ect the service life of the pavement, so it is necessary to carry out a lot of maintenance and expansion work to ensure normal use of the pavement and meet increased tra c volume. e asphalt pavement waste produced for each year pavement maintenance in China amounts to 2.2 million tons and increases year by year [4,5], if using asphalt mixture recycling technology during paving asphalt pavement engineering, and waste asphalt pavement materials for reuse, it can not only alleviate the development pressure caused by the shortage of resources such as oil and stone, but also can save the economic costs. How to rational, recycle, and utilize a large amount of waste asphalt mixture produced in pavement maintenance work and reduce a large amount of waste of preexisting resources is the core problem that needs to be solved now. Pavement recycling technology [6,7] is a technology that digs and recycles the waste asphalt mixture of old pavement and mixes it with virgin asphalt, virgin aggregate, recycling agent, and some additives in a certain proportion, to obtain an asphalt recycling mixture that meets the requirements of the speci cation.
Academic experts have studied the recycled mixture from various perspectives, such as the in uence of RAP content on the performance of the mixture, recycling agent, and recycling technology. Chen et al. [8] carried out various performance tests on mixed asphalt with di erent aged asphalt content and recycled asphalt mixtures with di erent RAP content. e study was found that with the increase in the aging asphalt content, the high-temperature performance of the mixed asphalt continued to improve and the low-temperature performance decreased signi cantly. At the same time, with the increase of RAP content, the water stability and high-temperature stability of recycled asphalt mixture increase, and the low-temperature crack resistance decreases. Tang et al. [9] studied the effects of ordinary and emulsified rejuvenator on the performances of recycled mixture through rutting test and freeze-thaw splitting tests.
e experimental results show that emulsified rejuvenator can improve the workability and high-temperature stability of reclaimed mixtures. Arambula-Mercado et al. [10] evaluated three recycling agent dosage selection methods based on the restoration of the performance grade (PG) of the recycled blend (virgin binder, recycled binder, and recycling agent). On the basis of the test result, the method to reduce high-temperature PG is recommended to determine the optimum recycling agent dosage. Hafeez et al. [11] studied the pavement performance of the recycled asphalt mixture based on aged asphalt in different aging states and showed that the performance of aging asphalt was improved in the recycling process. Grilli et al. [12] recovered the performance of aging asphalt by adding specific biological additives into the recycled mixture so that the addition of virgin asphalt can be significantly reduced under the condition that the pavement performance of the recycled mixture is not significantly changed, to achieve the purpose of cost saving. e study of Bernier et al. [13] showed that the compaction energy required by the mixture decreased with the increase of the incorporation rate of recycled aggregates, and the use of recycled aggregates had a significant influence on the compaction characteristics of the mixture skeleton.
In 2008, Technical Specification for recycling of highway asphalt pavement was formulated in China, which laid a foundation for the promotion and application of recycling technology in China, and was revised and supplemented in 2019. Shirodkar et al. [14] found that the degree of fusion of old and virgin asphalt in recycled asphalt mixture decreases with the increase of RAP content. Kaseer et al. [15] added a certain amount of recycling agent to the recycled asphalt mixture to improve the road performance of the recycled asphalt mixture and studied the influence of these admixtures on road performance. Laboratory test results demonstrated that the hardness of the recycled asphalt mixture is significantly reduced and the crack resistance is improved by adding recycling agent, which is conducive to the use of more recycled materials. Nie et al. [16] carried out fatigue, rutting, water damage, and cracking tests in the laboratory by using asphalt mixtures with different RAP content and determined that the RAP content when using plant mixed hot recycled asphalt mixture has good service performance. Ma et al. [17] studied the admixture content of the hot recycled asphalt mixture. By dividing different RAP content and testing their respective pavement performance, it was found that with the increase of RAP content, the dynamic modulus and mechanical strength of the mixture also increased, but the low-temperature properties and moisture susceptibility properties are first enhanced and then weakened. Guo et al. [18] studied the change rule of twodimensional morphological structure of recycled aggregates with different proportions of old and virgin, and found that the ellipticity change of old aggregates was smaller than that of virgin aggregates. According to Sabouri's [19] research, several mixtures containing different RAP content were evaluated in terms of fatigue and rutting performances using the S-VECD model and TSS testing, respectively. e study found that increasing the RAP content deteriorates fatigue resistance while improving the rutting performance of the asphalt mixtures.
All above studies show that RAP content significantly affects the pavement performance of recycled asphalt mixture. However, the bond weakening between RAP aggregate particles has not been quantitatively analyzed, resulting in inconsistency between the actual performance of the mixture and the theoretical analysis results. erefore, in this study, the discrete element method was used to analyze the mechanical parameters of recycled asphalt mixture with different RAP content, and the rational RAP content was discussed based on the results of the uniaxial compression test, to provide reference for the mix design of recycled asphalt mixture.

Virgin Asphalt.
e virgin asphalt used in this test is Shell ordinary 70# asphalt, and the relevant performance tests of asphalt are carried out in accordance with "Specification and Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering." e test results are shown in Table 1, all of which meet the specification requirements.

Aggregate.
e aggregate used in this test is diabase. e aggregate is used after screening, washing, drying, and other processes, and the performance test of the processed coarse and fine aggregate is carried out according to the relevant test method in the Testing Methods of Aggregate for Highway Engineering. e performance test results of coarse and fine aggregates are shown in Tables 2 and 3, and all related performances meet the requirements of the specification.

Asphalt Mixture Recycled Material.
e RAP used in this test is recycled waste materials from municipal pavements in Guangzhou, and the asphalt content of the RAP is 4.6%. According to the requirements of the Technical Specification for the Recycling of Asphalt Pavement on Highways, the recycled RAP is dried and screened. At the same time, the basic properties of the coarse aggregates are tested according to the relevant test methods in the Aggregate Testing Methods for Highway Engineering, and the results are shown in Table 4.

Mix Proportion of Recycled Asphalt Mixture.
Dense-graded asphalt mixture AC-13 was selected as the test gradation. e test gradation is shown in Table 5. A large number of studies show that the best range of RAP content is 30%∼50%. In this study, a recycled asphalt mixture with rap content of 0%∼50% was used for test. On the basis of considering RAP asphalt content, the oil stone ratio of recycled asphalt mixture is uniformly adopted 4.5%.

Uniaxial Compression Test.
Five groups of hot recycled asphalt mixture specimens (3 specimens in each group) with rap content of 0%∼50% are formed by gyratory compaction, and the specimens are cylindrical specimens with a diameter of 100 mm and height of 100 mm. e specimens were kept in an oven at 60°C for 6 h, and the uniaxial compression test was carried out at the test temperature of 60°C, with a loading speed of 1 mm/s. e stress deformation curve of each material is shown in Figure 1.

Discrete Element Model.
Recent studies have shown that the discrete element method is an ideal numerical simulation method for solving discontinuous media problems [20][21][22][23]. When using the discrete element method for simulation analysis, there is no need to pay too much attention to intermediate variables such as volume index and smaller error. Based on the PFC3D software, a cylindrical discrete element specimen with diameter of 100 mm and height of 100 mm is established to carry out virtual compression test. e loading speed is 1 mm/s, as shown in Figure 2.
Taking into account the efficiency of the software, the minimum particle size of the specimen of discrete element specimen is 1.18 mm and the other gradations are consistent with the actual specimen. e part less than 1.18 mm is equivalent to asphalt mortar, which is characterized by interface bonding parameters. To characterize the mechanical behavior of specimens with different RAP content, RAP particles and virgin aggregate particles were characterized by different elastic stiffness (35 GPa and 17 GPa) according to the crushing value test results of coarse aggregate and the aging state of aggregate. e contact model between particles adopts the contact bonding model, and the bonding parameters are consistent with the elastic stiffness of particles. e flowchart is shown in Figure 3

Uniaxial Compression Test Results.
Uniaxial compression test is also called unconfined compressive strength test. As the displacement of the pressed specimen increases, the pressure exerted by the indenter gradually increases. When the maximum compressive load of the specimen is reached, the specimen will be damaged. e displacement load curve of this process was obtained, and the peak load was taken as the maximum compressive load that the specimen can bear. Its compressive strength was calculated, and the test results are shown in Figure 4.
It can be seen from Figure 4 that the compressive strength of the recycled asphalt mixture changes with the increase of RAP content. e change trend is that when the content of RAP increased from 0% to 30%, the compressive strength increased and reached the peak at 30%. When the RAP content increased from 30% to 40%, the compressive strength decreased. When the content of RAP increased from 40% to 50%, the change of compressive strength was not significant.
is shows that 30% RAP is the best for compressive performance.
e results show that without recycling the agent, the increase of RAP content increases the proportion of old asphalt in asphalt mortar and increases the viscosity and stiffness of asphalt mortar, and improves the compressive performance of mixture. When the content of RAP is further increased, the stiffness of asphalt mortar increases significantly. In the low stress state, there is a large stress concentration in the material, resulting in brittle failure.    e virtual compression test of discrete element of recycled asphalt mixture with different RAP content is carried out, and the axial compression rate is 1 mm/s. When only the contact stiffness between the same particles is considered, the analysis results are shown in Figure 5.
As shown in Figure 5, if only the contact stiffness between the same particles is considered, the simulated compressive strength decreases significantly with the increase of RAP content. e results show that the discrete element virtual compressive strength of recycled asphalt mixture decreases monotonically with the increase of RAP content, and there is no peak of compressive strength. is result is not in line with the actual situation, because the model only defines the contact between the same particles without considering the previous contact between different particles, which will clearly lead to the failure of stress transfer between particles with different modulus. erefore, the definition of contact between the RAP particles and the virgin aggregate particles is added and the elastic stiffness at the interface between the RAP particles and the virgin aggregate particles is taken as 25 GPa for verification and analysis. e results of the analysis are shown in Figure 6.
It can be seen in Figure 6 that when the interface parameters of the two particles are added, the analysis   results are relatively consistent with the indoor test results. e mixture has a maximum value when the RAP content is 30%, indicating that the 30% RAP content is the best. e analysis shows that the contact stiffness between different particles should be considered in the virtual simulation of the recycled asphalt mixture to ensure that the analysis results are consistent with the actual test results.

Analysis of RAP Content Based on PFC.
To verify the effectiveness of the simulation results of the discrete element method, the virtual analysis results are compared with the indoor test results, as shown in Figure 7.
It can be seen from Figure 6 that although the trend of discrete element analysis is consistent with that of uniaxial compression test, and the conclusion that the optimal RAP content is 30% can be obtained at all; the correlation between them is general and the correlation coefficient is only 0.7229. e results show that there are many factors affecting the virtual mechanical analysis results of recycled asphalt mixture, and the simple contact stiffness model cannot consider the effects of asphalt aging, particle weakening, and asphalt fusion state. For this material with relatively complex composition, a more detailed theoretical model should be used for characterization. erefore, the above model can be used to carry out the virtual mechanical analysis of recycled asphalt mixture with different RAP content, and more detailed analysis results can be obtained.

Advances in Materials Science and Engineering
According to the results of the existing analysis, the virtual mechanical analysis with RAP content of 20%∼40% is carried out at an interval of 2%. e results are shown in Figure 8.
It can be seen from Figure 8 that when RAP content is 28%, the compressive strength of recycled asphalt mixture reaches the peak. If the compressive strength is used as a single evaluation standard, the optimum RAP content of the recycled asphalt mixture is 28%. It should be careful that this result is a theoretical solution obtained by using a simple discrete element model.

Conclusion
In this paper, the mechanical parameters of recycled asphalt mixture with different RAP content are analyzed by the discrete element method. Combined with the results of the uniaxial compression test, the following conclusions are obtained.
(1) e results of the indoor uniaxial compression test show that the optimum RAP content of the recycled asphalt mixture is 30%; (2) When using the discrete element model for analysis, the contact between different particles needs to be considered in order to ensure that the trend of the analysis results is consistent with the actual test results; (3) e change trend of discrete element analysis results is consistent with that of the uniaxial penetration test, but the two values are quite different and the correlation is general; (4) e analysis results of the optimal RAP content obtained based on the discrete element method are less than the indoor test results. When the compressive strength is taken as a single evaluation standard, the optimal theoretical RAP content of the recycled asphalt mixture is 28%.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.