Influences by Air Voids on the Low-Temperature Cracking Property of Dense-Graded Asphalt Concrete Based on Micromechanical Modeling

This study characterized the impacts of air voids on the low-temperature cracking behavior of dense-graded asphalt concrete. Virtual low-temperature bending beam test for dense-graded asphalt concrete was built and executed by discrete element method and PFC3D (particle flow code in three dimensions). Virtual tests were applied to analyze the impacts by content, distribution, and size of air voids on the low-temperature properties of dense-graded asphalt concrete. The results revealed that higher air void content results in worse low-temperature property of dense-graded asphalt concrete, especially when the air void content exceeds the designed air content; even with the same designed air void content, different distributing condition of air voids within asphalt concrete leads to different low-temperature properties of asphalt concrete, especially when the air void content in the central-lower part of testing sample varies. Bigger size of single air void which tends to form interconnected air voids within asphalt concrete has more harmful impacts on the low-temperature properties of asphalt concrete.Thus, to achieve satisfied low-temperature properties of dense-graded asphalt concrete, it is critical to ensure the designed air void content, improve the distribution of air voids, and reduce the interconnected air voids for dense-graded asphalt concrete.


Introduction
Low-temperature cracking is one of the main diseases of asphalt pavement especially in cold weather. Since asphalt concrete is typical heterogeneous composite materials, the composition ratios of different constituents within asphalt concrete and their microstructure distribution have important influences on the cracking behavior of asphalt concrete [1,2]. However, laboratory tests cannot fully evaluate the influences by different constituents of asphalt concrete on its cracking behavior [3]. Although finite element method can well depict the cracking behavior of asphalt concrete, it still has difficulties to characterize the heterogeneity of asphalt concrete and depict the microstructure of different constituents of asphalt concrete [4][5][6][7][8]. The discrete element method proposed by Cundall can evaluate the interacting behavior within discrete particles by characterizing the translational and rational movements of different particles based on Newton's second law of motion and a finite difference scheme [9,10]. It provides a more promising way to model and describe the heterogeneous microstructure and micromechanical behavior of asphalt concrete.
After contact-bonding relationships for asphalt concrete were built, DEM has been extensively used to characterize the performances of asphalt concrete. Although many different discrete element software have been developed, the particle flow code in two and three dimensions (PFC2D/3D) was used most popularly for asphalt concrete analysis due to its good modeling productivity and flexible capacity to characterize the moving behavior and interaction between the different ingredients of asphalt concrete [11]. Abbas et al. and Liu and Dai conducted micromechanical modeling for asphalt concrete and analyzed the viscoelastic behavior of asphalt concrete based on discrete element method [12,13]. Collop et al. performed uniaxial compressive creep test simulation for asphalt concrete based on elastic contacting model [14].   [25,26]. However, few researches were performed to evaluate and analyze the low-temperature cracking behavior based on three-dimensional discrete element modeling and the impacts by air voids on the low-temperature properties of asphalt concrete. This study focused on the impacts of different parameters of air voids on the low-temperature properties of dense-graded asphalt concrete. DEM and PFC3D were used to build three-dimensional digital sample and virtual low-temperature bending beam test for dense-graded asphalt concrete based on laboratory tests. And the influences of air void content, distribution of air voids, and size of single air void on the low-temperature properties of asphalt concrete were analyzed.

Materials and Experimental Test
2.1. Materials. A 13 mm dense-graded asphalt concrete (AC13) with nominal maximum aggregate size of 13.2 mm, which was widely used as the wearing course in China, was prepared for laboratory test and micromechanical modeling. The mix design of AC13 satisfied the specifications set forth by Chinese Ministry of Transportation and is shown in Table 1. If all of the aggregates especially the fine aggregates and mineral fillers were considered during micromechanical modeling for asphalt concrete, it is too time-consuming to generate virtual sample and conduct the virtual test during PFC3D. Thus, to facilitate micromechanical modeling in PFC3D, asphalt concrete was considered as a three-phase composition that consisted of three ingredients which are air voids, asphalt mortar composed of asphalt binder and fine aggregates passing 2.36 mm sieving size, and coarse aggregates retained on 2.36 mm sieving size.

Experimental Tests.
The low-temperature three-point bending beam test was performed for AC13 by Universal Testing Machine (UTM). The testing temperature was −10 ∘ C. And loading was applied by cylindrical pressure bar with diameter of 2 cm on the span center of the beam sample with dimensions of 250 × 30 × 35 mm 3 (length × width × height) at loading speed of 50 mm/min until the beam was ruptured. Based on the rupture load and the rupture displacement at the span center of beam sample immediately after the sample was ruptured, the fracture tensile stress, fracture tensile strain, and fracture strain energy density can be obtained and recorded. The low-temperature splitting test was conducted at −10 ∘ C for asphalt mortar. During the splitting test, loading was applied on the cylindrical sample with height of 63.5 mm and diameter of 101.6 mm at loading speed of 50 mm/min until the sample was split to get the splitting tensile stress and splitting tensile modulus for mortar sample. Figure 1 shows the test samples for the low-temperature three-point bending beam test and low-temperature splitting test, respectively.

Micromechanical Models and Parameters.
During PFC3D modeling, the microstructure of asphalt concrete was modeled as a three-ingredient system (coarse aggregates, asphalt mortar, and air voids) and different contact models were used to describe the micromechanical behavior of different ingredients. Based on PFC3D manual [27], the contact models at different contacts within asphalt concrete are summarized in Table 2.
The micromechanical parameters for different contact models can be determined by the macromechanical properties of coarse aggregates and asphalt mortar [27], as shown in the following: Advances in Materials Science and Engineering 3 where , , and are the normal stiffness, shear stiffness, and friction coefficient at contacts between aggregates; , , and are the normal stiffness, shear stiffness, and maximum tensile force at contacts within asphalt mortar; , , and are the normal stiffness, shear stiffness, and maximum tensile force at contacts within asphalt mortar; is the radius of the discrete ball element for aggregate and asphalt mortar which is 1 mm in this study; , ], and are the elastic modulus, Poisson ratio, and friction coefficient of aggregates; and and are the tensile modulus and strength from splitting test of asphalt mortar.
Based on previous research [15,26], the elastic modulus and friction coefficient of coarse aggregates are presented in Table 3. Based on splitting tests of asphalt mortar, the tensile stress and modulus of asphalt mortar are also summarized in Table 3. According to (1), the micromechanical modeling parameters at different contacts within asphalt concrete are determined and presented in Table 4.

Micromechanical Modeling of Virtual Test.
During micromechanical modeling by PFC3D, asphalt mortar was modeled by discrete ball elements with the same size, and air voids were considered to be distributed within asphalt mortar randomly and simulated by removing elements of asphalt mortar randomly to meet the designed air void content of asphalt concrete. However, PFC3D cannot generate irregular elements directly; thus, a user-defined modeling algorithm was performed in PFC3D to get polyhedrons with irregular shapes to simulate coarse aggregates. Based on the previous assumptions and the testing conditions of laboratory lowtemperature bending beam test, as shown in Figure 2, a micromechanical modeling procedure was proposed to build virtual low-temperature bending beam test. Figure 3 shows the critical generation process during PFC3D modeling for virtual low-temperature bending beam test.  Set up the virtual sample space by "Walls"

Results and Discussion
Generation of irregular aggregates based Apply loading by "Wall" according to laboratory test and collect data Generation of air voids by randomly deleting mortar elements according to target air void content Set appropriate contact models within the remaining discrete ball elements to simulate asphalt mortar Set the discrete ball elements within coarse aggregates as "clumps" and set appropriate contact models between aggregates Generation of uniform-sized discrete ball elements to fulfill the virtual sample on user-defined modeling algorithm Generation of spherical aggregates according to the designed gradation according to the geometry of real sample laboratory test is shown in Figure 4 while Figure 5 illustrates the different testing stages during virtual test. It can be seen that the virtual test can capture the developing process of cracking failure which is very similar to the cracking failure of the laboratory test. Figure 6 shows the test curves from laboratory test and virtual test. It can be seen that the testing curve of virtual test is similar to the testing curve of laboratory test. It proves the validity of using virtual bending beam test to predict the low-temperature property of asphalt concrete.

Effects by Content of Air Voids on Low-Temperature
Property. Based on the built modeling process, as shown in Figure 7, beam samples with different contents of air voids (2%, 4%, 6%, 8%, and 10%) were built for virtual lowtemperature bending beam test to analyze the influences by air void content on the low-temperature properties of asphalt concrete. The changing of tensile failure strength and failure strain with variation of air void contents are shown in Figure 8. It can be seen that all of the three indices including failure strength, failure strain, and strain energy density decrease with the air void contents increasing, especially for the strain energy density. It indicates that the low-temperature property of asphalt concrete gets worse with its air void content growing. When the air void content exceeds 6% especially, the degradation of low-temperature property becomes more serious. It well confirms with the idea that the common mix design of asphalt concrete tends to keep the target air void content lower than 6%.

Effects by Air Voids Distribution on Low-Temperature
Property. During the virtual bending beam test, while the total content of air voids of test sample was kept as 4%, the nonuniform vertical distribution and nonuniform horizontal distribution of air voids in test sample were simulated, respectively, as shown in Figures 9 and 10. In Figure 9, along the vertical direction, the samples were cut apart into two parts with equal volume. Five different air void content distributions, which are 8% in the upper part and 0% in the lower part (V8/0), 6% in the upper part and 2% in the lower part (V6/2), 4% in the upper part and 4% in the lower part (V4/4), 2% in the upper part and 6% in the lower part (V2/6), and 0% in the upper part and 8% in the lower part (V0/8), were generated. In Figure 10, along the horizontal direction, the samples were cut apart into three parts with the same volume. Six different air void content distributions, which are 0% in the side parts and 12% in the middle parts (H0/12/0), 1% in the side parts and 0% in the middle part (H1/10/1), 2% in the side parts and 8% in the middle part (H2/8/2), 4% in all of the three parts (H4/4/4), 5% in the side parts and 2% in the middle part (H5/2/5), and 6% in the side parts and 0% in the middle part (H6/0/6), were considered. Figures 11 and 12 show the testing results of asphalt concrete samples with different nonuniform air voids distribution. It is indicated that different air voids distributions within the samples result in different low-temperature properties. From Figure 11(a), it can be seen that the failure strength increases with the air void content of bottom lower part declining. From Figures 11(b) and 11(c), it is shown that Advances in Materials Science and Engineering 6% 0%  the sample with uniform distribution of air voids has the biggest failure strain and strain energy density; besides that both the failure strain and strain energy density increase with the air void content of lower part declining. It indicates that the air void content variation of lower part has more influences on the low-temperature property than that of the upper part. From Figure 12, it is shown that all of the three indices decrease with the air void content of middle part growing. When the air void content of middle part exceeds 6% especially, the degradation of all of the three indices becomes more sharp. Since the loading was applied in the center of the middle part, it confirms well with the previous analysis about the influences by air void contents on the lowtemperature properties. Thus, the variation of air void content within the middle part has important impacts on the lowtemperature property of the testing sample.

Effects by Air Void Size on Low-Temperature Property.
To analyze the effects by air void size on the low-temperature property, different numbers of asphalt mortar elements contacting with each other were removed to get air voids with different sizes. During PFC3D modeling, four different air void sizes were modeled by removing mortar element (named Size 1), two interconnected mortar elements (named Size 2), three interconnected mortar elements (named Size 3), and four interconnected mortar elements (named Size 4). As shown in Figure 13, while the total air void content was kept as 4%, samples with different single air void sizes were built for virtual bending beam tests. The testing results are shown in Figure 14. It can be seen that all of the three indices decline  with the air void size growing. It is shown that smaller air void size of asphalt concrete results in better low-temperature property of asphalt concrete.

Conclusions
Micromechanical modeling procedure based on discrete element method and PFC3D was built to simulate the lowtemperature bending beam test in laboratory. Based on laboratory testing data, the validity of virtual test to characterize the low-temperature property of asphalt concrete was proved. It provides an effective method to analyze the impacts by air voids on the low-temperature properties of dense-graded asphalt concrete which are difficult to be carried out by laboratory tests.
It is proved that the growing of air void content weakens the low-temperature properties of dense-graded asphalt concrete, especially when the content of air voids is bigger than the designed content of air voids. Even with the same mix design and content of air voids, asphalt concrete can still exhibit very different low-temperature properties. Nonuniform air voids distribution and air void sizes variation have important impacts on the low-temperature properties of asphalt concrete, especially when the air void content and size within the loading area of asphalt concrete vary. Therefore, lower air void content, uniform distribution of air voids, and small size of interconnected air voids are helpful to improve the low-temperature properties of asphalt concrete. Future study will focus on different types of asphalt concretes such as stone matrix asphalt concrete and porous asphalt concrete, different types of air voids such as impermeable void and permeable void, and the relationship between volumetric characteristics and asphalt concrete behaviors.