Numerical Simulation for Mechanical Behavior of Asphalt Pavement with Graded Aggregate Base

*e performance of asphalt pavement is determined by the combination of its material properties, road structure, and loading configurations. A DEM numerical simulation study was conducted to determine stress distribution and deformation behavior of asphalt pavement with graded aggregate base under standard traffic loading. Stress contour and displacement contour were presented via a self-made program. Compressive stress concentrated area located in both sides of wheel, while tensile stress concentrated area appeared in lower part of the asphalt layer. *e traffic loading transferred downward by graded aggregate base and to both sides at the same time, and has a trend to expand gradually with increasing depth within graded aggregate base. *erefore, stress was well distributed in the subgrade soil layer with a great action scope, and the value decreased obviously because of the stress dispersion of graded aggregate base. Vertical displacement was the main displacement of the asphalt layer, and on the both sides of traffic loading, displacement was downward and inclined slightly to the central of loading. Vertical and horizontal deformations included in both graded aggregate base layers, and displacement extended to both sides gradually with increasing depth corresponding to stress-distribution trends. Vertical displacement was dominated in the subgrade soil layer which was relatively small.


Introduction
In the built and rebuilt highways, approximately 90% of pavements in China are asphalt-surfaced pavements, and much of their subgrade was semirigid base.However, as the subgrade is used extensively, there are some problems that appear progressively, and subjected to repeated traffic loading, premature failures, and lower maintenance over the life cycle of the pavements [1][2][3][4].e common distress modes in pavements are likely fatigue cracking and rutting which decrease the service life of pavement.is is a phenomenon that pavement design and maintenance engineers stripping off asphalt in flexible pavement have had to contend with for years [5][6][7][8].Fatigue cracking and rutting were triggered by leading infiltration of rainwater into subgrade base, which has been found responsible for premature failures [8,9].
A series of investigation on mechanical properties of graded aggregate base material (referring to assembly of granular materials for construction of highway base layers) was performed alone [10][11][12][13][14][15] to meet the engineering needs, both under motonic and cyclic loading conditions.However, the behavior of pavements is complex and depends on many factors such as the axle/wheel loading configurations, the materials used, the thickness of the layers, and the environmental conditions [16].Mechanistic-empirical design methods use greatly simplified models [17] and is now moving to more mechanistic-based approaches [10,18].Stress level within each layer of a pavement structure is determined by magnitude of the load, individual and combined layer thickness, and layer material properties [16,19].And long-term stability of pavements can only be achieved with a properly designed and constructed system that consists of all pavement structural components and sufficient understanding of their interaction [6,20].erefore, it is imperative to investigate pavement stability by considering its structure.is paper presents a discrete element method (DEM) [21][22][23] numerical simulation study to determine stress distribution and deformation behavior of asphalt pavement with graded aggregate base under standard tra c loading.And stress and displacement contours were presented to describe them visually via a self-made program, which o ers trends of stress and displacement quantitatively.Subsequently, comparison of deformation performance and stress distribution was made to verify the interaction of layers, especially graded aggregate base.e method and conclusion provide a useful tool and guidance to pavement structure design for engineering.

Modelling Procedure
Over the years, DEM is broadly applied to simulate the mechanical performance of unboned granular materials [24][25][26][27].And particle ow code (PFC) has been successfully employed to study the mechanical behavior of granular materials, especially for railway ballast [28][29][30].
e numerical software PFC2D is used to study the graded aggregate, comprising particles, and in uence on pavement deformation.However, it must be noted that calculation e ciency signi cantly decreases with increase of particles, and this is also the disadvantage for almost all particle ow models.Furthermore, DEM concerns about micromechanics behavior with a small scope of study object.
erefore, a simpli ed model is employed to obtain reliable results and e cient calculation both, as follows.

Simpli cation.
Because of the aforementioned reasons, the object must be carefully planned and conducted to be successful.Firstly, good particle control is necessary to provide e cient calculation.Generally, a highway has a width up to tens of meters, but owing to symmetry of it, the scope of simulation can be reduced in half.Meanwhile, soil of the subgrade layer is not the focus of the current research, so it is default to deem that particle size used in simulation is greater than the minimum particle size of graded aggregate base material.However, particle size for the soil should be in a reasonable radius to prevent graded aggregate base material from entering the soil.On the other hand, the present study mainly focuses on the in uence of graded aggregate base on pavement performance; therefore, the selected gradation of granular materials is used as GanDing highway base materials with the maximum particle size of 37.5 mm.Particle size distributions of the graded aggregates are shown in Table 1.As illustrated in Table 1, the gradation of the particles in the numerical simulation met that in reality, and the maximum error was less than 0.8%.

Pavement Structure and Modelling.
rough the analysis, the partial pavements (Figures 1 and 2) were selected to investigate the in uence of granular material on pavement performance under tra c loading.As shown in Figure 1, the partial covers a half of single line, including a wheel width of 0.3 m and a width of 0.6 m on both sides of it.Figure 1 illustrates the highway structure for modelling, which could be categorized into four parts: (1) Asphalt layer: exible pavements with a thickness of 10 cm.(2) Graded aggregate base layer: composed of speci c gradation of granular material, with a thickness of 20 cm.It mainly bears the loads from the asphalt layer and disperses them, so the stress concentration is reduced, which could decrease vertical deformation of subgrade soil.At the same time, it can drain   2. (1) Asphalt layer: asphalt is typical of the viscoelastoplastic material, with prominent viscous properties at high temperature and elastic property at low temperature.us, the asphalt layer is stratiform elastomer, without considering the viscous properties, in the simulation.e assembly of balls is arranged regularly and tightly within a specified region, and contact and parallel bonds are used to meet the assumption.

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(2) Graded aggregate base layer: graded aggregate is unbound particles, and the assembly of balls is arranged randomly with given size distribution and within the specified region.
(3) Subgrade soil layer: this layer is regarded as elastic property and ignored the plastic deformation.Consequently, the generation of balls is the same as the asphalt layer but has relatively small size.(4) Loading plate: a clump, assembly of balls arranged regularly and tightly, is used to apply traffic loading.
After the particle assembly is generated and compacted, boundary and initial conditions are applied to achieve the desired initial equilibrium state.

Results and Discussion
3.1.Stress Distribution Characteristics.50 kN force was uniformly distributed on loading plate to simulate action of a wheel.As illustrated in Figure 3, it can be observed that generally the stress of the model is in a symmetrical distribution.
For the stress distribution in the asphalt layer, Figure 4 highlights that compressive stress concentrated area located in on both sides of wheel, while tensile stress concentrated area located in lower part of the asphalt layer.Meanwhile, under the traffic loading, the asphalt layer beneath the wheel suffers from shear and tensile action in the converging zone of compressive and tensile stress.After long-term repeated loading, fatigue cracking and rutting will arise owing to the fatigue failure of the asphalt layer and different vertical strains of two sides.
For the graded aggregate base layer, the stress distribution located mainly in a range beneath traffic loading, which has a double width of wheel approximately and has a trend to expand gradually with increasing depth within the graded aggregate base layer.e traffic load was transferred downward by the graded aggregate base layer and to both sides at the same time (as shown in Figure 5).Consequently, stress in the subgrade soil layer reduced greatly, and correspondingly, deformation is relatively small.

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For the subgrade soil layer, the stress was distributed well in the subgrade soil layer with a great action scope (as illustrated in Figure 6).And the maximum force between balls was 1.97 kN and, as expected, the maximum stress distribution was right below tra c loading.But due to the appearance of graded aggregate base, the e ect of stress dispersion diminished stress value in the subgrade soil layer.
In order to describe stress state visually, stress contour is presented in Figure 7 via a self-made program, which o ers a trend of stress quantitatively.It is noted that only presentation of stress value was available.So, for this reason, the failure mode for a speci c zone cannot be determined from it.As shown in Figure 8, stress concentration exhibited on the edge of wheel; the maximum stress 200 kPa was slightly greater than mean stress 167 kPa, under the tra c loading.us, accompanying irregular settlement, it will contribute fatigue cracking and rutting, and nally conform to the actual phenomenon for pavement.Additionally, stress value decreased obviously in the subgrade soil layer because of the stress dispersion of graded aggregate base.

Displacement
Characteristics. Figure 7 illustrates the particle displacement vector for each layer.For the asphalt layer, vertical displacement was the main displacement of the asphalt layer (as shown in Figure 9), with the maximum vertical displacement equal to 2.199 mm, located right below tra c loading.On the both sides of tra c loading, displacement was downward and inclined slightly to the central of loading.
For the graded aggregate base layer, vertical and horizontal deformations included both in graded aggregate base layers (as shown in Figure 10).Displacement concentrated in a nite region right below the loading with a maximum value of 2.159 mm and extended to both sides gradually with increasing depth.And because of unboned granular material of graded aggregate base, the displacement vector corresponds to stress distribution trends.6

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For the subgrade soil layer, vertical displacement is dominated in the subgrade soil layer with a maximum value of 1.225 mm located right below the traffic loading, and displacement has a trend to diffuse into both sides (as shown in Figure 11), which corresponds to stress dispersion.Figure 12 provides a visible vertical displacement contour via the selfmade program.Although discontinuity appears in this contour owing to the fact that it comes from DEM which is not a continuum problem, it does not affect the estimation of vertical displacement quantitatively for different regions.For the asphalt layer, the maximum vertical displacement varies between 2.0 and 2.25 mm; consequently vertical deformation is dominated in the asphalt layer as compared to the maximum displacement 2.199 mm (Figure 10).But for the graded aggregate base layer, the maximum vertical displacement varies between 1.25 and 1.5 mm, which is different significantly from the maximum displacement 2.159 mm (Figure 11); thus, horizontal displacement cannot be ignored in the graded aggregate base layer.Deformation of the subgrade soil layer was dominated by vertical displacement as the maximum vertical displacement varies between 1.0 and 1.25 mm (Figure 12), which is close to the maximum displacement 1.225 mm (Figure 12), and the displacement was relatively small because of the stress dispersion of graded aggregate base.

Conclusions
A PFC numerical simulation study was conducted to determine stress distribution and deformation behavior of asphalt pavement with graded aggregate base under standard traffic loading.
(1) Stress distribution characteristics demonstrated that compressive stress concentrated area located in on both sides of wheel, while tensile stress concentrated area located in lower part of the asphalt layer; consequently, fatigue cracking and rutting will arise with

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the fatigue failure of the asphalt layer after long-term repeated loading.e tra c load transferred downward by graded aggregate base and transferred to both sides at the same time and has a trend to expand gradually with increasing depth within the graded aggregate base layer.erefore, stress was distributed well in the subgrade soil layer with a great action scope, and the value decreased obviously in the subgrade soil layer because of the stress dispersion of graded aggregate base.(2) Displacement characteristics and the corresponding vertical displacement contour demonstrated that vertical displacement was the main displacement of the asphalt layer, and on the both sides of tra c loading, displacements were downward and inclined slightly to the central of loading.Vertical and horizontal deformations included in both graded aggregate base layers, and displacement extended to both sides gradually with increasing depth corresponding to stress-distribution trends.Vertical displacement was dominated in the subgrade soil layer which was relatively small.

Figure 3 :
Figure 3: Stress distribution of the model (black and red denote pressure and tension, resp.).

Figure 4 :
Figure 4: Stress distribution of the asphalt layer (black and red denote pressure and tension, resp.).

Figure 5 :
Figure 5: Stress distribution of graded aggregate base layer (black and red denote pressure and tension, resp.).

Figure 6 :
Figure 6: Stress distribution of subgrade soil layer (black and red denote pressure and tension, resp.).

Figure 7 :
Figure 7: Particle displacement vector for each layer.

Figure 8 :
Figure 8: Stress contour of the model.

Figure 9 :
Figure 9: Deformation characteristics of the asphalt layer.

Figure 10 :
Figure 10: Deformation characteristics of the graded aggregate base layer.

Figure 11 :
Figure 11: Deformation characteristics of the subgrade soil layer.

Figure 12 :
Figure 12: Vertical displacement contour of the model.

Table 1 :
Particle size distributions of the graded aggregate.

Table 2 :
Properties for each part.